test/source/blender/blenkernel/intern/mball_tessellate.cc

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

/** \file
 * \ingroup bke
 */

#include <cctype>
#include <cfloat>
#include <cmath>
#include <cstdio>
#include <cstdlib>
#include <cstring>

#include "MEM_guardedalloc.h"

#include "DNA_mesh_types.h"
#include "DNA_meshdata_types.h"
#include "DNA_meta_types.h"
#include "DNA_object_types.h"
#include "DNA_scene_types.h"

#include "BLI_listbase.h"
#include "BLI_math.h"
#include "BLI_memarena.h"
#include "BLI_string_utils.h"
#include "BLI_utildefines.h"

#include "BKE_displist.h"
#include "BKE_global.h"
#include "BKE_lib_id.h"
#include "BKE_mball_tessellate.h" /* own include */
#include "BKE_mesh.h"
#include "BKE_object.h"
#include "BKE_scene.h"

#include "DEG_depsgraph.h"
#include "DEG_depsgraph_query.h"

#include "BLI_strict_flags.h"

/* experimental (faster) normal calculation */
// #define USE_ACCUM_NORMAL

#define MBALL_ARRAY_LEN_INIT 4096

/* Data types */

/** Corner of a cube. */
typedef struct corner {
  int i, j, k;        /* (i, j, k) is index within lattice */
  float co[3], value; /* location and function value */
  struct corner *next;
} CORNER;

/** Partitioning cell (cube). */
typedef struct cube {
  int i, j, k;        /* lattice location of cube */
  CORNER *corners[8]; /* eight corners */
} CUBE;

/** Linked list of cubes acting as stack. */
typedef struct cubes {
  CUBE cube;          /* a single cube */
  struct cubes *next; /* remaining elements */
} CUBES;

/** List of cube locations. */
typedef struct centerlist {
  int i, j, k;             /* cube location */
  struct centerlist *next; /* remaining elements */
} CENTERLIST;

/** List of edges. */
typedef struct edgelist {
  int i1, j1, k1, i2, j2, k2; /* edge corner ids */
  int vid;                    /* vertex id */
  struct edgelist *next;      /* remaining elements */
} EDGELIST;

/** List of integers. */
typedef struct intlist {
  int i;                /* an integer */
  struct intlist *next; /* remaining elements */
} INTLIST;

/** List of list of integers. */
typedef struct intlists {
  INTLIST *list;         /* a list of integers */
  struct intlists *next; /* remaining elements */
} INTLISTS;

/** An AABB with pointer to metal-elem. */
typedef struct Box {
  float min[3], max[3];
  const MetaElem *ml;
} Box;

typedef struct MetaballBVHNode { /* BVH node */
  Box bb[2];                     /* AABB of children */
  struct MetaballBVHNode *child[2];
} MetaballBVHNode;

/** Parameters, storage. */
typedef struct process {
  float thresh, size; /* mball threshold, single cube size */
  float delta;        /* small delta for calculating normals */
  uint converge_res;  /* converge procedure resolution (more = slower) */

  MetaElem **mainb;  /* array of all meta-elems. */
  uint totelem, mem; /* number of meta-elems. */

  MetaballBVHNode metaball_bvh; /* The simplest bvh */
  Box allbb;                    /* Bounding box of all meta-elems */

  MetaballBVHNode **bvh_queue; /* Queue used during bvh traversal */
  uint bvh_queue_size;

  CUBES *cubes;         /* stack of cubes waiting for polygonization */
  CENTERLIST **centers; /* cube center hash table */
  CORNER **corners;     /* corner value hash table */
  EDGELIST **edges;     /* edge and vertex id hash table */

  int (*indices)[4]; /* output indices */
  uint totindex;     /* size of memory allocated for indices */
  uint curindex;     /* number of currently added indices */

  float (*co)[3], (*no)[3]; /* surface vertices - positions and normals */
  uint totvertex;           /* memory size */
  uint curvertex;           /* currently added vertices */

  /* memory allocation from common pool */
  MemArena *pgn_elements;
} PROCESS;

/* Forward declarations */
static int vertid(PROCESS *process, const CORNER *c1, const CORNER *c2);
static void add_cube(PROCESS *process, int i, int j, int k);
static void make_face(PROCESS *process, int i1, int i2, int i3, int i4);
static void converge(PROCESS *process, const CORNER *c1, const CORNER *c2, float r_p[3]);

/* ******************* SIMPLE BVH ********************* */

static void make_box_union(const BoundBox *a, const Box *b, Box *r_out)
{
  r_out->min[0] = min_ff(a->vec[0][0], b->min[0]);
  r_out->min[1] = min_ff(a->vec[0][1], b->min[1]);
  r_out->min[2] = min_ff(a->vec[0][2], b->min[2]);

  r_out->max[0] = max_ff(a->vec[6][0], b->max[0]);
  r_out->max[1] = max_ff(a->vec[6][1], b->max[1]);
  r_out->max[2] = max_ff(a->vec[6][2], b->max[2]);
}

static void make_box_from_metaelem(Box *r, const MetaElem *ml)
{
  copy_v3_v3(r->max, ml->bb->vec[6]);
  copy_v3_v3(r->min, ml->bb->vec[0]);
  r->ml = ml;
}

/**
 * Partitions part of #process.mainb array [start, end) along axis s. Returns i,
 * where centroids of elements in the [start, i) segment lie "on the right side" of div,
 * and elements in the [i, end) segment lie "on the left"
 */
static uint partition_mainb(MetaElem **mainb, uint start, uint end, uint s, float div)
{
  uint i = start, j = end - 1;
  div *= 2.0f;

  while (true) {
    while (i < j && div > (mainb[i]->bb->vec[6][s] + mainb[i]->bb->vec[0][s])) {
      i++;
    }
    while (j > i && div < (mainb[j]->bb->vec[6][s] + mainb[j]->bb->vec[0][s])) {
      j--;
    }

    if (i >= j) {
      break;
    }

    std::swap(mainb[i], mainb[j]);
    i++;
    j--;
  }

  if (i == start) {
    i++;
  }

  return i;
}

/**
 * Recursively builds a BVH, dividing elements along the middle of the longest axis of allbox.
 */
static void build_bvh_spatial(
    PROCESS *process, MetaballBVHNode *node, uint start, uint end, const Box *allbox)
{
  uint part, j, s;
  float dim[3], div;

