curve.cc

Go to the documentation of this file.

/* SPDX-FileCopyrightText: 2001-2002 NaN Holding BV. All rights reserved.
 *
 * SPDX-License-Identifier: GPL-2.0-or-later */

 
#include <algorithm>
#include <cmath> /* floor */
#include <cstdlib>
#include <cstring>
#include <optional>
 
#include "MEM_guardedalloc.h"
 
#include "BLI_ghash.h"
#include "BLI_index_range.hh"
#include "BLI_listbase.h"
#include "BLI_math_base_safe.h"
#include "BLI_math_geom.h"
#include "BLI_math_matrix.h"
#include "BLI_math_rotation.h"
#include "BLI_math_solvers.h"
#include "BLI_math_vector.h"
#include "BLI_math_vector_types.hh"
#include "BLI_string.h"
#include "BLI_string_utf8.h"
#include "BLI_utildefines.h"
#include "BLT_translation.hh"
 
/* Allow using deprecated functionality for .blend file I/O. */
#define DNA_DEPRECATED_ALLOW
 
#include "DNA_anim_types.h"
#include "DNA_curve_types.h"
#include "DNA_defaults.h"
#include "DNA_material_types.h"
 
/* For dereferencing pointers. */
#include "DNA_key_types.h"
#include "DNA_object_types.h"
#include "DNA_vfont_types.h"
 
#include "BKE_curve.hh"
#include "BKE_curveprofile.h"
#include "BKE_idtype.hh"
#include "BKE_key.hh"
#include "BKE_lib_id.hh"
#include "BKE_lib_query.hh"
#include "BKE_object_types.hh"
#include "BKE_vfont.hh"
 
#include "DEG_depsgraph.hh"
#include "DEG_depsgraph_query.hh"
 
#include "BLO_read_write.hh"
 
using blender::Array;
using blender::float3;
using blender::float4x4;
using blender::IndexRange;
using blender::MutableSpan;
using blender::Span;
 
/* globals */
 
/* local */
// static CLG_LogRef LOG = {"bke.curve"};
 
enum class NURBSValidationStatus {
  Valid,
  AtLeastTwoPointsRequired,
  MorePointsThanOrderRequired,
  MoreRowsForBezierRequired,
  MorePointsForBezierRequired
};
 
static void curve_init_data(ID *id)
{
  Curve *curve = (Curve *)id;
 
  BLI_assert(MEMCMP_STRUCT_AFTER_IS_ZERO(curve, id));
 
  MEMCPY_STRUCT_AFTER(curve, DNA_struct_default_get(Curve), id);
}
 
static void curve_copy_data(Main *bmain,
                            std::optional<Library *> owner_library,
                            ID *id_dst,
                            const ID *id_src,
                            const int flag)
{
  Curve *curve_dst = (Curve *)id_dst;
  const Curve *curve_src = (const Curve *)id_src;
 
  BLI_listbase_clear(&curve_dst->nurb);
  BKE_nurbList_duplicate(&(curve_dst->nurb), &(curve_src->nurb));
 
  curve_dst->mat = (Material **)MEM_dupallocN(curve_src->mat);
 
  curve_dst->str = (char *)MEM_dupallocN(curve_src->str);
  curve_dst->strinfo = (CharInfo *)MEM_dupallocN(curve_src->strinfo);
  curve_dst->tb = (TextBox *)MEM_dupallocN(curve_src->tb);
  curve_dst->batch_cache = nullptr;
 
  curve_dst->bevel_profile = BKE_curveprofile_copy(curve_src->bevel_profile);
 
  if (curve_src->key && (flag & LIB_ID_COPY_SHAPEKEY)) {
    BKE_id_copy_in_lib(bmain,
                       owner_library,
                       &curve_src->key->id,
                       &curve_dst->id,
                       reinterpret_cast<ID **>(&curve_dst->key),
                       flag);
  }
 
  curve_dst->editnurb = nullptr;
  curve_dst->editfont = nullptr;
}
 
static void curve_free_data(ID *id)
{
  Curve *curve = (Curve *)id;
 
  BKE_curve_batch_cache_free(curve);
 
  BKE_nurbList_free(&curve->nurb);
 
  if (!curve->edit_data_from_original) {
    BKE_curve_editfont_free(curve);
 
    BKE_curve_editNurb_free(curve);
  }
 
  BKE_curveprofile_free(curve->bevel_profile);
 
  MEM_SAFE_FREE(curve->mat);
  MEM_SAFE_FREE(curve->str);
  MEM_SAFE_FREE(curve->strinfo);
  MEM_SAFE_FREE(curve->tb);
}
 
static void curve_foreach_id(ID *id, LibraryForeachIDData *data)
{
  Curve *curve = reinterpret_cast<Curve *>(id);
  const int flag = BKE_lib_query_foreachid_process_flags_get(data);
 
  BKE_LIB_FOREACHID_PROCESS_IDSUPER(data, curve->bevobj, IDWALK_CB_NOP);
  BKE_LIB_FOREACHID_PROCESS_IDSUPER(data, curve->taperobj, IDWALK_CB_NOP);
  BKE_LIB_FOREACHID_PROCESS_IDSUPER(data, curve->textoncurve, IDWALK_CB_NOP);
  BKE_LIB_FOREACHID_PROCESS_IDSUPER(data, curve->key, IDWALK_CB_USER);
  for (int i = 0; i < curve->totcol; i++) {
    BKE_LIB_FOREACHID_PROCESS_IDSUPER(data, curve->mat[i], IDWALK_CB_USER);
  }
  BKE_LIB_FOREACHID_PROCESS_IDSUPER(data, curve->vfont, IDWALK_CB_USER);
  BKE_LIB_FOREACHID_PROCESS_IDSUPER(data, curve->vfontb, IDWALK_CB_USER);
  BKE_LIB_FOREACHID_PROCESS_IDSUPER(data, curve->vfonti, IDWALK_CB_USER);
  BKE_LIB_FOREACHID_PROCESS_IDSUPER(data, curve->vfontbi, IDWALK_CB_USER);
 
  if (flag & IDWALK_DO_DEPRECATED_POINTERS) {
    BKE_LIB_FOREACHID_PROCESS_ID_NOCHECK(data, curve->ipo, IDWALK_CB_USER);
  }
}
 
static void curve_blend_write(BlendWriter *writer, ID *id, const void *id_address)
{
  Curve *cu = (Curve *)id;
 
  /* Clean up, important in undo case to reduce false detection of changed datablocks. */
  cu->editnurb = nullptr;
  cu->editfont = nullptr;
  cu->batch_cache = nullptr;
 
  /* write LibData */
  BLO_write_id_struct(writer, Curve, id_address, &cu->id);
  BKE_id_blend_write(writer, &cu->id);
 
  /* direct data */
  BLO_write_pointer_array(writer, cu->totcol, cu->mat);
 
  if (cu->ob_type == OB_FONT) {
    BLO_write_string(writer, cu->str);
    BLO_write_struct_array(writer, CharInfo, cu->len_char32 + 1, cu->strinfo);
    BLO_write_struct_array(writer, TextBox, cu->totbox, cu->tb);
  }
  else {
    /* is also the order of reading */
    LISTBASE_FOREACH (Nurb *, nu, &cu->nurb) {
      BLO_write_struct(writer, Nurb, nu);
    }
    LISTBASE_FOREACH (Nurb *, nu, &cu->nurb) {
      if (nu->type == CU_BEZIER) {
        BLO_write_struct_array(writer, BezTriple, nu->pntsu, nu->bezt);
      }
      else {
        BLO_write_struct_array(writer, BPoint, nu->pntsu * nu->pntsv, nu->bp);
        if (nu->knotsu) {
          BLO_write_float_array(writer, KNOTSU(nu), nu->knotsu);
        }
        if (nu->knotsv) {
          BLO_write_float_array(writer, KNOTSV(nu), nu->knotsv);
        }
      }
    }
  }
 
  if (cu->bevel_profile != nullptr) {
    BKE_curveprofile_blend_write(writer, cu->bevel_profile);
  }
}
 
static void curve_blend_read_data(BlendDataReader *reader, ID *id)
{
  Curve *cu = (Curve *)id;
 
  BLO_read_string(reader, &cu->str);
 
  /* Old files don't have `cu->len_char32` set. */
  if ((cu->len_char32 == 0) && (cu->str != nullptr) && (cu->str[0] != '\0')) {
    size_t len_bytes;
    size_t len_char32 = BLI_strlen_utf8_ex(cu->str, &len_bytes);
    cu->len_char32 = len_char32;
  }
  /* Protect against integer overflow vulnerability. */
  CLAMP(cu->len_char32, 0, INT_MAX - 4);
 
  BLO_read_pointer_array(reader, cu->totcol, (void **)&cu->mat);
 
  BLO_read_struct_array(reader, CharInfo, cu->len_char32 + 1, &cu->strinfo);
  BLO_read_struct_array(reader, TextBox, cu->totbox, &cu->tb);
 
  /* WARNING: for old files `cu->ob_type` won't be initialized,
   * versioning detects fonts based on `cu->vfont` (which won't have run yet)
   * so do the same here. */
  const bool is_font = cu->ob_type ? (cu->ob_type == OB_FONT) : (cu->vfont != nullptr);
 
  if (is_font == false) {
    BLO_read_struct_list(reader, Nurb, &(cu->nurb));
  }
  else {
    cu->nurb.first = cu->nurb.last = nullptr;
 
    if (UNLIKELY(cu->str == nullptr)) {
      cu->len_char32 = 0;
      cu->str = MEM_calloc_arrayN<char>(cu->len_char32 + 1, "str new");
    }
    if (UNLIKELY(cu->strinfo == nullptr)) {
      cu->strinfo = MEM_calloc_arrayN<CharInfo>(cu->len_char32 + 1, "strinfo new");
    }
 
    TextBox *tb = MEM_calloc_arrayN<TextBox>(MAXTEXTBOX, "TextBoxread");
    if (cu->tb) {
      memcpy(tb, cu->tb, cu->totbox * sizeof(TextBox));
      MEM_freeN(cu->tb);
      cu->tb = tb;
    }
    else {
      cu->totbox = 1;
      cu->actbox = 1;
      cu->tb = tb;
      cu->tb[0].w = cu->linewidth;
    }
    if (cu->wordspace == 0.0f) {
      cu->wordspace = 1.0f;
    }
  }
 
  cu->editnurb = nullptr;
  cu->editfont = nullptr;
  cu->batch_cache = nullptr;
 
  LISTBASE_FOREACH (Nurb *, nu, &cu->nurb) {
    BLO_read_struct_array(reader, BezTriple, nu->pntsu, &nu->bezt);
    BLO_read_struct_array(reader, BPoint, nu->pntsu * nu->pntsv, &nu->bp);
    BLO_read_float_array(reader, KNOTSU(nu), &nu->knotsu);
    BLO_read_float_array(reader, KNOTSV(nu), &nu->knotsv);
    if (is_font == false) {
      nu->charidx = 0;
    }
  }
  cu->texspace_flag &= ~CU_TEXSPACE_FLAG_AUTO_EVALUATED;
 
  BLO_read_struct(reader, CurveProfile, &cu->bevel_profile);
  if (cu->bevel_profile != nullptr) {
    BKE_curveprofile_blend_read(reader, cu->bevel_profile);
  }
}
 
IDTypeInfo IDType_ID_CU_LEGACY = {
    /*id_code*/ Curve::id_type,
    /*id_filter*/ FILTER_ID_CU_LEGACY,
    /*dependencies_id_types*/ FILTER_ID_OB | FILTER_ID_MA | FILTER_ID_VF | FILTER_ID_KE,
    /*main_listbase_index*/ INDEX_ID_CU_LEGACY,
    /*struct_size*/ sizeof(Curve),
    /*name*/ "Curve",
    /*name_plural*/ N_("curves"),
    /*translation_context*/ BLT_I18NCONTEXT_ID_CURVE_LEGACY,
    /*flags*/ IDTYPE_FLAGS_APPEND_IS_REUSABLE,
    /*asset_type_info*/ nullptr,
 
    /*init_data*/ curve_init_data,
    /*copy_data*/ curve_copy_data,
    /*free_data*/ curve_free_data,
    /*make_local*/ nullptr,
    /*foreach_id*/ curve_foreach_id,
    /*foreach_cache*/ nullptr,
    /*foreach_path*/ nullptr,
    /*owner_pointer_get*/ nullptr,
 
    /*blend_write*/ curve_blend_write,
    /*blend_read_data*/ curve_blend_read_data,
    /*blend_read_after_liblink*/ nullptr,
 
    /*blend_read_undo_preserve*/ nullptr,
 
    /*lib_override_apply_post*/ nullptr,
};
 
void BKE_curve_editfont_free(Curve *cu)
{
  if (cu->editfont) {
    EditFont *ef = cu->editfont;
 
    if (ef->textbuf) {
      MEM_freeN(ef->textbuf);
    }
    if (ef->textbufinfo) {
      MEM_freeN(ef->textbufinfo);
    }
    if (ef->selboxes) {
      MEM_freeN(ef->selboxes);
    }
 
    MEM_freeN(ef);
    cu->editfont = nullptr;
  }
}
 
static void curve_editNurb_keyIndex_cv_free_cb(void *val)
{
  CVKeyIndex *index = (CVKeyIndex *)val;
  MEM_freeN(index->orig_cv);
  MEM_freeN(val);
}
 
void BKE_curve_editNurb_keyIndex_delCV(GHash *keyindex, const void *cv)
{
  BLI_assert(keyindex != nullptr);
  BLI_ghash_remove(keyindex, cv, nullptr, curve_editNurb_keyIndex_cv_free_cb);
}
 
void BKE_curve_editNurb_keyIndex_free(GHash **keyindex)
{
  if (!(*keyindex)) {
    return;
  }
  BLI_ghash_free(*keyindex, nullptr, curve_editNurb_keyIndex_cv_free_cb);
  *keyindex = nullptr;
}
 
void BKE_curve_editNurb_free(Curve *cu)
{
  if (cu->editnurb) {
    BKE_nurbList_free(&cu->editnurb->nurbs);
    BKE_curve_editNurb_keyIndex_free(&cu->editnurb->keyindex);
    MEM_freeN(cu->editnurb);
    cu->editnurb = nullptr;
  }
}
 
void BKE_curve_init(Curve *cu, const short curve_type)
{
  curve_init_data(&cu->id);
 
  cu->ob_type = curve_type;
 
  if (cu->ob_type == OB_FONT) {
    cu->flag |= CU_FRONT | CU_BACK;
    cu->vfont = cu->vfontb = cu->vfonti = cu->vfontbi = BKE_vfont_builtin_ensure();
    cu->vfont->id.us += 4;
 
    const char *str = DATA_("Text");
    size_t len_bytes;
    size_t len_char32 = BLI_strlen_utf8_ex(str, &len_bytes);
 
    cu->str = MEM_malloc_arrayN<char>(len_bytes + 1, "str");
    memcpy(cu->str, str, len_bytes + 1);
    BLI_assert(cu->str[len_bytes] == '\0');
 
    cu->len = len_bytes;
    cu->len_char32 = cu->pos = len_char32;
 
    cu->strinfo = MEM_calloc_arrayN<CharInfo>(len_char32 + 1, "strinfo new");
 
    cu->totbox = cu->actbox = 1;
    cu->tb = MEM_calloc_arrayN<TextBox>(MAXTEXTBOX, "textbox");
    cu->tb[0].w = cu->tb[0].h = 0.0;
  }
  else if (cu->ob_type == OB_SURF) {
    cu->flag |= CU_3D;
    cu->resolu = 4;
    cu->resolv = 4;
  }
  cu->bevel_profile = nullptr;
  /* Initialize the offset to 1.0, to compensate for it being set to -1.0
   * in the property getter. */
  cu->offset = 1.0f;
}
 
Curve *BKE_curve_add(Main *bmain, const char *name, int type)
{
  Curve *cu;
 
  /* We cannot use #BKE_id_new here as we need some custom initialization code. */
  cu = (Curve *)BKE_libblock_alloc(bmain, ID_CU_LEGACY, name, 0);
 
  BKE_curve_init(cu, type);
 
  return cu;
}
 
ListBase *BKE_curve_editNurbs_get(Curve *cu)
{
  if (cu->editnurb) {
    return &cu->editnurb->nurbs;
  }
 
  return nullptr;
}
 
const ListBase *BKE_curve_editNurbs_get_for_read(const Curve *cu)
{
  if (cu->editnurb) {
    return &cu->editnurb->nurbs;
  }
 
  return nullptr;
}
 
void BKE_curve_dimension_update(Curve *cu)
{
  ListBase *nurbs = BKE_curve_nurbs_get(cu);
  bool is_2d = CU_IS_2D(cu);
 
  LISTBASE_FOREACH (Nurb *, nu, nurbs) {
    if (is_2d) {
      BKE_nurb_project_2d(nu);
    }
 
    /* since the handles are moved they need to be auto-located again */
    if (nu->type == CU_BEZIER) {
      BKE_nurb_handles_calc(nu);
    }
  }
}
 
void BKE_curve_type_test(Object *ob, const bool dimension_update)
{
  Curve *cu = static_cast<Curve *>(ob->data);
  ob->type = cu->ob_type;
 
  if (dimension_update) {
    if (ob->type == OB_CURVES_LEGACY) {
      if (CU_IS_2D(cu)) {
        BKE_curve_dimension_update(cu);
      }
    }
  }
}
 
void BKE_curve_texspace_calc(Curve *cu)
{
  if (cu->texspace_flag & CU_TEXSPACE_FLAG_AUTO) {
    std::optional<blender::Bounds<blender::float3>> bounds = BKE_curve_minmax(cu, true);
    if (!bounds) {
      bounds = blender::Bounds<blender::float3>{float3(-FLT_MAX), -float3(FLT_MAX)};
    }
 
    float texspace_location[3], texspace_size[3];
    mid_v3_v3v3(texspace_location, bounds->min, bounds->max);
 
    texspace_size[0] = (bounds->max[0] - bounds->min[0]) / 2.0f;
    texspace_size[1] = (bounds->max[1] - bounds->min[1]) / 2.0f;
    texspace_size[2] = (bounds->max[2] - bounds->min[2]) / 2.0f;
 
    for (int a = 0; a < 3; a++) {
      if (texspace_size[a] == 0.0f) {
        texspace_size[a] = 1.0f;
      }
      else if (texspace_size[a] > 0.0f && texspace_size[a] < 0.00001f) {
        texspace_size[a] = 0.00001f;
      }
      else if (texspace_size[a] < 0.0f && texspace_size[a] > -0.00001f) {
        texspace_size[a] = -0.00001f;
      }
    }
 
    copy_v3_v3(cu->texspace_location, texspace_location);
    copy_v3_v3(cu->texspace_size, texspace_size);
 
    cu->texspace_flag |= CU_TEXSPACE_FLAG_AUTO_EVALUATED;
  }
}
 
void BKE_curve_texspace_ensure(Curve *cu)
{
  if ((cu->texspace_flag & CU_TEXSPACE_FLAG_AUTO) &&
      (cu->texspace_flag & CU_TEXSPACE_FLAG_AUTO_EVALUATED) == 0)
  {
    BKE_curve_texspace_calc(cu);
  }
}
 
bool BKE_nurbList_index_get_co(ListBase *nurb, const int index, float r_co[3])
{
  int tot = 0;
 
  LISTBASE_FOREACH (Nurb *, nu, nurb) {
    int tot_nu;
    if (nu->type == CU_BEZIER) {
      tot_nu = nu->pntsu;
      if (index - tot < tot_nu) {
        copy_v3_v3(r_co, nu->bezt[index - tot].vec[1]);
        return true;
      }
    }
    else {
      tot_nu = nu->pntsu * nu->pntsv;
      if (index - tot < tot_nu) {
        copy_v3_v3(r_co, nu->bp[index - tot].vec);
        return true;
      }
    }
    tot += tot_nu;
  }
 
  return false;
}
 
int BKE_nurbList_verts_count(const ListBase *nurb)
{
  int tot = 0;
 
  LISTBASE_FOREACH (const Nurb *, nu, nurb) {
    if (nu->bezt) {
      tot += 3 * nu->pntsu;
    }
    else if (nu->bp) {
      tot += nu->pntsu * nu->pntsv;
    }
  }
 
  return tot;
}
 
int BKE_nurbList_verts_count_without_handles(const ListBase *nurb)
{
  int tot = 0;
 
  LISTBASE_FOREACH (Nurb *, nu, nurb) {
    if (nu->bezt) {
      tot += nu->pntsu;
    }
    else if (nu->bp) {
      tot += nu->pntsu * nu->pntsv;
    }
  }
 
  return tot;
}
 
/* **************** NURBS ROUTINES ******************** */
 
void BKE_nurb_free(Nurb *nu)
{
  if (nu == nullptr) {
    return;
  }
 
  if (nu->bezt) {
    MEM_freeN(nu->bezt);
  }
  nu->bezt = nullptr;
  if (nu->bp) {
    MEM_freeN(nu->bp);
  }
  nu->bp = nullptr;
  if (nu->knotsu) {
    MEM_freeN(nu->knotsu);
  }
  nu->knotsu = nullptr;
  if (nu->knotsv) {
    MEM_freeN(nu->knotsv);
  }
  nu->knotsv = nullptr;
 
  MEM_freeN(nu);
}
 
void BKE_nurbList_free(ListBase *lb)
{
  if (lb == nullptr) {
    return;
  }
 
  LISTBASE_FOREACH_MUTABLE (Nurb *, nu, lb) {
    BKE_nurb_free(nu);
  }
  BLI_listbase_clear(lb);
}
 
Nurb *BKE_nurb_duplicate(const Nurb *nu)
{
  Nurb *newnu;
  int len;
 
  newnu = MEM_mallocN<Nurb>("duplicateNurb");
  if (newnu == nullptr) {
    return nullptr;
  }
  *newnu = blender::dna::shallow_copy(*nu);
 
  if (nu->bezt) {
    newnu->bezt = MEM_malloc_arrayN<BezTriple>(size_t(nu->pntsu), "duplicateNurb2");
    memcpy(newnu->bezt, nu->bezt, nu->pntsu * sizeof(BezTriple));
  }
  else {
    len = nu->pntsu * nu->pntsv;
    newnu->bp = MEM_malloc_arrayN<BPoint>(size_t(len), "duplicateNurb3");
    memcpy(newnu->bp, nu->bp, len * sizeof(BPoint));
 
    newnu->knotsu = newnu->knotsv = nullptr;
 
    if (nu->knotsu) {
      len = KNOTSU(nu);
      if (len) {
        newnu->knotsu = MEM_malloc_arrayN<float>(size_t(len), "duplicateNurb4");
        memcpy(newnu->knotsu, nu->knotsu, sizeof(float) * len);
      }
    }
    if (nu->pntsv > 1 && nu->knotsv) {
      len = KNOTSV(nu);
      if (len) {
        newnu->knotsv = MEM_malloc_arrayN<float>(size_t(len), "duplicateNurb5");
        memcpy(newnu->knotsv, nu->knotsv, sizeof(float) * len);
      }
    }
  }
  return newnu;
}
 
