voronoi_2d.c

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/*
 * This program is free software; you can redistribute it and/or
 * modify it under the terms of the GNU General Public License
 * as published by the Free Software Foundation; either version 2
 * of the License, or (at your option) any later version.
 *
 * This program is distributed in the hope that it will be useful,
 * but WITHOUT ANY WARRANTY; without even the implied warranty of
 * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
 * GNU General Public License for more details.
 *
 * You should have received a copy of the GNU General Public License
 * along with this program; if not, write to the Free Software Foundation,
 * Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301, USA.
 *
 * The Original Code is Copyright (C) 2012 Blender Foundation.
 * All rights reserved.
 */
 
#include "MEM_guardedalloc.h"
 
#include "BLI_listbase.h"
#include "BLI_math.h"
#include "BLI_utildefines.h"
#include "BLI_voronoi_2d.h"
 
#define VORONOI_EPS 1e-2f
 
enum {
  voronoiEventType_Site = 0,
  voronoiEventType_Circle = 1,
};
 
typedef struct VoronoiEvent {
  struct VoronoiEvent *next, *prev;
 
  int type;      /* type of event (site or circle) */
  float site[2]; /* site for which event was generated */
 
  struct VoronoiParabola *parabola; /* parabola for which event was generated */
} VoronoiEvent;
 
typedef struct VoronoiParabola {
  struct VoronoiParabola *left, *right, *parent;
  VoronoiEvent *event;
  VoronoiEdge *edge;
  float site[2];
  bool is_leaf;
} VoronoiParabola;
 
typedef struct VoronoiProcess {
  ListBase queue, edges;
  VoronoiParabola *root;
  int width, height;
  float current_y;
} VoronoiProcess;
 
/* event */
 
static void voronoi_insertEvent(VoronoiProcess *process, VoronoiEvent *event)
{
  VoronoiEvent *current_event = process->queue.first;
 
  while (current_event) {
    if (current_event->site[1] < event->site[1]) {
      break;
    }
    if (current_event->site[1] == event->site[1]) {
      event->site[1] -= VORONOI_EPS;
    }
 
    current_event = current_event->next;
  }
 
  BLI_insertlinkbefore(&process->queue, current_event, event);
}
 
/* edge */
static VoronoiEdge *voronoiEdge_new(const float start[2],
                                    const float left[2],
                                    const float right[2])
{
  VoronoiEdge *edge = MEM_callocN(sizeof(VoronoiEdge), "voronoi edge");
 
  copy_v2_v2(edge->start, start);
  copy_v2_v2(edge->left, left);
  copy_v2_v2(edge->right, right);
 
  edge->neighbor = NULL;
  edge->end[0] = 0;
  edge->end[1] = 0;
 
  edge->f = (right[0] - left[0]) / (left[1] - right[1]);
  edge->g = start[1] - edge->f * start[0];
 
  edge->direction[0] = right[1] - left[1];
  edge->direction[1] = -(right[0] - left[0]);
 
  return edge;
}
 
/* parabola */
 
static VoronoiParabola *voronoiParabola_new(void)
{
  VoronoiParabola *parabola = MEM_callocN(sizeof(VoronoiParabola), "voronoi parabola");
 
  parabola->is_leaf = false;
  parabola->event = NULL;
  parabola->edge = NULL;
  parabola->parent = NULL;
 
  return parabola;
}
 
static VoronoiParabola *voronoiParabola_newSite(const float site[2])
{
  VoronoiParabola *parabola = MEM_callocN(sizeof(VoronoiParabola), "voronoi parabola site");
 
  copy_v2_v2(parabola->site, site);
  parabola->is_leaf = true;
  parabola->event = NULL;
  parabola->edge = NULL;
  parabola->parent = NULL;
 
  return parabola;
}
 
/* returns the closest leave which is on the left of current node */
static VoronoiParabola *voronoiParabola_getLeftChild(VoronoiParabola *parabola)
{
  VoronoiParabola *current_parabola;
 
  if (!parabola) {
    return NULL;
  }
 
  current_parabola = parabola->left;
  while (!current_parabola->is_leaf) {
    current_parabola = current_parabola->right;
  }
 
  return current_parabola;
}
 
/* returns the closest leave which is on the right of current node */
static VoronoiParabola *voronoiParabola_getRightChild(VoronoiParabola *parabola)
{
  VoronoiParabola *current_parabola;
 