  /* Maximum bvh queue size is number of nodes which are made, equals calls to this function. */
  process->bvh_queue_size++;

  dim[0] = allbox->max[0] - allbox->min[0];
  dim[1] = allbox->max[1] - allbox->min[1];
  dim[2] = allbox->max[2] - allbox->min[2];

  s = 0;
  if (dim[1] > dim[0] && dim[1] > dim[2]) {
    s = 1;
  }
  else if (dim[2] > dim[1] && dim[2] > dim[0]) {
    s = 2;
  }

  div = allbox->min[s] + (dim[s] / 2.0f);

  part = partition_mainb(process->mainb, start, end, s, div);

  make_box_from_metaelem(&node->bb[0], process->mainb[start]);
  node->child[0] = nullptr;

  if (part > start + 1) {
    for (j = start; j < part; j++) {
      make_box_union(process->mainb[j]->bb, &node->bb[0], &node->bb[0]);
    }

    node->child[0] = static_cast<MetaballBVHNode *>(
        BLI_memarena_alloc(process->pgn_elements, sizeof(MetaballBVHNode)));
    build_bvh_spatial(process, node->child[0], start, part, &node->bb[0]);
  }

  node->child[1] = nullptr;
  if (part < end) {
    make_box_from_metaelem(&node->bb[1], process->mainb[part]);

    if (part < end - 1) {
      for (j = part; j < end; j++) {
        make_box_union(process->mainb[j]->bb, &node->bb[1], &node->bb[1]);
      }

      node->child[1] = static_cast<MetaballBVHNode *>(
          BLI_memarena_alloc(process->pgn_elements, sizeof(MetaballBVHNode)));
      build_bvh_spatial(process, node->child[1], part, end, &node->bb[1]);
    }
  }
  else {
    INIT_MINMAX(node->bb[1].min, node->bb[1].max);
  }
}

/* ******************** ARITH ************************* */

/**
 * BASED AT CODE (but mostly rewritten) :
 * C code from the article
 * "An Implicit Surface Polygonizer"
 * by Jules Bloomenthal <jbloom@beauty.gmu.edu>
 * in "Graphics Gems IV", Academic Press, 1994
 *
 * Authored by Jules Bloomenthal, Xerox PARC.
 * Copyright (c) Xerox Corporation, 1991.  All rights reserved.
 * Permission is granted to reproduce, use and distribute this code for
 * any and all purposes, provided that this notice appears in all copies.
 */

#define L 0   /* Left direction:   -x, -i. */
#define R 1   /* Right direction:  +x, +i. */
#define B 2   /* Bottom direction: -y, -j. */
#define T 3   /* Top direction:    +y, +j. */
#define N 4   /* Near direction:   -z, -k. */
#define F 5   /* Far direction:    +z, +k. */
#define LBN 0 /* Left bottom near corner. */
#define LBF 1 /* Left bottom far corner. */
#define LTN 2 /* Left top near corner. */
#define LTF 3 /* Left top far corner. */
#define RBN 4 /* Right bottom near corner. */
#define RBF 5 /* Right bottom far corner. */
#define RTN 6 /* Right top near corner. */
#define RTF 7 /* Right top far corner. */

/**
 * the LBN corner of cube (i, j, k), corresponds with location
 * (i-0.5)*size, (j-0.5)*size, (k-0.5)*size)
 */

#define HASHBIT (5)
/** Hash table size (32768). */
#define HASHSIZE size_t(1 << (3 * HASHBIT))

#define HASH(i, j, k) ((((((i)&31) << 5) | ((j)&31)) << 5) | ((k)&31))

#define MB_BIT(i, bit) (((i) >> (bit)) & 1)
// #define FLIP(i, bit) ((i) ^ 1 << (bit)) /* flip the given bit of i */

/* ******************** DENSITY COPMPUTATION ********************* */

/**
 * Computes density from given metaball at given position.
 * Metaball equation is: `(1 - r^2 / R^2)^3 * s`
 *
 * r = distance from center
 * R = metaball radius
 * s - metaball stiffness
 */
static float densfunc(const MetaElem *ball, float x, float y, float z)
{
  float dist2;
  float dvec[3] = {x, y, z};

  mul_m4_v3((const float(*)[4])ball->imat, dvec);

  switch (ball->type) {
    case MB_BALL:
      /* do nothing */
      break;
    case MB_CUBE:
      if (dvec[2] > ball->expz) {
        dvec[2] -= ball->expz;
      }
      else if (dvec[2] < -ball->expz) {
        dvec[2] += ball->expz;
      }
      else {
        dvec[2] = 0.0;
      }
      ATTR_FALLTHROUGH;
    case MB_PLANE:
      if (dvec[1] > ball->expy) {
        dvec[1] -= ball->expy;
      }
      else if (dvec[1] < -ball->expy) {
        dvec[1] += ball->expy;
      }
      else {
        dvec[1] = 0.0;
      }
      ATTR_FALLTHROUGH;
    case MB_TUBE:
      if (dvec[0] > ball->expx) {
        dvec[0] -= ball->expx;
      }
      else if (dvec[0] < -ball->expx) {
        dvec[0] += ball->expx;
      }
      else {
        dvec[0] = 0.0;
      }
      break;
    case MB_ELIPSOID:
      dvec[0] /= ball->expx;
      dvec[1] /= ball->expy;
      dvec[2] /= ball->expz;
      break;

    /* *** deprecated, could be removed?, do-versioned at least *** */
    case MB_TUBEX:
      if (dvec[0] > ball->len) {
        dvec[0] -= ball->len;
      }
      else if (dvec[0] < -ball->len) {
        dvec[0] += ball->len;
      }
      else {
        dvec[0] = 0.0;
      }
      break;
    case MB_TUBEY:
      if (dvec[1] > ball->len) {
        dvec[1] -= ball->len;
      }
      else if (dvec[1] < -ball->len) {
        dvec[1] += ball->len;
      }
      else {
        dvec[1] = 0.0;
      }
      break;
    case MB_TUBEZ:
      if (dvec[2] > ball->len) {
        dvec[2] -= ball->len;
      }
      else if (dvec[2] < -ball->len) {
        dvec[2] += ball->len;
      }
      else {
        dvec[2] = 0.0;
      }
      break;
      /* *** end deprecated *** */
  }