Nurb *BKE_nurb_copy(Nurb *src, int pntsu, int pntsv)
{
  Nurb *newnu = MEM_mallocN<Nurb>("copyNurb");
  *newnu = blender::dna::shallow_copy(*src);
 
  if (pntsu == 1) {
    std::swap(pntsu, pntsv);
  }
  newnu->pntsu = pntsu;
  newnu->pntsv = pntsv;
 
  /* caller can manually handle these arrays */
  newnu->knotsu = nullptr;
  newnu->knotsv = nullptr;
 
  if (src->bezt) {
    newnu->bezt = MEM_malloc_arrayN<BezTriple>(size_t(pntsu) * size_t(pntsv), "copyNurb2");
  }
  else {
    newnu->bp = MEM_malloc_arrayN<BPoint>(size_t(pntsu) * size_t(pntsv), "copyNurb3");
  }
 
  return newnu;
}
 
void BKE_nurbList_duplicate(ListBase *lb1, const ListBase *lb2)
{
  BKE_nurbList_free(lb1);
 
  LISTBASE_FOREACH (const Nurb *, nu, lb2) {
    Nurb *nurb_new = BKE_nurb_duplicate(nu);
    BLI_addtail(lb1, nurb_new);
  }
}
 
void BKE_nurb_project_2d(Nurb *nu)
{
  BezTriple *bezt;
  BPoint *bp;
  int a;
 
  if (nu->type == CU_BEZIER) {
    a = nu->pntsu;
    bezt = nu->bezt;
    while (a--) {
      bezt->vec[0][2] = 0.0;
      bezt->vec[1][2] = 0.0;
      bezt->vec[2][2] = 0.0;
      bezt++;
    }
  }
  else {
    a = nu->pntsu * nu->pntsv;
    bp = nu->bp;
    while (a--) {
      bp->vec[2] = 0.0;
      bp++;
    }
  }
}
 
static void calc_nurb_minmax(const Nurb *nu, bool use_radius, float min[3], float max[3])
{
  BezTriple *bezt;
  BPoint *bp;
  int a;
  float point[3];
 
  if (nu->type == CU_BEZIER) {
    a = nu->pntsu;
    bezt = nu->bezt;
    while (a--) {
      if (use_radius) {
        float radius_vector[3];
        radius_vector[0] = radius_vector[1] = radius_vector[2] = bezt->radius;
 
        add_v3_v3v3(point, bezt->vec[1], radius_vector);
        minmax_v3v3_v3(min, max, point);
 
        sub_v3_v3v3(point, bezt->vec[1], radius_vector);
        minmax_v3v3_v3(min, max, point);
      }
      else {
        minmax_v3v3_v3(min, max, bezt->vec[1]);
      }
      minmax_v3v3_v3(min, max, bezt->vec[0]);
      minmax_v3v3_v3(min, max, bezt->vec[2]);
      bezt++;
    }
  }
  else {
    a = nu->pntsu * nu->pntsv;
    bp = nu->bp;
    while (a--) {
      if (nu->pntsv == 1 && use_radius) {
        float radius_vector[3];
        radius_vector[0] = radius_vector[1] = radius_vector[2] = bp->radius;
 
        add_v3_v3v3(point, bp->vec, radius_vector);
        minmax_v3v3_v3(min, max, point);
 
        sub_v3_v3v3(point, bp->vec, radius_vector);
        minmax_v3v3_v3(min, max, point);
      }
      else {
        /* Surfaces doesn't use bevel, so no need to take radius into account. */
        minmax_v3v3_v3(min, max, bp->vec);
      }
      bp++;
    }
  }
}
 
float BKE_nurb_calc_length(const Nurb *nu, int resolution)
{
  BezTriple *bezt, *prevbezt;
  BPoint *bp, *prevbp;
  int a, b;
  float length = 0.0f;
  int resolu = resolution ? resolution : nu->resolu;
  int pntsu = nu->pntsu;
  float *points, *pntsit, *prevpntsit;
 
  if (nu->type == CU_POLY) {
    a = nu->pntsu - 1;
    bp = nu->bp;
    if (nu->flagu & CU_NURB_CYCLIC) {
      a++;
      prevbp = nu->bp + (nu->pntsu - 1);
    }
    else {
      prevbp = bp;
      bp++;
    }
 
    while (a--) {
      length += len_v3v3(prevbp->vec, bp->vec);
      prevbp = bp;
      bp++;
    }
  }
  else if (nu->type == CU_BEZIER) {
    points = MEM_malloc_arrayN<float>(3 * (size_t(resolu) + 1), "getLength_bezier");
    a = nu->pntsu - 1;
    bezt = nu->bezt;
    if (nu->flagu & CU_NURB_CYCLIC) {
      a++;
      prevbezt = nu->bezt + (nu->pntsu - 1);
    }
    else {
      prevbezt = bezt;
      bezt++;
    }
 
    while (a--) {
      if (prevbezt->h2 == HD_VECT && bezt->h1 == HD_VECT) {
        length += len_v3v3(prevbezt->vec[1], bezt->vec[1]);
      }
      else {
        for (int j = 0; j < 3; j++) {
          BKE_curve_forward_diff_bezier(prevbezt->vec[1][j],
                                        prevbezt->vec[2][j],
                                        bezt->vec[0][j],
                                        bezt->vec[1][j],
                                        points + j,
                                        resolu,
                                        sizeof(float[3]));
        }
 
        prevpntsit = pntsit = points;
        b = resolu;
        while (b--) {
          pntsit += 3;
          length += len_v3v3(prevpntsit, pntsit);
          prevpntsit = pntsit;
        }
      }
      prevbezt = bezt;
      bezt++;
    }
 
    MEM_freeN(points);
  }
  else if (nu->type == CU_NURBS) {
    if (nu->pntsv == 1) {
      /* important to zero for BKE_nurb_makeCurve. */
      points = MEM_calloc_arrayN<float>(3 * size_t(pntsu) * size_t(resolu), "getLength_nurbs");
 
      BKE_nurb_makeCurve(nu, points, nullptr, nullptr, nullptr, resolu, sizeof(float[3]));
 
      if (nu->flagu & CU_NURB_CYCLIC) {
        b = pntsu * resolu + 1;
        prevpntsit = points + 3 * (pntsu * resolu - 1);
        pntsit = points;
      }
      else {
        b = (pntsu - 1) * resolu;
        prevpntsit = points;
        pntsit = points + 3;
      }
 
      while (--b > 0) {
        length += len_v3v3(prevpntsit, pntsit);
        prevpntsit = pntsit;
        pntsit += 3;
      }
 
      MEM_freeN(points);
    }
  }
 
  return length;
}
 
void BKE_nurb_points_add(Nurb *nu, int number)
{
  nu->bp = (BPoint *)MEM_recallocN(nu->bp, (nu->pntsu + number) * sizeof(BPoint));
 
  BPoint *bp;
  int i;
  for (i = 0, bp = &nu->bp[nu->pntsu]; i < number; i++, bp++) {
    bp->radius = 1.0f;
  }
 
  nu->pntsu += number;
}
 
void BKE_nurb_bezierPoints_add(Nurb *nu, int number)
{
  BezTriple *bezt;
  int i;
 
  nu->bezt = (BezTriple *)MEM_recallocN(nu->bezt, (nu->pntsu + number) * sizeof(BezTriple));
 
  for (i = 0, bezt = &nu->bezt[nu->pntsu]; i < number; i++, bezt++) {
    bezt->radius = 1.0f;
  }
 
  nu->pntsu += number;
}
 
int BKE_nurb_index_from_uv(Nurb *nu, int u, int v)
{
  const int totu = nu->pntsu;
  const int totv = nu->pntsv;
 
  if (nu->flagu & CU_NURB_CYCLIC) {
    u = mod_i(u, totu);
  }
  else if (u < 0 || u >= totu) {
    return -1;
  }
 
  if (nu->flagv & CU_NURB_CYCLIC) {
    v = mod_i(v, totv);
  }
  else if (v < 0 || v >= totv) {
    return -1;
  }
 
  return (v * totu) + u;
}
 
void BKE_nurb_index_to_uv(Nurb *nu, int index, int *r_u, int *r_v)
{
  const int totu = nu->pntsu;
  const int totv = nu->pntsv;
  BLI_assert(index >= 0 && index < (nu->pntsu * nu->pntsv));
  *r_u = (index % totu);
  *r_v = (index / totu) % totv;
}
 
BezTriple *BKE_nurb_bezt_get_next(Nurb *nu, BezTriple *bezt)
{
  BezTriple *bezt_next;
 
  BLI_assert(ARRAY_HAS_ITEM(bezt, nu->bezt, nu->pntsu));
 
  if (bezt == &nu->bezt[nu->pntsu - 1]) {
    if (nu->flagu & CU_NURB_CYCLIC) {
      bezt_next = nu->bezt;
    }
    else {
      bezt_next = nullptr;
    }
  }
  else {
    bezt_next = bezt + 1;
  }
 
  return bezt_next;
}
 
BPoint *BKE_nurb_bpoint_get_next(Nurb *nu, BPoint *bp)
{
  BPoint *bp_next;
 
  BLI_assert(ARRAY_HAS_ITEM(bp, nu->bp, nu->pntsu));
 
  if (bp == &nu->bp[nu->pntsu - 1]) {
    if (nu->flagu & CU_NURB_CYCLIC) {
      bp_next = nu->bp;
    }
    else {
      bp_next = nullptr;
    }
  }
  else {
    bp_next = bp + 1;
  }
 
  return bp_next;
}
 
BezTriple *BKE_nurb_bezt_get_prev(Nurb *nu, BezTriple *bezt)
{
  BezTriple *bezt_prev;
 
  BLI_assert(ARRAY_HAS_ITEM(bezt, nu->bezt, nu->pntsu));
  BLI_assert(nu->pntsv <= 1);
 
  if (bezt == nu->bezt) {
    if (nu->flagu & CU_NURB_CYCLIC) {
      bezt_prev = &nu->bezt[nu->pntsu - 1];
    }
    else {
      bezt_prev = nullptr;
    }
  }
  else {
    bezt_prev = bezt - 1;
  }
 
  return bezt_prev;
}
 
BPoint *BKE_nurb_bpoint_get_prev(Nurb *nu, BPoint *bp)
{
  BPoint *bp_prev;
 
  BLI_assert(ARRAY_HAS_ITEM(bp, nu->bp, nu->pntsu));
  BLI_assert(nu->pntsv == 1);
 
  if (bp == nu->bp) {
    if (nu->flagu & CU_NURB_CYCLIC) {
      bp_prev = &nu->bp[nu->pntsu - 1];
    }
    else {
      bp_prev = nullptr;
    }
  }
  else {
    bp_prev = bp - 1;
  }
 
  return bp_prev;
}
 
void BKE_nurb_bezt_calc_normal(Nurb * /*nu*/, BezTriple *bezt, float r_normal[3])
{
  /* calculate the axis matrix from the spline */
  float dir_prev[3], dir_next[3];
 
  sub_v3_v3v3(dir_prev, bezt->vec[0], bezt->vec[1]);
  sub_v3_v3v3(dir_next, bezt->vec[1], bezt->vec[2]);
 
  normalize_v3(dir_prev);
  normalize_v3(dir_next);
 
  add_v3_v3v3(r_normal, dir_prev, dir_next);
  normalize_v3(r_normal);
}
 
void BKE_nurb_bezt_calc_plane(Nurb *nu, BezTriple *bezt, float r_plane[3])
{
  float dir_prev[3], dir_next[3];
 
  sub_v3_v3v3(dir_prev, bezt->vec[0], bezt->vec[1]);
  sub_v3_v3v3(dir_next, bezt->vec[1], bezt->vec[2]);
 
  normalize_v3(dir_prev);
  normalize_v3(dir_next);
 
  cross_v3_v3v3(r_plane, dir_prev, dir_next);
  if (normalize_v3(r_plane) < FLT_EPSILON) {
    BezTriple *bezt_prev = BKE_nurb_bezt_get_prev(nu, bezt);
    BezTriple *bezt_next = BKE_nurb_bezt_get_next(nu, bezt);
 
    if (bezt_prev) {
      sub_v3_v3v3(dir_prev, bezt_prev->vec[1], bezt->vec[1]);
      normalize_v3(dir_prev);
    }
    if (bezt_next) {
      sub_v3_v3v3(dir_next, bezt->vec[1], bezt_next->vec[1]);
      normalize_v3(dir_next);
    }
    cross_v3_v3v3(r_plane, dir_prev, dir_next);
  }
 
  /* matches with bones more closely */
  {
    float dir_mid[3], tvec[3];
    add_v3_v3v3(dir_mid, dir_prev, dir_next);
    cross_v3_v3v3(tvec, r_plane, dir_mid);
    copy_v3_v3(r_plane, tvec);
  }
 
  normalize_v3(r_plane);
}
 
void BKE_nurb_bpoint_calc_normal(Nurb *nu, BPoint *bp, float r_normal[3])
{
  BPoint *bp_prev = BKE_nurb_bpoint_get_prev(nu, bp);
  BPoint *bp_next = BKE_nurb_bpoint_get_next(nu, bp);
 
  zero_v3(r_normal);
 
  if (bp_prev) {
    float dir_prev[3];
    sub_v3_v3v3(dir_prev, bp_prev->vec, bp->vec);
    normalize_v3(dir_prev);
    add_v3_v3(r_normal, dir_prev);
  }
  if (bp_next) {
    float dir_next[3];
    sub_v3_v3v3(dir_next, bp->vec, bp_next->vec);
    normalize_v3(dir_next);
    add_v3_v3(r_normal, dir_next);
  }
 
  normalize_v3(r_normal);
}
 
void BKE_nurb_bpoint_calc_plane(Nurb *nu, BPoint *bp, float r_plane[3])
{
  BPoint *bp_prev = BKE_nurb_bpoint_get_prev(nu, bp);
  BPoint *bp_next = BKE_nurb_bpoint_get_next(nu, bp);
 
  float dir_prev[3] = {0.0f}, dir_next[3] = {0.0f};
 
  if (bp_prev) {
    sub_v3_v3v3(dir_prev, bp_prev->vec, bp->vec);
    normalize_v3(dir_prev);
  }
  if (bp_next) {
    sub_v3_v3v3(dir_next, bp->vec, bp_next->vec);
    normalize_v3(dir_next);
  }
  cross_v3_v3v3(r_plane, dir_prev, dir_next);
 
  /* matches with bones more closely */
  {
    float dir_mid[3], tvec[3];
    add_v3_v3v3(dir_mid, dir_prev, dir_next);
    cross_v3_v3v3(tvec, r_plane, dir_mid);
    copy_v3_v3(r_plane, tvec);
  }
 
  normalize_v3(r_plane);
}
 
/* ~~~~~~~~~~~~~~~~~~~~Non Uniform Rational B Spline calculations ~~~~~~~~~~~ */
 
static void calcknots(float *knots, const int pnts, const short order, const short flag)
{
  const bool is_cyclic = flag & CU_NURB_CYCLIC;
  const bool is_bezier = flag & CU_NURB_BEZIER;
  const bool is_end_point = flag & CU_NURB_ENDPOINT;
  /* Inner knots are always repeated once except on Bezier case. */
  const int repeat_inner = is_bezier ? order - 1 : 1;
  /* How many times to repeat 0.0 at the beginning of knot. */
  const int head = is_end_point ? (order - (is_cyclic ? 1 : 0)) :
                                  (is_bezier ? min_ii(2, repeat_inner) : 1);
  /* Number of knots replicating widths of the starting knots.
   * Covers both Cyclic and EndPoint cases. */
  const int tail = is_cyclic ? 2 * order - 1 : (is_end_point ? order : 0);
 
  const int knot_count = pnts + order + (is_cyclic ? order - 1 : 0);
 
  int r = head;
  float current = 0.0f;
 
  const int offset = is_end_point && is_cyclic ? 1 : 0;
  if (offset) {
    knots[0] = current;
    current += 1.0f;
  }
 
  for (const int i : IndexRange(offset, knot_count - offset - tail)) {
    knots[i] = current;
    r--;
    if (r == 0) {
      current += 1.0f;
      r = repeat_inner;
    }
  }
 
  const int tail_index = knot_count - tail;
  for (const int i : IndexRange(tail)) {
    knots[tail_index + i] = current + (knots[i] - knots[0]);
  }
}
 
static void makeknots(Nurb *nu, short uv)
{
  if (nu->type == CU_NURBS) {
    if (uv == 1) {
      if (nu->knotsu) {
        MEM_freeN(nu->knotsu);
      }
      if (BKE_nurb_check_valid_u(nu)) {
        nu->knotsu = MEM_calloc_arrayN<float>(size_t(KNOTSU(nu)) + 1, "makeknots");
        calcknots(nu->knotsu, nu->pntsu, nu->orderu, nu->flagu);
        nu->flagu &= ~CU_NURB_CUSTOM;
      }
      else {
        nu->knotsu = nullptr;
      }
    }
    else if (uv == 2) {
      if (nu->knotsv) {
        MEM_freeN(nu->knotsv);
      }
      if (BKE_nurb_check_valid_v(nu)) {
        nu->knotsv = MEM_calloc_arrayN<float>(size_t(KNOTSV(nu)) + 1, "makeknots");
        calcknots(nu->knotsv, nu->pntsv, nu->orderv, nu->flagv);
        nu->flagv &= ~CU_NURB_CUSTOM;
      }
      else {
        nu->knotsv = nullptr;
      }
    }
  }
}
 
void BKE_nurb_knot_alloc_u(Nurb *nu)
{
  nu->knotsu = MEM_calloc_arrayN<float>(KNOTSU(nu) + 1, __func__);
}
 
void BKE_nurb_knot_calc_u(Nurb *nu)
{
  makeknots(nu, 1);
}
 
void BKE_nurb_knot_calc_v(Nurb *nu)
{
  makeknots(nu, 2);
}
 
static void basisNurb(
    float t, short order, int pnts, const float *knots, float *basis, int *start, int *end)
{
  float d, e;
  int i, i1 = 0, i2 = 0, j, orderpluspnts, opp2, o2;
 
  orderpluspnts = order + pnts;
  opp2 = orderpluspnts - 1;
 
  /* this is for float inaccuracy */
  if (t < knots[0]) {
    t = knots[0];
  }
  else if (t > knots[opp2]) {
    t = knots[opp2];
  }
 
  /* this part is order '1' */
  o2 = order + 1;
  for (i = 0; i < opp2; i++) {
    if (knots[i] != knots[i + 1] && t >= knots[i] && t <= knots[i + 1]) {
      basis[i] = 1.0;
      i1 = i - o2;
      i1 = std::max(i1, 0);
      i2 = i;
      i++;
      while (i < opp2) {
        basis[i] = 0.0;
        i++;
      }
      break;
    }
 
    basis[i] = 0.0;
  }
  basis[i] = 0.0;
 
  /* this is order 2, 3, ... */
  for (j = 2; j <= order; j++) {
 
    if (i2 + j >= orderpluspnts) {
      i2 = opp2 - j;
    }
 
    for (i = i1; i <= i2; i++) {
      if (basis[i] != 0.0f) {
        d = ((t - knots[i]) * basis[i]) / (knots[i + j - 1] - knots[i]);
      }
      else {
        d = 0.0f;
      }
 
      if (basis[i + 1] != 0.0f) {
        e = ((knots[i + j] - t) * basis[i + 1]) / (knots[i + j] - knots[i + 1]);
      }
      else {
        e = 0.0;
      }
 
      basis[i] = d + e;
    }
  }
 
  *start = 1000;
  *end = 0;
 
  for (i = i1; i <= i2; i++) {
    if (basis[i] > 0.0f) {
      *end = i;
      if (*start == 1000) {
        *start = i;
      }
    }
  }
}
 
void BKE_nurb_makeFaces(const Nurb *nu, float *coord_array, int rowstride, int resolu, int resolv)
{
  BPoint *bp;
  float *basisu, *basis, *basisv, *sum, *fp, *in;
  float u, v, ustart, uend, ustep, vstart, vend, vstep, sumdiv;
  int i, j, iofs, jofs, cycl, len, curu, curv;
  int istart, iend, jsta, jen, *jstart, *jend, ratcomp;
 
  int totu = nu->pntsu * resolu, totv = nu->pntsv * resolv;
 
  if (nu->knotsu == nullptr || nu->knotsv == nullptr) {
    return;
  }
  if (nu->orderu > nu->pntsu) {
    return;
  }
  if (nu->orderv > nu->pntsv) {
    return;
  }
  if (coord_array == nullptr) {
    return;
  }
 
  /* allocate and initialize */
  len = totu * totv;
  if (len == 0) {
    return;
  }
 
  sum = MEM_calloc_arrayN<float>(len, "makeNurbfaces1");
 
  bp = nu->bp;
  i = nu->pntsu * nu->pntsv;
  ratcomp = 0;
  while (i--) {
    if (bp->vec[3] != 1.0f) {
      ratcomp = 1;
      break;
    }
    bp++;
  }
 
  fp = nu->knotsu;
  ustart = fp[nu->orderu - 1];
  if (nu->flagu & CU_NURB_CYCLIC) {
    uend = fp[nu->pntsu + nu->orderu - 1];
  }
  else {
    uend = fp[nu->pntsu];
  }
  ustep = (uend - ustart) / ((nu->flagu & CU_NURB_CYCLIC) ? totu : totu - 1);
 
  basisu = MEM_malloc_arrayN<float>(size_t(KNOTSU(nu)), "makeNurbfaces3");
 
  fp = nu->knotsv;
  vstart = fp[nu->orderv - 1];
 
  if (nu->flagv & CU_NURB_CYCLIC) {
    vend = fp[nu->pntsv + nu->orderv - 1];
  }
  else {
    vend = fp[nu->pntsv];
  }
  vstep = (vend - vstart) / ((nu->flagv & CU_NURB_CYCLIC) ? totv : totv - 1);
 
  len = KNOTSV(nu);
  basisv = MEM_malloc_arrayN<float>(size_t(len) * size_t(totv), "makeNurbfaces3");
  jstart = MEM_malloc_arrayN<int>(size_t(totv), "makeNurbfaces4");
  jend = MEM_malloc_arrayN<int>(size_t(totv), "makeNurbfaces5");
 
