Cleanup: Move uv_parametrizer.c to C++

Differential Review: https://developer.blender.org/D15618

1 files changed, 4409 insertions, 0 deletions

diff --git a/source/blender/geometry/intern/uv_parametrizer.cc b/source/blender/geometry/intern/uv_parametrizer.cc
new file mode 100644
index 00000000000..efda55e2669
--- /dev/null
+++ b/source/blender/geometry/intern/uv_parametrizer.cc
@@ -0,0 +1,4409 @@
+/* SPDX-License-Identifier: GPL-2.0-or-later */
+
+/** \file
+ * \ingroup eduv
+ */
+
+#include "GEO_uv_parametrizer.h"
+
+#include "MEM_guardedalloc.h"
+
+#include "BLI_boxpack_2d.h"
+#include "BLI_convexhull_2d.h"
+#include "BLI_ghash.h"
+#include "BLI_heap.h"
+#include "BLI_memarena.h"
+#include "BLI_polyfill_2d.h"
+#include "BLI_polyfill_2d_beautify.h"
+#include "BLI_rand.h"
+
+#include "eigen_capi.h"
+
+/* Utils */
+
+#define param_assert(condition) \
+  if (!(condition)) { /*printf("Assertion %s:%d\n", __FILE__, __LINE__); abort();*/ \
+  } \
+  (void)0
+#define param_warning(message) \
+  {/*printf("Warning %s:%d: %s\n", __FILE__, __LINE__, message);*/}(void)0
+
+/* Special Purpose Hash */
+
+typedef intptr_t PHashKey;
+
+typedef struct PHashLink {
+  struct PHashLink *next;
+  PHashKey key;
+} PHashLink;
+
+typedef struct PHash {
+  PHashLink **list;
+  PHashLink **buckets;
+  int size, cursize, cursize_id;
+} PHash;
+
+/* Simplices */
+
+typedef struct PVert {
+  struct PVert *nextlink;
+
+  union PVertUnion {
+    PHashKey key;       /* Construct. */
+    int id;             /* ABF/LSCM matrix index. */
+    HeapNode *heaplink; /* Edge collapsing. */
+  } u;
+
+  struct PEdge *edge;
+  float co[3];
+  float uv[2];
+  uint flag;
+} PVert;
+
+typedef struct PEdge {
+  struct PEdge *nextlink;
+
+  union PEdgeUnion {
+    PHashKey key;               /* Construct. */
+    int id;                     /* ABF matrix index. */
+    HeapNode *heaplink;         /* Fill holes. */
+    struct PEdge *nextcollapse; /* Simplification. */
+  } u;
+
+  struct PVert *vert;
+  struct PEdge *pair;
+  struct PEdge *next;
+  struct PFace *face;
+  float *orig_uv, old_uv[2];
+  uint flag;
+} PEdge;
+
+typedef struct PFace {
+  struct PFace *nextlink;
+
+  union PFaceUnion {
+    PHashKey key; /* Construct. */
+    int chart;    /* Construct splitting. */
+    float area3d; /* Stretch. */
+    int id;       /* ABF matrix index. */
+  } u;
+
+  struct PEdge *edge;
+  uchar flag;
+} PFace;
+
+enum PVertFlag {
+  PVERT_PIN = 1,
+  PVERT_SELECT = 2,
+  PVERT_INTERIOR = 4,
+  PVERT_COLLAPSE = 8,
+  PVERT_SPLIT = 16,
+};
+
+enum PEdgeFlag {
+  PEDGE_SEAM = 1,
+  PEDGE_VERTEX_SPLIT = 2,
+  PEDGE_PIN = 4,
+  PEDGE_SELECT = 8,
+  PEDGE_DONE = 16,
+  PEDGE_FILLED = 32,
+  PEDGE_COLLAPSE = 64,
+  PEDGE_COLLAPSE_EDGE = 128,
+  PEDGE_COLLAPSE_PAIR = 256,
+};
+
+/* for flipping faces */
+#define PEDGE_VERTEX_FLAGS (PEDGE_PIN)
+
+enum PFaceFlag {
+  PFACE_CONNECTED = 1,
+  PFACE_FILLED = 2,
+  PFACE_COLLAPSE = 4,
+};
+
+/* Chart */
+
+typedef struct PChart {
+  PVert *verts;
+  PEdge *edges;
+  PFace *faces;
+  int nverts, nedges, nfaces;
+  int nboundaries;
+
+  PVert *collapsed_verts;
+  PEdge *collapsed_edges;
+  PFace *collapsed_faces;
+
+  union PChartUnion {
+    struct PChartLscm {
+      LinearSolver *context;
+      float *abf_alpha;
+      PVert *pin1, *pin2;
+      PVert *single_pin;
+      float single_pin_area;
+      float single_pin_uv[2];
+    } lscm;
+    struct PChartPack {
+      float rescale, area;
+      float size[2];
+      float origin[2];
+    } pack;
+  } u;
+
+  bool has_pins;
+} PChart;
+
+enum PHandleState {
+  PHANDLE_STATE_ALLOCATED,
+  PHANDLE_STATE_CONSTRUCTED,
+  PHANDLE_STATE_LSCM,
+  PHANDLE_STATE_STRETCH,
+};
+
+typedef struct ParamHandle {
+  enum PHandleState state;
+  MemArena *arena;
+  MemArena *polyfill_arena;
+  Heap *polyfill_heap;
+
+  PChart *construction_chart;
+  PHash *hash_verts;
+  PHash *hash_edges;
+  PHash *hash_faces;
+
+  struct GHash *pin_hash;
+  int unique_pin_count;
+
+  PChart **charts;
+  int ncharts;
+
+  float aspx, aspy;
+
+  RNG *rng;
+  float blend;
+} ParamHandle;
+
+/* PHash
+ * - special purpose hash that keeps all its elements in a single linked list.
+ * - after construction, this hash is thrown away, and the list remains.
+ * - removing elements is not possible efficiently.