  /* ball->rad2 is inverse of squared rad */
  dist2 = 1.0f - (len_squared_v3(dvec) * ball->rad2);

  /* ball->s is negative if metaball is negative */
  return (dist2 < 0.0f) ? 0.0f : (ball->s * dist2 * dist2 * dist2);
}

/**
 * Computes density at given position form all meta-balls which contain this point in their box.
 * Traverses BVH using a queue.
 */
static float metaball(PROCESS *process, float x, float y, float z)
{
  float dens = 0.0f;
  uint front = 0, back = 0;
  MetaballBVHNode *node;

  process->bvh_queue[front++] = &process->metaball_bvh;

  while (front != back) {
    node = process->bvh_queue[back++];

    for (int i = 0; i < 2; i++) {
      if ((node->bb[i].min[0] <= x) && (node->bb[i].max[0] >= x) && (node->bb[i].min[1] <= y) &&
          (node->bb[i].max[1] >= y) && (node->bb[i].min[2] <= z) && (node->bb[i].max[2] >= z)) {
        if (node->child[i]) {
          process->bvh_queue[front++] = node->child[i];
        }
        else {
          dens += densfunc(node->bb[i].ml, x, y, z);
        }
      }
    }
  }

  return process->thresh - dens;
}

/**
 * Adds face to indices, expands memory if needed.
 */
static void make_face(PROCESS *process, int i1, int i2, int i3, int i4)
{
#ifdef USE_ACCUM_NORMAL
  float n[3];
#endif

  if (UNLIKELY(process->totindex == process->curindex)) {
    process->totindex = process->totindex ? (process->totindex * 2) : MBALL_ARRAY_LEN_INIT;
    process->indices = static_cast<int(*)[4]>(
        MEM_reallocN(process->indices, sizeof(int[4]) * process->totindex));
  }

  int *cur = process->indices[process->curindex++];

  /* Treat triangles as fake quads. */
  cur[0] = i1;
  cur[1] = i2;
  cur[2] = i3;
  cur[3] = i4;

#ifdef USE_ACCUM_NORMAL
  if (i4 == i3) {
    normal_tri_v3(n, process->co[i1], process->co[i2], process->co[i3]);
    accumulate_vertex_normals_v3(process->no[i1],
                                 process->no[i2],
                                 process->no[i3],
                                 nullptr,
                                 n,
                                 process->co[i1],
                                 process->co[i2],
                                 process->co[i3],
                                 nullptr);
  }
  else {
    normal_quad_v3(n, process->co[i1], process->co[i2], process->co[i3], process->co[i4]);
    accumulate_vertex_normals_v3(process->no[i1],
                                 process->no[i2],
                                 process->no[i3],
                                 process->no[i4],
                                 n,
                                 process->co[i1],
                                 process->co[i2],
                                 process->co[i3],
                                 process->co[i4]);
  }
#endif
}

/* Frees allocated memory */
static void freepolygonize(PROCESS *process)
{
  if (process->corners) {
    MEM_freeN(process->corners);
  }
  if (process->edges) {
    MEM_freeN(process->edges);
  }
  if (process->centers) {
    MEM_freeN(process->centers);
  }
  if (process->mainb) {
    MEM_freeN(process->mainb);
  }
  if (process->bvh_queue) {
    MEM_freeN(process->bvh_queue);
  }
  if (process->pgn_elements) {
    BLI_memarena_free(process->pgn_elements);
  }
}

/* **************** POLYGONIZATION ************************ */

/**** Cubical Polygonization (optional) ****/

#define LB 0  /* left bottom edge */
#define LT 1  /* left top edge */
#define LN 2  /* left near edge */
#define LF 3  /* left far edge */
#define RB 4  /* right bottom edge */
#define RT 5  /* right top edge */
#define RN 6  /* right near edge */
#define RF 7  /* right far edge */
#define BN 8  /* bottom near edge */
#define BF 9  /* bottom far edge */
#define TN 10 /* top near edge */
#define TF 11 /* top far edge */

static INTLISTS *cubetable[256];
static char faces[256];

/* edge: LB, LT, LN, LF, RB, RT, RN, RF, BN, BF, TN, TF */
static int corner1[12] = {
    LBN,
    LTN,
    LBN,
    LBF,
    RBN,
    RTN,
    RBN,
    RBF,
    LBN,
    LBF,
    LTN,
    LTF,
};
static int corner2[12] = {
    LBF,
    LTF,
    LTN,
    LTF,
    RBF,
    RTF,
    RTN,
    RTF,
    RBN,
    RBF,
    RTN,
    RTF,
};
static int leftface[12] = {
    B,
    L,
    L,
    F,
    R,
    T,
    N,
    R,
    N,
    B,
    T,
    F,
};
/* face on left when going corner1 to corner2 */
static int rightface[12] = {
    L,
    T,
    N,
    L,
    B,
    R,
    R,
    F,
    B,
    F,
    N,
    T,
};
/* face on right when going corner1 to corner2 */

/**
 * triangulate the cube directly, without decomposition
 */
static void docube(PROCESS *process, CUBE *cube)
{
  INTLISTS *polys;
  CORNER *c1, *c2;
  int i, index = 0, count, indexar[8];

  /* Determine which case cube falls into. */
  for (i = 0; i < 8; i++) {
    if (cube->corners[i]->value > 0.0f) {
      index += (1 << i);
    }
  }