  /* Pre-calculation of `basisv` and `jstart`, `jend`. */
  if (nu->flagv & CU_NURB_CYCLIC) {
    cycl = nu->orderv - 1;
  }
  else {
    cycl = 0;
  }
  v = vstart;
  basis = basisv;
  curv = totv;
  while (curv--) {
    basisNurb(v, nu->orderv, nu->pntsv + cycl, nu->knotsv, basis, jstart + curv, jend + curv);
    basis += KNOTSV(nu);
    v += vstep;
  }
 
  if (nu->flagu & CU_NURB_CYCLIC) {
    cycl = nu->orderu - 1;
  }
  else {
    cycl = 0;
  }
  in = coord_array;
  u = ustart;
  curu = totu;
  while (curu--) {
    basisNurb(u, nu->orderu, nu->pntsu + cycl, nu->knotsu, basisu, &istart, &iend);
 
    basis = basisv;
    curv = totv;
    while (curv--) {
      jsta = jstart[curv];
      jen = jend[curv];
 
      /* calculate sum */
      sumdiv = 0.0;
      fp = sum;
 
      for (j = jsta; j <= jen; j++) {
 
        if (j >= nu->pntsv) {
          jofs = (j - nu->pntsv);
        }
        else {
          jofs = j;
        }
        bp = nu->bp + nu->pntsu * jofs + istart - 1;
 
        for (i = istart; i <= iend; i++, fp++) {
          if (i >= nu->pntsu) {
            iofs = i - nu->pntsu;
            bp = nu->bp + nu->pntsu * jofs + iofs;
          }
          else {
            bp++;
          }
 
          if (ratcomp) {
            *fp = basisu[i] * basis[j] * bp->vec[3];
            sumdiv += *fp;
          }
          else {
            *fp = basisu[i] * basis[j];
          }
        }
      }
 
      if (ratcomp) {
        fp = sum;
        for (j = jsta; j <= jen; j++) {
          for (i = istart; i <= iend; i++, fp++) {
            *fp /= sumdiv;
          }
        }
      }
 
      zero_v3(in);
 
      /* one! (1.0) real point now */
      fp = sum;
      for (j = jsta; j <= jen; j++) {
 
        if (j >= nu->pntsv) {
          jofs = (j - nu->pntsv);
        }
        else {
          jofs = j;
        }
        bp = nu->bp + nu->pntsu * jofs + istart - 1;
 
        for (i = istart; i <= iend; i++, fp++) {
          if (i >= nu->pntsu) {
            iofs = i - nu->pntsu;
            bp = nu->bp + nu->pntsu * jofs + iofs;
          }
          else {
            bp++;
          }
 
          if (*fp != 0.0f) {
            madd_v3_v3fl(in, bp->vec, *fp);
          }
        }
      }
 
      in += 3;
      basis += KNOTSV(nu);
    }
    u += ustep;
    if (rowstride != 0) {
      in = (float *)(((uchar *)in) + (rowstride - 3 * totv * sizeof(*in)));
    }
  }
 
  /* free */
  MEM_freeN(sum);
  MEM_freeN(basisu);
  MEM_freeN(basisv);
  MEM_freeN(jstart);
  MEM_freeN(jend);
}
 
void BKE_nurb_makeCurve(const Nurb *nu,
                        float *coord_array,
                        float *tilt_array,
                        float *radius_array,
                        float *weight_array,
                        int resolu,
                        int stride)
{
  const float eps = 1e-6f;
  BPoint *bp;
  float u, ustart, uend, ustep, sumdiv;
  float *basisu, *sum, *fp;
  float *coord_fp = coord_array, *tilt_fp = tilt_array, *radius_fp = radius_array,
        *weight_fp = weight_array;
  int i, len, istart, iend, cycl;
 
  if (nu->knotsu == nullptr) {
    return;
  }
  if (nu->orderu > nu->pntsu) {
    return;
  }
  if (coord_array == nullptr) {
    return;
  }
 
  /* allocate and initialize */
  len = nu->pntsu;
  if (len == 0) {
    return;
  }
  sum = MEM_calloc_arrayN<float>(len, "makeNurbcurve1");
 
  resolu = (resolu * SEGMENTSU(nu));
 
  if (resolu == 0) {
    MEM_freeN(sum);
    return;
  }
 
  fp = nu->knotsu;
  ustart = fp[nu->orderu - 1];
  if (nu->flagu & CU_NURB_CYCLIC) {
    uend = fp[nu->pntsu + nu->orderu - 1];
  }
  else {
    uend = fp[nu->pntsu];
  }
  ustep = (uend - ustart) / (resolu - ((nu->flagu & CU_NURB_CYCLIC) ? 0 : 1));
 
  basisu = MEM_malloc_arrayN<float>(size_t(KNOTSU(nu)), "makeNurbcurve3");
 
  if (nu->flagu & CU_NURB_CYCLIC) {
    cycl = nu->orderu - 1;
  }
  else {
    cycl = 0;
  }
 
  u = ustart;
  while (resolu--) {
    basisNurb(u, nu->orderu, nu->pntsu + cycl, nu->knotsu, basisu, &istart, &iend);
 
    /* calc sum */
    sumdiv = 0.0;
    fp = sum;
    bp = nu->bp + istart - 1;
    for (i = istart; i <= iend; i++, fp++) {
      if (i >= nu->pntsu) {
        bp = nu->bp + (i - nu->pntsu);
      }
      else {
        bp++;
      }
 
      *fp = basisu[i] * bp->vec[3];
      sumdiv += *fp;
    }
    if ((sumdiv != 0.0f) && (sumdiv < 1.0f - eps || sumdiv > 1.0f + eps)) {
      /* is normalizing needed? */
      fp = sum;
      for (i = istart; i <= iend; i++, fp++) {
        *fp /= sumdiv;
      }
    }
 
    zero_v3(coord_fp);
 
    /* one! (1.0) real point */
    fp = sum;
    bp = nu->bp + istart - 1;
    for (i = istart; i <= iend; i++, fp++) {
      if (i >= nu->pntsu) {
        bp = nu->bp + (i - nu->pntsu);
      }
      else {
        bp++;
      }
 
      if (*fp != 0.0f) {
        madd_v3_v3fl(coord_fp, bp->vec, *fp);
 
        if (tilt_fp) {
          (*tilt_fp) += (*fp) * bp->tilt;
        }
 
        if (radius_fp) {
          (*radius_fp) += (*fp) * bp->radius;
        }
 
        if (weight_fp) {
          (*weight_fp) += (*fp) * bp->weight;
        }
      }
    }
 
    coord_fp = (float *)POINTER_OFFSET(coord_fp, stride);
 
    if (tilt_fp) {
      tilt_fp = (float *)POINTER_OFFSET(tilt_fp, stride);
    }
    if (radius_fp) {
      radius_fp = (float *)POINTER_OFFSET(radius_fp, stride);
    }
    if (weight_fp) {
      weight_fp = (float *)POINTER_OFFSET(weight_fp, stride);
    }
 
    u += ustep;
  }
 
  /* free */
  MEM_freeN(sum);
  MEM_freeN(basisu);
}
 
uint BKE_curve_calc_coords_axis_len(const uint bezt_array_len,
                                    const uint resolu,
                                    const bool is_cyclic,
                                    const bool use_cyclic_duplicate_endpoint)
{
  const uint segments = bezt_array_len - (is_cyclic ? 0 : 1);
  const uint points_len = (segments * resolu) + (is_cyclic ? (use_cyclic_duplicate_endpoint) : 1);
  return points_len;
}
 
void BKE_curve_calc_coords_axis(const BezTriple *bezt_array,
                                const uint bezt_array_len,
                                const uint resolu,
                                const bool is_cyclic,
                                const bool use_cyclic_duplicate_endpoint,
                                /* Array parameters. */
                                const uint axis,
                                const uint stride,
                                float *r_points)
{
  const uint points_len = BKE_curve_calc_coords_axis_len(
      bezt_array_len, resolu, is_cyclic, use_cyclic_duplicate_endpoint);
  float *r_points_offset = r_points;
 
  const uint resolu_stride = resolu * stride;
  const uint bezt_array_last = bezt_array_len - 1;
 
  for (uint i = 0; i < bezt_array_last; i++) {
    const BezTriple *bezt_curr = &bezt_array[i];
    const BezTriple *bezt_next = &bezt_array[i + 1];
    BKE_curve_forward_diff_bezier(bezt_curr->vec[1][axis],
                                  bezt_curr->vec[2][axis],
                                  bezt_next->vec[0][axis],
                                  bezt_next->vec[1][axis],
                                  r_points_offset,
                                  int(resolu),
                                  stride);
    r_points_offset = (float *)POINTER_OFFSET(r_points_offset, resolu_stride);
  }
 
  if (is_cyclic) {
    const BezTriple *bezt_curr = &bezt_array[bezt_array_last];
    const BezTriple *bezt_next = &bezt_array[0];
    BKE_curve_forward_diff_bezier(bezt_curr->vec[1][axis],
                                  bezt_curr->vec[2][axis],
                                  bezt_next->vec[0][axis],
                                  bezt_next->vec[1][axis],
                                  r_points_offset,
                                  int(resolu),
                                  stride);
    r_points_offset = (float *)POINTER_OFFSET(r_points_offset, resolu_stride);
    if (use_cyclic_duplicate_endpoint) {
      *r_points_offset = *r_points;
      r_points_offset = (float *)POINTER_OFFSET(r_points_offset, stride);
    }
  }
  else {
    float *r_points_last = (float *)POINTER_OFFSET(r_points, bezt_array_last * resolu_stride);
    *r_points_last = bezt_array[bezt_array_last].vec[1][axis];
    r_points_offset = (float *)POINTER_OFFSET(r_points_offset, stride);
  }
 
  BLI_assert((float *)POINTER_OFFSET(r_points, points_len * stride) == r_points_offset);
  UNUSED_VARS_NDEBUG(points_len);
}
 
void BKE_curve_forward_diff_bezier(
    float q0, float q1, float q2, float q3, float *p, int it, int stride)
{
  float rt0, rt1, rt2, rt3, f;
  int a;
 
  f = float(it);
  rt0 = q0;
  rt1 = 3.0f * (q1 - q0) / f;
  f *= f;
  rt2 = 3.0f * (q0 - 2.0f * q1 + q2) / f;
  f *= it;
  rt3 = (q3 - q0 + 3.0f * (q1 - q2)) / f;
 
  q0 = rt0;
  q1 = rt1 + rt2 + rt3;
  q2 = 2 * rt2 + 6 * rt3;
  q3 = 6 * rt3;
 
  for (a = 0; a <= it; a++) {
    *p = q0;
    p = (float *)POINTER_OFFSET(p, stride);
    q0 += q1;
    q1 += q2;
    q2 += q3;
  }
}
 
void BKE_curve_forward_diff_tangent_bezier(
    float q0, float q1, float q2, float q3, float *p, int it, int stride)
{
  float rt0, rt1, rt2, f;
  int a;
 
  f = 1.0f / float(it);
 
  rt0 = 3.0f * (q1 - q0);
  rt1 = f * (3.0f * (q3 - q0) + 9.0f * (q1 - q2));
  rt2 = 6.0f * (q0 + q2) - 12.0f * q1;
 
  q0 = rt0;
  q1 = f * (rt1 + rt2);
  q2 = 2.0f * f * rt1;
 
  for (a = 0; a <= it; a++) {
    *p = q0;
    p = (float *)POINTER_OFFSET(p, stride);
    q0 += q1;
    q1 += q2;
  }
}
 
static void forward_diff_bezier_cotangent(const float p0[3],
                                          const float p1[3],
                                          const float p2[3],
                                          const float p3[3],
                                          float p[3],
                                          int it,
                                          int stride)
{
  /* note that these are not perpendicular to the curve
   * they need to be rotated for this,
   *
   * This could also be optimized like BKE_curve_forward_diff_bezier */
  for (int a = 0; a <= it; a++) {
    float t = float(a) / float(it);
 
    for (int i = 0; i < 3; i++) {
      p[i] = (-6.0f * t + 6.0f) * p0[i] + (18.0f * t - 12.0f) * p1[i] +
             (-18.0f * t + 6.0f) * p2[i] + (6.0f * t) * p3[i];
    }
    normalize_v3(p);
    p = (float *)POINTER_OFFSET(p, stride);
  }
}
 
static int cu_isectLL(const float v1[3],
                      const float v2[3],
                      const float v3[3],
                      const float v4[3],
                      short cox,
                      short coy,
                      float *lambda,
                      float *mu,
                      float vec[3])
{
  /* return:
   * -1: collinear
   *  0: no intersection of segments
   *  1: exact intersection of segments
   *  2: cross-intersection of segments
   */
  float deler;
 
  deler = (v1[cox] - v2[cox]) * (v3[coy] - v4[coy]) - (v3[cox] - v4[cox]) * (v1[coy] - v2[coy]);
  if (deler == 0.0f) {
    return -1;
  }
 
  *lambda = (v1[coy] - v3[coy]) * (v3[cox] - v4[cox]) - (v1[cox] - v3[cox]) * (v3[coy] - v4[coy]);
  *lambda = -(*lambda / deler);
 
  deler = v3[coy] - v4[coy];
  if (deler == 0) {
    deler = v3[cox] - v4[cox];
    *mu = -(*lambda * (v2[cox] - v1[cox]) + v1[cox] - v3[cox]) / deler;
  }
  else {
    *mu = -(*lambda * (v2[coy] - v1[coy]) + v1[coy] - v3[coy]) / deler;
  }
  vec[cox] = *lambda * (v2[cox] - v1[cox]) + v1[cox];
  vec[coy] = *lambda * (v2[coy] - v1[coy]) + v1[coy];
 
  if (*lambda >= 0.0f && *lambda <= 1.0f && *mu >= 0.0f && *mu <= 1.0f) {
    if (*lambda == 0.0f || *lambda == 1.0f || *mu == 0.0f || *mu == 1.0f) {
      return 1;
    }
    return 2;
  }
  return 0;
}
 
static bool bevelinside(const BevList *bl1, const BevList *bl2)
{
  /* is bl2 INSIDE bl1 ? with left-right method and "lambda's" */
  /* returns '1' if correct hole. */
  BevPoint *bevp, *prevbevp;
  float min, max, vec[3], hvec1[3], hvec2[3], lab, mu;
  int nr, links = 0, rechts = 0, mode;
 
  /* take first vertex of possible hole */
 
  bevp = bl2->bevpoints;
  hvec1[0] = bevp->vec[0];
  hvec1[1] = bevp->vec[1];
  hvec1[2] = 0.0;
  copy_v3_v3(hvec2, hvec1);
  hvec2[0] += 1000;
 
  /* test it with all edges of potential surrounding poly */
  /* count number of transitions left-right. */
 
  bevp = bl1->bevpoints;
  nr = bl1->nr;
  prevbevp = bevp + (nr - 1);
 
  while (nr--) {
    min = prevbevp->vec[1];
    max = bevp->vec[1];
    if (max < min) {
      min = max;
      max = prevbevp->vec[1];
    }
    if (min != max) {
      if (min <= hvec1[1] && max >= hvec1[1]) {
        /* there's a transition, calc intersection point */
        mode = cu_isectLL(prevbevp->vec, bevp->vec, hvec1, hvec2, 0, 1, &lab, &mu, vec);
        /* if lab==0.0 or lab==1.0 then the edge intersects exactly a transition
         * only allow for one situation: we choose lab= 1.0
         */
        if (mode >= 0 && lab != 0.0f) {
          if (vec[0] < hvec1[0]) {
            links++;
          }
          else {
            rechts++;
          }
        }
      }
    }
    prevbevp = bevp;
    bevp++;
  }
 
  return (links & 1) && (rechts & 1);
}
 
struct BevelSort {
  BevList *bl;
  float left;
  int dir;
};
 
static int vergxcobev(const void *a1, const void *a2)
{
  const BevelSort *x1 = (BevelSort *)a1, *x2 = (BevelSort *)a2;
 
  if (x1->left > x2->left) {
    return 1;
  }
  if (x1->left < x2->left) {
    return -1;
  }
  return 0;
}
 
/* this function cannot be replaced with atan2, but why? */
 
static void calc_bevel_sin_cos(
    float x1, float y1, float x2, float y2, float *r_sina, float *r_cosa)
{
  float t01, t02, x3, y3;
 
  t01 = sqrtf(x1 * x1 + y1 * y1);
  t02 = sqrtf(x2 * x2 + y2 * y2);
  if (t01 == 0.0f) {
    t01 = 1.0f;
  }
  if (t02 == 0.0f) {
    t02 = 1.0f;
  }
 
  x1 /= t01;
  y1 /= t01;
  x2 /= t02;
  y2 /= t02;
 
  t02 = x1 * x2 + y1 * y2;
  if (fabsf(t02) >= 1.0f) {
    t02 = M_PI_2;
  }
  else {
    t02 = safe_acosf(t02) / 2.0f;
  }
 
  t02 = sinf(t02);
  if (t02 == 0.0f) {
    t02 = 1.0f;
  }
 
  x3 = x1 - x2;
  y3 = y1 - y2;
  if (x3 == 0 && y3 == 0) {
    x3 = y1;
    y3 = -x1;
  }
  else {
    t01 = sqrtf(x3 * x3 + y3 * y3);
    x3 /= t01;
    y3 /= t01;
  }
 
  *r_sina = -y3 / t02;
  *r_cosa = x3 / t02;
}
 
static void tilt_bezpart(const BezTriple *prevbezt,
                         const BezTriple *bezt,
                         const Nurb *nu,
                         float *tilt_array,
                         float *radius_array,
                         float *weight_array,
                         int resolu,
                         int stride)
{
  const BezTriple *pprev, *next, *last;
  float fac, dfac, t[4];
  int a;
 
  if (tilt_array == nullptr && radius_array == nullptr) {
    return;
  }
 
  last = nu->bezt + (nu->pntsu - 1);
 
  /* returns a point */
  if (prevbezt == nu->bezt) {
    if (nu->flagu & CU_NURB_CYCLIC) {
      pprev = last;
    }
    else {
      pprev = prevbezt;
    }
  }
  else {
    pprev = prevbezt - 1;
  }
 
  /* next point */
  if (bezt == last) {
    if (nu->flagu & CU_NURB_CYCLIC) {
      next = nu->bezt;
    }
    else {
      next = bezt;
    }
  }
  else {
    next = bezt + 1;
  }
 
  fac = 0.0;
  dfac = 1.0f / float(resolu);
 
  for (a = 0; a < resolu; a++, fac += dfac) {
    if (tilt_array) {
      if (nu->tilt_interp == KEY_CU_EASE) {
        /* May as well support for tilt also 2.47 ease interp. */
        *tilt_array = prevbezt->tilt +
                      (bezt->tilt - prevbezt->tilt) * (3.0f * fac * fac - 2.0f * fac * fac * fac);
      }
      else {
        key_curve_position_weights(fac, t, KeyInterpolationType(nu->tilt_interp));
        *tilt_array = t[0] * pprev->tilt + t[1] * prevbezt->tilt + t[2] * bezt->tilt +
                      t[3] * next->tilt;
      }
 
      tilt_array = (float *)POINTER_OFFSET(tilt_array, stride);
    }
 
    if (radius_array) {
      if (nu->radius_interp == KEY_CU_EASE) {
        /* Support 2.47 ease interp
         * NOTE: this only takes the 2 points into account,
         * giving much more localized results to changes in radius, sometimes you want that. */
        *radius_array = prevbezt->radius + (bezt->radius - prevbezt->radius) *
                                               (3.0f * fac * fac - 2.0f * fac * fac * fac);
      }
      else {
 
        /* reuse interpolation from tilt if we can */
        if (tilt_array == nullptr || nu->tilt_interp != nu->radius_interp) {
          key_curve_position_weights(fac, t, KeyInterpolationType(nu->radius_interp));
        }
        *radius_array = t[0] * pprev->radius + t[1] * prevbezt->radius + t[2] * bezt->radius +
                        t[3] * next->radius;
      }
 
      radius_array = (float *)POINTER_OFFSET(radius_array, stride);
    }
 
    if (weight_array) {
      /* Basic interpolation for now, could copy tilt interp too. */
      *weight_array = prevbezt->weight + (bezt->weight - prevbezt->weight) *
                                             (3.0f * fac * fac - 2.0f * fac * fac * fac);
 
      weight_array = (float *)POINTER_OFFSET(weight_array, stride);
    }
  }
}
 
/* `make_bevel_list_3D_*` functions, at a minimum these must
 * fill in the #BevPoint.quat and #BevPoint.dir values. */

static void bevel_list_calc_bisect(BevList *bl)
{
  BevPoint *bevp2, *bevp1, *bevp0;
  int nr;
  const bool is_cyclic = bl->poly != -1;
 
  if (is_cyclic) {
    bevp2 = bl->bevpoints;
    bevp1 = bevp2 + (bl->nr - 1);
    bevp0 = bevp1 - 1;
    nr = bl->nr;
  }
  else {
    /* If spline is not cyclic, direction of first and
     * last bevel points matches direction of CV handle.
     *
     * This is getting calculated earlier when we know
     * CV's handles and here we might simply skip evaluation
     * of direction for this guys.
     */
 
    bevp0 = bl->bevpoints;
    bevp1 = bevp0 + 1;
    bevp2 = bevp1 + 1;
 
    nr = bl->nr - 2;
  }
 
  while (nr--) {
    /* totally simple */
    bisect_v3_v3v3v3(bevp1->dir, bevp0->vec, bevp1->vec, bevp2->vec);
 
    bevp0 = bevp1;
    bevp1 = bevp2;
    bevp2++;
  }
 
  /* In the unlikely situation that handles define a zeroed direction,
   * calculate it from the adjacent points, see #80742.
   *
   * Only do this as a fallback since we typically want the end-point directions
   * to be exactly aligned with the handles at the end-point, see #83117. */
  if (is_cyclic == false) {
    bevp0 = &bl->bevpoints[0];
    bevp1 = &bl->bevpoints[1];
    if (UNLIKELY(is_zero_v3(bevp0->dir))) {
      sub_v3_v3v3(bevp0->dir, bevp1->vec, bevp0->vec);
      if (normalize_v3(bevp0->dir) == 0.0f) {
        copy_v3_v3(bevp0->dir, bevp1->dir);
      }
    }
 
    bevp0 = &bl->bevpoints[bl->nr - 2];
    bevp1 = &bl->bevpoints[bl->nr - 1];
    if (UNLIKELY(is_zero_v3(bevp1->dir))) {
      sub_v3_v3v3(bevp1->dir, bevp1->vec, bevp0->vec);
      if (normalize_v3(bevp1->dir) == 0.0f) {
        copy_v3_v3(bevp1->dir, bevp0->dir);
      }
    }
  }
}
static void bevel_list_flip_tangents(BevList *bl)
{
  BevPoint *bevp2, *bevp1, *bevp0;
  int nr;
 
  bevp2 = bl->bevpoints;
  bevp1 = bevp2 + (bl->nr - 1);
  bevp0 = bevp1 - 1;
 
  nr = bl->nr;
  while (nr--) {
    if (angle_normalized_v3v3(bevp0->tan, bevp1->tan) > DEG2RADF(90.0f)) {
      negate_v3(bevp1->tan);
    }
 
    bevp0 = bevp1;
    bevp1 = bevp2;
    bevp2++;
  }
}
/* apply user tilt */
static void bevel_list_apply_tilt(BevList *bl)
{
  BevPoint *bevp2, *bevp1;
  int nr;
  float q[4];
 
  bevp2 = bl->bevpoints;
  bevp1 = bevp2 + (bl->nr - 1);
 
  nr = bl->nr;
  while (nr--) {
    axis_angle_to_quat(q, bevp1->dir, bevp1->tilt);
    mul_qt_qtqt(bevp1->quat, q, bevp1->quat);
    normalize_qt(bevp1->quat);
 
    bevp1 = bevp2;
    bevp2++;
  }
}

static void bevel_list_smooth(BevList *bl, int smooth_iter)
{
  BevPoint *bevp2, *bevp1, *bevp0;
  int nr;
 
  float q[4];
  float bevp0_quat[4];
  int a;
 
  for (a = 0; a < smooth_iter; a++) {
    bevp2 = bl->bevpoints;
    bevp1 = bevp2 + (bl->nr - 1);
    bevp0 = bevp1 - 1;
 
    nr = bl->nr;
 
    if (bl->poly == -1) { /* check its not cyclic */
      /* Skip the first point. */
      // bevp0 = bevp1;
      bevp1 = bevp2;
      bevp2++;
      nr--;
 
      bevp0 = bevp1;
      bevp1 = bevp2;
      bevp2++;
      nr--;
    }
 
    copy_qt_qt(bevp0_quat, bevp0->quat);
 
    while (nr--) {
      /* Interpolate quaternions. */
      float zaxis[3] = {0, 0, 1}, cross[3], q2[4];
      interp_qt_qtqt(q, bevp0_quat, bevp2->quat, 0.5);
      normalize_qt(q);
 
      mul_qt_v3(q, zaxis);
      cross_v3_v3v3(cross, zaxis, bevp1->dir);
      axis_angle_to_quat(q2, cross, angle_normalized_v3v3(zaxis, bevp1->dir));
      normalize_qt(q2);
 
      copy_qt_qt(bevp0_quat, bevp1->quat);
      mul_qt_qtqt(q, q2, q);
      interp_qt_qtqt(bevp1->quat, bevp1->quat, q, 0.5);
      normalize_qt(bevp1->quat);
 