+ */
+
+static int PHashSizes[] = {
+    1,       3,       5,       11,      17,       37,       67,       131,       257,       521,
+    1031,    2053,    4099,    8209,    16411,    32771,    65537,    131101,    262147,    524309,
+    1048583, 2097169, 4194319, 8388617, 16777259, 33554467, 67108879, 134217757, 268435459,
+};
+
+#define PHASH_hash(ph, item) (((uintptr_t)(item)) % ((uint)(ph)->cursize))
+#define PHASH_edge(v1, v2) (((v1) < (v2)) ? ((v1)*39) ^ ((v2)*31) : ((v1)*31) ^ ((v2)*39))
+
+static PHash *phash_new(PHashLink **list, int sizehint)
+{
+  PHash *ph = (PHash *)MEM_callocN(sizeof(PHash), "PHash");
+  ph->size = 0;
+  ph->cursize_id = 0;
+  ph->list = list;
+
+  while (PHashSizes[ph->cursize_id] < sizehint) {
+    ph->cursize_id++;
+  }
+
+  ph->cursize = PHashSizes[ph->cursize_id];
+  ph->buckets = (PHashLink **)MEM_callocN(ph->cursize * sizeof(*ph->buckets), "PHashBuckets");
+
+  return ph;
+}
+
+static void phash_delete(PHash *ph)
+{
+  if (ph) {
+    MEM_SAFE_FREE(ph->buckets);
+  }
+  MEM_SAFE_FREE(ph);
+}
+
+static int phash_size(PHash *ph)
+{
+  return ph->size;
+}
+
+static void phash_insert(PHash *ph, PHashLink *link)
+{
+  int size = ph->cursize;
+  uintptr_t hash = PHASH_hash(ph, link->key);
+  PHashLink *lookup = ph->buckets[hash];
+
+  if (lookup == NULL) {
+    /* insert in front of the list */
+    ph->buckets[hash] = link;
+    link->next = *(ph->list);
+    *(ph->list) = link;
+  }
+  else {
+    /* insert after existing element */
+    link->next = lookup->next;
+    lookup->next = link;
+  }
+
+  ph->size++;
+
+  if (ph->size > (size * 3)) {
+    PHashLink *next = NULL, *first = *(ph->list);
+
+    ph->cursize = PHashSizes[++ph->cursize_id];
+    MEM_freeN(ph->buckets);
+    ph->buckets = (PHashLink **)MEM_callocN(ph->cursize * sizeof(*ph->buckets), "PHashBuckets");
+    ph->size = 0;
+    *(ph->list) = NULL;
+
+    for (link = first; link; link = next) {
+      next = link->next;
+      phash_insert(ph, link);
+    }
+  }
+}
+
+static PHashLink *phash_lookup(PHash *ph, PHashKey key)
+{
+  PHashLink *link;
+  uintptr_t hash = PHASH_hash(ph, key);
+
+  for (link = ph->buckets[hash]; link; link = link->next) {
+    if (link->key == key) {
+      return link;
+    }
+    if (PHASH_hash(ph, link->key) != hash) {
+      return NULL;
+    }
+  }
+
+  return link;
+}
+
+static PHashLink *phash_next(PHash *ph, PHashKey key, PHashLink *link)
+{
+  uintptr_t hash = PHASH_hash(ph, key);
+
+  for (link = link->next; link; link = link->next) {
+    if (link->key == key) {
+      return link;
+    }
+    if (PHASH_hash(ph, link->key) != hash) {
+      return NULL;
+    }
+  }
+
+  return link;
+}
+
+/* Geometry */
+
+static float p_vec_angle(const float v1[3], const float v2[3], const float v3[3])
+{
+  return angle_v3v3v3(v1, v2, v3);
+}
+static float p_vec2_angle(const float v1[2], const float v2[2], const float v3[2])
+{
+  return angle_v2v2v2(v1, v2, v3);
+}
+static void p_triangle_angles(
+    const float v1[3], const float v2[3], const float v3[3], float *r_a1, float *r_a2, float *r_a3)
+{
+  *r_a1 = p_vec_angle(v3, v1, v2);
+  *r_a2 = p_vec_angle(v1, v2, v3);
+  *r_a3 = (float)M_PI - *r_a2 - *r_a1;
+}
+
+static void p_face_angles(PFace *f, float *r_a1, float *r_a2, float *r_a3)
+{
+  PEdge *e1 = f->edge, *e2 = e1->next, *e3 = e2->next;
+  PVert *v1 = e1->vert, *v2 = e2->vert, *v3 = e3->vert;
+
+  p_triangle_angles(v1->co, v2->co, v3->co, r_a1, r_a2, r_a3);
+}
+
+static float p_face_area(PFace *f)
+{
+  PEdge *e1 = f->edge, *e2 = e1->next, *e3 = e2->next;
+  PVert *v1 = e1->vert, *v2 = e2->vert, *v3 = e3->vert;
+
+  return area_tri_v3(v1->co, v2->co, v3->co);
+}
+
+static float p_area_signed(const float v1[2], const float v2[2], const float v3[2])
+{
+  return 0.5f * (((v2[0] - v1[0]) * (v3[1] - v1[1])) - ((v3[0] - v1[0]) * (v2[1] - v1[1])));
+}
+
+static float p_face_uv_area_signed(PFace *f)
+{
+  PEdge *e1 = f->edge, *e2 = e1->next, *e3 = e2->next;
+  PVert *v1 = e1->vert, *v2 = e2->vert, *v3 = e3->vert;
+
+  return 0.5f * (((v2->uv[0] - v1->uv[0]) * (v3->uv[1] - v1->uv[1])) -
+                 ((v3->uv[0] - v1->uv[0]) * (v2->uv[1] - v1->uv[1])));
+}
+
+static float p_edge_length(PEdge *e)
+{
+  return len_v3v3(e->vert->co, e->next->vert->co);
+}
+
+static float p_edge_uv_length(PEdge *e)
+{
+  return len_v2v2(e->vert->uv, e->next->vert->uv);
+}
+
+static void p_chart_uv_bbox(PChart *chart, float minv[2], float maxv[2])
+{
+  PVert *v;
+
+  INIT_MINMAX2(minv, maxv);
+
+  for (v = chart->verts; v; v = v->nextlink) {
+    minmax_v2v2_v2(minv, maxv, v->uv);
+  }
+}
+
+static float p_chart_uv_area(PChart *chart)
+{
+  float area = 0.0f;
+
+  for (PFace *f = chart->faces; f; f = f->nextlink) {
+    area += fabsf(p_face_uv_area_signed(f));
+  }
+
+  return area;
+}
+
+static void p_chart_uv_scale(PChart *chart, float scale)
+{
+  PVert *v;
+
+  for (v = chart->verts; v; v = v->nextlink) {
+    v->uv[0] *= scale;
+    v->uv[1] *= scale;
+  }
+}
+
+static void p_chart_uv_scale_xy(PChart *chart, float x, float y)
+{
+  PVert *v;
+
+  for (v = chart->verts; v; v = v->nextlink) {
+    v->uv[0] *= x;
+    v->uv[1] *= y;
+  }
+}
+
+static void p_chart_uv_translate(PChart *chart, const float trans[2])
+{
+  PVert *v;
+
+  for (v = chart->verts; v; v = v->nextlink) {
+    v->uv[0] += trans[0];
+    v->uv[1] += trans[1];
+  }
+}
+
+static void p_chart_uv_transform(PChart *chart, const float mat[2][2])
+{
+  PVert *v;
+
+  for (v = chart->verts; v; v = v->nextlink) {