  /* Using faces[] table, adds neighboring cube if surface intersects face in this direction. */
  if (MB_BIT(faces[index], 0)) {
    add_cube(process, cube->i - 1, cube->j, cube->k);
  }
  if (MB_BIT(faces[index], 1)) {
    add_cube(process, cube->i + 1, cube->j, cube->k);
  }
  if (MB_BIT(faces[index], 2)) {
    add_cube(process, cube->i, cube->j - 1, cube->k);
  }
  if (MB_BIT(faces[index], 3)) {
    add_cube(process, cube->i, cube->j + 1, cube->k);
  }
  if (MB_BIT(faces[index], 4)) {
    add_cube(process, cube->i, cube->j, cube->k - 1);
  }
  if (MB_BIT(faces[index], 5)) {
    add_cube(process, cube->i, cube->j, cube->k + 1);
  }

  /* Using cubetable[], determines polygons for output. */
  for (polys = cubetable[index]; polys; polys = polys->next) {
    INTLIST *edges;

    count = 0;
    /* Sets needed vertex id's lying on the edges. */
    for (edges = polys->list; edges; edges = edges->next) {
      c1 = cube->corners[corner1[edges->i]];
      c2 = cube->corners[corner2[edges->i]];

      indexar[count] = vertid(process, c1, c2);
      count++;
    }

    /* Adds faces to output. */
    if (count > 2) {
      switch (count) {
        case 3:
          make_face(process, indexar[2], indexar[1], indexar[0], indexar[0]); /* triangle */
          break;
        case 4:
          make_face(process, indexar[3], indexar[2], indexar[1], indexar[0]);
          break;
        case 5:
          make_face(process, indexar[3], indexar[2], indexar[1], indexar[0]);
          make_face(process, indexar[4], indexar[3], indexar[0], indexar[0]); /* triangle */
          break;
        case 6:
          make_face(process, indexar[3], indexar[2], indexar[1], indexar[0]);
          make_face(process, indexar[5], indexar[4], indexar[3], indexar[0]);
          break;
        case 7:
          make_face(process, indexar[3], indexar[2], indexar[1], indexar[0]);
          make_face(process, indexar[5], indexar[4], indexar[3], indexar[0]);
          make_face(process, indexar[6], indexar[5], indexar[0], indexar[0]); /* triangle */
          break;
      }
    }
  }
}

/**
 * return corner with the given lattice location
 * set (and cache) its function value
 */
static CORNER *setcorner(PROCESS *process, int i, int j, int k)
{
  /* for speed, do corner value caching here */
  CORNER *c;
  int index;

  /* does corner exist? */
  index = HASH(i, j, k);
  c = process->corners[index];

  for (; c != nullptr; c = c->next) {
    if (c->i == i && c->j == j && c->k == k) {
      return c;
    }
  }

  c = static_cast<CORNER *>(BLI_memarena_alloc(process->pgn_elements, sizeof(CORNER)));

  c->i = i;
  c->co[0] = (float(i) - 0.5f) * process->size;
  c->j = j;
  c->co[1] = (float(j) - 0.5f) * process->size;
  c->k = k;
  c->co[2] = (float(k) - 0.5f) * process->size;

  c->value = metaball(process, c->co[0], c->co[1], c->co[2]);

  c->next = process->corners[index];
  process->corners[index] = c;

  return c;
}

/**
 * return next clockwise edge from given edge around given face
 */
static int nextcwedge(int edge, int face)
{
  switch (edge) {
    case LB:
      return (face == L) ? LF : BN;
    case LT:
      return (face == L) ? LN : TF;
    case LN:
      return (face == L) ? LB : TN;
    case LF:
      return (face == L) ? LT : BF;
    case RB:
      return (face == R) ? RN : BF;
    case RT:
      return (face == R) ? RF : TN;
    case RN:
      return (face == R) ? RT : BN;
    case RF:
      return (face == R) ? RB : TF;
    case BN:
      return (face == B) ? RB : LN;
    case BF:
      return (face == B) ? LB : RF;
    case TN:
      return (face == T) ? LT : RN;
    case TF:
      return (face == T) ? RT : LF;
  }
  return 0;
}

/**
 * \return the face adjoining edge that is not the given face
 */
static int otherface(int edge, int face)
{
  int other = leftface[edge];
  return face == other ? rightface[edge] : other;
}

/**
 * create the 256 entry table for cubical polygonization
 */
static void makecubetable()
{
  static bool is_done = false;
  int i, e, c, done[12], pos[8];

  if (is_done) {
    return;
  }
  is_done = true;

  for (i = 0; i < 256; i++) {
    for (e = 0; e < 12; e++) {
      done[e] = 0;
    }
    for (c = 0; c < 8; c++) {
      pos[c] = MB_BIT(i, c);
    }
    for (e = 0; e < 12; e++) {
      if (!done[e] && (pos[corner1[e]] != pos[corner2[e]])) {
        INTLIST *ints = nullptr;
        INTLISTS *lists = static_cast<INTLISTS *>(MEM_callocN(sizeof(INTLISTS), "mball_intlist"));
        int start = e, edge = e;

        /* get face that is to right of edge from pos to neg corner: */
        int face = pos[corner1[e]] ? rightface[e] : leftface[e];

        while (true) {
          edge = nextcwedge(edge, face);
          done[edge] = 1;
          if (pos[corner1[edge]] != pos[corner2[edge]]) {
            INTLIST *tmp = ints;

            ints = static_cast<INTLIST *>(MEM_callocN(sizeof(INTLIST), "mball_intlist"));
            ints->i = edge;
            ints->next = tmp; /* add edge to head of list */

            if (edge == start) {
              break;
            }
            face = otherface(edge, face);
          }
        }
        lists->list = ints; /* add ints to head of table entry */
        lists->next = cubetable[i];
        cubetable[i] = lists;
      }
    }
  }

  for (i = 0; i < 256; i++) {
    INTLISTS *polys;
    faces[i] = 0;
    for (polys = cubetable[i]; polys; polys = polys->next) {
      INTLIST *edges;

      for (edges = polys->list; edges; edges = edges->next) {
        if (ELEM(edges->i, LB, LT, LN, LF)) {
          faces[i] |= 1 << L;
        }
        if (ELEM(edges->i, RB, RT, RN, RF)) {
          faces[i] |= 1 << R;
        }
        if (ELEM(edges->i, LB, RB, BN, BF)) {
          faces[i] |= 1 << B;
        }
        if (ELEM(edges->i, LT, RT, TN, TF)) {
          faces[i] |= 1 << T;
        }
        if (ELEM(edges->i, LN, RN, BN, TN)) {
          faces[i] |= 1 << N;
        }
        if (ELEM(edges->i, LF, RF, BF, TF)) {
          faces[i] |= 1 << F;
        }
      }
    }
  }
}

void BKE_mball_cubeTable_free(void)
{
  for (int i = 0; i < 256; i++) {
    INTLISTS *lists = cubetable[i];
    while (lists) {
      INTLISTS *nlists = lists->next;