      // bevp0 = bevp1; /* UNUSED */
      bevp1 = bevp2;
      bevp2++;
    }
  }
}
 
static void make_bevel_list_3D_zup(BevList *bl)
{
  BevPoint *bevp = bl->bevpoints;
  int nr = bl->nr;
 
  bevel_list_calc_bisect(bl);
 
  while (nr--) {
    vec_to_quat(bevp->quat, bevp->dir, 5, 1);
    bevp++;
  }
}
 
static void minimum_twist_between_two_points(BevPoint *bevp_curr, const BevPoint *bevp_prev)
{
  float angle = angle_normalized_v3v3(bevp_prev->dir, bevp_curr->dir);
 
  if (angle > 0.0f) { /* otherwise we can keep as is */
    float q[4];
    float cross_tmp[3];
    cross_v3_v3v3(cross_tmp, bevp_prev->dir, bevp_curr->dir);
    axis_angle_to_quat(q, cross_tmp, angle);
    mul_qt_qtqt(bevp_curr->quat, q, bevp_prev->quat);
  }
  else {
    copy_qt_qt(bevp_curr->quat, bevp_prev->quat);
  }
}
 
static void make_bevel_list_3D_minimum_twist(BevList *bl)
{
  BevPoint *bevp2, *bevp1, *bevp0; /* Standard for all make_bevel_list_3D_* functions. */
  int nr;
  float q[4];
  const bool is_cyclic = bl->poly != -1;
  /* NOTE(@ideasman42): For non-cyclic curves only initialize the first direction
   * (via `vec_to_quat`), necessary for symmetry, see #71137.
   * Otherwise initialize the first and second points before propagating rotation forward.
   * This is historical as changing this can cause significantly different output.
   * Specifically: `deform_modifiers` test: (`CurveMeshDeform`).
   *
   * While it would seem correct to only use the first point for non-cyclic curves as well
   * the end-points direction is initialized from the input handles (instead of the directions
   * between points), there is often a bigger difference in the first and second directions
   * than you'd otherwise expect. So using only the first direction breaks compatibility
   * enough it's best to leave it as-is. */
  const int nr_init = bl->nr - (is_cyclic ? 1 : 2);
 
  bevel_list_calc_bisect(bl);
 
  bevp2 = bl->bevpoints;
  bevp1 = bevp2 + (bl->nr - 1);
  bevp0 = bevp1 - 1;
 
  nr = bl->nr;
  while (nr--) {
 
    if (nr >= nr_init) {
      /* Initialize the rotation, otherwise propagate the previous rotation forward. */
      vec_to_quat(bevp1->quat, bevp1->dir, 5, 1);
    }
    else {
      minimum_twist_between_two_points(bevp1, bevp0);
    }
 
    bevp0 = bevp1;
    bevp1 = bevp2;
    bevp2++;
  }
 
  if (bl->poly != -1) { /* check for cyclic */
 
    /* Need to correct for the start/end points not matching
     * do this by calculating the tilt angle difference, then apply
     * the rotation gradually over the entire curve.
     *
     * Note that the split is between last and second last, rather than first/last as you'd expect.
     *
     * real order is like this
     * 0,1,2,3,4 --> 1,2,3,4,0
     *
     * This is why we compare last with second last.
     */
    float vec_1[3] = {0, 1, 0}, vec_2[3] = {0, 1, 0}, angle, ang_fac, cross_tmp[3];
 
    BevPoint *bevp_first;
    BevPoint *bevp_last;
 
    bevp_first = bl->bevpoints;
    bevp_first += bl->nr - 1;
    bevp_last = bevp_first;
    bevp_last--;
 
    /* Quaternions and vectors are normalized, should not need to re-normalize. */
    mul_qt_v3(bevp_first->quat, vec_1);
    mul_qt_v3(bevp_last->quat, vec_2);
    normalize_v3(vec_1);
    normalize_v3(vec_2);
 
    /* align the vector, can avoid this and it looks 98% OK but
     * better to align the angle quat roll's before comparing */
    {
      cross_v3_v3v3(cross_tmp, bevp_last->dir, bevp_first->dir);
      angle = angle_normalized_v3v3(bevp_first->dir, bevp_last->dir);
      axis_angle_to_quat(q, cross_tmp, angle);
      mul_qt_v3(q, vec_2);
    }
 
    angle = angle_normalized_v3v3(vec_1, vec_2);
 
    /* flip rotation if needs be */
    cross_v3_v3v3(cross_tmp, vec_1, vec_2);
    normalize_v3(cross_tmp);
    if (angle_normalized_v3v3(bevp_first->dir, cross_tmp) < DEG2RADF(90.0f)) {
      angle = -angle;
    }
 
    bevp2 = bl->bevpoints;
    bevp1 = bevp2 + (bl->nr - 1);
    bevp0 = bevp1 - 1;
 
    nr = bl->nr;
    while (nr--) {
      ang_fac = angle * (1.0f - (float(nr) / bl->nr)); /* also works */
 
      axis_angle_to_quat(q, bevp1->dir, ang_fac);
      mul_qt_qtqt(bevp1->quat, q, bevp1->quat);
 
      bevp0 = bevp1;
      bevp1 = bevp2;
      bevp2++;
    }
  }
  else {
    /* Need to correct quat for the first/last point,
     * this is so because previously it was only calculated
     * using its own direction, which might not correspond
     * the twist of neighbor point.
     */
    bevp1 = bl->bevpoints;
    bevp0 = bevp1 + 1;
    minimum_twist_between_two_points(bevp1, bevp0);
 
    bevp2 = bl->bevpoints;
    bevp1 = bevp2 + (bl->nr - 1);
    bevp0 = bevp1 - 1;
    minimum_twist_between_two_points(bevp1, bevp0);
  }
}
 
static void make_bevel_list_3D_tangent(BevList *bl)
{
  BevPoint *bevp2, *bevp1, *bevp0; /* Standard for all make_bevel_list_3D_* functions. */
  int nr;
 
  float bevp0_tan[3];
 
  bevel_list_calc_bisect(bl);
  bevel_list_flip_tangents(bl);
 
  /* correct the tangents */
  bevp2 = bl->bevpoints;
  bevp1 = bevp2 + (bl->nr - 1);
  bevp0 = bevp1 - 1;
 
  nr = bl->nr;
  while (nr--) {
    float cross_tmp[3];
    cross_v3_v3v3(cross_tmp, bevp1->tan, bevp1->dir);
    cross_v3_v3v3(bevp1->tan, cross_tmp, bevp1->dir);
    normalize_v3(bevp1->tan);
 
    bevp0 = bevp1;
    bevp1 = bevp2;
    bevp2++;
  }
 
  /* now for the real twist calc */
  bevp2 = bl->bevpoints;
  bevp1 = bevp2 + (bl->nr - 1);
  bevp0 = bevp1 - 1;
 
  copy_v3_v3(bevp0_tan, bevp0->tan);
 
  nr = bl->nr;
  while (nr--) {
    /* make perpendicular, modify tan in place, is ok */
    float cross_tmp[3];
    const float zero[3] = {0, 0, 0};
 
    cross_v3_v3v3(cross_tmp, bevp1->tan, bevp1->dir);
    normalize_v3(cross_tmp);
    tri_to_quat(bevp1->quat, zero, cross_tmp, bevp1->tan); /* XXX: could be faster. */
 
    // bevp0 = bevp1; /* UNUSED */
    bevp1 = bevp2;
    bevp2++;
  }
}
 
static void make_bevel_list_3D(BevList *bl, int smooth_iter, int twist_mode)
{
  switch (twist_mode) {
    case CU_TWIST_TANGENT:
      make_bevel_list_3D_tangent(bl);
      break;
    case CU_TWIST_MINIMUM:
      make_bevel_list_3D_minimum_twist(bl);
      break;
    default: /* CU_TWIST_Z_UP default, pre 2.49c */
      make_bevel_list_3D_zup(bl);
      break;
  }
 
  if (smooth_iter) {
    bevel_list_smooth(bl, smooth_iter);
  }
 
  bevel_list_apply_tilt(bl);
}
 
/* only for 2 points */
static void make_bevel_list_segment_3D(BevList *bl)
{
  float q[4];
 
  BevPoint *bevp2 = bl->bevpoints;
  BevPoint *bevp1 = bevp2 + 1;
 
  /* simple quat/dir */
  sub_v3_v3v3(bevp1->dir, bevp1->vec, bevp2->vec);
  normalize_v3(bevp1->dir);
 
  vec_to_quat(bevp1->quat, bevp1->dir, 5, 1);
  axis_angle_to_quat(q, bevp1->dir, bevp1->tilt);
  mul_qt_qtqt(bevp1->quat, q, bevp1->quat);
  normalize_qt(bevp1->quat);
 
  copy_v3_v3(bevp2->dir, bevp1->dir);
  vec_to_quat(bevp2->quat, bevp2->dir, 5, 1);
  axis_angle_to_quat(q, bevp2->dir, bevp2->tilt);
  mul_qt_qtqt(bevp2->quat, q, bevp2->quat);
  normalize_qt(bevp2->quat);
}
 
/* only for 2 points */
static void make_bevel_list_segment_2D(BevList *bl)
{
  BevPoint *bevp2 = bl->bevpoints;
  BevPoint *bevp1 = bevp2 + 1;
 
  const float x1 = bevp1->vec[0] - bevp2->vec[0];
  const float y1 = bevp1->vec[1] - bevp2->vec[1];
 
  calc_bevel_sin_cos(x1, y1, -x1, -y1, &(bevp1->sina), &(bevp1->cosa));
  bevp2->sina = bevp1->sina;
  bevp2->cosa = bevp1->cosa;
 
  /* fill in dir & quat */
  make_bevel_list_segment_3D(bl);
}
 
static void make_bevel_list_2D(BevList *bl)
{
  /* NOTE(@ideasman42): `bevp->dir` and `bevp->quat` are not needed for beveling but are
   * used when making a path from a 2D curve, therefore they need to be set. */
 
  BevPoint *bevp0, *bevp1, *bevp2;
  int nr;
 
  if (bl->poly != -1) {
    bevp2 = bl->bevpoints;
    bevp1 = bevp2 + (bl->nr - 1);
    bevp0 = bevp1 - 1;
    nr = bl->nr;
  }
  else {
    bevp0 = bl->bevpoints;
    bevp1 = bevp0 + 1;
    bevp2 = bevp1 + 1;
 
    nr = bl->nr - 2;
  }
 
  while (nr--) {
    const float x1 = bevp1->vec[0] - bevp0->vec[0];
    const float x2 = bevp1->vec[0] - bevp2->vec[0];
    const float y1 = bevp1->vec[1] - bevp0->vec[1];
    const float y2 = bevp1->vec[1] - bevp2->vec[1];
 
    calc_bevel_sin_cos(x1, y1, x2, y2, &(bevp1->sina), &(bevp1->cosa));
 
    /* from: make_bevel_list_3D_zup, could call but avoid a second loop.
     * no need for tricky tilt calculation as with 3D curves */
    bisect_v3_v3v3v3(bevp1->dir, bevp0->vec, bevp1->vec, bevp2->vec);
    vec_to_quat(bevp1->quat, bevp1->dir, 5, 1);
    /* done with inline make_bevel_list_3D_zup */
 
    bevp0 = bevp1;
    bevp1 = bevp2;
    bevp2++;
  }
 
  /* correct non-cyclic cases */
  if (bl->poly == -1) {
    BevPoint *bevp;
    float angle;
 
    /* first */
    bevp = bl->bevpoints;
    angle = atan2f(bevp->dir[0], bevp->dir[1]) - float(M_PI_2);
    bevp->sina = sinf(angle);
    bevp->cosa = cosf(angle);
    vec_to_quat(bevp->quat, bevp->dir, 5, 1);
 
    /* last */
    bevp = bl->bevpoints;
    bevp += (bl->nr - 1);
    angle = atan2f(bevp->dir[0], bevp->dir[1]) - float(M_PI_2);
    bevp->sina = sinf(angle);
    bevp->cosa = cosf(angle);
    vec_to_quat(bevp->quat, bevp->dir, 5, 1);
  }
}
 
static void bevlist_firstlast_direction_calc_from_bpoint(const Nurb *nu, BevList *bl)
{
  if (nu->pntsu > 1) {
    BPoint *first_bp = nu->bp, *last_bp = nu->bp + (nu->pntsu - 1);
    BevPoint *first_bevp, *last_bevp;
 
    first_bevp = bl->bevpoints;
    last_bevp = first_bevp + (bl->nr - 1);
 
    sub_v3_v3v3(first_bevp->dir, (first_bp + 1)->vec, first_bp->vec);
    normalize_v3(first_bevp->dir);
 
    sub_v3_v3v3(last_bevp->dir, last_bp->vec, (last_bp - 1)->vec);
    normalize_v3(last_bevp->dir);
  }
}
 
void BKE_curve_bevelList_free(ListBase *bev)
{
  LISTBASE_FOREACH_MUTABLE (BevList *, bl, bev) {
    if (bl->seglen != nullptr) {
      MEM_freeN(bl->seglen);
    }
    if (bl->segbevcount != nullptr) {
      MEM_freeN(bl->segbevcount);
    }
    if (bl->bevpoints != nullptr) {
      MEM_freeN(bl->bevpoints);
    }
    MEM_freeN(bl);
  }
 
  BLI_listbase_clear(bev);
}
 
void BKE_curve_bevelList_make(Object *ob, const ListBase *nurbs, const bool for_render)
{
  /* - Convert all curves to polys, with indication of resolution and flags for double-vertices.
   * - Possibly; do a smart vertex removal (in case #Nurb).
   * - Separate in individual blocks with #BoundBox.
   * - Auto-hole detection.
   */
 
  /* This function needs an object, because of `tflag` and `upflag`. */
  Curve *cu = (Curve *)ob->data;
  BezTriple *bezt, *prevbezt;
  BPoint *bp;
  BevList *blnew;
  BevPoint *bevp2, *bevp1 = nullptr, *bevp0;
  const float threshold = 0.00001f;
  float min, inp;
  float *seglen = nullptr;
  BevelSort *sortdata, *sd, *sd1;
  int a, b, nr, poly, resolu = 0, len = 0, segcount;
  int *segbevcount;
  bool do_tilt, do_radius, do_weight;
  bool is_editmode = false;
  ListBase *bev;
 
  /* segbevcount also requires seglen. */
  const bool need_seglen = ELEM(
                               cu->bevfac1_mapping, CU_BEVFAC_MAP_SEGMENT, CU_BEVFAC_MAP_SPLINE) ||
                           ELEM(cu->bevfac2_mapping, CU_BEVFAC_MAP_SEGMENT, CU_BEVFAC_MAP_SPLINE);
 
  bev = &ob->runtime->curve_cache->bev;
 
#if 0
  /* do we need to calculate the radius for each point? */
  do_radius = (cu->bevobj || cu->taperobj || (cu->flag & CU_FRONT) || (cu->flag & CU_BACK)) ? 0 :
                                                                                              1;
#endif
 
  /* STEP 1: MAKE POLYS */
 
  BKE_curve_bevelList_free(&ob->runtime->curve_cache->bev);
  if (cu->editnurb && ob->type != OB_FONT) {
    is_editmode = true;
  }
 
  LISTBASE_FOREACH (const Nurb *, nu, nurbs) {
    if (nu->hide && is_editmode) {
      continue;
    }
 
    /* check we are a single point? also check we are not a surface and that the orderu is sane,
     * enforced in the UI but can go wrong possibly */
    if (!BKE_nurb_check_valid_u(nu)) {
      BevList *bl = MEM_callocN<BevList>("makeBevelList1");
      bl->bevpoints = MEM_calloc_arrayN<BevPoint>(1, "makeBevelPoints1");
      BLI_addtail(bev, bl);
      bl->nr = 0;
      bl->charidx = nu->charidx;
      continue;
    }
 
    /* Tilt, as the rotation angle of curve control points, is only calculated for 3D curves,
     * (since this transformation affects the 3D space). */
    do_tilt = (cu->flag & CU_3D) != 0;
 
    /* Normal display uses the radius, better just to calculate them. */
    do_radius = CU_DO_RADIUS(cu, nu);
 
    do_weight = true;
 
    BevPoint *bevp;
 
    if (for_render && cu->resolu_ren != 0) {
      resolu = cu->resolu_ren;
    }
    else {
      resolu = nu->resolu;
    }
 
    segcount = SEGMENTSU(nu);
 
    if (nu->type == CU_POLY) {
      len = nu->pntsu;
      BevList *bl = MEM_callocN<BevList>(__func__);
      bl->bevpoints = MEM_calloc_arrayN<BevPoint>(len, __func__);
      if (need_seglen && (nu->flagu & CU_NURB_CYCLIC) == 0) {
        bl->seglen = MEM_malloc_arrayN<float>(size_t(segcount), __func__);
        bl->segbevcount = MEM_malloc_arrayN<int>(size_t(segcount), __func__);
      }
      BLI_addtail(bev, bl);
 
      bl->poly = (nu->flagu & CU_NURB_CYCLIC) ? 0 : -1;
      bl->nr = len;
      bl->dupe_nr = 0;
      bl->charidx = nu->charidx;
      bevp = bl->bevpoints;
      bevp->offset = 0;
      bp = nu->bp;
      seglen = bl->seglen;
      segbevcount = bl->segbevcount;
 
      while (len--) {
        copy_v3_v3(bevp->vec, bp->vec);
        bevp->tilt = bp->tilt;
        bevp->radius = bp->radius;
        bevp->weight = bp->weight;
        bp++;
        if (seglen != nullptr && len != 0) {
          *seglen = len_v3v3(bevp->vec, bp->vec);
          bevp++;
          bevp->offset = *seglen;
          if (*seglen > threshold) {
            *segbevcount = 1;
          }
          else {
            *segbevcount = 0;
          }
          seglen++;
          segbevcount++;
        }
        else {
          bevp++;
        }
      }
 
      if ((nu->flagu & CU_NURB_CYCLIC) == 0) {
        bevlist_firstlast_direction_calc_from_bpoint(nu, bl);
      }
    }
    else if (nu->type == CU_BEZIER) {
      /* in case last point is not cyclic */
      len = segcount * resolu + 1;
 
      BevList *bl = MEM_callocN<BevList>(__func__);
      bl->bevpoints = MEM_calloc_arrayN<BevPoint>(len, __func__);
      if (need_seglen && (nu->flagu & CU_NURB_CYCLIC) == 0) {
        bl->seglen = MEM_malloc_arrayN<float>(size_t(segcount), __func__);
        bl->segbevcount = MEM_malloc_arrayN<int>(size_t(segcount), __func__);
      }
      BLI_addtail(bev, bl);
 
      bl->poly = (nu->flagu & CU_NURB_CYCLIC) ? 0 : -1;
      bl->charidx = nu->charidx;
 
      bevp = bl->bevpoints;
      seglen = bl->seglen;
      segbevcount = bl->segbevcount;
 
      bevp->offset = 0;
      if (seglen != nullptr) {
        *seglen = 0;
        *segbevcount = 0;
      }
 
      a = nu->pntsu - 1;
      bezt = nu->bezt;
      if (nu->flagu & CU_NURB_CYCLIC) {
        a++;
        prevbezt = nu->bezt + (nu->pntsu - 1);
      }
      else {
        prevbezt = bezt;
        bezt++;
      }
 
      sub_v3_v3v3(bevp->dir, prevbezt->vec[2], prevbezt->vec[1]);
      normalize_v3(bevp->dir);
 
      BLI_assert(segcount >= a);
 
      while (a--) {
        if (prevbezt->h2 == HD_VECT && bezt->h1 == HD_VECT) {
 
          copy_v3_v3(bevp->vec, prevbezt->vec[1]);
          bevp->tilt = prevbezt->tilt;
          bevp->radius = prevbezt->radius;
          bevp->weight = prevbezt->weight;
          bevp->dupe_tag = false;
          bevp++;
          bl->nr++;
          bl->dupe_nr = 1;
          if (seglen != nullptr) {
            *seglen = len_v3v3(prevbezt->vec[1], bezt->vec[1]);
            bevp->offset = *seglen;
            seglen++;
            /* match segbevcount to the cleaned up bevel lists (see STEP 2) */
            if (bevp->offset > threshold) {
              *segbevcount = 1;
            }
            segbevcount++;
          }
        }
        else {
          /* Always do all three, to prevent data hanging around. */
          int j;
 
          /* #BevPoint must stay aligned to 4 so `sizeof(BevPoint) / sizeof(float)` works. */
          for (j = 0; j < 3; j++) {
            BKE_curve_forward_diff_bezier(prevbezt->vec[1][j],
                                          prevbezt->vec[2][j],
                                          bezt->vec[0][j],
                                          bezt->vec[1][j],
                                          &(bevp->vec[j]),
                                          resolu,
                                          sizeof(BevPoint));
          }
 