+    mul_m2_v2(mat, v->uv);
+  }
+}
+
+static void p_chart_uv_to_array(PChart *chart, float (*points)[2])
+{
+  PVert *v;
+  uint i = 0;
+
+  for (v = chart->verts; v; v = v->nextlink) {
+    copy_v2_v2(points[i++], v->uv);
+  }
+}
+
+static bool p_intersect_line_2d_dir(const float v1[2],
+                                    const float dir1[2],
+                                    const float v2[2],
+                                    const float dir2[2],
+                                    float r_isect[2])
+{
+  float lmbda, div;
+
+  div = dir2[0] * dir1[1] - dir2[1] * dir1[0];
+
+  if (div == 0.0f) {
+    return false;
+  }
+
+  lmbda = ((v1[1] - v2[1]) * dir1[0] - (v1[0] - v2[0]) * dir1[1]) / div;
+  r_isect[0] = v1[0] + lmbda * dir2[0];
+  r_isect[1] = v1[1] + lmbda * dir2[1];
+
+  return true;
+}
+
+/* Topological Utilities */
+
+static PEdge *p_wheel_edge_next(PEdge *e)
+{
+  return e->next->next->pair;
+}
+
+static PEdge *p_wheel_edge_prev(PEdge *e)
+{
+  return (e->pair) ? e->pair->next : NULL;
+}
+
+static PEdge *p_boundary_edge_next(PEdge *e)
+{
+  return e->next->vert->edge;
+}
+
+static PEdge *p_boundary_edge_prev(PEdge *e)
+{
+  PEdge *we = e, *last;
+
+  do {
+    last = we;
+    we = p_wheel_edge_next(we);
+  } while (we && (we != e));
+
+  return last->next->next;
+}
+
+static bool p_vert_interior(PVert *v)
+{
+  return v->edge->pair;
+}
+
+static void p_face_flip(PFace *f)
+{
+  PEdge *e1 = f->edge, *e2 = e1->next, *e3 = e2->next;
+  PVert *v1 = e1->vert, *v2 = e2->vert, *v3 = e3->vert;
+  int f1 = e1->flag, f2 = e2->flag, f3 = e3->flag;
+  float *orig_uv1 = e1->orig_uv, *orig_uv2 = e2->orig_uv, *orig_uv3 = e3->orig_uv;
+
+  e1->vert = v2;
+  e1->next = e3;
+  e1->orig_uv = orig_uv2;
+  e1->flag = (f1 & ~PEDGE_VERTEX_FLAGS) | (f2 & PEDGE_VERTEX_FLAGS);
+
+  e2->vert = v3;
+  e2->next = e1;
+  e2->orig_uv = orig_uv3;
+  e2->flag = (f2 & ~PEDGE_VERTEX_FLAGS) | (f3 & PEDGE_VERTEX_FLAGS);
+
+  e3->vert = v1;
+  e3->next = e2;
+  e3->orig_uv = orig_uv1;
+  e3->flag = (f3 & ~PEDGE_VERTEX_FLAGS) | (f1 & PEDGE_VERTEX_FLAGS);
+}
+
+#if 0
+static void p_chart_topological_sanity_check(PChart *chart)
+{
+  PVert *v;
+  PEdge *e;
+
+  for (v = chart->verts; v; v = v->nextlink) {
+    GEO_uv_parametrizer_test_equals_ptr("v->edge->vert", v, v->edge->vert);
+  }
+
+  for (e = chart->edges; e; e = e->nextlink) {
+    if (e->pair) {
+      GEO_uv_parametrizer_test_equals_ptr("e->pair->pair", e, e->pair->pair);
+      GEO_uv_parametrizer_test_equals_ptr("pair->vert", e->vert, e->pair->next->vert);
+      GEO_uv_parametrizer_test_equals_ptr("pair->next->vert", e->next->vert, e->pair->vert);
+    }
+  }
+}
+#endif
+
+/* Loading / Flushing */
+
+static void p_vert_load_pin_select_uvs(ParamHandle *handle, PVert *v)
+{
+  PEdge *e;
+  int nedges = 0, npins = 0;
+  float pinuv[2];
+
+  v->uv[0] = v->uv[1] = 0.0f;
+  pinuv[0] = pinuv[1] = 0.0f;
+  e = v->edge;
+  do {
+    if (e->orig_uv) {
+      if (e->flag & PEDGE_SELECT) {
+        v->flag |= PVERT_SELECT;
+      }
+
+      if (e->flag & PEDGE_PIN) {
+        pinuv[0] += e->orig_uv[0] * handle->aspx;
+        pinuv[1] += e->orig_uv[1] * handle->aspy;
+        npins++;
+      }
+      else {
+        v->uv[0] += e->orig_uv[0] * handle->aspx;
+        v->uv[1] += e->orig_uv[1] * handle->aspy;
+      }
+
+      nedges++;
+    }
+
+    e = p_wheel_edge_next(e);
+  } while (e && e != (v->edge));
+
+  if (npins > 0) {
+    v->uv[0] = pinuv[0] / npins;
+    v->uv[1] = pinuv[1] / npins;
+    v->flag |= PVERT_PIN;
+  }
+  else if (nedges > 0) {
+    v->uv[0] /= nedges;
+    v->uv[1] /= nedges;
+  }
+}
+
+static void p_flush_uvs(ParamHandle *handle, PChart *chart)
+{
+  PEdge *e;
+
+  for (e = chart->edges; e; e = e->nextlink) {
+    if (e->orig_uv) {
+      e->orig_uv[0] = e->vert->uv[0] / handle->aspx;
+      e->orig_uv[1] = e->vert->uv[1] / handle->aspy;
+    }
+  }
+}
+
+static void p_flush_uvs_blend(ParamHandle *handle, PChart *chart, float blend)
+{
+  PEdge *e;
+  float invblend = 1.0f - blend;
+
+  for (e = chart->edges; e; e = e->nextlink) {
+    if (e->orig_uv) {
+      e->orig_uv[0] = blend * e->old_uv[0] + invblend * e->vert->uv[0] / handle->aspx;
+      e->orig_uv[1] = blend * e->old_uv[1] + invblend * e->vert->uv[1] / handle->aspy;
+    }
+  }
+}
+
+static void p_face_backup_uvs(PFace *f)
+{
+  PEdge *e1 = f->edge, *e2 = e1->next, *e3 = e2->next;
+
+  if (e1->orig_uv) {
+    e1->old_uv[0] = e1->orig_uv[0];
+    e1->old_uv[1] = e1->orig_uv[1];
+  }
+  if (e2->orig_uv) {
+    e2->old_uv[0] = e2->orig_uv[0];
+    e2->old_uv[1] = e2->orig_uv[1];
+  }
+  if (e3->orig_uv) {
+    e3->old_uv[0] = e3->orig_uv[0];
+    e3->old_uv[1] = e3->orig_uv[1];
+  }
+}
+
+static void p_face_restore_uvs(PFace *f)
+{
+  PEdge *e1 = f->edge, *e2 = e1->next, *e3 = e2->next;
+
+  if (e1->orig_uv) {
+    e1->orig_uv[0] = e1->old_uv[0];
+    e1->orig_uv[1] = e1->old_uv[1];
+  }
+  if (e2->orig_uv) {
+    e2->orig_uv[0] = e2->old_uv[0];
+    e2->orig_uv[1] = e2->old_uv[1];
+  }
+  if (e3->orig_uv) {
+    e3->orig_uv[0] = e3->old_uv[0];
+    e3->orig_uv[1] = e3->old_uv[1];
+  }
+}
+
+/* Construction (use only during construction, relies on u.key being set */
+
+static PVert *p_vert_add(ParamHandle *handle, PHashKey key, const float co[3], PEdge *e)
+{
+  PVert *v = (PVert *)BLI_memarena_alloc(handle->arena, sizeof(*v));
+  copy_v3_v3(v->co, co);
+
+  /* Sanity check, a single nan/inf point causes the entire result to be invalid.