  if (!parabola) {
    return NULL;
  }
 
  current_parabola = parabola->right;
  while (!current_parabola->is_leaf) {
    current_parabola = current_parabola->left;
  }
 
  return current_parabola;
}
 
/* returns the closest parent which is on the left */
static VoronoiParabola *voronoiParabola_getLeftParent(VoronoiParabola *parabola)
{
  VoronoiParabola *current_par = parabola->parent;
  VoronoiParabola *last_parabola = parabola;
 
  while (current_par->left == last_parabola) {
    if (!current_par->parent) {
      return NULL;
    }
 
    last_parabola = current_par;
    current_par = current_par->parent;
  }
 
  return current_par;
}
 
/* returns the closest parent which is on the right */
static VoronoiParabola *voronoiParabola_getRightParent(VoronoiParabola *parabola)
{
  VoronoiParabola *current_parabola = parabola->parent;
  VoronoiParabola *last_parabola = parabola;
 
  while (current_parabola->right == last_parabola) {
    if (!current_parabola->parent) {
      return NULL;
    }
 
    last_parabola = current_parabola;
    current_parabola = current_parabola->parent;
  }
 
  return current_parabola;
}
 
static void voronoiParabola_setLeft(VoronoiParabola *parabola, VoronoiParabola *left)
{
  parabola->left = left;
  left->parent = parabola;
}
 
static void voronoiParabola_setRight(VoronoiParabola *parabola, VoronoiParabola *right)
{
  parabola->right = right;
  right->parent = parabola;
}
 
static float voronoi_getY(VoronoiProcess *process, const float p[2], float x)
{
  float ly = process->current_y;
 
  float dp = 2 * (p[1] - ly);
  float a1 = 1 / dp;
  float b1 = -2 * p[0] / dp;
  float c1 = ly + dp / 4 + p[0] * p[0] / dp;
 
  return a1 * x * x + b1 * x + c1;
}
 
static float voronoi_getXOfEdge(VoronoiProcess *process, VoronoiParabola *par, float y)
{
  VoronoiParabola *left = voronoiParabola_getLeftChild(par);
  VoronoiParabola *right = voronoiParabola_getRightChild(par);
  float p[2], r[2];
  float dp, a1, b1, c1, a2, b2, c2, a, b, c, disc, ry, x1, x2;
  float ly = process->current_y;
 
  copy_v2_v2(p, left->site);
  copy_v2_v2(r, right->site);
 
  dp = 2.0f * (p[1] - y);
  a1 = 1.0f / dp;
  b1 = -2.0f * p[0] / dp;
  c1 = y + dp / 4 + p[0] * p[0] / dp;
 
  dp = 2.0f * (r[1] - y);
  a2 = 1.0f / dp;
  b2 = -2.0f * r[0] / dp;
  c2 = ly + dp / 4 + r[0] * r[0] / dp;
 
  a = a1 - a2;
  b = b1 - b2;
  c = c1 - c2;
 
  disc = b * b - 4 * a * c;
  x1 = (-b + sqrtf(disc)) / (2 * a);
  x2 = (-b - sqrtf(disc)) / (2 * a);
 
  if (p[1] < r[1]) {
    ry = max_ff(x1, x2);
  }
  else {
    ry = min_ff(x1, x2);
  }
 
  return ry;
}
 
static VoronoiParabola *voronoi_getParabolaByX(VoronoiProcess *process, float xx)
{
  VoronoiParabola *par = process->root;
  float x = 0.0f;
  float ly = process->current_y;
 
  while (!par->is_leaf) {
    x = voronoi_getXOfEdge(process, par, ly);
 
    if (x > xx) {
      par = par->left;
    }
    else {
      par = par->right;
    }
  }
 
  return par;
}
 
static int voronoi_getEdgeIntersection(VoronoiEdge *a, VoronoiEdge *b, float p[2])
{
  float x = (b->g - a->g) / (a->f - b->f);
  float y = a->f * x + a->g;
 
  if ((x - a->start[0]) / a->direction[0] < 0) {
    return 0;
  }
 
  if ((y - a->start[1]) / a->direction[1] < 0) {
    return 0;
  }
 
  if ((x - b->start[0]) / b->direction[0] < 0) {
    return 0;
  }
 
  if ((y - b->start[1]) / b->direction[1] < 0) {
    return 0;
  }
 
  p[0] = x;
  p[1] = y;
 
  return 1;
}
 
static void voronoi_checkCircle(VoronoiProcess *process, VoronoiParabola *b)
{
  VoronoiParabola *lp = voronoiParabola_getLeftParent(b);
  VoronoiParabola *rp = voronoiParabola_getRightParent(b);
 