          /* If both arrays are `nullptr` do nothing. */
          tilt_bezpart(prevbezt,
                       bezt,
                       nu,
                       do_tilt ? &bevp->tilt : nullptr,
                       do_radius ? &bevp->radius : nullptr,
                       do_weight ? &bevp->weight : nullptr,
                       resolu,
                       sizeof(BevPoint));
 
          if (cu->twist_mode == CU_TWIST_TANGENT) {
            forward_diff_bezier_cotangent(prevbezt->vec[1],
                                          prevbezt->vec[2],
                                          bezt->vec[0],
                                          bezt->vec[1],
                                          bevp->tan,
                                          resolu,
                                          sizeof(BevPoint));
          }
 
          /* `seglen`. */
          if (seglen != nullptr) {
            *seglen = 0;
            *segbevcount = 0;
            for (j = 0; j < resolu; j++) {
              bevp0 = bevp;
              bevp++;
              bevp->offset = len_v3v3(bevp0->vec, bevp->vec);
              /* Match `seglen` and `segbevcount` to the cleaned up bevel lists (see STEP 2). */
              if (bevp->offset > threshold) {
                *seglen += bevp->offset;
                *segbevcount += 1;
              }
            }
            seglen++;
            segbevcount++;
          }
          else {
            bevp += resolu;
          }
          bl->nr += resolu;
        }
        prevbezt = bezt;
        bezt++;
      }
 
      if ((nu->flagu & CU_NURB_CYCLIC) == 0) { /* not cyclic: endpoint */
        copy_v3_v3(bevp->vec, prevbezt->vec[1]);
        bevp->tilt = prevbezt->tilt;
        bevp->radius = prevbezt->radius;
        bevp->weight = prevbezt->weight;
 
        sub_v3_v3v3(bevp->dir, prevbezt->vec[1], prevbezt->vec[0]);
        normalize_v3(bevp->dir);
 
        bl->nr++;
      }
    }
    else if (nu->type == CU_NURBS) {
      if (nu->pntsv == 1) {
        len = (resolu * segcount);
 
        BevList *bl = MEM_callocN<BevList>(__func__);
        bl->bevpoints = MEM_calloc_arrayN<BevPoint>(len, __func__);
        if (need_seglen && (nu->flagu & CU_NURB_CYCLIC) == 0) {
          bl->seglen = MEM_malloc_arrayN<float>(size_t(segcount), __func__);
          bl->segbevcount = MEM_malloc_arrayN<int>(size_t(segcount), __func__);
        }
        BLI_addtail(bev, bl);
        bl->nr = len;
        bl->dupe_nr = 0;
        bl->poly = (nu->flagu & CU_NURB_CYCLIC) ? 0 : -1;
        bl->charidx = nu->charidx;
 
        bevp = bl->bevpoints;
        seglen = bl->seglen;
        segbevcount = bl->segbevcount;
 
        BKE_nurb_makeCurve(nu,
                           &bevp->vec[0],
                           do_tilt ? &bevp->tilt : nullptr,
                           do_radius ? &bevp->radius : nullptr,
                           do_weight ? &bevp->weight : nullptr,
                           resolu,
                           sizeof(BevPoint));
 
        /* match seglen and segbevcount to the cleaned up bevel lists (see STEP 2) */
        if (seglen != nullptr) {
          nr = segcount;
          bevp0 = bevp;
          bevp++;
          while (nr) {
            int j;
            *seglen = 0;
            *segbevcount = 0;
            /* We keep last bevel segment zero-length. */
            for (j = 0; j < ((nr == 1) ? (resolu - 1) : resolu); j++) {
              bevp->offset = len_v3v3(bevp0->vec, bevp->vec);
              if (bevp->offset > threshold) {
                *seglen += bevp->offset;
                *segbevcount += 1;
              }
              bevp0 = bevp;
              bevp++;
            }
            seglen++;
            segbevcount++;
            nr--;
          }
        }
 
        if ((nu->flagu & CU_NURB_CYCLIC) == 0) {
          bevlist_firstlast_direction_calc_from_bpoint(nu, bl);
        }
      }
    }
  }
 
  /* STEP 2: DOUBLE POINTS AND AUTOMATIC RESOLUTION, REDUCE DATABLOCKS */
  LISTBASE_FOREACH (BevList *, bl, bev) {
    if (bl->nr == 0) { /* null bevel items come from single points */
      continue;
    }
 
    /* Scale the threshold so high resolution shapes don't get over reduced, see: #49850. */
    const float threshold_resolu = 0.00001f / resolu;
    const bool is_cyclic = bl->poly != -1;
    nr = bl->nr;
    if (is_cyclic) {
      bevp1 = bl->bevpoints;
      bevp0 = bevp1 + (nr - 1);
    }
    else {
      bevp0 = bl->bevpoints;
      bevp0->offset = 0;
      bevp1 = bevp0 + 1;
    }
    nr--;
    while (nr--) {
      if (seglen != nullptr) {
        if (fabsf(bevp1->offset) < threshold) {
          bevp0->dupe_tag = true;
          bl->dupe_nr++;
        }
      }
      else {
        if (compare_v3v3(bevp0->vec, bevp1->vec, threshold_resolu)) {
          bevp0->dupe_tag = true;
          bl->dupe_nr++;
        }
      }
      bevp0 = bevp1;
      bevp1++;
    }
  }
 
  LISTBASE_FOREACH_MUTABLE (BevList *, bl, bev) {
    if (bl->nr == 0 || bl->dupe_nr == 0) {
      continue;
    }
 
    nr = bl->nr - bl->dupe_nr + 1; /* +1 because vector-bezier sets flag too. */
    blnew = MEM_mallocN<BevList>("makeBevelList4");
    memcpy(blnew, bl, sizeof(BevList));
    blnew->bevpoints = MEM_calloc_arrayN<BevPoint>(nr, "makeBevelPoints4");
    if (!blnew->bevpoints) {
      MEM_freeN(blnew);
      break;
    }
    blnew->segbevcount = bl->segbevcount;
    blnew->seglen = bl->seglen;
    blnew->nr = 0;
    BLI_remlink(bev, bl);
    BLI_insertlinkbefore(bev, bl->next, blnew); /* Ensure `bevlist` is tuned with `nurblist`. */
    bevp0 = bl->bevpoints;
    bevp1 = blnew->bevpoints;
    nr = bl->nr;
    while (nr--) {
      if (bevp0->dupe_tag == 0) {
        memcpy(bevp1, bevp0, sizeof(BevPoint));
        bevp1++;
        blnew->nr++;
      }
      bevp0++;
    }
    if (bl->bevpoints != nullptr) {
      MEM_freeN(bl->bevpoints);
    }
    MEM_freeN(bl);
    blnew->dupe_nr = 0;
  }
 
  /* STEP 3: POLYS COUNT AND AUTOHOLE */
  poly = 0;
  LISTBASE_FOREACH (BevList *, bl, bev) {
    if (bl->nr && bl->poly >= 0) {
      poly++;
      bl->poly = poly;
      bl->hole = 0;
    }
  }
 
  /* find extreme left points, also test (turning) direction */
  if (poly > 0) {
    sd = sortdata = MEM_malloc_arrayN<BevelSort>(size_t(poly), __func__);
    LISTBASE_FOREACH (BevList *, bl, bev) {
      if (bl->poly > 0) {
        BevPoint *bevp;
 
        bevp = bl->bevpoints;
        bevp1 = bl->bevpoints;
        min = bevp1->vec[0];
        nr = bl->nr;
        while (nr--) {
          if (min > bevp->vec[0]) {
            min = bevp->vec[0];
            bevp1 = bevp;
          }
          bevp++;
        }
        sd->bl = bl;
        sd->left = min;
 
        bevp = bl->bevpoints;
        if (bevp1 == bevp) {
          bevp0 = bevp + (bl->nr - 1);
        }
        else {
          bevp0 = bevp1 - 1;
        }
        bevp = bevp + (bl->nr - 1);
        if (bevp1 == bevp) {
          bevp2 = bl->bevpoints;
        }
        else {
          bevp2 = bevp1 + 1;
        }
 
        inp = ((bevp1->vec[0] - bevp0->vec[0]) * (bevp0->vec[1] - bevp2->vec[1]) +
               (bevp0->vec[1] - bevp1->vec[1]) * (bevp0->vec[0] - bevp2->vec[0]));
 
        if (inp > 0.0f) {
          sd->dir = 1;
        }
        else {
          sd->dir = 0;
        }
 
        sd++;
      }
    }
    qsort(sortdata, poly, sizeof(BevelSort), vergxcobev);
 
    sd = sortdata + 1;
    for (a = 1; a < poly; a++, sd++) {
      BevList *bl = sd->bl; /* is bl a hole? */
      sd1 = sortdata + (a - 1);
      for (b = a - 1; b >= 0; b--, sd1--) {    /* all polys to the left */
        if (sd1->bl->charidx == bl->charidx) { /* for text, only check matching char */
          if (bevelinside(sd1->bl, bl)) {
            bl->hole = 1 - sd1->bl->hole;
            break;
          }
        }
      }
    }
 
    /* turning direction */
    if (CU_IS_2D(cu)) {
      sd = sortdata;
      for (a = 0; a < poly; a++, sd++) {
        if (sd->bl->hole == sd->dir) {
          BevList *bl = sd->bl;
          bevp1 = bl->bevpoints;
          bevp2 = bevp1 + (bl->nr - 1);
          nr = bl->nr / 2;
          while (nr--) {
            std::swap(*bevp1, *bevp2);
            bevp1++;
            bevp2--;
          }
        }
      }
    }
    MEM_freeN(sortdata);
  }
 
  /* STEP 4: 2D-COSINES or 3D ORIENTATION */
  if (CU_IS_2D(cu)) {
    /* 2D Curves */
    LISTBASE_FOREACH (BevList *, bl, bev) {
      if (bl->nr < 2) {
        BevPoint *bevp = bl->bevpoints;
        unit_qt(bevp->quat);
      }
      else if (bl->nr == 2) { /* 2 points, treat separately. */
        make_bevel_list_segment_2D(bl);
      }
      else {
        make_bevel_list_2D(bl);
      }
    }
  }
  else {
    /* 3D Curves */
    LISTBASE_FOREACH (BevList *, bl, bev) {
      if (bl->nr < 2) {
        BevPoint *bevp = bl->bevpoints;
        unit_qt(bevp->quat);
      }
      else if (bl->nr == 2) { /* 2 points, treat separately. */
        make_bevel_list_segment_3D(bl);
      }
      else {
        make_bevel_list_3D(bl, int(resolu * cu->twist_smooth), cu->twist_mode);
      }
    }
  }
}
 
/* ****************** HANDLES ************** */
 
static void calchandleNurb_intern(BezTriple *bezt,
                                  const BezTriple *prev,
                                  const BezTriple *next,
                                  eBezTriple_Flag handle_sel_flag,
                                  bool is_fcurve,
                                  bool skip_align,
                                  char fcurve_smoothing)
{
  /* defines to avoid confusion */
#define p2_h1 ((p2)-3)
#define p2_h2 ((p2) + 3)
 
  const float *p1, *p3;
  float *p2;
  float pt[3];
  float dvec_a[3], dvec_b[3];
  float len, len_a, len_b;
  const float eps = 1e-5;
 
  /* assume normal handle until we check */
  bezt->auto_handle_type = HD_AUTOTYPE_NORMAL;
 
  if (bezt->h1 == 0 && bezt->h2 == 0) {
    return;
  }
 
  p2 = bezt->vec[1];
 
  if (prev == nullptr) {
    p3 = next->vec[1];
    pt[0] = 2.0f * p2[0] - p3[0];
    pt[1] = 2.0f * p2[1] - p3[1];
    pt[2] = 2.0f * p2[2] - p3[2];
    p1 = pt;
  }
  else {
    p1 = prev->vec[1];
  }
 
  if (next == nullptr) {
    pt[0] = 2.0f * p2[0] - p1[0];
    pt[1] = 2.0f * p2[1] - p1[1];
    pt[2] = 2.0f * p2[2] - p1[2];
    p3 = pt;
  }
  else {
    p3 = next->vec[1];
  }
 
  sub_v3_v3v3(dvec_a, p2, p1);
  sub_v3_v3v3(dvec_b, p3, p2);
 
  if (is_fcurve) {
    len_a = dvec_a[0];
    len_b = dvec_b[0];
  }
  else {
    len_a = len_v3(dvec_a);
    len_b = len_v3(dvec_b);
  }
 
  if (len_a == 0.0f) {
    len_a = 1.0f;
  }
  if (len_b == 0.0f) {
    len_b = 1.0f;
  }
 
  if (ELEM(bezt->h1, HD_AUTO, HD_AUTO_ANIM) || ELEM(bezt->h2, HD_AUTO, HD_AUTO_ANIM)) { /* auto */
    float tvec[3];
    tvec[0] = dvec_b[0] / len_b + dvec_a[0] / len_a;
    tvec[1] = dvec_b[1] / len_b + dvec_a[1] / len_a;
    tvec[2] = dvec_b[2] / len_b + dvec_a[2] / len_a;
 
    if (is_fcurve) {
      if (fcurve_smoothing != FCURVE_SMOOTH_NONE) {
        /* force the horizontal handle size to be 1/3 of the key interval so that
         * the X component of the parametric bezier curve is a linear spline */
        len = 6.0f / 2.5614f;
      }
      else {
        len = tvec[0];
      }
    }
    else {
      len = len_v3(tvec);
    }
    len *= 2.5614f;
 
    if (len != 0.0f) {
      /* Only for F-Curves. */
      bool leftviolate = false, rightviolate = false;
 
      if (!is_fcurve || fcurve_smoothing == FCURVE_SMOOTH_NONE) {
        len_a = std::min(len_a, 5.0f * len_b);
        len_b = std::min(len_b, 5.0f * len_a);
      }
 
      if (ELEM(bezt->h1, HD_AUTO, HD_AUTO_ANIM)) {
        len_a /= len;
        madd_v3_v3v3fl(p2_h1, p2, tvec, -len_a);
 
        if ((bezt->h1 == HD_AUTO_ANIM) && next && prev) { /* keep horizontal if extrema */
          float ydiff1 = prev->vec[1][1] - bezt->vec[1][1];
          float ydiff2 = next->vec[1][1] - bezt->vec[1][1];
          if ((ydiff1 <= 0.0f && ydiff2 <= 0.0f) || (ydiff1 >= 0.0f && ydiff2 >= 0.0f)) {
            bezt->vec[0][1] = bezt->vec[1][1];
            bezt->auto_handle_type = HD_AUTOTYPE_LOCKED_FINAL;
          }
          else { /* handles should not be beyond y coord of two others */
            if (ydiff1 <= 0.0f) {
              if (prev->vec[1][1] > bezt->vec[0][1]) {
                bezt->vec[0][1] = prev->vec[1][1];
                leftviolate = true;
              }
            }
            else {
              if (prev->vec[1][1] < bezt->vec[0][1]) {
                bezt->vec[0][1] = prev->vec[1][1];
                leftviolate = true;
              }
            }
          }
        }
      }
      if (ELEM(bezt->h2, HD_AUTO, HD_AUTO_ANIM)) {
        len_b /= len;
        madd_v3_v3v3fl(p2_h2, p2, tvec, len_b);
 
        if ((bezt->h2 == HD_AUTO_ANIM) && next && prev) { /* keep horizontal if extrema */
          float ydiff1 = prev->vec[1][1] - bezt->vec[1][1];
          float ydiff2 = next->vec[1][1] - bezt->vec[1][1];
          if ((ydiff1 <= 0.0f && ydiff2 <= 0.0f) || (ydiff1 >= 0.0f && ydiff2 >= 0.0f)) {
            bezt->vec[2][1] = bezt->vec[1][1];
            bezt->auto_handle_type = HD_AUTOTYPE_LOCKED_FINAL;
          }
          else { /* handles should not be beyond y coord of two others */
            if (ydiff1 <= 0.0f) {
              if (next->vec[1][1] < bezt->vec[2][1]) {
                bezt->vec[2][1] = next->vec[1][1];
                rightviolate = true;
              }
            }
            else {
              if (next->vec[1][1] > bezt->vec[2][1]) {
                bezt->vec[2][1] = next->vec[1][1];
                rightviolate = true;
              }
            }
          }
        }
      }
      if (leftviolate || rightviolate) { /* align left handle */
        BLI_assert(is_fcurve);
        /* simple 2d calculation */
        float h1_x = p2_h1[0] - p2[0];
        float h2_x = p2[0] - p2_h2[0];
 
        if (leftviolate) {
          p2_h2[1] = p2[1] + ((p2[1] - p2_h1[1]) / h1_x) * h2_x;
        }
        else {
          p2_h1[1] = p2[1] + ((p2[1] - p2_h2[1]) / h2_x) * h1_x;
        }
      }
    }
  }
 
  if (bezt->h1 == HD_VECT) { /* vector */
    madd_v3_v3v3fl(p2_h1, p2, dvec_a, -1.0f / 3.0f);
  }
  if (bezt->h2 == HD_VECT) {
    madd_v3_v3v3fl(p2_h2, p2, dvec_b, 1.0f / 3.0f);
  }
 
  if (skip_align ||
      /* When one handle is free, aligning makes no sense, see: #35952 */
      ELEM(HD_FREE, bezt->h1, bezt->h2) ||
      /* Also when no handles are aligned, skip this step. */
      (!ELEM(HD_ALIGN, bezt->h1, bezt->h2) && !ELEM(HD_ALIGN_DOUBLESIDE, bezt->h1, bezt->h2)))
  {
    /* Handles need to be updated during animation and applying stuff like hooks,
     * but in such situations it's quite difficult to distinguish in which order
     * align handles should be aligned so skip them for now. */
    return;
  }
 
  len_a = len_v3v3(p2, p2_h1);
  len_b = len_v3v3(p2, p2_h2);
 
  if (len_a == 0.0f) {
    len_a = 1.0f;
  }
  if (len_b == 0.0f) {
    len_b = 1.0f;
  }
 
  const float len_ratio = len_a / len_b;
 
  if (bezt->f1 & handle_sel_flag) {                      /* order of calculation */
    if (ELEM(bezt->h2, HD_ALIGN, HD_ALIGN_DOUBLESIDE)) { /* aligned */
      if (len_a > eps) {
        len = 1.0f / len_ratio;
        p2_h2[0] = p2[0] + len * (p2[0] - p2_h1[0]);
        p2_h2[1] = p2[1] + len * (p2[1] - p2_h1[1]);
        p2_h2[2] = p2[2] + len * (p2[2] - p2_h1[2]);
      }
    }
    if (ELEM(bezt->h1, HD_ALIGN, HD_ALIGN_DOUBLESIDE)) {
      if (len_b > eps) {
        len = len_ratio;
        p2_h1[0] = p2[0] + len * (p2[0] - p2_h2[0]);
        p2_h1[1] = p2[1] + len * (p2[1] - p2_h2[1]);
        p2_h1[2] = p2[2] + len * (p2[2] - p2_h2[2]);
      }
    }
  }
  else {
    if (ELEM(bezt->h1, HD_ALIGN, HD_ALIGN_DOUBLESIDE)) {
      if (len_b > eps) {
        len = len_ratio;
        p2_h1[0] = p2[0] + len * (p2[0] - p2_h2[0]);
        p2_h1[1] = p2[1] + len * (p2[1] - p2_h2[1]);
        p2_h1[2] = p2[2] + len * (p2[2] - p2_h2[2]);
      }
    }
    if (ELEM(bezt->h2, HD_ALIGN, HD_ALIGN_DOUBLESIDE)) { /* aligned */
      if (len_a > eps) {
        len = 1.0f / len_ratio;
        p2_h2[0] = p2[0] + len * (p2[0] - p2_h1[0]);
        p2_h2[1] = p2[1] + len * (p2[1] - p2_h1[1]);
        p2_h2[2] = p2[2] + len * (p2[2] - p2_h1[2]);
      }
    }
  }
 
#undef p2_h1
#undef p2_h2
}
 
static void calchandlesNurb_intern(Nurb *nu, eBezTriple_Flag handle_sel_flag, bool skip_align)
{
  BezTriple *bezt, *prev, *next;
  int a;
 
  if (nu->type != CU_BEZIER) {
    return;
  }
  if (nu->pntsu < 2) {
    return;
  }
 
  a = nu->pntsu;
  bezt = nu->bezt;
  if (nu->flagu & CU_NURB_CYCLIC) {
    prev = bezt + (a - 1);
  }
  else {
    prev = nullptr;
  }
  next = bezt + 1;
 
  while (a--) {
    calchandleNurb_intern(bezt, prev, next, handle_sel_flag, false, skip_align, 0);
    prev = bezt;
    if (a == 1) {
      if (nu->flagu & CU_NURB_CYCLIC) {
        next = nu->bezt;
      }
      else {
        next = nullptr;
      }
    }
    else if (next != nullptr) {
      next++;
    }
 
    bezt++;
  }
}

static void *allocate_arrays(int count, float ***floats, char ***chars, const char *name)
{
  size_t num_floats = 0, num_chars = 0;
 
  while (floats && floats[num_floats]) {
    num_floats++;
  }
 
  while (chars && chars[num_chars]) {
    num_chars++;
  }
 
  void *buffer = MEM_malloc_arrayN(count, (sizeof(float) * num_floats + num_chars), name);
 
  if (!buffer) {
    return nullptr;
  }
 
  float *fptr = (float *)buffer;
 
  for (int i = 0; i < num_floats; i++, fptr += count) {
    *floats[i] = fptr;
  }
 
  char *cptr = (char *)fptr;
 
  for (int i = 0; i < num_chars; i++, cptr += count) {
    *chars[i] = cptr;
  }
 
  return buffer;
}
 
static void free_arrays(void *buffer)
{
  MEM_freeN(buffer);
}
 
/* computes in which direction to change h[i] to satisfy conditions better */
static float bezier_relax_direction(const float *a,
                                    const float *b,
                                    const float *c,
                                    const float *d,
                                    const float *h,
                                    int i,
                                    int count)
{
  /* current deviation between sides of the equation */
  float state = a[i] * h[(i + count - 1) % count] + b[i] * h[i] + c[i] * h[(i + 1) % count] - d[i];
 