+   * Note that values within the calculation may _become_ non-finite,
+   * so the rest of the code still needs to take this possibility into account. */
+  for (int i = 0; i < 3; i++) {
+    if (UNLIKELY(!isfinite(v->co[i]))) {
+      v->co[i] = 0.0f;
+    }
+  }
+
+  v->u.key = key;
+  v->edge = e;
+  v->flag = 0;
+
+  phash_insert(handle->hash_verts, (PHashLink *)v);
+
+  return v;
+}
+
+static PVert *p_vert_lookup(ParamHandle *handle, PHashKey key, const float co[3], PEdge *e)
+{
+  PVert *v = (PVert *)phash_lookup(handle->hash_verts, key);
+
+  if (v) {
+    return v;
+  }
+  return p_vert_add(handle, key, co, e);
+}
+
+static PVert *p_vert_copy(ParamHandle *handle, PVert *v)
+{
+  PVert *nv = (PVert *)BLI_memarena_alloc(handle->arena, sizeof(*nv));
+
+  copy_v3_v3(nv->co, v->co);
+  nv->uv[0] = v->uv[0];
+  nv->uv[1] = v->uv[1];
+  nv->u.key = v->u.key;
+  nv->edge = v->edge;
+  nv->flag = v->flag;
+
+  return nv;
+}
+
+static PEdge *p_edge_lookup(ParamHandle *handle, const PHashKey *vkeys)
+{
+  PHashKey key = PHASH_edge(vkeys[0], vkeys[1]);
+  PEdge *e = (PEdge *)phash_lookup(handle->hash_edges, key);
+
+  while (e) {
+    if ((e->vert->u.key == vkeys[0]) && (e->next->vert->u.key == vkeys[1])) {
+      return e;
+    }
+    if ((e->vert->u.key == vkeys[1]) && (e->next->vert->u.key == vkeys[0])) {
+      return e;
+    }
+
+    e = (PEdge *)phash_next(handle->hash_edges, key, (PHashLink *)e);
+  }
+
+  return NULL;
+}
+
+static int p_face_exists(ParamHandle *handle, const ParamKey *pvkeys, int i1, int i2, int i3)
+{
+  PHashKey *vkeys = (PHashKey *)pvkeys;
+  PHashKey key = PHASH_edge(vkeys[i1], vkeys[i2]);
+  PEdge *e = (PEdge *)phash_lookup(handle->hash_edges, key);
+
+  while (e) {
+    if ((e->vert->u.key == vkeys[i1]) && (e->next->vert->u.key == vkeys[i2])) {
+      if (e->next->next->vert->u.key == vkeys[i3]) {
+        return true;
+      }
+    }
+    else if ((e->vert->u.key == vkeys[i2]) && (e->next->vert->u.key == vkeys[i1])) {
+      if (e->next->next->vert->u.key == vkeys[i3]) {
+        return true;
+      }
+    }
+
+    e = (PEdge *)phash_next(handle->hash_edges, key, (PHashLink *)e);
+  }
+
+  return false;
+}
+
+static bool p_edge_implicit_seam(PEdge *e, PEdge *ep)
+{
+  float *uv1, *uv2, *uvp1, *uvp2;
+  float limit[2];
+
+  limit[0] = 0.00001;
+  limit[1] = 0.00001;
+
+  uv1 = e->orig_uv;
+  uv2 = e->next->orig_uv;
+
+  if (e->vert->u.key == ep->vert->u.key) {
+    uvp1 = ep->orig_uv;
+    uvp2 = ep->next->orig_uv;
+  }
+  else {
+    uvp1 = ep->next->orig_uv;
+    uvp2 = ep->orig_uv;
+  }
+
+  if ((fabsf(uv1[0] - uvp1[0]) > limit[0]) || (fabsf(uv1[1] - uvp1[1]) > limit[1])) {
+    e->flag |= PEDGE_SEAM;
+    ep->flag |= PEDGE_SEAM;
+    return true;
+  }
+  if ((fabsf(uv2[0] - uvp2[0]) > limit[0]) || (fabsf(uv2[1] - uvp2[1]) > limit[1])) {
+    e->flag |= PEDGE_SEAM;
+    ep->flag |= PEDGE_SEAM;
+    return true;
+  }
+
+  return false;
+}
+
+static bool p_edge_has_pair(ParamHandle *handle, PEdge *e, bool topology_from_uvs, PEdge **r_pair)
+{
+  PHashKey key;
+  PEdge *pe;
+  PVert *v1, *v2;
+  PHashKey key1 = e->vert->u.key;
+  PHashKey key2 = e->next->vert->u.key;
+
+  if (e->flag & PEDGE_SEAM) {
+    return false;
+  }
+
+  key = PHASH_edge(key1, key2);
+  pe = (PEdge *)phash_lookup(handle->hash_edges, key);
+  *r_pair = NULL;
+
+  while (pe) {
+    if (pe != e) {
+      v1 = pe->vert;
+      v2 = pe->next->vert;
+
+      if (((v1->u.key == key1) && (v2->u.key == key2)) ||
+          ((v1->u.key == key2) && (v2->u.key == key1))) {
+
+        /* don't connect seams and t-junctions */
+        if ((pe->flag & PEDGE_SEAM) || *r_pair ||
+            (topology_from_uvs && p_edge_implicit_seam(e, pe))) {
+          *r_pair = NULL;
+          return false;
+        }
+
+        *r_pair = pe;
+      }
+    }
+
+    pe = (PEdge *)phash_next(handle->hash_edges, key, (PHashLink *)pe);
+  }
+
+  if (*r_pair && (e->vert == (*r_pair)->vert)) {
+    if ((*r_pair)->next->pair || (*r_pair)->next->next->pair) {
+      /* non unfoldable, maybe mobius ring or klein bottle */
+      *r_pair = NULL;
+      return false;
+    }
+  }
+
+  return (*r_pair != NULL);
+}
+
+static bool p_edge_connect_pair(ParamHandle *handle,
+                                PEdge *e,
+                                bool topology_from_uvs,
+                                PEdge ***stack)
+{
+  PEdge *pair = NULL;
+
+  if (!e->pair && p_edge_has_pair(handle, e, topology_from_uvs, &pair)) {
+    if (e->vert == pair->vert) {
+      p_face_flip(pair->face);
+    }
+
+    e->pair = pair;
+    pair->pair = e;
+
+    if (!(pair->face->flag & PFACE_CONNECTED)) {
+      **stack = pair;
+      (*stack)++;
+    }
+  }
+
+  return (e->pair != NULL);
+}
+
+static int p_connect_pairs(ParamHandle *handle, bool topology_from_uvs)
+{
+  PEdge **stackbase = (PEdge **)MEM_mallocN(sizeof(*stackbase) * phash_size(handle->hash_faces),
+                                            "Pstackbase");
+  PEdge **stack = stackbase;
+  PFace *f, *first;
+  PEdge *e, *e1, *e2;
+  PChart *chart = handle->construction_chart;
+  int ncharts = 0;
+
+  /* Connect pairs, count edges, set vertex-edge pointer to a pair-less edge. */
+  for (first = chart->faces; first; first = first->nextlink) {
+    if (first->flag & PFACE_CONNECTED) {
+      continue;
+    }
+
+    *stack = first->edge;
+    stack++;
+
+    while (stack != stackbase) {
+      stack--;
+      e = *stack;
+      e1 = e->next;
+      e2 = e1->next;
+
+      f = e->face;
+      f->flag |= PFACE_CONNECTED;
+
+      /* assign verts to charts so we can sort them later */
+      f->u.chart = ncharts;
+
+      if (!p_edge_connect_pair(handle, e, topology_from_uvs, &stack)) {
+        e->vert->edge = e;
+      }
+      if (!p_edge_connect_pair(handle, e1, topology_from_uvs, &stack)) {
+        e1->vert->edge = e1;
+      }
+      if (!p_edge_connect_pair(handle, e2, topology_from_uvs, &stack)) {
+        e2->vert->edge = e2;
+      }
+    }
+
+    ncharts++;
+  }
+
+  MEM_SAFE_FREE(stackbase);
+
+  return ncharts;
+}
+
+static void p_split_vert(ParamHandle *handle, PChart *chart, PEdge *e)