  VoronoiParabola *a = voronoiParabola_getLeftChild(lp);
  VoronoiParabola *c = voronoiParabola_getRightChild(rp);
 
  VoronoiEvent *event;
 
  float ly = process->current_y;
  float s[2], dx, dy, d;
 
  if (!a || !c || len_squared_v2v2(a->site, c->site) < VORONOI_EPS) {
    return;
  }
 
  if (!voronoi_getEdgeIntersection(lp->edge, rp->edge, s)) {
    return;
  }
 
  dx = a->site[0] - s[0];
  dy = a->site[1] - s[1];
 
  d = sqrtf((dx * dx) + (dy * dy));
 
  if (s[1] - d >= ly) {
    return;
  }
 
  event = MEM_callocN(sizeof(VoronoiEvent), "voronoi circle event");
 
  event->type = voronoiEventType_Circle;
 
  event->site[0] = s[0];
  event->site[1] = s[1] - d;
 
  b->event = event;
  event->parabola = b;
 
  voronoi_insertEvent(process, event);
}
 
static void voronoi_addParabola(VoronoiProcess *process, float site[2])
{
  VoronoiParabola *root = process->root;
  VoronoiParabola *par, *p0, *p1, *p2;
  VoronoiEdge *el, *er;
  float start[2];
 
  if (!process->root) {
    process->root = voronoiParabola_newSite(site);
 
    return;
  }
 
  if (root->is_leaf && root->site[1] - site[1] < 0) {
    float *fp = root->site;
    float s[2];
 
    root->is_leaf = false;
    voronoiParabola_setLeft(root, voronoiParabola_newSite(fp));
    voronoiParabola_setRight(root, voronoiParabola_newSite(site));
 
    s[0] = (site[0] + fp[0]) / 2.0f;
    s[1] = process->height;
 
    if (site[0] > fp[0]) {
      root->edge = voronoiEdge_new(s, fp, site);
    }
    else {
      root->edge = voronoiEdge_new(s, site, fp);
    }
 
    BLI_addtail(&process->edges, root->edge);
 
    return;
  }
 
  par = voronoi_getParabolaByX(process, site[0]);
 
  if (par->event) {
    BLI_freelinkN(&process->queue, par->event);
 
    par->event = NULL;
  }
 
  start[0] = site[0];
  start[1] = voronoi_getY(process, par->site, site[0]);
 
  el = voronoiEdge_new(start, par->site, site);
  er = voronoiEdge_new(start, site, par->site);
 
  el->neighbor = er;
  BLI_addtail(&process->edges, el);
 
  par->edge = er;
  par->is_leaf = false;
 
  p0 = voronoiParabola_newSite(par->site);
  p1 = voronoiParabola_newSite(site);
  p2 = voronoiParabola_newSite(par->site);
 
  voronoiParabola_setRight(par, p2);
  voronoiParabola_setLeft(par, voronoiParabola_new());
  par->left->edge = el;
 
  voronoiParabola_setLeft(par->left, p0);
  voronoiParabola_setRight(par->left, p1);
 
  voronoi_checkCircle(process, p0);
  voronoi_checkCircle(process, p2);
}
 
static void voronoi_removeParabola(VoronoiProcess *process, VoronoiEvent *event)
{
  VoronoiParabola *p1 = event->parabola;
 
  VoronoiParabola *xl = voronoiParabola_getLeftParent(p1);
  VoronoiParabola *xr = voronoiParabola_getRightParent(p1);
 
  VoronoiParabola *p0 = voronoiParabola_getLeftChild(xl);
  VoronoiParabola *p2 = voronoiParabola_getRightChild(xr);
 