      INTLIST *ints = lists->list;
      while (ints) {
        INTLIST *nints = ints->next;
        MEM_freeN(ints);
        ints = nints;
      }

      MEM_freeN(lists);
      lists = nlists;
    }
    cubetable[i] = nullptr;
  }
}

/**** Storage ****/

/**
 * Inserts cube at lattice i, j, k into hash table, marking it as "done"
 */
static int setcenter(PROCESS *process, CENTERLIST *table[], const int i, const int j, const int k)
{
  int index;
  CENTERLIST *newc, *l, *q;

  index = HASH(i, j, k);
  q = table[index];

  for (l = q; l != nullptr; l = l->next) {
    if (l->i == i && l->j == j && l->k == k) {
      return 1;
    }
  }

  newc = static_cast<CENTERLIST *>(BLI_memarena_alloc(process->pgn_elements, sizeof(CENTERLIST)));
  newc->i = i;
  newc->j = j;
  newc->k = k;
  newc->next = q;
  table[index] = newc;

  return 0;
}

/**
 * Sets vid of vertex lying on given edge.
 */
static void setedge(PROCESS *process, int i1, int j1, int k1, int i2, int j2, int k2, int vid)
{
  int index;
  EDGELIST *newe;

  if (i1 > i2 || (i1 == i2 && (j1 > j2 || (j1 == j2 && k1 > k2)))) {
    int t = i1;
    i1 = i2;
    i2 = t;
    t = j1;
    j1 = j2;
    j2 = t;
    t = k1;
    k1 = k2;
    k2 = t;
  }
  index = HASH(i1, j1, k1) + HASH(i2, j2, k2);
  newe = static_cast<EDGELIST *>(BLI_memarena_alloc(process->pgn_elements, sizeof(EDGELIST)));

  newe->i1 = i1;
  newe->j1 = j1;
  newe->k1 = k1;
  newe->i2 = i2;
  newe->j2 = j2;
  newe->k2 = k2;
  newe->vid = vid;
  newe->next = process->edges[index];
  process->edges[index] = newe;
}

/**
 * \return vertex id for edge; return -1 if not set
 */
static int getedge(EDGELIST *table[], int i1, int j1, int k1, int i2, int j2, int k2)
{
  EDGELIST *q;

  if (i1 > i2 || (i1 == i2 && (j1 > j2 || (j1 == j2 && k1 > k2)))) {
    int t = i1;
    i1 = i2;
    i2 = t;
    t = j1;
    j1 = j2;
    j2 = t;
    t = k1;
    k1 = k2;
    k2 = t;
  }
  q = table[HASH(i1, j1, k1) + HASH(i2, j2, k2)];
  for (; q != nullptr; q = q->next) {
    if (q->i1 == i1 && q->j1 == j1 && q->k1 == k1 && q->i2 == i2 && q->j2 == j2 && q->k2 == k2) {
      return q->vid;
    }
  }
  return -1;
}

/**
 * Adds a vertex, expands memory if needed.
 */
static void addtovertices(PROCESS *process, const float v[3], const float no[3])
{
  if (UNLIKELY(process->curvertex == process->totvertex)) {
    process->totvertex = process->totvertex ? process->totvertex * 2 : MBALL_ARRAY_LEN_INIT;
    process->co = static_cast<float(*)[3]>(
        MEM_reallocN(process->co, process->totvertex * sizeof(float[3])));
    process->no = static_cast<float(*)[3]>(
        MEM_reallocN(process->no, process->totvertex * sizeof(float[3])));
  }

  copy_v3_v3(process->co[process->curvertex], v);
  copy_v3_v3(process->no[process->curvertex], no);

  process->curvertex++;
}

#ifndef USE_ACCUM_NORMAL
/**
 * Computes normal from density field at given point.
 *
 * \note Doesn't do normalization!
 */
static void vnormal(PROCESS *process, const float point[3], float r_no[3])
{
  const float delta = process->delta;
  const float f = metaball(process, point[0], point[1], point[2]);

  r_no[0] = metaball(process, point[0] + delta, point[1], point[2]) - f;
  r_no[1] = metaball(process, point[0], point[1] + delta, point[2]) - f;
  r_no[2] = metaball(process, point[0], point[1], point[2] + delta) - f;
}
#endif /* USE_ACCUM_NORMAL */

/**
 * \return the id of vertex between two corners.
 *
 * If it wasn't previously computed, does #converge() and adds vertex to process.
 */
static int vertid(PROCESS *process, const CORNER *c1, const CORNER *c2)
{
  float v[3], no[3];
  int vid = getedge(process->edges, c1->i, c1->j, c1->k, c2->i, c2->j, c2->k);

  if (vid != -1) {
    return vid; /* previously computed */
  }

  converge(process, c1, c2, v); /* position */

#ifdef USE_ACCUM_NORMAL
  zero_v3(no);
#else
  vnormal(process, v, no);
#endif

  addtovertices(process, v, no); /* save vertex */
  vid = int(process->curvertex) - 1;
  setedge(process, c1->i, c1->j, c1->k, c2->i, c2->j, c2->k, vid);

  return vid;
}

/**
 * Given two corners, computes approximation of surface intersection point between them.
 * In case of small threshold, do bisection.
 */
static void converge(PROCESS *process, const CORNER *c1, const CORNER *c2, float r_p[3])
{
  float c1_value, c1_co[3];
  float c2_value, c2_co[3];

  if (c1->value < c2->value) {
    c1_value = c2->value;
    copy_v3_v3(c1_co, c2->co);
    c2_value = c1->value;
    copy_v3_v3(c2_co, c1->co);
  }
  else {
    c1_value = c1->value;
    copy_v3_v3(c1_co, c1->co);
    c2_value = c2->value;
    copy_v3_v3(c2_co, c2->co);
  }

  for (uint i = 0; i < process->converge_res; i++) {
    interp_v3_v3v3(r_p, c1_co, c2_co, 0.5f);
    float dens = metaball(process, r_p[0], r_p[1], r_p[2]);

    if (dens > 0.0f) {
      c1_value = dens;
      copy_v3_v3(c1_co, r_p);
    }
    else {
      c2_value = dens;
      copy_v3_v3(c2_co, r_p);
    }
  }

  float tmp = -c1_value / (c2_value - c1_value);
  interp_v3_v3v3(r_p, c1_co, c2_co, tmp);
}