+{
+  PEdge *we, *lastwe = NULL;
+  PVert *v = e->vert;
+  bool copy = true;
+
+  if (e->flag & PEDGE_PIN) {
+    chart->has_pins = true;
+  }
+
+  if (e->flag & PEDGE_VERTEX_SPLIT) {
+    return;
+  }
+
+  /* rewind to start */
+  lastwe = e;
+  for (we = p_wheel_edge_prev(e); we && (we != e); we = p_wheel_edge_prev(we)) {
+    lastwe = we;
+  }
+
+  /* go over all edges in wheel */
+  for (we = lastwe; we; we = p_wheel_edge_next(we)) {
+    if (we->flag & PEDGE_VERTEX_SPLIT) {
+      break;
+    }
+
+    we->flag |= PEDGE_VERTEX_SPLIT;
+
+    if (we == v->edge) {
+      /* found it, no need to copy */
+      copy = false;
+      v->nextlink = chart->verts;
+      chart->verts = v;
+      chart->nverts++;
+    }
+  }
+
+  if (copy) {
+    /* not found, copying */
+    v->flag |= PVERT_SPLIT;
+    v = p_vert_copy(handle, v);
+    v->flag |= PVERT_SPLIT;
+
+    v->nextlink = chart->verts;
+    chart->verts = v;
+    chart->nverts++;
+
+    v->edge = lastwe;
+
+    we = lastwe;
+    do {
+      we->vert = v;
+      we = p_wheel_edge_next(we);
+    } while (we && (we != lastwe));
+  }
+}
+
+static PChart **p_split_charts(ParamHandle *handle, PChart *chart, int ncharts)
+{
+  PChart **charts = (PChart **)MEM_callocN(sizeof(*charts) * ncharts, "PCharts");
+
+  for (int i = 0; i < ncharts; i++) {
+    charts[i] = (PChart *)MEM_callocN(sizeof(*chart), "PChart");
+  }
+
+  PFace *f = chart->faces;
+  while (f) {
+    PEdge *e1 = f->edge, *e2 = e1->next, *e3 = e2->next;
+    PFace *nextf = f->nextlink;
+
+    PChart *nchart = charts[f->u.chart];
+
+    f->nextlink = nchart->faces;
+    nchart->faces = f;
+    e1->nextlink = nchart->edges;
+    nchart->edges = e1;
+    e2->nextlink = nchart->edges;
+    nchart->edges = e2;
+    e3->nextlink = nchart->edges;
+    nchart->edges = e3;
+
+    nchart->nfaces++;
+    nchart->nedges += 3;
+
+    p_split_vert(handle, nchart, e1);
+    p_split_vert(handle, nchart, e2);
+    p_split_vert(handle, nchart, e3);
+
+    f = nextf;
+  }
+
+  return charts;
+}
+
+static PFace *p_face_add(ParamHandle *handle)
+{
+  PFace *f;
+  PEdge *e1, *e2, *e3;
+
+  /* allocate */
+  f = (PFace *)BLI_memarena_alloc(handle->arena, sizeof(*f));
+  f->flag = 0; /* init ! */
+
+  e1 = (PEdge *)BLI_memarena_alloc(handle->arena, sizeof(*e1));
+  e2 = (PEdge *)BLI_memarena_alloc(handle->arena, sizeof(*e2));
+  e3 = (PEdge *)BLI_memarena_alloc(handle->arena, sizeof(*e3));
+
+  /* set up edges */
+  f->edge = e1;
+  e1->face = e2->face = e3->face = f;
+
+  e1->next = e2;
+  e2->next = e3;
+  e3->next = e1;
+
+  e1->pair = NULL;
+  e2->pair = NULL;
+  e3->pair = NULL;
+
+  e1->flag = 0;
+  e2->flag = 0;
+  e3->flag = 0;
+
+  return f;
+}
+
+static PFace *p_face_add_construct(ParamHandle *handle,
+                                   ParamKey key,
+                                   const ParamKey *vkeys,
+                                   const float **co,
+                                   float **uv,
+                                   int i1,
+                                   int i2,
+                                   int i3,
+                                   const bool *pin,
+                                   const bool *select)
+{
+  PFace *f = p_face_add(handle);
+  PEdge *e1 = f->edge, *e2 = e1->next, *e3 = e2->next;
+
+  e1->vert = p_vert_lookup(handle, vkeys[i1], co[i1], e1);
+  e2->vert = p_vert_lookup(handle, vkeys[i2], co[i2], e2);
+  e3->vert = p_vert_lookup(handle, vkeys[i3], co[i3], e3);
+
+  e1->orig_uv = uv[i1];
+  e2->orig_uv = uv[i2];
+  e3->orig_uv = uv[i3];
+
+  if (pin) {
+    if (pin[i1]) {
+      e1->flag |= PEDGE_PIN;
+    }
+    if (pin[i2]) {
+      e2->flag |= PEDGE_PIN;
+    }
+    if (pin[i3]) {
+      e3->flag |= PEDGE_PIN;
+    }
+  }
+
+  if (select) {
+    if (select[i1]) {
+      e1->flag |= PEDGE_SELECT;
+    }
+    if (select[i2]) {
+      e2->flag |= PEDGE_SELECT;
+    }
+    if (select[i3]) {
+      e3->flag |= PEDGE_SELECT;
+    }
+  }
+
+  f->u.key = key;
+  phash_insert(handle->hash_faces, (PHashLink *)f);
+
+  e1->u.key = PHASH_edge(vkeys[i1], vkeys[i2]);
+  e2->u.key = PHASH_edge(vkeys[i2], vkeys[i3]);
+  e3->u.key = PHASH_edge(vkeys[i3], vkeys[i1]);
+
+  phash_insert(handle->hash_edges, (PHashLink *)e1);
+  phash_insert(handle->hash_edges, (PHashLink *)e2);
+  phash_insert(handle->hash_edges, (PHashLink *)e3);
+
+  return f;
+}
+
+static PFace *p_face_add_fill(ParamHandle *handle, PChart *chart, PVert *v1, PVert *v2, PVert *v3)
+{
+  PFace *f = p_face_add(handle);
+  PEdge *e1 = f->edge, *e2 = e1->next, *e3 = e2->next;
+
+  e1->vert = v1;
+  e2->vert = v2;
+  e3->vert = v3;
+
+  e1->orig_uv = e2->orig_uv = e3->orig_uv = NULL;
+
+  f->nextlink = chart->faces;
+  chart->faces = f;
+  e1->nextlink = chart->edges;
+  chart->edges = e1;
+  e2->nextlink = chart->edges;
+  chart->edges = e2;
+  e3->nextlink = chart->edges;
+  chart->edges = e3;
+
+  chart->nfaces++;
+  chart->nedges += 3;
+
+  return f;
+}
+
+static bool p_quad_split_direction(ParamHandle *handle, const float **co, const ParamKey *vkeys)
+{
+  /* Slight bias to prefer one edge over the other in case they are equal, so
+   * that in symmetric models we choose the same split direction instead of
+   * depending on floating point errors to decide. */
+  float bias = 1.0f + 1e-6f;
+  float fac = len_v3v3(co[0], co[2]) * bias - len_v3v3(co[1], co[3]);
+  bool dir = (fac <= 0.0f);
+
+  /* The face exists check is there because of a special case:
+   * when two quads share three vertices, they can each be split into two triangles,
+   * resulting in two identical triangles. For example in Suzanne's nose. */
+  if (dir) {
+    if (p_face_exists(handle, vkeys, 0, 1, 2) || p_face_exists(handle, vkeys, 0, 2, 3)) {
+      return !dir;
+    }
+  }
+  else {
+    if (p_face_exists(handle, vkeys, 0, 1, 3) || p_face_exists(handle, vkeys, 1, 2, 3)) {
+      return !dir;
+    }
+  }
+
+  return dir;
+}
+
+/* Construction: boundary filling */
+
+static void p_chart_boundaries(PChart *chart, PEdge **r_outer)
+{
+  PEdge *e, *be;
+  float len, maxlen = -1.0;