  VoronoiParabola *higher = NULL, *par, *gparent;
 
  float p[2];
 
  if (p0->event) {
    BLI_freelinkN(&process->queue, p0->event);
    p0->event = NULL;
  }
 
  if (p2->event) {
    BLI_freelinkN(&process->queue, p2->event);
    p2->event = NULL;
  }
 
  p[0] = event->site[0];
  p[1] = voronoi_getY(process, p1->site, event->site[0]);
 
  copy_v2_v2(xl->edge->end, p);
  copy_v2_v2(xr->edge->end, p);
 
  par = p1;
  while (par != process->root) {
    par = par->parent;
 
    if (par == xl) {
      higher = xl;
    }
    if (par == xr) {
      higher = xr;
    }
  }
 
  higher->edge = voronoiEdge_new(p, p0->site, p2->site);
  BLI_addtail(&process->edges, higher->edge);
 
  gparent = p1->parent->parent;
  if (p1->parent->left == p1) {
    if (gparent->left == p1->parent) {
      voronoiParabola_setLeft(gparent, p1->parent->right);
    }
    if (gparent->right == p1->parent) {
      voronoiParabola_setRight(gparent, p1->parent->right);
    }
  }
  else {
    if (gparent->left == p1->parent) {
      voronoiParabola_setLeft(gparent, p1->parent->left);
    }
    if (gparent->right == p1->parent) {
      voronoiParabola_setRight(gparent, p1->parent->left);
    }
  }
 
  MEM_freeN(p1->parent);
  MEM_freeN(p1);
 
  voronoi_checkCircle(process, p0);
  voronoi_checkCircle(process, p2);
}
 
static void voronoi_finishEdge(VoronoiProcess *process, VoronoiParabola *parabola)
{
  float mx;
 
  if (parabola->is_leaf) {
    MEM_freeN(parabola);
    return;
  }
 
  if (parabola->edge->direction[0] > 0.0f) {
    mx = max_ff(process->width, parabola->edge->start[0] + 10);
  }
  else {
    mx = min_ff(0.0f, parabola->edge->start[0] - 10.0f);
  }
 
  parabola->edge->end[0] = mx;
  parabola->edge->end[1] = mx * parabola->edge->f + parabola->edge->g;
 
  voronoi_finishEdge(process, parabola->left);
  voronoi_finishEdge(process, parabola->right);
 
  MEM_freeN(parabola);
}
 
static void voronoi_clampEdgeVertex(int width, int height, float *coord, float *other_coord)
{
  const float corners[4][2] = {
      {0.0f, 0.0f}, {width - 1, 0.0f}, {width - 1, height - 1}, {0.0f, height - 1}};
  int i;
 
  if (IN_RANGE_INCL(coord[0], 0, width - 1) && IN_RANGE_INCL(coord[1], 0, height - 1)) {
    return;
  }
 
  for (i = 0; i < 4; i++) {
    float v1[2], v2[2];
    float p[2];
 
    copy_v2_v2(v1, corners[i]);
 
    if (i == 3) {
      copy_v2_v2(v2, corners[0]);
    }
    else {
      copy_v2_v2(v2, corners[i + 1]);
    }
 
    if (isect_seg_seg_v2_point(v1, v2, coord, other_coord, p) == 1) {
      if (i == 0 && coord[1] > p[1]) {
        continue;
      }
      if (i == 1 && coord[0] < p[0]) {
        continue;
      }
      if (i == 2 && coord[1] < p[1]) {
        continue;
      }
      if (i == 3 && coord[0] > p[0]) {
        continue;
      }
 
      copy_v2_v2(coord, p);
    }
  }
}
 
static void voronoi_clampEdges(ListBase *edges, int width, int height, ListBase *clamped_edges)
{
  VoronoiEdge *edge;
 
  edge = edges->first;
  while (edge) {
    VoronoiEdge *new_edge = MEM_callocN(sizeof(VoronoiEdge), "clamped edge");
 
    *new_edge = *edge;
    BLI_addtail(clamped_edges, new_edge);
 
    voronoi_clampEdgeVertex(width, height, new_edge->start, new_edge->end);
    voronoi_clampEdgeVertex(width, height, new_edge->end, new_edge->start);
 
    edge = edge->next;
  }
}
 
static int voronoi_getNextSideCoord(
    ListBase *edges, const float coord[2], int dim, int dir, float next_coord[2])
{
  VoronoiEdge *edge = edges->first;
  float distance = FLT_MAX;
  int other_dim = dim ? 0 : 1;
 
  while (edge) {
    bool ok = false;
    float co[2], cur_distance;
 