/**
 * Adds cube at given lattice position to cube stack of process.
 */
static void add_cube(PROCESS *process, int i, int j, int k)
{
  CUBES *ncube;
  int n;

  /* test if cube has been found before */
  if (setcenter(process, process->centers, i, j, k) == 0) {
    /* push cube on stack: */
    ncube = static_cast<CUBES *>(BLI_memarena_alloc(process->pgn_elements, sizeof(CUBES)));
    ncube->next = process->cubes;
    process->cubes = ncube;

    ncube->cube.i = i;
    ncube->cube.j = j;
    ncube->cube.k = k;

    /* set corners of initial cube: */
    for (n = 0; n < 8; n++) {
      ncube->cube.corners[n] = setcorner(
          process, i + MB_BIT(n, 2), j + MB_BIT(n, 1), k + MB_BIT(n, 0));
    }
  }
}

static void next_lattice(int r[3], const float pos[3], const float size)
{
  r[0] = int(ceil((pos[0] / size) + 0.5f));
  r[1] = int(ceil((pos[1] / size) + 0.5f));
  r[2] = int(ceil((pos[2] / size) + 0.5f));
}
static void prev_lattice(int r[3], const float pos[3], const float size)
{
  next_lattice(r, pos, size);
  r[0]--;
  r[1]--;
  r[2]--;
}
static void closest_latice(int r[3], const float pos[3], const float size)
{
  r[0] = int(floorf(pos[0] / size + 1.0f));
  r[1] = int(floorf(pos[1] / size + 1.0f));
  r[2] = int(floorf(pos[2] / size + 1.0f));
}

/**
 * Find at most 26 cubes to start polygonization from.
 */
static void find_first_points(PROCESS *process, const uint em)
{
  const MetaElem *ml;
  int center[3], lbn[3], rtf[3], it[3], dir[3], add[3];
  float tmp[3], a, b;

  ml = process->mainb[em];

  mid_v3_v3v3(tmp, ml->bb->vec[0], ml->bb->vec[6]);
  closest_latice(center, tmp, process->size);
  prev_lattice(lbn, ml->bb->vec[0], process->size);
  next_lattice(rtf, ml->bb->vec[6], process->size);

  for (dir[0] = -1; dir[0] <= 1; dir[0]++) {
    for (dir[1] = -1; dir[1] <= 1; dir[1]++) {
      for (dir[2] = -1; dir[2] <= 1; dir[2]++) {
        if (dir[0] == 0 && dir[1] == 0 && dir[2] == 0) {
          continue;
        }

        copy_v3_v3_int(it, center);

        b = setcorner(process, it[0], it[1], it[2])->value;
        do {
          it[0] += dir[0];
          it[1] += dir[1];
          it[2] += dir[2];
          a = b;
          b = setcorner(process, it[0], it[1], it[2])->value;

          if (a * b < 0.0f) {
            add[0] = it[0] - dir[0];
            add[1] = it[1] - dir[1];
            add[2] = it[2] - dir[2];
            DO_MIN(it, add);
            add_cube(process, add[0], add[1], add[2]);
            break;
          }
        } while ((it[0] > lbn[0]) && (it[1] > lbn[1]) && (it[2] > lbn[2]) && (it[0] < rtf[0]) &&
                 (it[1] < rtf[1]) && (it[2] < rtf[2]));
      }
    }
  }
}

/**
 * The main polygonization processing function.
 * Allocates memory, makes cube-table,
 * finds starting surface points
 * and processes cubes on the stack until none left.
 */
static void polygonize(PROCESS *process)
{
  CUBE c;

  process->centers = static_cast<CENTERLIST **>(
      MEM_callocN(HASHSIZE * sizeof(CENTERLIST *), "mbproc->centers"));
  process->corners = static_cast<CORNER **>(
      MEM_callocN(HASHSIZE * sizeof(CORNER *), "mbproc->corners"));
  process->edges = static_cast<EDGELIST **>(
      MEM_callocN(2 * HASHSIZE * sizeof(EDGELIST *), "mbproc->edges"));
  process->bvh_queue = static_cast<MetaballBVHNode **>(
      MEM_callocN(sizeof(MetaballBVHNode *) * process->bvh_queue_size, "Metaball BVH Queue"));

  makecubetable();

  for (uint i = 0; i < process->totelem; i++) {
    find_first_points(process, i);
  }

  while (process->cubes != nullptr) {
    c = process->cubes->cube;
    process->cubes = process->cubes->next;

    docube(process, &c);
  }
}

/**
 * Iterates over ALL objects in the scene and all of its sets, including
 * making all duplis (not only meta-elements). Copies meta-elements to #process.mainb array.
 * Computes bounding boxes for building BVH.
 */
static void init_meta(Depsgraph *depsgraph, PROCESS *process, Scene *scene, Object *ob)
{
  Scene *sce_iter = scene;
  Base *base;
  Object *bob;
  MetaBall *mb;
  const MetaElem *ml;
  float obinv[4][4], obmat[4][4];
  uint i;
  int obnr, zero_size = 0;
  char obname[MAX_ID_NAME];
  SceneBaseIter iter;
  const eEvaluationMode deg_eval_mode = DEG_get_mode(depsgraph);
  const short parenting_dupli_transflag = (OB_DUPLIFACES | OB_DUPLIVERTS);

  copy_m4_m4(obmat,
             ob->object_to_world); /* to cope with duplicators from BKE_scene_base_iter_next */
  invert_m4_m4(obinv, ob->object_to_world);