  /* only the sign is meaningful */
  return -state * b[i];
}
 
static void bezier_lock_unknown(float *a, float *b, float *c, float *d, int i, float value)
{
  a[i] = c[i] = 0.0f;
  b[i] = 1.0f;
  d[i] = value;
}
 
static void bezier_restore_equation(float *a,
                                    float *b,
                                    float *c,
                                    float *d,
                                    const float *a0,
                                    const float *b0,
                                    const float *c0,
                                    const float *d0,
                                    int i)
{
  a[i] = a0[i];
  b[i] = b0[i];
  c[i] = c0[i];
  d[i] = d0[i];
}
 
static bool tridiagonal_solve_with_limits(float *a,
                                          float *b,
                                          float *c,
                                          float *d,
                                          float *h,
                                          const float *hmin,
                                          const float *hmax,
                                          int solve_count)
{
  float *a0, *b0, *c0, *d0;
  float **arrays[] = {&a0, &b0, &c0, &d0, nullptr};
  char *is_locked, *num_unlocks;
  char **flagarrays[] = {&is_locked, &num_unlocks, nullptr};
 
  void *tmps = allocate_arrays(solve_count, arrays, flagarrays, "tridiagonal_solve_with_limits");
  if (!tmps) {
    return false;
  }
 
  memcpy(a0, a, sizeof(float) * solve_count);
  memcpy(b0, b, sizeof(float) * solve_count);
  memcpy(c0, c, sizeof(float) * solve_count);
  memcpy(d0, d, sizeof(float) * solve_count);
 
  memset(is_locked, 0, solve_count);
  memset(num_unlocks, 0, solve_count);
 
  bool overshoot, unlocked;
 
  do {
    if (!BLI_tridiagonal_solve_cyclic(a, b, c, d, h, solve_count)) {
      free_arrays(tmps);
      return false;
    }
 
    /* first check if any handles overshoot the limits, and lock them */
    bool all = false, locked = false;
 
    overshoot = unlocked = false;
 
    do {
      for (int i = 0; i < solve_count; i++) {
        if (h[i] >= hmin[i] && h[i] <= hmax[i]) {
          continue;
        }
 
        overshoot = true;
 
        float target = h[i] > hmax[i] ? hmax[i] : hmin[i];
 
        /* heuristically only lock handles that go in the right direction if there are such ones */
        if (target != 0.0f || all) {
          /* mark item locked */
          is_locked[i] = 1;
 
          bezier_lock_unknown(a, b, c, d, i, target);
          locked = true;
        }
      }
 
      all = true;
    } while (overshoot && !locked);
 
    /* If no handles overshot and were locked,
     * see if it may be a good idea to unlock some handles. */
    if (!locked) {
      for (int i = 0; i < solve_count; i++) {
        /* to definitely avoid infinite loops limit this to 2 times */
        if (!is_locked[i] || num_unlocks[i] >= 2) {
          continue;
        }
 
        /* if the handle wants to move in allowable direction, release it */
        float relax = bezier_relax_direction(a0, b0, c0, d0, h, i, solve_count);
 
        if ((relax > 0 && h[i] < hmax[i]) || (relax < 0 && h[i] > hmin[i])) {
          bezier_restore_equation(a, b, c, d, a0, b0, c0, d0, i);
 
          is_locked[i] = 0;
          num_unlocks[i]++;
          unlocked = true;
        }
      }
    }
  } while (overshoot || unlocked);
 
  free_arrays(tmps);
  return true;
}
 
/* Keep ASCII art. */
/* clang-format off */
/*
 * This function computes the handles of a series of auto bezier points
 * on the basis of 'no acceleration discontinuities' at the points.
 * The first and last bezier points are considered 'fixed' (their handles are not touched)
 * The result is the smoothest possible trajectory going through intermediate points.
 * The difficulty is that the handles depends on their neighbors.
 *
 * The exact solution is found by solving a tridiagonal matrix equation formed
 * by the continuity and boundary conditions. Although theoretically handle position
 * is affected by all other points of the curve segment, in practice the influence
 * decreases exponentially with distance.
 *
 * NOTE: this algorithm assumes that the handle horizontal size is always 1/3 of the
 * of the interval to the next point. This rule ensures linear interpolation of time.
 *
 * ^ height (co 1)
 * |                                            yN
 * |                                   yN-1     |
 * |                      y2           |        |
 * |           y1         |            |        |
 * |    y0     |          |            |        |
 * |    |      |          |            |        |
 * |    |      |          |            |        |
 * |    |      |          |            |        |
 * |------dx1--------dx2--------- ~ -------dxN-------------------> time (co 0)
 *
 * Notation:
 *
 *   x[i], y[i] - keyframe coordinates
 *   h[i]       - right handle y offset from y[i]
 *
 *   dx[i] = x[i] - x[i-1]
 *   dy[i] = y[i] - y[i-1]
 *
 * Mathematical basis:
 *
 * 1. Handle lengths on either side of each point are connected by a factor
 *    ensuring continuity of the first derivative:
 *
 *    l[i] = dx[i+1]/dx[i]
 *
 * 2. The tridiagonal system is formed by the following equation, which is derived
 *    by differentiating the bezier curve and specifies second derivative continuity
 *    at every point:
 *
 *    l[i]^2 * h[i-1] + (2*l[i]+2) * h[i] + 1/l[i+1] * h[i+1] = dy[i]*l[i]^2 + dy[i+1]
 *
 * 3. If this point is adjacent to a manually set handle with X size not equal to 1/3
 *    of the horizontal interval, this equation becomes slightly more complex:
 *
 *    l[i]^2 * h[i-1] + (3*(1-R[i-1])*l[i] + 3*(1-L[i+1])) * h[i] + 1/l[i+1] * h[i+1] = dy[i]*l[i]^2 + dy[i+1]
 *
 *    The difference between equations amounts to this, and it's obvious that when R[i-1]
 *    and L[i+1] are both 1/3, it becomes zero:
 *
 *    ( (1-3*R[i-1])*l[i] + (1-3*L[i+1]) ) * h[i]
 *
 * 4. The equations for zero acceleration border conditions are basically the above
 *    equation with parts omitted, so the handle size correction also applies.
 *
 * 5. The fully cyclic curve case is handled by eliminating one of the end points,
 *    and instead of border conditions connecting the curve via a set of equations:
 *
 *    l[0] = l[N] = dx[1] / dx[N]
 *    dy[0] = dy[N]
 *    Continuity equation (item 2) for i = 0.
 *    Substitute h[0] for h[N] and h[N-1] for h[-1]
 */
/* clang-format on */
 
static void bezier_eq_continuous(
    float *a, float *b, float *c, float *d, const float *dy, const float *l, int i)
{
  a[i] = l[i] * l[i];
  b[i] = 2.0f * (l[i] + 1);
  c[i] = 1.0f / l[i + 1];
  d[i] = dy[i] * l[i] * l[i] + dy[i + 1];
}
 
static void bezier_eq_noaccel_right(
    float *a, float *b, float *c, float *d, const float *dy, const float *l, int i)
{
  a[i] = 0.0f;
  b[i] = 2.0f;
  c[i] = 1.0f / l[i + 1];
  d[i] = dy[i + 1];
}
 
static void bezier_eq_noaccel_left(
    float *a, float *b, float *c, float *d, const float *dy, const float *l, int i)
{
  a[i] = l[i] * l[i];
  b[i] = 2.0f * l[i];
  c[i] = 0.0f;
  d[i] = dy[i] * l[i] * l[i];
}
 
/* auto clamp prevents its own point going the wrong way, and adjacent handles overshooting */
static void bezier_clamp(
    float *hmax, float *hmin, int i, float dy, bool no_reverse, bool no_overshoot)
{
  if (dy > 0) {
    if (no_overshoot) {
      hmax[i] = min_ff(hmax[i], dy);
    }
    if (no_reverse) {
      hmin[i] = 0.0f;
    }
  }
  else if (dy < 0) {
    if (no_reverse) {
      hmax[i] = 0.0f;
    }
    if (no_overshoot) {
      hmin[i] = max_ff(hmin[i], dy);
    }
  }
  else if (no_reverse || no_overshoot) {
    hmax[i] = hmin[i] = 0.0f;
  }
}
 
/* write changes to a bezier handle */
static void bezier_output_handle_inner(BezTriple *bezt,
                                       bool right,
                                       const float newval[3],
                                       bool endpoint)
{
  float tmp[3];
 
  int idx = right ? 2 : 0;
  char hr = right ? bezt->h2 : bezt->h1;
  char hm = right ? bezt->h1 : bezt->h2;
 
  /* only assign Auto/Vector handles */
  if (!ELEM(hr, HD_AUTO, HD_AUTO_ANIM, HD_VECT)) {
    return;
  }
 
  copy_v3_v3(bezt->vec[idx], newval);
 
  /* fix up the Align handle if any */
  if (ELEM(hm, HD_ALIGN, HD_ALIGN_DOUBLESIDE)) {
    float hlen = len_v3v3(bezt->vec[1], bezt->vec[2 - idx]);
    float h2len = len_v3v3(bezt->vec[1], bezt->vec[idx]);
 
    sub_v3_v3v3(tmp, bezt->vec[1], bezt->vec[idx]);
    madd_v3_v3v3fl(bezt->vec[2 - idx], bezt->vec[1], tmp, hlen / h2len);
  }
  /* at end points of the curve, mirror handle to the other side */
  else if (endpoint && ELEM(hm, HD_AUTO, HD_AUTO_ANIM, HD_VECT)) {
    sub_v3_v3v3(tmp, bezt->vec[1], bezt->vec[idx]);
    add_v3_v3v3(bezt->vec[2 - idx], bezt->vec[1], tmp);
  }
}
 
static void bezier_output_handle(BezTriple *bezt, bool right, float dy, bool endpoint)
{
  float tmp[3];
 
  copy_v3_v3(tmp, bezt->vec[right ? 2 : 0]);
 
  tmp[1] = bezt->vec[1][1] + dy;
 
  bezier_output_handle_inner(bezt, right, tmp, endpoint);
}
 
static bool bezier_check_solve_end_handle(BezTriple *bezt, char htype, bool end)
{
  return (htype == HD_VECT) || (end && ELEM(htype, HD_AUTO, HD_AUTO_ANIM) &&
                                bezt->auto_handle_type == HD_AUTOTYPE_NORMAL);
}
 
static float bezier_calc_handle_adj(float hsize[2], float dx)
{
  /* if handles intersect in x direction, they are scaled to fit */
  float fac = dx / (hsize[0] + dx / 3.0f);
  if (fac < 1.0f) {
    mul_v2_fl(hsize, fac);
  }
  return 1.0f - 3.0f * hsize[0] / dx;
}
 
static void bezier_handle_calc_smooth_fcurve(
    BezTriple *bezt, int total, int start, int count, bool cycle)
{
  float *dx, *dy, *l, *a, *b, *c, *d, *h, *hmax, *hmin;
  float **arrays[] = {&dx, &dy, &l, &a, &b, &c, &d, &h, &hmax, &hmin, nullptr};
 
  int solve_count = count;
 
  /* verify index ranges */
 
  if (count < 2) {
    return;
  }
 
  BLI_assert(start < total - 1 && count <= total);
  BLI_assert(start + count <= total || cycle);
 
  bool full_cycle = (start == 0 && count == total && cycle);
 
  BezTriple *bezt_first = &bezt[start];
  BezTriple *bezt_last =
      &bezt[(start + count > total) ? start + count - total : start + count - 1];
 
  bool solve_first = bezier_check_solve_end_handle(bezt_first, bezt_first->h2, start == 0);
  bool solve_last = bezier_check_solve_end_handle(
      bezt_last, bezt_last->h1, start + count == total);
 
  if (count == 2 && !full_cycle && solve_first == solve_last) {
    return;
  }
 
  /* allocate all */
 
  void *tmp_buffer = allocate_arrays(count, arrays, nullptr, "bezier_calc_smooth_tmp");
  if (!tmp_buffer) {
    return;
  }
 
  /* point locations */
 
  dx[0] = dy[0] = NAN_FLT;
 
  for (int i = 1, j = start + 1; i < count; i++, j++) {
    dx[i] = bezt[j].vec[1][0] - bezt[j - 1].vec[1][0];
    dy[i] = bezt[j].vec[1][1] - bezt[j - 1].vec[1][1];
 
    /* when cyclic, jump from last point to first */
    if (cycle && j == total - 1) {
      j = 0;
    }
  }
 
  /* ratio of x intervals */
 
  if (full_cycle) {
    dx[0] = dx[count - 1];
    dy[0] = dy[count - 1];
 
    l[0] = l[count - 1] = dx[1] / dx[0];
  }
  else {
    l[0] = l[count - 1] = 1.0f;
  }
 
  for (int i = 1; i < count - 1; i++) {
    l[i] = dx[i + 1] / dx[i];
  }
 
  /* compute handle clamp ranges */
 
  bool clamped_prev = false, clamped_cur = ELEM(HD_AUTO_ANIM, bezt_first->h1, bezt_first->h2);
 
  for (int i = 0; i < count; i++) {
    hmax[i] = FLT_MAX;
    hmin[i] = -FLT_MAX;
  }
 
  for (int i = 1, j = start + 1; i < count; i++, j++) {
    clamped_prev = clamped_cur;
    clamped_cur = ELEM(HD_AUTO_ANIM, bezt[j].h1, bezt[j].h2);
 
    if (cycle && j == total - 1) {
      j = 0;
      clamped_cur = clamped_cur || ELEM(HD_AUTO_ANIM, bezt[j].h1, bezt[j].h2);
    }
 
    bezier_clamp(hmax, hmin, i - 1, dy[i], clamped_prev, clamped_prev);
    bezier_clamp(hmax, hmin, i, dy[i] * l[i], clamped_cur, clamped_cur);
  }
 
  /* full cycle merges first and last points into continuous loop */
 
  float first_handle_adj = 0.0f, last_handle_adj = 0.0f;
 
  if (full_cycle) {
    /* reduce the number of unknowns by one */
    int i = solve_count = count - 1;
 
    hmin[0] = max_ff(hmin[0], hmin[i]);
    hmax[0] = min_ff(hmax[0], hmax[i]);
 
    solve_first = solve_last = true;
 
    bezier_eq_continuous(a, b, c, d, dy, l, 0);
  }
  else {
    float tmp[2];
 
    /* boundary condition: fixed handles or zero curvature */
    if (!solve_first) {
      sub_v2_v2v2(tmp, bezt_first->vec[2], bezt_first->vec[1]);
      first_handle_adj = bezier_calc_handle_adj(tmp, dx[1]);
 
      bezier_lock_unknown(a, b, c, d, 0, tmp[1]);
    }
    else {
      bezier_eq_noaccel_right(a, b, c, d, dy, l, 0);
    }
 
    if (!solve_last) {
      sub_v2_v2v2(tmp, bezt_last->vec[1], bezt_last->vec[0]);
      last_handle_adj = bezier_calc_handle_adj(tmp, dx[count - 1]);
 
      bezier_lock_unknown(a, b, c, d, count - 1, tmp[1]);
    }
    else {
      bezier_eq_noaccel_left(a, b, c, d, dy, l, count - 1);
    }
  }
 
  /* main tridiagonal system of equations */
 
  for (int i = 1; i < count - 1; i++) {
    bezier_eq_continuous(a, b, c, d, dy, l, i);
  }
 
  /* apply correction for user-defined handles with nonstandard x positions */
 
  if (!full_cycle) {
    if (count > 2 || solve_last) {
      b[1] += l[1] * first_handle_adj;
    }
 
    if (count > 2 || solve_first) {
      b[count - 2] += last_handle_adj;
    }
  }
 
  /* solve and output results */
 
  if (tridiagonal_solve_with_limits(a, b, c, d, h, hmin, hmax, solve_count)) {
    if (full_cycle) {
      h[count - 1] = h[0];
    }
 
    for (int i = 1, j = start + 1; i < count - 1; i++, j++) {
      bool end = (j == total - 1);
 
      bezier_output_handle(&bezt[j], false, -h[i] / l[i], end);
 
      if (end) {
        j = 0;
      }
 
      bezier_output_handle(&bezt[j], true, h[i], end);
    }
 
    if (solve_first) {
      bezier_output_handle(bezt_first, true, h[0], start == 0);
    }
 
    if (solve_last) {
      bezier_output_handle(bezt_last, false, -h[count - 1] / l[count - 1], start + count == total);
    }
  }
 
  /* free all */
 
  free_arrays(tmp_buffer);
}
 
static bool is_free_auto_point(BezTriple *bezt)
{
  return BEZT_IS_AUTOH(bezt) && bezt->auto_handle_type == HD_AUTOTYPE_NORMAL;
}
 
void BKE_nurb_handle_smooth_fcurve(BezTriple *bezt, int total, bool cyclic)
{
  /* ignore cyclic extrapolation if end points are locked */
  cyclic = cyclic && is_free_auto_point(&bezt[0]) && is_free_auto_point(&bezt[total - 1]);
 
  /* if cyclic, try to find a sequence break point */
  int search_base = 0;
 
  if (cyclic) {
    for (int i = 1; i < total - 1; i++) {
      if (!is_free_auto_point(&bezt[i])) {
        search_base = i;
        break;
      }
    }
 
    /* all points of the curve are freely changeable auto handles - solve as full cycle */
    if (search_base == 0) {
      bezier_handle_calc_smooth_fcurve(bezt, total, 0, total, cyclic);
      return;
    }
  }
 
  /* Find continuous sub-sequences of free auto handles and smooth them, starting at search_base.
   * In cyclic mode these sub-sequences can span the cycle boundary. */
  int start = search_base, count = 1;
 
  for (int i = 1, j = start + 1; i < total; i++, j++) {
    /* in cyclic mode: jump from last to first point when necessary */
    if (j == total - 1 && cyclic) {
      j = 0;
    }
 
    /* non auto handle closes the list (we come here at least for the last handle, see above) */
    if (!is_free_auto_point(&bezt[j])) {
      bezier_handle_calc_smooth_fcurve(bezt, total, start, count + 1, cyclic);
      start = j;
      count = 1;
    }
    else {
      count++;
    }
  }
 
  if (count > 1) {
    bezier_handle_calc_smooth_fcurve(bezt, total, start, count, cyclic);
  }
}
 
void BKE_nurb_handle_calc(
    BezTriple *bezt, BezTriple *prev, BezTriple *next, const bool is_fcurve, const char smoothing)
{
  calchandleNurb_intern(bezt, prev, next, (eBezTriple_Flag)SELECT, is_fcurve, false, smoothing);
}
 
void BKE_nurb_handle_calc_ex(BezTriple *bezt,
                             BezTriple *prev,
                             BezTriple *next,
                             const eBezTriple_Flag__Alias handle_sel_flag,
                             const bool is_fcurve,
                             const char smoothing)
{
  calchandleNurb_intern(
      bezt, prev, next, (eBezTriple_Flag)handle_sel_flag, is_fcurve, false, smoothing);
}
 
void BKE_nurb_handles_calc(Nurb *nu) /* first, if needed, set handle flags */
{
  calchandlesNurb_intern(nu, (eBezTriple_Flag)SELECT, false);
}

static void nurbList_handles_swap_select(Nurb *nu)
{
  BezTriple *bezt;
  int i;
 
  for (i = nu->pntsu, bezt = nu->bezt; i--; bezt++) {
    if ((bezt->f1 & SELECT) != (bezt->f3 & SELECT)) {
      bezt->f1 ^= SELECT;
      bezt->f3 ^= SELECT;
    }
  }
}
 
/* internal use only (weak) */
static void nurb_handles_calc__align_selected(Nurb *nu)
{
  nurbList_handles_swap_select(nu);
  BKE_nurb_handles_calc(nu);
  nurbList_handles_swap_select(nu);
}
 
void BKE_nurb_handle_calc_simple(Nurb *nu, BezTriple *bezt)
{
  if (nu->pntsu > 1) {
    BezTriple *prev = BKE_nurb_bezt_get_prev(nu, bezt);
    BezTriple *next = BKE_nurb_bezt_get_next(nu, bezt);
    BKE_nurb_handle_calc(bezt, prev, next, false, 0);
  }
}
 
void BKE_nurb_handle_calc_simple_auto(Nurb *nu, BezTriple *bezt)
{
  if (nu->pntsu > 1) {
    const char h1_back = bezt->h1, h2_back = bezt->h2;
 
    bezt->h1 = bezt->h2 = HD_AUTO;
 
    /* Override handle types to HD_AUTO and recalculate */
    BKE_nurb_handle_calc_simple(nu, bezt);
 
    bezt->h1 = h1_back;
    bezt->h2 = h2_back;
  }
}
 
#define SEL_F1 (1 << 0)
#define SEL_F2 (1 << 1)
#define SEL_F3 (1 << 2)
 
short BKE_nurb_bezt_handle_test_calc_flag(const BezTriple *bezt,
                                          const eBezTriple_Flag__Alias sel_flag,
                                          const eNurbHandleTest_Mode handle_mode)
{
  short flag = 0;
 
  switch (handle_mode) {
    case NURB_HANDLE_TEST_KNOT_ONLY: {
      flag = (bezt->f2 & sel_flag) ? (SEL_F1 | SEL_F2 | SEL_F3) : 0;
      break;
    }
    case NURB_HANDLE_TEST_KNOT_OR_EACH:
      if (bezt->f2 & sel_flag) {
        flag = (bezt->f2 & sel_flag) ? (SEL_F1 | SEL_F2 | SEL_F3) : 0;
        break;
      }
      [[fallthrough]];
    case NURB_HANDLE_TEST_EACH: {
      if (bezt->f1 & sel_flag) {
        flag |= SEL_F1;
      }
      if (bezt->f2 & sel_flag) {
        flag |= SEL_F2;
      }
      if (bezt->f3 & sel_flag) {
        flag |= SEL_F3;
      }
      break;
    }
  }
  return flag;
}
 
void BKE_nurb_bezt_handle_test(BezTriple *bezt,
                               const eBezTriple_Flag__Alias sel_flag,
                               const eNurbHandleTest_Mode handle_mode,
                               const bool use_around_local)
{
  short flag = BKE_nurb_bezt_handle_test_calc_flag(bezt, sel_flag, handle_mode);
  if (use_around_local) {
    flag &= ~SEL_F2;
  }
 
  /* check for partial selection */
  if (!ELEM(flag, 0, SEL_F1 | SEL_F2 | SEL_F3)) {
    if (ELEM(bezt->h1, HD_AUTO, HD_AUTO_ANIM)) {
      bezt->h1 = HD_ALIGN;
    }
    if (ELEM(bezt->h2, HD_AUTO, HD_AUTO_ANIM)) {
      bezt->h2 = HD_ALIGN;
    }
 
    if (bezt->h1 == HD_VECT) {
      if (!(flag & SEL_F1) != !(flag & SEL_F2)) {
        bezt->h1 = HD_FREE;
      }
    }
    if (bezt->h2 == HD_VECT) {
      if (!(flag & SEL_F3) != !(flag & SEL_F2)) {
        bezt->h2 = HD_FREE;
      }
    }
  }
}
 
#undef SEL_F1
#undef SEL_F2
#undef SEL_F3
 
void BKE_nurb_handles_test(Nurb *nu,
                           const eNurbHandleTest_Mode handle_mode,
                           const bool use_around_local)
{
  BezTriple *bezt;
  int a;
 
  if (nu->type != CU_BEZIER) {
    return;
  }
 
  bezt = nu->bezt;
  a = nu->pntsu;
  while (a--) {
    BKE_nurb_bezt_handle_test(bezt, SELECT, handle_mode, use_around_local);
    bezt++;
  }
 