    if (fabsf(edge->start[other_dim] - coord[other_dim]) < VORONOI_EPS &&
        len_squared_v2v2(coord, edge->start) > VORONOI_EPS) {
      copy_v2_v2(co, edge->start);
      ok = true;
    }
 
    if (fabsf(edge->end[other_dim] - coord[other_dim]) < VORONOI_EPS &&
        len_squared_v2v2(coord, edge->end) > VORONOI_EPS) {
      copy_v2_v2(co, edge->end);
      ok = true;
    }
 
    if (ok) {
      if (dir > 0 && coord[dim] > co[dim]) {
        ok = false;
      }
      else if (dir < 0 && coord[dim] < co[dim]) {
        ok = false;
      }
    }
 
    if (ok) {
      cur_distance = len_squared_v2v2(coord, co);
      if (cur_distance < distance) {
        copy_v2_v2(next_coord, co);
        distance = cur_distance;
      }
    }
 
    edge = edge->next;
  }
 
  return distance < FLT_MAX;
}
 
static void voronoi_createBoundaryEdges(ListBase *edges, int width, int height)
{
  const float corners[4][2] = {
      {width - 1, 0.0f}, {width - 1, height - 1}, {0.0f, height - 1}, {0.0f, 0.0f}};
  int i, dim = 0, dir = 1;
 
  float coord[2] = {0.0f, 0.0f};
  float next_coord[2] = {0.0f, 0.0f};
 
  for (i = 0; i < 4; i++) {
    while (voronoi_getNextSideCoord(edges, coord, dim, dir, next_coord)) {
      VoronoiEdge *edge = MEM_callocN(sizeof(VoronoiEdge), "boundary edge");
 
      copy_v2_v2(edge->start, coord);
      copy_v2_v2(edge->end, next_coord);
      BLI_addtail(edges, edge);
 
      copy_v2_v2(coord, next_coord);
    }
 
    if (len_squared_v2v2(coord, corners[i]) > VORONOI_EPS) {
      VoronoiEdge *edge = MEM_callocN(sizeof(VoronoiEdge), "boundary edge");
 
      copy_v2_v2(edge->start, coord);
      copy_v2_v2(edge->end, corners[i]);
      BLI_addtail(edges, edge);
      copy_v2_v2(coord, corners[i]);
    }
 
    dim = dim ? 0 : 1;
    if (i == 1) {
      dir = -1;
    }
  }
}
 
void BLI_voronoi_compute(
    const VoronoiSite *sites, int sites_total, int width, int height, ListBase *edges)
{
  VoronoiProcess process;
  VoronoiEdge *edge;
  int i;
 
  memset(&process, 0, sizeof(VoronoiProcess));
 
  process.width = width;
  process.height = height;
 
  for (i = 0; i < sites_total; i++) {
    VoronoiEvent *event = MEM_callocN(sizeof(VoronoiEvent), "voronoi site event");
 
    event->type = voronoiEventType_Site;
    copy_v2_v2(event->site, sites[i].co);
 
    voronoi_insertEvent(&process, event);
  }
 
  while (process.queue.first) {
    VoronoiEvent *event = process.queue.first;
 
    process.current_y = event->site[1];
 
    if (event->type == voronoiEventType_Site) {
      voronoi_addParabola(&process, event->site);
    }
    else {
      voronoi_removeParabola(&process, event);
    }
 
    BLI_freelinkN(&process.queue, event);
  }
 
  voronoi_finishEdge(&process, process.root);
 
  edge = process.edges.first;
  while (edge) {
    if (edge->neighbor) {
      copy_v2_v2(edge->start, edge->neighbor->end);
      MEM_freeN(edge->neighbor);
    }
 
    edge = edge->next;
  }
 
  BLI_movelisttolist(edges, &process.edges);
}
 
static bool testVoronoiEdge(const float site[2], const float point[2], const VoronoiEdge *edge)
{
  float p[2];
 
  if (isect_seg_seg_v2_point(site, point, edge->start, edge->end, p) == 1) {
    if (len_squared_v2v2(p, edge->start) > VORONOI_EPS &&
        len_squared_v2v2(p, edge->end) > VORONOI_EPS) {
      return false;
    }
  }
 