  BLI_split_name_num(obname, &obnr, ob->id.name + 2, '.');

  /* make main array */
  BKE_scene_base_iter_next(depsgraph, &iter, &sce_iter, 0, nullptr, nullptr);
  while (BKE_scene_base_iter_next(depsgraph, &iter, &sce_iter, 1, &base, &bob)) {
    if (bob->type == OB_MBALL) {
      zero_size = 0;
      ml = nullptr;

      /* If this metaball is the original that's used for duplication, only have it visible when
       * the instancer is visible too. */
      if ((base->flag_legacy & OB_FROMDUPLI) == 0 && ob->parent != nullptr &&
          (ob->parent->transflag & parenting_dupli_transflag) != 0 &&
          (BKE_object_visibility(ob->parent, deg_eval_mode) & OB_VISIBLE_SELF) == 0) {
        continue;
      }

      if (bob == ob && (base->flag_legacy & OB_FROMDUPLI) == 0) {
        mb = static_cast<MetaBall *>(ob->data);

        if (mb->editelems) {
          ml = static_cast<const MetaElem *>(mb->editelems->first);
        }
        else {
          ml = static_cast<const MetaElem *>(mb->elems.first);
        }
      }
      else {
        char name[MAX_ID_NAME];
        int nr;

        BLI_split_name_num(name, &nr, bob->id.name + 2, '.');
        if (STREQ(obname, name)) {
          mb = static_cast<MetaBall *>(bob->data);

          if (mb->editelems) {
            ml = static_cast<const MetaElem *>(mb->editelems->first);
          }
          else {
            ml = static_cast<const MetaElem *>(mb->elems.first);
          }
        }
      }

      /* when metaball object has zero scale, then MetaElem to this MetaBall
       * will not be put to mainb array */
      if (has_zero_axis_m4(bob->object_to_world)) {
        zero_size = 1;
      }
      else if (bob->parent) {
        struct Object *pob = bob->parent;
        while (pob) {
          if (has_zero_axis_m4(pob->object_to_world)) {
            zero_size = 1;
            break;
          }
          pob = pob->parent;
        }
      }

      if (zero_size) {
        while (ml) {
          ml = ml->next;
        }
      }
      else {
        while (ml) {
          if (!(ml->flag & MB_HIDE)) {
            float pos[4][4], rot[4][4];
            float expx, expy, expz;
            float tempmin[3], tempmax[3];

            MetaElem *new_ml;

            /* make a copy because of duplicates */
            new_ml = static_cast<MetaElem *>(
                BLI_memarena_alloc(process->pgn_elements, sizeof(MetaElem)));
            *(new_ml) = *ml;
            new_ml->bb = static_cast<BoundBox *>(
                BLI_memarena_alloc(process->pgn_elements, sizeof(BoundBox)));
            new_ml->mat = static_cast<float *>(
                BLI_memarena_alloc(process->pgn_elements, sizeof(float[4][4])));
            new_ml->imat = static_cast<float *>(
                BLI_memarena_alloc(process->pgn_elements, sizeof(float[4][4])));

            /* too big stiffness seems only ugly due to linear interpolation
             * no need to have possibility for too big stiffness */
            if (ml->s > 10.0f) {
              new_ml->s = 10.0f;
            }
            else {
              new_ml->s = ml->s;
            }

            /* if metaball is negative, set stiffness negative */
            if (new_ml->flag & MB_NEGATIVE) {
              new_ml->s = -new_ml->s;
            }

            /* Translation of MetaElem */
            unit_m4(pos);
            pos[3][0] = ml->x;
            pos[3][1] = ml->y;
            pos[3][2] = ml->z;

            /* Rotation of MetaElem is stored in quat */
            quat_to_mat4(rot, ml->quat);

            /* Matrix multiply is as follows:
             *   basis object space ->
             *   world ->
             *   ml object space ->
             *   position ->
             *   rotation ->
             *   ml local space
             */
            mul_m4_series((float(*)[4])new_ml->mat, obinv, bob->object_to_world, pos, rot);
            /* ml local space -> basis object space */
            invert_m4_m4((float(*)[4])new_ml->imat, (float(*)[4])new_ml->mat);

            /* rad2 is inverse of squared radius */
            new_ml->rad2 = 1 / (ml->rad * ml->rad);

            /* initial dimensions = radius */
            expx = ml->rad;
            expy = ml->rad;
            expz = ml->rad;

            switch (ml->type) {
              case MB_BALL:
                break;
              case MB_CUBE: /* cube is "expanded" by expz, expy and expx */
                expz += ml->expz;
                ATTR_FALLTHROUGH;
              case MB_PLANE: /* plane is "expanded" by expy and expx */
                expy += ml->expy;
                ATTR_FALLTHROUGH;
              case MB_TUBE: /* tube is "expanded" by expx */
                expx += ml->expx;
                break;
              case MB_ELIPSOID: /* ellipsoid is "stretched" by exp* */
                expx *= ml->expx;
                expy *= ml->expy;
                expz *= ml->expz;
                break;
            }

            /* untransformed Bounding Box of MetaElem */
            /* TODO: its possible the elem type has been changed and the exp*
             * values can use a fallback. */
            copy_v3_fl3(new_ml->bb->vec[0], -expx, -expy, -expz); /* 0 */
            copy_v3_fl3(new_ml->bb->vec[1], +expx, -expy, -expz); /* 1 */
            copy_v3_fl3(new_ml->bb->vec[2], +expx, +expy, -expz); /* 2 */
            copy_v3_fl3(new_ml->bb->vec[3], -expx, +expy, -expz); /* 3 */
            copy_v3_fl3(new_ml->bb->vec[4], -expx, -expy, +expz); /* 4 */
            copy_v3_fl3(new_ml->bb->vec[5], +expx, -expy, +expz); /* 5 */
            copy_v3_fl3(new_ml->bb->vec[6], +expx, +expy, +expz); /* 6 */
            copy_v3_fl3(new_ml->bb->vec[7], -expx, +expy, +expz); /* 7 */