  BKE_nurb_handles_calc(nu);
}
 
void BKE_nurb_handles_autocalc(Nurb *nu, uint8_t flag)
{
  /* checks handle coordinates and calculates type */
  const float eps = 0.0001f;
  const float eps_sq = eps * eps;
 
  if (nu == nullptr || nu->bezt == nullptr) {
    return;
  }
 
  BezTriple *bezt2 = nu->bezt;
  BezTriple *bezt1 = bezt2 + (nu->pntsu - 1);
  BezTriple *bezt0 = bezt1 - 1;
  int i = nu->pntsu;
 
  while (i--) {
    bool align = false, leftsmall = false, rightsmall = false;
 
    /* left handle: */
    if (flag == 0 || (bezt1->f1 & flag)) {
      bezt1->h1 = HD_FREE;
      /* Distance too short: vector-handle. */
      if (len_squared_v3v3(bezt1->vec[1], bezt0->vec[1]) < eps_sq) {
        bezt1->h1 = HD_VECT;
        leftsmall = true;
      }
      else {
        /* Aligned handle? */
        if (dist_squared_to_line_v3(bezt1->vec[1], bezt1->vec[0], bezt1->vec[2]) < eps_sq) {
          align = true;
          bezt1->h1 = HD_ALIGN;
        }
        /* or vector handle? */
        if (dist_squared_to_line_v3(bezt1->vec[0], bezt1->vec[1], bezt0->vec[1]) < eps_sq) {
          bezt1->h1 = HD_VECT;
        }
      }
    }
    /* right handle: */
    if (flag == 0 || (bezt1->f3 & flag)) {
      bezt1->h2 = HD_FREE;
      /* Distance too short: vector-handle. */
      if (len_squared_v3v3(bezt1->vec[1], bezt2->vec[1]) < eps_sq) {
        bezt1->h2 = HD_VECT;
        rightsmall = true;
      }
      else {
        /* Aligned handle? */
        if (align) {
          bezt1->h2 = HD_ALIGN;
        }
 
        /* or vector handle? */
        if (dist_squared_to_line_v3(bezt1->vec[2], bezt1->vec[1], bezt2->vec[1]) < eps_sq) {
          bezt1->h2 = HD_VECT;
        }
      }
    }
    if (leftsmall && bezt1->h2 == HD_ALIGN) {
      bezt1->h2 = HD_FREE;
    }
    if (rightsmall && bezt1->h1 == HD_ALIGN) {
      bezt1->h1 = HD_FREE;
    }
 
    /* undesired combination: */
    if (bezt1->h1 == HD_ALIGN && bezt1->h2 == HD_VECT) {
      bezt1->h1 = HD_FREE;
    }
    if (bezt1->h2 == HD_ALIGN && bezt1->h1 == HD_VECT) {
      bezt1->h2 = HD_FREE;
    }
 
    bezt0 = bezt1;
    bezt1 = bezt2;
    bezt2++;
  }
 
  BKE_nurb_handles_calc(nu);
}
 
void BKE_nurbList_handles_autocalc(ListBase *editnurb, uint8_t flag)
{
  LISTBASE_FOREACH (Nurb *, nu, editnurb) {
    BKE_nurb_handles_autocalc(nu, flag);
  }
}
 
void BKE_nurbList_handles_set(ListBase *editnurb,
                              eNurbHandleTest_Mode handle_mode,
                              const char code)
{
  BezTriple *bezt;
  int a;
 
  if (ELEM(code, HD_AUTO, HD_VECT)) {
    LISTBASE_FOREACH (Nurb *, nu, editnurb) {
      if (nu->type == CU_BEZIER) {
        bezt = nu->bezt;
        a = nu->pntsu;
        while (a--) {
          const short flag = BKE_nurb_bezt_handle_test_calc_flag(bezt, SELECT, handle_mode);
          if ((flag & (1 << 0)) || (flag & (1 << 2))) {
            if (flag & (1 << 0)) {
              bezt->h1 = code;
            }
            if (flag & (1 << 2)) {
              bezt->h2 = code;
            }
            if (bezt->h1 != bezt->h2) {
              if (ELEM(bezt->h1, HD_ALIGN, HD_AUTO)) {
                bezt->h1 = HD_FREE;
              }
              if (ELEM(bezt->h2, HD_ALIGN, HD_AUTO)) {
                bezt->h2 = HD_FREE;
              }
            }
          }
          bezt++;
        }
 
        /* like BKE_nurb_handles_calc but moves selected */
        nurb_handles_calc__align_selected(nu);
      }
    }
  }
  else {
    char h_new = HD_FREE;
 
    /* There is 1 handle not FREE: FREE it all, else make ALIGNED. */
    if (code == 5) {
      h_new = HD_ALIGN;
    }
    else if (code == 6) {
      h_new = HD_FREE;
    }
    else {
      /* Toggle */
      LISTBASE_FOREACH (Nurb *, nu, editnurb) {
        if (nu->type == CU_BEZIER) {
          bezt = nu->bezt;
          a = nu->pntsu;
          while (a--) {
            const short flag = BKE_nurb_bezt_handle_test_calc_flag(bezt, SELECT, handle_mode);
            if (((flag & (1 << 0)) && bezt->h1 != HD_FREE) ||
                ((flag & (1 << 2)) && bezt->h2 != HD_FREE))
            {
              h_new = HD_AUTO;
              break;
            }
            bezt++;
          }
        }
      }
      h_new = (h_new == HD_FREE) ? HD_ALIGN : HD_FREE;
    }
    LISTBASE_FOREACH (Nurb *, nu, editnurb) {
      if (nu->type == CU_BEZIER) {
        bezt = nu->bezt;
        a = nu->pntsu;
        while (a--) {
          const short flag = BKE_nurb_bezt_handle_test_calc_flag(bezt, SELECT, handle_mode);
          if (flag & (1 << 0)) {
            bezt->h1 = h_new;
          }
          if (flag & (1 << 2)) {
            bezt->h2 = h_new;
          }
 
          bezt++;
        }
 
        /* like BKE_nurb_handles_calc but moves selected */
        nurb_handles_calc__align_selected(nu);
      }
    }
  }
}
 
void BKE_nurbList_handles_recalculate(ListBase *editnurb,
                                      const bool calc_length,
                                      const uint8_t flag)
{
  BezTriple *bezt;
  int a;
 
  LISTBASE_FOREACH (Nurb *, nu, editnurb) {
    if (nu->type != CU_BEZIER) {
      continue;
    }
 
    bool changed = false;
 
    for (a = nu->pntsu, bezt = nu->bezt; a--; bezt++) {
 
      const bool h1_select = (bezt->f1 & flag) == flag;
      const bool h2_select = (bezt->f3 & flag) == flag;
 
      if (h1_select || h2_select) {
 
        float co1_back[3], co2_back[3];
 
        copy_v3_v3(co1_back, bezt->vec[0]);
        copy_v3_v3(co2_back, bezt->vec[2]);
 
        BKE_nurb_handle_calc_simple_auto(nu, bezt);
 
        if (h1_select) {
          if (!calc_length) {
            dist_ensure_v3_v3fl(bezt->vec[0], bezt->vec[1], len_v3v3(co1_back, bezt->vec[1]));
          }
        }
        else {
          copy_v3_v3(bezt->vec[0], co1_back);
        }
 
        if (h2_select) {
          if (!calc_length) {
            dist_ensure_v3_v3fl(bezt->vec[2], bezt->vec[1], len_v3v3(co2_back, bezt->vec[1]));
          }
        }
        else {
          copy_v3_v3(bezt->vec[2], co2_back);
        }
 
        changed = true;
      }
    }
 
    if (changed) {
      /* Recalculate the whole curve */
      BKE_nurb_handles_calc(nu);
    }
  }
}
 
void BKE_nurbList_flag_set(ListBase *editnurb, uint8_t flag, bool set)
{
  BezTriple *bezt;
  BPoint *bp;
  int a;
 
  LISTBASE_FOREACH (Nurb *, nu, editnurb) {
    if (nu->type == CU_BEZIER) {
      a = nu->pntsu;
      bezt = nu->bezt;
      while (a--) {
        if (set) {
          bezt->f1 |= flag;
          bezt->f2 |= flag;
          bezt->f3 |= flag;
        }
        else {
          bezt->f1 &= ~flag;
          bezt->f2 &= ~flag;
          bezt->f3 &= ~flag;
        }
        bezt++;
      }
    }
    else {
      a = nu->pntsu * nu->pntsv;
      bp = nu->bp;
      while (a--) {
        SET_FLAG_FROM_TEST(bp->f1, set, flag);
        bp++;
      }
    }
  }
}
 
bool BKE_nurbList_flag_set_from_flag(ListBase *editnurb, uint8_t from_flag, uint8_t flag)
{
  bool changed = false;
 
  LISTBASE_FOREACH (Nurb *, nu, editnurb) {
    if (nu->type == CU_BEZIER) {
      for (int i = 0; i < nu->pntsu; i++) {
        BezTriple *bezt = &nu->bezt[i];
        uint8_t old_f1 = bezt->f1, old_f2 = bezt->f2, old_f3 = bezt->f3;
 
        SET_FLAG_FROM_TEST(bezt->f1, bezt->f1 & from_flag, flag);
        SET_FLAG_FROM_TEST(bezt->f2, bezt->f2 & from_flag, flag);
        SET_FLAG_FROM_TEST(bezt->f3, bezt->f3 & from_flag, flag);
 
        changed |= (old_f1 != bezt->f1) || (old_f2 != bezt->f2) || (old_f3 != bezt->f3);
      }
    }
    else {
      for (int i = 0; i < nu->pntsu * nu->pntsv; i++) {
        BPoint *bp = &nu->bp[i];
        uint8_t old_f1 = bp->f1;
 
        SET_FLAG_FROM_TEST(bp->f1, bp->f1 & from_flag, flag);
        changed |= (old_f1 != bp->f1);
      }
    }
  }
 
  return changed;
}
 
void BKE_nurb_direction_switch(Nurb *nu)
{
  BezTriple *bezt1, *bezt2;
  BPoint *bp1, *bp2;
  float *fp1, *fp2, *tempf;
  int a, b;
 
  if (nu->pntsu == 1 && nu->pntsv == 1) {
    return;
  }
 
  if (nu->type == CU_BEZIER) {
    a = nu->pntsu;
    bezt1 = nu->bezt;
    bezt2 = bezt1 + (a - 1);
    if (a & 1) {
      a += 1; /* if odd, also swap middle content */
    }
    a /= 2;
    while (a > 0) {
      if (bezt1 != bezt2) {
        std::swap(*bezt1, *bezt2);
      }
 
      swap_v3_v3(bezt1->vec[0], bezt1->vec[2]);
 
      if (bezt1 != bezt2) {
        swap_v3_v3(bezt2->vec[0], bezt2->vec[2]);
      }
 
      std::swap(bezt1->h1, bezt1->h2);
      std::swap(bezt1->f1, bezt1->f3);
 
      if (bezt1 != bezt2) {
        std::swap(bezt2->h1, bezt2->h2);
        std::swap(bezt2->f1, bezt2->f3);
        bezt1->tilt = -bezt1->tilt;
        bezt2->tilt = -bezt2->tilt;
      }
      else {
        bezt1->tilt = -bezt1->tilt;
      }
      a--;
      bezt1++;
      bezt2--;
    }
  }
  else if (nu->pntsv == 1) {
    a = nu->pntsu;
    bp1 = nu->bp;
    bp2 = bp1 + (a - 1);
    a /= 2;
    while (bp1 != bp2 && a > 0) {
      std::swap(*bp1, *bp2);
      a--;
      bp1->tilt = -bp1->tilt;
      bp2->tilt = -bp2->tilt;
      bp1++;
      bp2--;
    }
    /* If there are odd number of points no need to touch coord of middle one,
     * but still need to change its tilt.
     */
    if (nu->pntsu & 1) {
      bp1->tilt = -bp1->tilt;
    }
    if (nu->type == CU_NURBS) {
      /* no knots for too short paths */
      if (nu->knotsu) {
        /* inverse knots */
        a = KNOTSU(nu);
        fp1 = nu->knotsu;
        fp2 = fp1 + (a - 1);
        a /= 2;
        while (fp1 != fp2 && a > 0) {
          std::swap(*fp1, *fp2);
          a--;
          fp1++;
          fp2--;
        }
        /* and make in increasing order again */
        a = KNOTSU(nu);
        fp1 = nu->knotsu;
        fp2 = tempf = MEM_malloc_arrayN<float>(size_t(a), "switchdirect");
        a--;
        fp2[a] = fp1[a];
        while (a--) {
          fp2[0] = fabsf(fp1[1] - fp1[0]);
          fp1++;
          fp2++;
        }
 
        a = KNOTSU(nu) - 1;
        fp1 = nu->knotsu;
        fp2 = tempf;
        fp1[0] = 0.0;
        fp1++;
        while (a--) {
          fp1[0] = fp1[-1] + fp2[0];
          fp1++;
          fp2++;
        }
        MEM_freeN(tempf);
      }
    }
  }
  else {
    for (b = 0; b < nu->pntsv; b++) {
      bp1 = nu->bp + b * nu->pntsu;
      a = nu->pntsu;
      bp2 = bp1 + (a - 1);
      a /= 2;
 
      while (bp1 != bp2 && a > 0) {
        std::swap(*bp1, *bp2);
        a--;
        bp1++;
        bp2--;
      }
    }
  }
}
 
void BKE_curve_nurbs_vert_coords_get(const ListBase *lb, MutableSpan<float3> vert_coords)
{
  int index = 0;
  LISTBASE_FOREACH (const Nurb *, nu, lb) {
    if (nu->type == CU_BEZIER) {
      const BezTriple *bezt = nu->bezt;
      for (int i = 0; i < nu->pntsu; i++, bezt++) {
        vert_coords[index] = bezt->vec[0];
        index++;
        vert_coords[index] = bezt->vec[1];
        index++;
        vert_coords[index] = bezt->vec[2];
        index++;
      }
    }
    else {
      const BPoint *bp = nu->bp;
      for (int i = 0; i < nu->pntsu * nu->pntsv; i++, bp++) {
        vert_coords[index] = bp->vec;
        index++;
      }
    }
  }
}
 
Array<float3> BKE_curve_nurbs_vert_coords_alloc(const ListBase *lb)
{
  Array<float3> vert_coords(BKE_nurbList_verts_count(lb));
  BKE_curve_nurbs_vert_coords_get(lb, vert_coords);
  return vert_coords;
}
 
void BKE_curve_nurbs_vert_coords_apply_with_mat4(ListBase *lb,
                                                 const Span<float3> vert_coords,
                                                 const float4x4 &transform,
                                                 const bool constrain_2d)
{
  int index = 0;
  LISTBASE_FOREACH (Nurb *, nu, lb) {
    if (nu->type == CU_BEZIER) {
      BezTriple *bezt = nu->bezt;
 
      for (int i = 0; i < nu->pntsu; i++, bezt++) {
        mul_v3_m4v3(bezt->vec[0], transform.ptr(), vert_coords[index]);
        index++;
        mul_v3_m4v3(bezt->vec[1], transform.ptr(), vert_coords[index]);
        index++;
        mul_v3_m4v3(bezt->vec[2], transform.ptr(), vert_coords[index]);
        index++;
      }
    }
    else {
      BPoint *bp = nu->bp;
 
      for (int i = 0; i < nu->pntsu * nu->pntsv; i++, bp++) {
        mul_v3_m4v3(bp->vec, transform.ptr(), vert_coords[index]);
        index++;
      }
    }
 
    if (constrain_2d) {
      BKE_nurb_project_2d(nu);
    }
 
    calchandlesNurb_intern(nu, (eBezTriple_Flag)SELECT, true);
  }
}
 
void BKE_curve_nurbs_vert_coords_apply(ListBase *lb,
                                       const Span<float3> vert_coords,
                                       const bool constrain_2d)
{
  int index = 0;
  LISTBASE_FOREACH (Nurb *, nu, lb) {
    if (nu->type == CU_BEZIER) {
      BezTriple *bezt = nu->bezt;
 
      for (int i = 0; i < nu->pntsu; i++, bezt++) {
        copy_v3_v3(bezt->vec[0], vert_coords[index]);
        index++;
        copy_v3_v3(bezt->vec[1], vert_coords[index]);
        index++;
        copy_v3_v3(bezt->vec[2], vert_coords[index]);
        index++;
      }
    }
    else {
      BPoint *bp = nu->bp;
 
      for (int i = 0; i < nu->pntsu * nu->pntsv; i++, bp++) {
        copy_v3_v3(bp->vec, vert_coords[index]);
        index++;
      }
    }
 
    if (constrain_2d) {
      BKE_nurb_project_2d(nu);
    }
 
    calchandlesNurb_intern(nu, (eBezTriple_Flag)SELECT, true);
  }
}
 
Array<float3> BKE_curve_nurbs_key_vert_coords_alloc(const ListBase *lb, const float *key)
{
  Array<float3> vert_coords(BKE_nurbList_verts_count(lb));
 
  int index = 0;
  LISTBASE_FOREACH (const Nurb *, nu, lb) {
    if (nu->type == CU_BEZIER) {
      const BezTriple *bezt = nu->bezt;
 
      for (int i = 0; i < nu->pntsu; i++, bezt++) {
        vert_coords[index] = &key[0];
        index++;
        vert_coords[index] = &key[3];
        index++;
        vert_coords[index] = &key[6];
        index++;
        key += KEYELEM_FLOAT_LEN_BEZTRIPLE;
      }
    }
    else {
      const BPoint *bp = nu->bp;
 
      for (int i = 0; i < nu->pntsu * nu->pntsv; i++, bp++) {
        vert_coords[index] = key;
        index++;
        key += KEYELEM_FLOAT_LEN_BPOINT;
      }
    }
  }
  return vert_coords;
}
 
void BKE_curve_nurbs_key_vert_tilts_apply(ListBase *lb, const float *key)
{
  LISTBASE_FOREACH (Nurb *, nu, lb) {
    if (nu->type == CU_BEZIER) {
      BezTriple *bezt = nu->bezt;
 
      for (int i = 0; i < nu->pntsu; i++, bezt++) {
        bezt->tilt = key[9];
        bezt->radius = key[10];
        key += KEYELEM_FLOAT_LEN_BEZTRIPLE;
      }
    }
    else {
      BPoint *bp = nu->bp;
 
      for (int i = 0; i < nu->pntsu * nu->pntsv; i++, bp++) {
        bp->tilt = key[3];
        bp->radius = key[4];
        key += KEYELEM_FLOAT_LEN_BPOINT;
      }
    }
  }
}
 
static NURBSValidationStatus nurb_check_valid(const int pnts,
                                              const short order,
                                              const short flag,
                                              const short type,
                                              const bool is_surf,
                                              int *r_points_needed)
{
  if (pnts <= 1) {
    return NURBSValidationStatus::AtLeastTwoPointsRequired;
  }
  if (type == CU_NURBS) {
    if (pnts < order) {
      return NURBSValidationStatus::MorePointsThanOrderRequired;
    }
    if (flag & CU_NURB_BEZIER) {
      int points_needed = 0;
      if (flag & CU_NURB_CYCLIC) {
        const int remainder = pnts % (order - 1);
        points_needed = remainder > 0 ? order - 1 - remainder : 0;
      }
      else if (((flag & CU_NURB_ENDPOINT) == 0) && pnts <= order) {
        points_needed = order + 1 - pnts;
      }
      if (points_needed) {
        *r_points_needed = points_needed;
        return is_surf ? NURBSValidationStatus::MoreRowsForBezierRequired :
                         NURBSValidationStatus::MorePointsForBezierRequired;
      }
    }
  }
  return NURBSValidationStatus::Valid;
}
 
bool BKE_nurb_valid_message(const int pnts,
                            const short order,
                            const short flag,
                            const short type,
                            const bool is_surf,
                            const int dir,
                            char *message_dst,
                            const size_t maxncpy)
{
  int points_needed;
  NURBSValidationStatus status = nurb_check_valid(
      pnts, order, flag, type, is_surf, &points_needed);
 
  switch (status) {
    case NURBSValidationStatus::Valid:
      message_dst[0] = 0;
      return false;
    case NURBSValidationStatus::AtLeastTwoPointsRequired:
      if (dir == 1) {
        /* Exception made for curves as their pntsv == 1. */
        message_dst[0] = 0;
        return false;
      }
      BLI_strncpy(message_dst, RPT_("At least two points required"), maxncpy);
      break;
    case NURBSValidationStatus::MorePointsThanOrderRequired:
      BLI_strncpy(message_dst, RPT_("Must have more control points than Order"), maxncpy);
      break;
    case NURBSValidationStatus::MoreRowsForBezierRequired:
      BLI_snprintf(message_dst,
                   maxncpy,
                   RPT_("%d more %s row(s) needed for Bézier"),
                   points_needed,
                   dir == 0 ? "U" : "V");
      break;
    case NURBSValidationStatus::MorePointsForBezierRequired:
      BLI_snprintf(
          message_dst, maxncpy, RPT_("%d more point(s) needed for Bézier"), points_needed);
      break;
  }
 
  return true;
}
 
bool BKE_nurb_check_valid_u(const Nurb *nu)
{
  int points_needed;
  return NURBSValidationStatus::Valid ==
         nurb_check_valid(
             nu->pntsu, nu->orderu, nu->flagu, nu->type, nu->pntsv > 1, &points_needed);
}
 
bool BKE_nurb_check_valid_v(const Nurb *nu)
{
  int points_needed;
  return NURBSValidationStatus::Valid ==
         nurb_check_valid(
             nu->pntsv, nu->orderv, nu->flagv, nu->type, nu->pntsv > 1, &points_needed);
}
 
bool BKE_nurb_check_valid_uv(const Nurb *nu)
{
  if (!BKE_nurb_check_valid_u(nu)) {
    return false;
  }
  if ((nu->pntsv > 1) && !BKE_nurb_check_valid_v(nu)) {
    return false;
  }
 
  return true;
}
 
bool BKE_nurb_order_clamp_u(Nurb *nu)
{
  bool changed = false;
  if (nu->pntsu < nu->orderu) {
    nu->orderu = max_ii(2, nu->pntsu);
    changed = true;
  }
  return changed;
}
 
bool BKE_nurb_order_clamp_v(Nurb *nu)
{
  bool changed = false;
  if (nu->pntsv < nu->orderv) {
    nu->orderv = max_ii(2, nu->pntsv);
    changed = true;
  }
  return changed;
}
 
bool BKE_nurb_type_convert(Nurb *nu,
                           const short type,
                           const bool use_handles,
                           const char **r_err_msg)
{
  BezTriple *bezt;
  BPoint *bp;
  int a, c, nr;
 