+
+  chart->nboundaries = 0;
+  if (r_outer) {
+    *r_outer = NULL;
+  }
+
+  for (e = chart->edges; e; e = e->nextlink) {
+    if (e->pair || (e->flag & PEDGE_DONE)) {
+      continue;
+    }
+
+    chart->nboundaries++;
+
+    len = 0.0f;
+
+    be = e;
+    do {
+      be->flag |= PEDGE_DONE;
+      len += p_edge_length(be);
+      be = be->next->vert->edge;
+    } while (be != e);
+
+    if (r_outer && (len > maxlen)) {
+      *r_outer = e;
+      maxlen = len;
+    }
+  }
+
+  for (e = chart->edges; e; e = e->nextlink) {
+    e->flag &= ~PEDGE_DONE;
+  }
+}
+
+static float p_edge_boundary_angle(PEdge *e)
+{
+  PEdge *we;
+  PVert *v, *v1, *v2;
+  float angle;
+  int n = 0;
+
+  v = e->vert;
+
+  /* concave angle check -- could be better */
+  angle = M_PI;
+
+  we = v->edge;
+  do {
+    v1 = we->next->vert;
+    v2 = we->next->next->vert;
+    angle -= p_vec_angle(v1->co, v->co, v2->co);
+
+    we = we->next->next->pair;
+    n++;
+  } while (we && (we != v->edge));
+
+  return angle;
+}
+
+static void p_chart_fill_boundary(ParamHandle *handle, PChart *chart, PEdge *be, int nedges)
+{
+  PEdge *e, *e1, *e2;
+
+  PFace *f;
+  struct Heap *heap = BLI_heap_new();
+  float angle;
+
+  e = be;
+  do {
+    angle = p_edge_boundary_angle(e);
+    e->u.heaplink = BLI_heap_insert(heap, angle, e);
+
+    e = p_boundary_edge_next(e);
+  } while (e != be);
+
+  if (nedges == 2) {
+    /* no real boundary, but an isolated seam */
+    e = be->next->vert->edge;
+    e->pair = be;
+    be->pair = e;
+
+    BLI_heap_remove(heap, e->u.heaplink);
+    BLI_heap_remove(heap, be->u.heaplink);
+  }
+  else {
+    while (nedges > 2) {
+      PEdge *ne, *ne1, *ne2;
+
+      e = (PEdge *)BLI_heap_pop_min(heap);
+
+      e1 = p_boundary_edge_prev(e);
+      e2 = p_boundary_edge_next(e);
+
+      BLI_heap_remove(heap, e1->u.heaplink);
+      BLI_heap_remove(heap, e2->u.heaplink);
+      e->u.heaplink = e1->u.heaplink = e2->u.heaplink = NULL;
+
+      e->flag |= PEDGE_FILLED;
+      e1->flag |= PEDGE_FILLED;
+
+      f = p_face_add_fill(handle, chart, e->vert, e1->vert, e2->vert);
+      f->flag |= PFACE_FILLED;
+
+      ne = f->edge->next->next;
+      ne1 = f->edge;
+      ne2 = f->edge->next;
+
+      ne->flag = ne1->flag = ne2->flag = PEDGE_FILLED;
+
+      e->pair = ne;
+      ne->pair = e;
+      e1->pair = ne1;
+      ne1->pair = e1;
+
+      ne->vert = e2->vert;
+      ne1->vert = e->vert;
+      ne2->vert = e1->vert;
+
+      if (nedges == 3) {
+        e2->pair = ne2;
+        ne2->pair = e2;
+      }
+      else {
+        ne2->vert->edge = ne2;
+
+        ne2->u.heaplink = BLI_heap_insert(heap, p_edge_boundary_angle(ne2), ne2);
+        e2->u.heaplink = BLI_heap_insert(heap, p_edge_boundary_angle(e2), e2);
+      }
+
+      nedges--;
+    }
+  }
+
+  BLI_heap_free(heap, NULL);
+}
+
+static void p_chart_fill_boundaries(ParamHandle *handle, PChart *chart, PEdge *outer)
+{
+  PEdge *e, *be; /* *enext - as yet unused */
+  int nedges;
+
+  for (e = chart->edges; e; e = e->nextlink) {
+    /* enext = e->nextlink; - as yet unused */
+
+    if (e->pair || (e->flag & PEDGE_FILLED)) {
+      continue;
+    }
+
+    nedges = 0;
+    be = e;
+    do {
+      be->flag |= PEDGE_FILLED;
+      be = be->next->vert->edge;
+      nedges++;
+    } while (be != e);
+
+    if (e != outer) {
+      p_chart_fill_boundary(handle, chart, e, nedges);
+    }
+  }
+}
+
+#if 0
+/* Polygon kernel for inserting uv's non overlapping */
+
+static int p_polygon_point_in(const float cp1[2], const float cp2[2], const float p[2])
+{
+  if ((cp1[0] == p[0]) && (cp1[1] == p[1])) {
+    return 2;
+  }
+  else if ((cp2[0] == p[0]) && (cp2[1] == p[1])) {
+    return 3;
+  }
+  else {
+    return (p_area_signed(cp1, cp2, p) >= 0.0f);
+  }
+}
+
+static void p_polygon_kernel_clip(float (*oldpoints)[2],
+                                  int noldpoints,
+                                  float (*newpoints)[2],
+                                  int *r_nnewpoints,
+                                  const float cp1[2],
+                                  const float cp2[2])
+{
+  float *p2, *p1, isect[2];
+  int i, p2in, p1in;
+
+  p1 = oldpoints[noldpoints - 1];
+  p1in = p_polygon_point_in(cp1, cp2, p1);
+  *r_nnewpoints = 0;
+
+  for (i = 0; i < noldpoints; i++) {
+    p2 = oldpoints[i];
+    p2in = p_polygon_point_in(cp1, cp2, p2);
+
+    if ((p2in >= 2) || (p1in && p2in)) {
+      newpoints[*r_nnewpoints][0] = p2[0];
+      newpoints[*r_nnewpoints][1] = p2[1];
+      (*r_nnewpoints)++;
+    }
+    else if (p1in && !p2in) {
+      if (p1in != 3) {
+        p_intersect_line_2d(p1, p2, cp1, cp2, isect);
+        newpoints[*r_nnewpoints][0] = isect[0];
+        newpoints[*r_nnewpoints][1] = isect[1];
+        (*r_nnewpoints)++;
+      }
+    }
+    else if (!p1in && p2in) {
+      p_intersect_line_2d(p1, p2, cp1, cp2, isect);
+      newpoints[*r_nnewpoints][0] = isect[0];
+      newpoints[*r_nnewpoints][1] = isect[1];
+      (*r_nnewpoints)++;
+
+      newpoints[*r_nnewpoints][0] = p2[0];
+      newpoints[*r_nnewpoints][1] = p2[1];
+      (*r_nnewpoints)++;
+    }
+
+    p1in = p2in;
+    p1 = p2;
+  }
+}
+
+static void p_polygon_kernel_center(float (*points)[2], int npoints, float *center)
+{
+  int i, size, nnewpoints = npoints;
+  float(*oldpoints)[2], (*newpoints)[2], *p1, *p2;
+
+  size = npoints * 3;
+  oldpoints = MEM_mallocN(sizeof(float[2]) * size, "PPolygonOldPoints");
+  newpoints = MEM_mallocN(sizeof(float[2]) * size, "PPolygonNewPoints");
+
+  memcpy(oldpoints, points, sizeof(float[2]) * npoints);
+
+  for (i = 0; i < npoints; i++) {
+    p1 = points[i];
+    p2 = points[(i + 1) % npoints];
+    p_polygon_kernel_clip(oldpoints, nnewpoints, newpoints, &nnewpoints, p1, p2);
+
+    if (nnewpoints == 0) {
+      /* degenerate case, use center of original polygon */
+      memcpy(oldpoints, points, sizeof(float[2]) * npoints);
+      nnewpoints = npoints;
+      break;
+    }
+    else if (nnewpoints == 1) {
+      /* degenerate case, use remaining point */
+      center[0] = newpoints[0][0];