            /* Transformation of meta-elem bounding-box. */
            for (i = 0; i < 8; i++) {
              mul_m4_v3((float(*)[4])new_ml->mat, new_ml->bb->vec[i]);
            }

            /* Find max and min of transformed bounding-box. */
            INIT_MINMAX(tempmin, tempmax);
            for (i = 0; i < 8; i++) {
              DO_MINMAX(new_ml->bb->vec[i], tempmin, tempmax);
            }

            /* Set only point 0 and 6 - AABB of meta-elem. */
            copy_v3_v3(new_ml->bb->vec[0], tempmin);
            copy_v3_v3(new_ml->bb->vec[6], tempmax);

            /* add new_ml to mainb[] */
            if (UNLIKELY(process->totelem == process->mem)) {
              process->mem = process->mem * 2 + 10;
              process->mainb = static_cast<MetaElem **>(
                  MEM_reallocN(process->mainb, sizeof(MetaElem *) * process->mem));
            }
            process->mainb[process->totelem++] = new_ml;
          }
          ml = ml->next;
        }
      }
    }
  }

  /* Compute AABB of all meta-elems. */
  if (process->totelem > 0) {
    copy_v3_v3(process->allbb.min, process->mainb[0]->bb->vec[0]);
    copy_v3_v3(process->allbb.max, process->mainb[0]->bb->vec[6]);
    for (i = 1; i < process->totelem; i++) {
      make_box_union(process->mainb[i]->bb, &process->allbb, &process->allbb);
    }
  }
}

Mesh *BKE_mball_polygonize(Depsgraph *depsgraph, Scene *scene, Object *ob)
{
  PROCESS process = {0};
  const bool is_render = DEG_get_mode(depsgraph) == DAG_EVAL_RENDER;

  MetaBall *mb = static_cast<MetaBall *>(ob->data);

  process.thresh = mb->thresh;

  if (process.thresh < 0.001f) {
    process.converge_res = 16;
  }
  else if (process.thresh < 0.01f) {
    process.converge_res = 8;
  }
  else if (process.thresh < 0.1f) {
    process.converge_res = 4;
  }
  else {
    process.converge_res = 2;
  }

  if (!is_render && (mb->flag == MB_UPDATE_NEVER)) {
    return nullptr;
  }
  if ((G.moving & (G_TRANSFORM_OBJ | G_TRANSFORM_EDIT)) && mb->flag == MB_UPDATE_FAST) {
    return nullptr;
  }

  if (is_render) {
    process.size = mb->rendersize;
  }
  else {
    process.size = mb->wiresize;
    if ((G.moving & (G_TRANSFORM_OBJ | G_TRANSFORM_EDIT)) && mb->flag == MB_UPDATE_HALFRES) {
      process.size *= 2.0f;
    }
  }

  process.delta = process.size * 0.001f;

  process.pgn_elements = BLI_memarena_new(BLI_MEMARENA_STD_BUFSIZE, "Metaball memarena");

  /* initialize all mainb (MetaElems) */
  init_meta(depsgraph, &process, scene, ob);
  if (process.totelem == 0) {
    freepolygonize(&process);
    return nullptr;
  }

  build_bvh_spatial(&process, &process.metaball_bvh, 0, process.totelem, &process.allbb);

  /* Don't polygonize meta-balls with too high resolution (base meta-ball too small).
   * NOTE: Epsilon was 0.0001f but this was giving problems for blood animation for
   * the open movie "Sintel", using 0.00001f. */
  if (ob->scale[0] < 0.00001f * (process.allbb.max[0] - process.allbb.min[0]) ||
      ob->scale[1] < 0.00001f * (process.allbb.max[1] - process.allbb.min[1]) ||
      ob->scale[2] < 0.00001f * (process.allbb.max[2] - process.allbb.min[2])) {
    freepolygonize(&process);
    return nullptr;
  }

  polygonize(&process);
  if (process.curindex == 0) {
    freepolygonize(&process);
    return nullptr;
  }

  freepolygonize(&process);

  Mesh *mesh = (Mesh *)BKE_id_new_nomain(ID_ME, ((ID *)ob->data)->name + 2);

  mesh->totvert = int(process.curvertex);
  CustomData_add_layer_named(
      &mesh->vdata, CD_PROP_FLOAT3, CD_ASSIGN, process.co, mesh->totvert, "position");
  process.co = nullptr;

  mesh->totpoly = int(process.curindex);
  MPoly *mpoly = static_cast<MPoly *>(
      CustomData_add_layer(&mesh->pdata, CD_MPOLY, CD_CONSTRUCT, nullptr, mesh->totpoly));
  MLoop *mloop = static_cast<MLoop *>(
      CustomData_add_layer(&mesh->ldata, CD_MLOOP, CD_CONSTRUCT, nullptr, mesh->totpoly * 4));

  int loop_offset = 0;
  for (int i = 0; i < mesh->totpoly; i++) {
    const int *indices = process.indices[i];

    const int count = indices[2] != indices[3] ? 4 : 3;
    mpoly[i].loopstart = loop_offset;
    mpoly[i].totloop = count;
    mpoly[i].flag = ME_SMOOTH;

    mloop[loop_offset].v = uint32_t(indices[0]);
    mloop[loop_offset + 1].v = uint32_t(indices[1]);
    mloop[loop_offset + 2].v = uint32_t(indices[2]);
    if (count == 4) {
      mloop[loop_offset + 3].v = uint32_t(indices[3]);
    }

    loop_offset += count;
  }
  MEM_freeN(process.indices);

  for (int i = 0; i < mesh->totvert; i++) {
    normalize_v3(process.no[i]);
  }
  memcpy(BKE_mesh_vertex_normals_for_write(mesh),
         process.no,
         sizeof(float[3]) * size_t(mesh->totvert));
  MEM_freeN(process.no);
  BKE_mesh_vertex_normals_clear_dirty(mesh);

  mesh->totloop = loop_offset;

  BKE_mesh_calc_edges(mesh, false, false);

  return mesh;
}