  return true;
}
 
static int voronoi_addTriangulationPoint(const float coord[2],
                                         const float color[3],
                                         VoronoiTriangulationPoint **triangulated_points,
                                         int *triangulated_points_total)
{
  VoronoiTriangulationPoint *triangulation_point;
  int i;
 
  for (i = 0; i < *triangulated_points_total; i++) {
    if (equals_v2v2(coord, (*triangulated_points)[i].co)) {
      triangulation_point = &(*triangulated_points)[i];
 
      add_v3_v3(triangulation_point->color, color);
      triangulation_point->power++;
 
      return i;
    }
  }
 
  if (*triangulated_points) {
    *triangulated_points = MEM_reallocN(*triangulated_points,
                                        sizeof(VoronoiTriangulationPoint) *
                                            (*triangulated_points_total + 1));
  }
  else {
    *triangulated_points = MEM_callocN(sizeof(VoronoiTriangulationPoint), "triangulation points");
  }
 
  triangulation_point = &(*triangulated_points)[(*triangulated_points_total)];
  copy_v2_v2(triangulation_point->co, coord);
  copy_v3_v3(triangulation_point->color, color);
 
  triangulation_point->power = 1;
 
  (*triangulated_points_total)++;
 
  return (*triangulated_points_total) - 1;
}
 
static void voronoi_addTriangle(
    int v1, int v2, int v3, int (**r_triangles)[3], int *r_triangles_total)
{
  int *triangle;
 
  if (*r_triangles) {
    *r_triangles = MEM_reallocN(*r_triangles, sizeof(int[3]) * (*r_triangles_total + 1));
  }
  else {
    *r_triangles = MEM_callocN(sizeof(int[3]), "trianglulation triangles");
  }
 
  triangle = (int *)&(*r_triangles)[(*r_triangles_total)];
 
  triangle[0] = v1;
  triangle[1] = v2;
  triangle[2] = v3;
 
  (*r_triangles_total)++;
}
 
void BLI_voronoi_triangulate(const VoronoiSite *sites,
                             int sites_total,
                             ListBase *edges,
                             int width,
                             int height,
                             VoronoiTriangulationPoint **r_triangulated_points,
                             int *r_triangulated_points_total,
                             int (**r_triangles)[3],
                             int *r_triangles_total)
{
  VoronoiTriangulationPoint *triangulated_points = NULL;
  int(*triangles)[3] = NULL;
  int triangulated_points_total = 0, triangles_total = 0;
  int i;
  ListBase boundary_edges = {NULL, NULL};
 
  voronoi_clampEdges(edges, width, height, &boundary_edges);
  voronoi_createBoundaryEdges(&boundary_edges, width, height);
 
  for (i = 0; i < sites_total; i++) {
    VoronoiEdge *edge;
    int v1;
 
    v1 = voronoi_addTriangulationPoint(
        sites[i].co, sites[i].color, &triangulated_points, &triangulated_points_total);
 
    edge = boundary_edges.first;
    while (edge) {
      VoronoiEdge *test_edge = boundary_edges.first;
      bool ok_start = true, ok_end = true;
 
      while (test_edge) {
        if (ok_start && !testVoronoiEdge(sites[i].co, edge->start, test_edge)) {
          ok_start = false;
          break;
        }
 
        if (ok_end && !testVoronoiEdge(sites[i].co, edge->end, test_edge)) {
          ok_end = false;
          break;
        }
 
        test_edge = test_edge->next;
      }
 
      if (ok_start && ok_end) {
        int v2, v3;
 
        v2 = voronoi_addTriangulationPoint(
            edge->start, sites[i].color, &triangulated_points, &triangulated_points_total);
        v3 = voronoi_addTriangulationPoint(
            edge->end, sites[i].color, &triangulated_points, &triangulated_points_total);
 
        voronoi_addTriangle(v1, v2, v3, &triangles, &triangles_total);
      }
 
      edge = edge->next;
    }
  }
 
  for (i = 0; i < triangulated_points_total; i++) {
    VoronoiTriangulationPoint *triangulation_point = &triangulated_points[i];
 
    mul_v3_fl(triangulation_point->color, 1.0f / triangulation_point->power);
  }
 
  *r_triangulated_points = triangulated_points;
  *r_triangulated_points_total = triangulated_points_total;
 
  *r_triangles = triangles;
  *r_triangles_total = triangles_total;
 
  BLI_freelistN(&boundary_edges);
}