  if (nu->type == CU_POLY) {
    if (type == CU_BEZIER) { /* To Bezier with vector-handles. */
      nr = nu->pntsu;
      bezt = MEM_calloc_arrayN<BezTriple>(nr, "setsplinetype2");
      nu->bezt = bezt;
      a = nr;
      bp = nu->bp;
      while (a--) {
        copy_v3_v3(bezt->vec[1], bp->vec);
        bezt->f1 = bezt->f2 = bezt->f3 = bp->f1;
        bezt->h1 = bezt->h2 = HD_VECT;
        bezt->weight = bp->weight;
        bezt->radius = bp->radius;
        bp++;
        bezt++;
      }
      MEM_freeN(nu->bp);
      nu->bp = nullptr;
      nu->pntsu = nr;
      nu->pntsv = 0;
      nu->type = CU_BEZIER;
      BKE_nurb_handles_calc(nu);
    }
    else if (type == CU_NURBS) {
      nu->type = CU_NURBS;
      nu->orderu = 4;
      nu->flagu &= CU_NURB_CYCLIC; /* disable all flags except for cyclic */
      BKE_nurb_knot_calc_u(nu);
      a = nu->pntsu * nu->pntsv;
      bp = nu->bp;
      while (a--) {
        bp->vec[3] = 1.0;
        bp++;
      }
    }
  }
  else if (nu->type == CU_BEZIER) { /* Bezier */
    if (ELEM(type, CU_POLY, CU_NURBS)) {
      nr = use_handles ? (3 * nu->pntsu) : nu->pntsu;
      nu->bp = MEM_calloc_arrayN<BPoint>(nr, "setsplinetype");
      a = nu->pntsu;
      bezt = nu->bezt;
      bp = nu->bp;
      while (a--) {
        if ((type == CU_POLY && bezt->h1 == HD_VECT && bezt->h2 == HD_VECT) ||
            (use_handles == false))
        {
          /* vector handle becomes one poly vertex */
          copy_v3_v3(bp->vec, bezt->vec[1]);
          bp->vec[3] = 1.0;
          bp->f1 = bezt->f2;
          if (use_handles) {
            nr -= 2;
          }
          bp->radius = bezt->radius;
          bp->weight = bezt->weight;
          bp++;
        }
        else {
          const uint8_t *f = &bezt->f1;
          for (c = 0; c < 3; c++, f++) {
            copy_v3_v3(bp->vec, bezt->vec[c]);
            bp->vec[3] = 1.0;
            bp->f1 = *f;
            bp->radius = bezt->radius;
            bp->weight = bezt->weight;
            bp++;
          }
        }
        bezt++;
      }
      MEM_freeN(nu->bezt);
      nu->bezt = nullptr;
      nu->pntsu = nr;
      nu->pntsv = 1;
      nu->orderu = 4;
      nu->orderv = 1;
      nu->type = type;
 
      if (type == CU_NURBS) {
        nu->flagu &= CU_NURB_CYCLIC; /* disable all flags except for cyclic */
        nu->flagu |= CU_NURB_BEZIER;
        BKE_nurb_knot_calc_u(nu);
      }
    }
  }
  else if (nu->type == CU_NURBS) {
    if (type == CU_POLY) {
      nu->type = CU_POLY;
      if (nu->knotsu) {
        MEM_freeN(nu->knotsu); /* python created nurbs have a knotsu of zero */
      }
      nu->knotsu = nullptr;
      MEM_SAFE_FREE(nu->knotsv);
    }
    else if (type == CU_BEZIER) { /* to Bezier */
      nr = nu->pntsu / 3;
 
      if (nr < 2) {
        if (r_err_msg != nullptr) {
          *r_err_msg = "At least 6 points required for conversion";
        }
        return false; /* conversion impossible */
      }
 
      bezt = MEM_calloc_arrayN<BezTriple>(nr, "setsplinetype2");
      nu->bezt = bezt;
      a = nr;
      bp = nu->bp;
      while (a--) {
        copy_v3_v3(bezt->vec[0], bp->vec);
        bezt->f1 = bp->f1;
        bp++;
        copy_v3_v3(bezt->vec[1], bp->vec);
        bezt->f2 = bp->f1;
        bp++;
        copy_v3_v3(bezt->vec[2], bp->vec);
        bezt->f3 = bp->f1;
        bezt->radius = bp->radius;
        bezt->weight = bp->weight;
        bp++;
        bezt++;
      }
      MEM_freeN(nu->bp);
      nu->bp = nullptr;
      MEM_freeN(nu->knotsu);
      nu->knotsu = nullptr;
      nu->pntsu = nr;
      nu->type = CU_BEZIER;
    }
  }
 
  return true;
}
 
ListBase *BKE_curve_nurbs_get(Curve *cu)
{
  if (cu->editnurb) {
    return BKE_curve_editNurbs_get(cu);
  }
 
  return &cu->nurb;
}
 
const ListBase *BKE_curve_nurbs_get_for_read(const Curve *cu)
{
  if (cu->editnurb) {
    return BKE_curve_editNurbs_get_for_read(cu);
  }
 
  return &cu->nurb;
}
 
void BKE_curve_nurb_active_set(Curve *cu, const Nurb *nu)
{
  if (nu == nullptr) {
    cu->actnu = CU_ACT_NONE;
  }
  else {
    BLI_assert(!nu->hide);
    ListBase *nurbs = BKE_curve_editNurbs_get(cu);
    cu->actnu = BLI_findindex(nurbs, nu);
  }
}
 
Nurb *BKE_curve_nurb_active_get(Curve *cu)
{
  ListBase *nurbs = BKE_curve_editNurbs_get(cu);
  return (Nurb *)BLI_findlink(nurbs, cu->actnu);
}
 
void *BKE_curve_vert_active_get(Curve *cu)
{
  Nurb *nu = nullptr;
  void *vert = nullptr;
 
  BKE_curve_nurb_vert_active_get(cu, &nu, &vert);
  return vert;
}
 
int BKE_curve_nurb_vert_index_get(const Nurb *nu, const void *vert)
{
  if (nu->type == CU_BEZIER) {
    BLI_assert(ARRAY_HAS_ITEM((BezTriple *)vert, nu->bezt, nu->pntsu));
    return (BezTriple *)vert - nu->bezt;
  }
 
  BLI_assert(ARRAY_HAS_ITEM((BPoint *)vert, nu->bp, nu->pntsu * nu->pntsv));
  return (BPoint *)vert - nu->bp;
}
 
void BKE_curve_nurb_vert_active_set(Curve *cu, const Nurb *nu, const void *vert)
{
  if (nu) {
    BKE_curve_nurb_active_set(cu, nu);
 
    if (vert) {
      cu->actvert = BKE_curve_nurb_vert_index_get(nu, vert);
    }
    else {
      cu->actvert = CU_ACT_NONE;
    }
  }
  else {
    cu->actnu = cu->actvert = CU_ACT_NONE;
  }
}
 
bool BKE_curve_nurb_vert_active_get(Curve *cu, Nurb **r_nu, void **r_vert)
{
  Nurb *nu = nullptr;
  void *vert = nullptr;
 
  if (cu->actvert != CU_ACT_NONE) {
    ListBase *nurbs = BKE_curve_editNurbs_get(cu);
    nu = (Nurb *)BLI_findlink(nurbs, cu->actnu);
 
    if (nu) {
      if (nu->type == CU_BEZIER) {
        BLI_assert(nu->pntsu > cu->actvert);
        vert = &nu->bezt[cu->actvert];
      }
      else {
        BLI_assert((nu->pntsu * nu->pntsv) > cu->actvert);
        vert = &nu->bp[cu->actvert];
      }
    }
  }
 
  *r_nu = nu;
  *r_vert = vert;
 
  return (*r_vert != nullptr);
}
 
void BKE_curve_nurb_vert_active_validate(Curve *cu)
{
  Nurb *nu;
  void *vert;
 
  if (BKE_curve_nurb_vert_active_get(cu, &nu, &vert)) {
    if (nu->type == CU_BEZIER) {
      BezTriple *bezt = (BezTriple *)vert;
      if (BEZT_ISSEL_ANY(bezt) == 0) {
        cu->actvert = CU_ACT_NONE;
      }
    }
    else {
      BPoint *bp = (BPoint *)vert;
      if ((bp->f1 & SELECT) == 0) {
        cu->actvert = CU_ACT_NONE;
      }
    }
 
    if (nu->hide) {
      cu->actnu = CU_ACT_NONE;
    }
  }
}
 
static std::optional<blender::Bounds<blender::float3>> calc_nurblist_bounds(const ListBase *nurbs,
                                                                            const bool use_radius)
{
  if (BLI_listbase_is_empty(nurbs)) {
    return std::nullopt;
  }
  float3 min(std::numeric_limits<float>::max());
  float3 max(std::numeric_limits<float>::lowest());
  LISTBASE_FOREACH (const Nurb *, nu, nurbs) {
    calc_nurb_minmax(nu, use_radius, min, max);
  }
  return blender::Bounds<float3>{min, max};
}
 
std::optional<blender::Bounds<blender::float3>> BKE_curve_minmax(const Curve *cu, bool use_radius)
{
  const ListBase *nurb_lb = BKE_curve_nurbs_get_for_read(cu);
  const bool is_font = BLI_listbase_is_empty(nurb_lb) && (cu->len != 0);
  /* For font curves we generate temp list of splines.
   *
   * This is likely to be fine, this function is not supposed to be called
   * often, and it's the only way to get meaningful bounds for fonts.
   */
  if (is_font) {
    ListBase temp_nurb_lb{};
    BKE_vfont_to_curve_ex(nullptr,
                          const_cast<Curve *>(cu),
                          FO_EDIT,
                          &temp_nurb_lb,
                          nullptr,
                          nullptr,
                          nullptr,
                          nullptr,
                          nullptr);
    BLI_SCOPED_DEFER([&]() { BKE_nurbList_free(&temp_nurb_lb); });
    return calc_nurblist_bounds(&temp_nurb_lb, false);
  }
 
  return calc_nurblist_bounds(nurb_lb, use_radius);
}
 
bool BKE_curve_center_median(Curve *cu, float cent[3])
{
  ListBase *nurb_lb = BKE_curve_nurbs_get(cu);
  int total = 0;
 
  zero_v3(cent);
 
  LISTBASE_FOREACH (Nurb *, nu, nurb_lb) {
    int i;
 
    if (nu->type == CU_BEZIER) {
      BezTriple *bezt;
      i = nu->pntsu;
      total += i * 3;
      for (bezt = nu->bezt; i--; bezt++) {
        add_v3_v3(cent, bezt->vec[0]);
        add_v3_v3(cent, bezt->vec[1]);
        add_v3_v3(cent, bezt->vec[2]);
      }
    }
    else {
      BPoint *bp;
      i = nu->pntsu * nu->pntsv;
      total += i;
      for (bp = nu->bp; i--; bp++) {
        add_v3_v3(cent, bp->vec);
      }
    }
  }
 
  if (total) {
    mul_v3_fl(cent, 1.0f / float(total));
  }
 
  return (total != 0);
}
 
void BKE_curve_transform_ex(Curve *cu,
                            const float mat[4][4],
                            const bool do_keys,
                            const bool do_props,
                            const float unit_scale)
{
  BPoint *bp;
  BezTriple *bezt;
  int i;
 
  const bool is_uniform_scaled = is_uniform_scaled_m4(mat);
 
  LISTBASE_FOREACH (Nurb *, nu, &cu->nurb) {
    if (nu->type == CU_BEZIER) {
      i = nu->pntsu;
      for (bezt = nu->bezt; i--; bezt++) {
        mul_m4_v3(mat, bezt->vec[0]);
        mul_m4_v3(mat, bezt->vec[1]);
        mul_m4_v3(mat, bezt->vec[2]);
        if (do_props) {
          bezt->radius *= unit_scale;
        }
        if (!is_uniform_scaled) {
          if (ELEM(bezt->h1, HD_AUTO, HD_AUTO_ANIM) || ELEM(bezt->h2, HD_AUTO, HD_AUTO_ANIM)) {
            bezt->h1 = bezt->h2 = HD_ALIGN;
          }
        }
      }
      BKE_nurb_handles_calc(nu);
    }
    else {
      i = nu->pntsu * nu->pntsv;
      for (bp = nu->bp; i--; bp++) {
        mul_m4_v3(mat, bp->vec);
        if (do_props) {
          bp->radius *= unit_scale;
        }
      }
    }
  }
 
  if (do_keys && cu->key) {
    LISTBASE_FOREACH (KeyBlock *, kb, &cu->key->block) {
      float *fp = (float *)kb->data;
      int n = kb->totelem;
 
      LISTBASE_FOREACH (Nurb *, nu, &cu->nurb) {
        if (nu->type == CU_BEZIER) {
          for (i = nu->pntsu; i && (n -= KEYELEM_ELEM_LEN_BEZTRIPLE) >= 0; i--) {
            mul_m4_v3(mat, &fp[0]);
            mul_m4_v3(mat, &fp[3]);
            mul_m4_v3(mat, &fp[6]);
            if (do_props) {
              fp[10] *= unit_scale; /* radius */
            }
            fp += KEYELEM_FLOAT_LEN_BEZTRIPLE;
          }
        }
        else {
          for (i = nu->pntsu * nu->pntsv; i && (n -= KEYELEM_ELEM_LEN_BPOINT) >= 0; i--) {
            mul_m4_v3(mat, fp);
            if (do_props) {
              fp[4] *= unit_scale; /* radius */
            }
            fp += KEYELEM_FLOAT_LEN_BPOINT;
          }
        }
      }
    }
  }
}
 
void BKE_curve_transform(Curve *cu, const float mat[4][4], const bool do_keys, const bool do_props)
{
  float unit_scale = mat4_to_scale(mat);
  BKE_curve_transform_ex(cu, mat, do_keys, do_props, unit_scale);
}
 
void BKE_curve_translate(Curve *cu, const float offset[3], const bool do_keys)
{
  ListBase *nurb_lb = BKE_curve_nurbs_get(cu);
 
  LISTBASE_FOREACH (Nurb *, nu, nurb_lb) {
    if (nu->type == CU_BEZIER) {
      int i = nu->pntsu;
      for (BezTriple *bezt = nu->bezt; i--; bezt++) {
        add_v3_v3(bezt->vec[0], offset);
        add_v3_v3(bezt->vec[1], offset);
        add_v3_v3(bezt->vec[2], offset);
      }
    }
    else {
      int i = nu->pntsu * nu->pntsv;
      for (BPoint *bp = nu->bp; i--; bp++) {
        add_v3_v3(bp->vec, offset);
      }
    }
  }
 
  if (do_keys && cu->key) {
    LISTBASE_FOREACH (KeyBlock *, kb, &cu->key->block) {
      float *fp = (float *)kb->data;
      int n = kb->totelem;
 
      LISTBASE_FOREACH (Nurb *, nu, &cu->nurb) {
        if (nu->type == CU_BEZIER) {
          for (int i = nu->pntsu; i && (n -= KEYELEM_ELEM_LEN_BEZTRIPLE) >= 0; i--) {
            add_v3_v3(&fp[0], offset);
            add_v3_v3(&fp[3], offset);
            add_v3_v3(&fp[6], offset);
            fp += KEYELEM_FLOAT_LEN_BEZTRIPLE;
          }
        }
        else {
          for (int i = nu->pntsu * nu->pntsv; i && (n -= KEYELEM_ELEM_LEN_BPOINT) >= 0; i--) {
            add_v3_v3(fp, offset);
            fp += KEYELEM_FLOAT_LEN_BPOINT;
          }
        }
      }
    }
  }
}
 
void BKE_curve_material_index_remove(Curve *cu, int index)
{
  if (cu->ob_type == OB_FONT) {
    CharInfo *info = cu->strinfo;
    for (int i = cu->len_char32 - 1; i >= 0; i--, info++) {
      if (info->mat_nr && info->mat_nr >= index) {
        info->mat_nr--;
      }
    }
  }
  else {
    LISTBASE_FOREACH (Nurb *, nu, &cu->nurb) {
      if (nu->mat_nr && nu->mat_nr >= index) {
        nu->mat_nr--;
      }
    }
  }
}
 
bool BKE_curve_material_index_used(const Curve *cu, int index)
{
  if (cu->ob_type == OB_FONT) {
    const CharInfo *info = cu->strinfo;
    for (int i = cu->len_char32 - 1; i >= 0; i--, info++) {
      if (info->mat_nr == index) {
        return true;
      }
    }
  }
  else {
    LISTBASE_FOREACH (const Nurb *, nu, &cu->nurb) {
      if (nu->mat_nr == index) {
        return true;
      }
    }
  }
 
  return false;
}
 
void BKE_curve_material_index_clear(Curve *cu)
{
  if (cu->ob_type == OB_FONT) {
    CharInfo *info = cu->strinfo;
    for (int i = cu->len_char32 - 1; i >= 0; i--, info++) {
      info->mat_nr = 0;
    }
  }
  else {
    LISTBASE_FOREACH (Nurb *, nu, &cu->nurb) {
      nu->mat_nr = 0;
    }
  }
}
 
bool BKE_curve_material_index_validate(Curve *cu)
{
  bool is_valid = true;
 
  if (cu->ob_type == OB_FONT) {
    CharInfo *info = cu->strinfo;
    const int max_idx = max_ii(0, cu->totcol); /* OB_FONT use 1 as first mat index, not 0!!! */
    int i;
    for (i = cu->len_char32 - 1; i >= 0; i--, info++) {
      if (info->mat_nr > max_idx) {
        info->mat_nr = 0;
        is_valid = false;
      }
    }
  }
  else {
    const int max_idx = max_ii(0, cu->totcol - 1);
    LISTBASE_FOREACH (Nurb *, nu, &cu->nurb) {
      if (nu->mat_nr > max_idx) {
        nu->mat_nr = 0;
        is_valid = false;
      }
    }
  }
 
  if (!is_valid) {
    DEG_id_tag_update(&cu->id, ID_RECALC_GEOMETRY);
    return true;
  }
  return false;
}
 
void BKE_curve_material_remap(Curve *cu, const uint *remap, uint remap_len)
{
  const short remap_len_short = short(remap_len);
 
#define MAT_NR_REMAP(n) \
  if (n < remap_len_short) { \
    BLI_assert(n >= 0 && remap[n] < remap_len_short); \
    n = remap[n]; \
  } \
  ((void)0)
 
  if (cu->ob_type == OB_FONT) {
    CharInfo *strinfo;
    int charinfo_len, i;
 
    if (cu->editfont) {
      EditFont *ef = cu->editfont;
      strinfo = ef->textbufinfo;
      charinfo_len = ef->len;
    }
    else {
      strinfo = cu->strinfo;
      charinfo_len = cu->len_char32;
    }
 
    for (i = 0; i <= charinfo_len; i++) {
      MAT_NR_REMAP(strinfo[i].mat_nr);
    }
  }
  else {
    ListBase *nurbs = BKE_curve_editNurbs_get(cu);
 
    if (nurbs) {
      LISTBASE_FOREACH (Nurb *, nu, nurbs) {
        MAT_NR_REMAP(nu->mat_nr);
      }
    }
  }
 
#undef MAT_NR_REMAP
}
 
void BKE_curve_smooth_flag_set(Curve *cu, const bool use_smooth)
{
  if (use_smooth) {
    LISTBASE_FOREACH (Nurb *, nu, &cu->nurb) {
      nu->flag |= CU_SMOOTH;
    }
  }
  else {
    LISTBASE_FOREACH (Nurb *, nu, &cu->nurb) {
      nu->flag &= ~CU_SMOOTH;
    }
  }
}
 
void BKE_curve_rect_from_textbox(const Curve *cu, const TextBox *tb, rctf *r_rect)
{
  r_rect->xmin = cu->xof + tb->x;
  r_rect->ymax = cu->yof + tb->y + cu->fsize;
 
  r_rect->xmax = r_rect->xmin + tb->w;
  r_rect->ymin = r_rect->ymax - tb->h;
}
 
void BKE_curve_correct_bezpart(const float v1[2], float v2[2], float v3[2], const float v4[2])
{
  float h1[2], h2[2], len1, len2, len, fac;
 
  /* Calculate handle deltas. */
  h1[0] = v1[0] - v2[0];
  h1[1] = v1[1] - v2[1];
 
  h2[0] = v4[0] - v3[0];
  h2[1] = v4[1] - v3[1];
 
  /* Calculate distances:
   * - len  = span of time between keyframes
   * - len1 = length of handle of start key
   * - len2 = length of handle of end key
   */
  len = v4[0] - v1[0];
  len1 = fabsf(h1[0]);
  len2 = fabsf(h2[0]);
 
  /* If the handles have no length, no need to do any corrections. */
  if ((len1 + len2) == 0.0f) {
    return;
  }
 
  /* the two handles cross over each other, so force them
   * apart using the proportion they overlap
   */
  if ((len1 + len2) > len) {
    fac = len / (len1 + len2);
 
    v2[0] = (v1[0] - fac * h1[0]);
    v2[1] = (v1[1] - fac * h1[1]);
 
    v3[0] = (v4[0] - fac * h2[0]);
    v3[1] = (v4[1] - fac * h2[1]);
  }
}
 
std::optional<int> Curve::material_index_max() const
{
  if (BLI_listbase_is_empty(&this->nurb)) {
    return std::nullopt;
  }
  int max_index = 0;
  LISTBASE_FOREACH (const Nurb *, nurb, &this->nurb) {
    max_index = std::max<int>(max_index, nurb->mat_nr);
  }
  return clamp_i(max_index, 0, MAXMAT);
}
 
/* **** Depsgraph evaluation **** */
 
void BKE_curve_eval_geometry(Depsgraph *depsgraph, Curve *curve)
{
  DEG_debug_print_eval(depsgraph, __func__, curve->id.name, curve);
  BKE_curve_texspace_calc(curve);
  if (DEG_is_active(depsgraph)) {
    Curve *curve_orig = DEG_get_original(curve);
    if (curve->texspace_flag & CU_TEXSPACE_FLAG_AUTO_EVALUATED) {
      curve_orig->texspace_flag |= CU_TEXSPACE_FLAG_AUTO_EVALUATED;
      copy_v3_v3(curve_orig->texspace_location, curve->texspace_location);
      copy_v3_v3(curve_orig->texspace_size, curve->texspace_size);
    }
  }
}
 
/* Draw Engine */
 
void (*BKE_curve_batch_cache_dirty_tag_cb)(Curve *cu, int mode) = nullptr;
void (*BKE_curve_batch_cache_free_cb)(Curve *cu) = nullptr;
 
void BKE_curve_batch_cache_dirty_tag(Curve *cu, int mode)
{
  if (cu->batch_cache) {
    BKE_curve_batch_cache_dirty_tag_cb(cu, mode);
  }
}
void BKE_curve_batch_cache_free(Curve *cu)
{
  if (cu->batch_cache) {
    BKE_curve_batch_cache_free_cb(cu);
  }
}