+      center[1] = newpoints[0][1];
+
+      MEM_freeN(oldpoints);
+      MEM_freeN(newpoints);
+
+      return;
+    }
+
+    if (nnewpoints * 2 > size) {
+      size *= 2;
+      MEM_freeN(oldpoints);
+      oldpoints = MEM_mallocN(sizeof(float[2]) * size, "oldpoints");
+      memcpy(oldpoints, newpoints, sizeof(float[2]) * nnewpoints);
+      MEM_freeN(newpoints);
+      newpoints = MEM_mallocN(sizeof(float[2]) * size, "newpoints");
+    }
+    else {
+      float(*sw_points)[2] = oldpoints;
+      oldpoints = newpoints;
+      newpoints = sw_points;
+    }
+  }
+
+  center[0] = center[1] = 0.0f;
+
+  for (i = 0; i < nnewpoints; i++) {
+    center[0] += oldpoints[i][0];
+    center[1] += oldpoints[i][1];
+  }
+
+  center[0] /= nnewpoints;
+  center[1] /= nnewpoints;
+
+  MEM_freeN(oldpoints);
+  MEM_freeN(newpoints);
+}
+#endif
+
+#if 0
+/* Edge Collapser */
+
+int NCOLLAPSE = 1;
+int NCOLLAPSEX = 0;
+
+static float p_vert_cotan(const float v1[3], const float v2[3], const float v3[3])
+{
+  float a[3], b[3], c[3], clen;
+
+  sub_v3_v3v3(a, v2, v1);
+  sub_v3_v3v3(b, v3, v1);
+  cross_v3_v3v3(c, a, b);
+
+  clen = len_v3(c);
+
+  if (clen == 0.0f) {
+    return 0.0f;
+  }
+
+  return dot_v3v3(a, b) / clen;
+}
+
+static bool p_vert_flipped_wheel_triangle(PVert *v)
+{
+  PEdge *e = v->edge;
+
+  do {
+    if (p_face_uv_area_signed(e->face) < 0.0f) {
+      return true;
+    }
+
+    e = p_wheel_edge_next(e);
+  } while (e && (e != v->edge));
+
+  return false;
+}
+
+static bool p_vert_map_harmonic_weights(PVert *v)
+{
+  float weightsum, positionsum[2], olduv[2];
+
+  weightsum = 0.0f;
+  positionsum[0] = positionsum[1] = 0.0f;
+
+  if (p_vert_interior(v)) {
+    PEdge *e = v->edge;
+
+    do {
+      float t1, t2, weight;
+      PVert *v1, *v2;
+
+      v1 = e->next->vert;
+      v2 = e->next->next->vert;
+      t1 = p_vert_cotan(v2->co, e->vert->co, v1->co);
+
+      v1 = e->pair->next->vert;
+      v2 = e->pair->next->next->vert;
+      t2 = p_vert_cotan(v2->co, e->pair->vert->co, v1->co);
+
+      weight = 0.5f * (t1 + t2);
+      weightsum += weight;
+      positionsum[0] += weight * e->pair->vert->uv[0];
+      positionsum[1] += weight * e->pair->vert->uv[1];
+
+      e = p_wheel_edge_next(e);
+    } while (e && (e != v->edge));
+  }
+  else {
+    PEdge *e = v->edge;
+
+    do {
+      float t1, t2;
+      PVert *v1, *v2;
+
+      v2 = e->next->vert;
+      v1 = e->next->next->vert;
+
+      t1 = p_vert_cotan(v1->co, v->co, v2->co);
+      t2 = p_vert_cotan(v2->co, v->co, v1->co);
+
+      weightsum += t1 + t2;
+      positionsum[0] += (v2->uv[1] - v1->uv[1]) + (t1 * v2->uv[0] + t2 * v1->uv[0]);
+      positionsum[1] += (v1->uv[0] - v2->uv[0]) + (t1 * v2->uv[1] + t2 * v1->uv[1]);
+
+      e = p_wheel_edge_next(e);
+    } while (e && (e != v->edge));
+  }
+
+  if (weightsum != 0.0f) {
+    weightsum = 1.0f / weightsum;
+    positionsum[0] *= weightsum;
+    positionsum[1] *= weightsum;
+  }
+
+  olduv[0] = v->uv[0];
+  olduv[1] = v->uv[1];
+  v->uv[0] = positionsum[0];
+  v->uv[1] = positionsum[1];
+
+  if (p_vert_flipped_wheel_triangle(v)) {
+    v->uv[0] = olduv[0];
+    v->uv[1] = olduv[1];
+
+    return false;
+  }
+
+  return true;
+}
+
+static void p_vert_harmonic_insert(PVert *v)
+{
+  PEdge *e;
+
+  if (!p_vert_map_harmonic_weights(v)) {
+    /* do polygon kernel center insertion: this is quite slow, but should
+     * only be needed for 0.01 % of verts or so, when insert with harmonic
+     * weights fails */
+
+    int npoints = 0, i;
+    float(*points)[2];
+
+    e = v->edge;
+    do {
+      npoints++;
+      e = p_wheel_edge_next(e);
+    } while (e && (e != v->edge));
+
+    if (e == NULL) {
+      npoints++;
+    }
+
+    points = MEM_mallocN(sizeof(float[2]) * npoints, "PHarmonicPoints");
+
+    e = v->edge;
+    i = 0;
+    do {
+      PEdge *nexte = p_wheel_edge_next(e);
+
+      points[i][0] = e->next->vert->uv[0];
+      points[i][1] = e->next->vert->uv[1];
+
+      if (nexte == NULL) {
+        i++;
+        points[i][0] = e->next->next->vert->uv[0];
+        points[i][1] = e->next->next->vert->uv[1];
+        break;
+      }
+
+      e = nexte;
+      i++;
+    } while (e != v->edge);
+
+    p_polygon_kernel_center(points, npoints, v->uv);
+
+    MEM_freeN(points);
+  }
+
+  e = v->edge;
+  do {
+    if (!(e->next->vert->flag & PVERT_PIN)) {
+      p_vert_map_harmonic_weights(e->next->vert);
+    }
+    e = p_wheel_edge_next(e);
+  } while (e && (e != v->edge));
+
+  p_vert_map_harmonic_weights(v);
+}
+
+static void p_vert_fix_edge_pointer(PVert *v)
+{
+  PEdge *start = v->edge;
+
+  /* set v->edge pointer to the edge with no pair, if there is one */
+  while (v->edge->pair) {
+    v->edge = p_wheel_edge_prev(v->edge);
+
+    if (v->edge == start) {
+      break;
+    }
+  }
+}
+
+static void p_collapsing_verts(PEdge *edge, PEdge *pair, PVert **r_newv, PVert **r_keepv)
+{
+  /* the two vertices that are involved in the collapse */
+  if (edge) {
+    *r_newv = edge->vert;
+    *r_keepv = edge->next->vert;
+  }
+  else {
+    *r_newv = pair->next->vert;
+    *r_keepv = pair->vert;
+  }
+}
+
+static void p_collapse_edge(PEdge *edge, PEdge *pair)
+{
+  PVert *oldv, *keepv;
+  PEdge *e;
+
+  p_collapsing_verts(edge, pair, &oldv, &keepv);
+
+  /* change e->vert pointers from old vertex to the target vertex */
+  e = oldv->edge;
+  do {
+    if ((e != edge) && !(pair && pair->next == e)) {
+      e->vert = keepv;
+    }
+
+    e = p_wheel_edge_next(e);
+  } while (e && (e != oldv->edge));
+
+  /* set keepv->edge pointer */
+  if ((edge && (keepv->edge == edge->next)) || (keepv->edge == pair)) {
+    if (edge && edge->next->pair) {
+      keepv->edge = edge->next->pair->next;
+    }
+    else if (pair && pair->next->next->pair) {
+      keepv->edge = pair->next->next->pair;
+    }
+    else if (edge && edge->next->next->pair) {
+      keepv->edge = edge->next->next->pair;
+    }
+    else {
+      keepv->edge = pair->next->pair->next;
+    }
+  }
+
+  /* update pairs and v->edge pointers */
+  if (edge) {
+    PEdge *e1 = edge->next, *e2 = e1->next;
+
+    if (e1->pair) {
+      e1->pair->pair = e2->pair;
+    }
+
+    if (e2->pair) {
+      e2->pair->pair = e1->pair;
+      e2->vert->edge = p_wheel_edge_prev(e2);
+    }
+    else {
+      e2->vert->edge = p_wheel_edge_next(e2);
+    }
+
+    p_vert_fix_edge_pointer(e2->vert);
+  }
+
+  if (pair) {
+    PEdge *e1 = pair->next, *e2 = e1->next;
+
+    if (e1->pair) {
+      e1->pair->pair = e2->pair;
+    }
+
+    if (e2->pair) {
+      e2->pair->pair = e1->pair;
+      e2->vert->edge = p_wheel_edge_prev(e2);
+    }
+    else {
+      e2->vert->edge = p_wheel_edge_next(e2);
+    }
+
+    p_vert_fix_edge_pointer(e2->vert);
+  }
+
+  p_vert_fix_edge_pointer(keepv);
+
+  /* mark for move to collapsed list later */
+  oldv->flag |= PVERT_COLLAPSE;
+
+  if (edge) {
+    PFace *f = edge->face;
+    PEdge *e1 = edge->next, *e2 = e1->next;
+
+    f->flag |= PFACE_COLLAPSE;
+    edge->flag |= PEDGE_COLLAPSE;
+    e1->flag |= PEDGE_COLLAPSE;
+    e2->flag |= PEDGE_COLLAPSE;
+  }
+
+  if (pair) {
+    PFace *f = pair->face;
+    PEdge *e1 = pair->next, *e2 = e1->next;
+
+    f->flag |= PFACE_COLLAPSE;
+    pair->flag |= PEDGE_COLLAPSE;
+    e1->flag |= PEDGE_COLLAPSE;
+    e2->flag |= PEDGE_COLLAPSE;
+  }
+}
+
+static void p_split_vertex(PEdge *edge, PEdge *pair)
+{
+  PVert *newv, *keepv;
+  PEdge *e;
+
+  p_collapsing_verts(edge, pair, &newv, &keepv);
+
+  /* update edge pairs */
+  if (edge) {
+    PEdge *e1 = edge->next, *e2 = e1->next;
+
+    if (e1->pair) {
+      e1->pair->pair = e1;
+    }
+    if (e2->pair) {
+      e2->pair->pair = e2;
+    }
+
+    e2->vert->edge = e2;
+    p_vert_fix_edge_pointer(e2->vert);
+    keepv->edge = e1;
+  }
+
+  if (pair) {
+    PEdge *e1 = pair->next, *e2 = e1->next;
+
+    if (e1->pair) {
+      e1->pair->pair = e1;
+    }
+    if (e2->pair) {
+      e2->pair->pair = e2;
+    }
+
+    e2->vert->edge = e2;
+    p_vert_fix_edge_pointer(e2->vert);
+    keepv->edge = pair;
+  }
+
+  p_vert_fix_edge_pointer(keepv);
+
+  /* set e->vert pointers to restored vertex */
+  e = newv->edge;
+  do {
+    e->vert = newv;
+    e = p_wheel_edge_next(e);
+  } while (e && (e != newv->edge));
+}
+
+static bool p_collapse_allowed_topologic(PEdge *edge, PEdge *pair)
+{
+  PVert *oldv, *keepv;
+
+  p_collapsing_verts(edge, pair, &oldv, &keepv);
+
+  /* boundary edges */
+  if (!edge || !pair) {
+    /* avoid collapsing chart into an edge */
+    if (edge && !edge->next->pair && !edge->next->next->pair) {
+      return false;
+    }
+    else if (pair && !pair->next->pair && !pair->next->next->pair) {
+      return false;
+    }
+  }
+  /* avoid merging two boundaries (oldv and keepv are on the 'other side' of
+   * the chart) */
+  else if (!p_vert_interior(oldv) && !p_vert_interior(keepv)) {
+    return false;
+  }
+
+  return true;
+}
+
+static bool p_collapse_normal_flipped(float *v1, float *v2, float *vold, float *vnew)
+{
+  float nold[3], nnew[3], sub1[3], sub2[3];
+
+  sub_v3_v3v3(sub1, vold, v1);
+  sub_v3_v3v3(sub2, vold, v2);
+  cross_v3_v3v3(nold, sub1, sub2);
+
+  sub_v3_v3v3(sub1, vnew, v1);
+  sub_v3_v3v3(sub2, vnew, v2);
+  cross_v3_v3v3(nnew, sub1, sub2);
+
+  return (dot_v3v3(nold, nnew) <= 0.0f);
+}
+
+static bool p_collapse_allowed_geometric(PEdge *edge, PEdge *pair)
+{
+  PVert *oldv, *keepv;
+  PEdge *e;
+  float angulardefect, angle;
+
+  p_collapsing_verts(edge, pair, &oldv, &keepv);
+
+  angulardefect = 2 * M_PI;
+
+  e = oldv->edge;
+  do {
+    float a[3], b[3], minangle, maxangle;
+    PEdge *e1 = e->next, *e2 = e1->next;
+    PVert *v1 = e1->vert, *v2 = e2->vert;
+    int i;
+
+    angle = p_vec_angle(v1->co, oldv->co, v2->co);
+    angulardefect -= angle;
+
+    /* skip collapsing faces */
+    if (v1 == keepv || v2 == keepv) {
+      e = p_wheel_edge_next(e);
+      continue;
+    }
+
+    if (p_collapse_normal_flipped(v1->co, v2->co, oldv->co, keepv->co)) {
+      return false;
+    }
+
+    a[0] = angle;
+    a[1] = p_vec_angle(v2->co, v1->co, oldv->co);
+    a[2] = M_PI - a[0] - a[1];
+
+    b[0] = p_vec_angle(v1->co, keepv->co, v2->co);
+    b[1] = p_vec_angle(v2->co, v1->co, keepv->co);
+    b[2] = M_PI - b[0] - b[1];
+
+    /* ABF criterion 1: avoid sharp and obtuse angles. */
+    minangle = 15.0f * M_PI / 180.0f;
+    maxangle = M_PI - minangle;
+
+    for (i = 0; i < 3; i++) {
+      if ((b[i] < a[i]) && (b[i] < minangle)) {
+        return false;
+      }
+      else if ((b[i] > a[i]) && (b[i] > maxangle)) {
+        return false;
+      }
+    }
+
+    e = p_wheel_edge_next(e);
+  } while (e && (e != oldv->edge));
+
+  if (p_vert_interior(oldv)) {
+    /* HLSCM criterion: angular defect smaller than threshold. */
+    if (fabsf(angulardefect) > (float)(M_PI * 30.0 / 180.0)) {
+      return false;
+    }
+  }
+  else {
+    PVert *v1 = p_boundary_edge_next(oldv->edge)->vert;
+    PVert *v2 = p_boundary_edge_prev(oldv->edge)->vert;
+
+    /* ABF++ criterion 2: avoid collapsing verts inwards. */
+    if (p_vert_interior(keepv)) {
+      return false;
+    }
+
+    /* Don't collapse significant boundary changes. */
+    angle = p_vec_angle(v1->co, oldv->co, v2->co);
+    if (angle < (M_PI * 160.0 / 180.0)) {
+      return false;
+    }
+  }
+
+  return true;
+}
+
+static bool p_collapse_allowed(PEdge *edge, PEdge *pair)
+{
+  PVert *oldv, *keepv;
+
+  p_collapsing_verts(edge, pair, &oldv, &keepv);
+
+  if (oldv->flag & PVERT_PIN) {
+    return false;
+  }
+
+  return (p_collapse_allowed_topologic(edge, pair) && p_collapse_allowed_geometric(edge, pair));
+}
+
+static float p_collapse_cost(PEdge *edge, PEdge *pair)
+{
+  /* based on volume and boundary optimization from:
+   * "Fast and Memory Efficient Polygonal Simplification" P. Lindstrom, G. Turk */
+
+  PVert *oldv, *keepv;
+  PEdge *e;
+  PFace *oldf1, *oldf2;
+  float volumecost = 0.0f, areacost = 0.0f, edgevec[3], cost, weight, elen;
+  float shapecost = 0.0f;
+  float shapeold = 0.0f, shapenew = 0.0f;
+  int nshapeold = 0, nshapenew = 0;
+
+  p_collapsing_verts(edge, pair, &oldv, &keepv);
+  oldf1 = (edge) ? edge->face : NULL;
+  oldf2 = (pair) ? pair->face : NULL;
+
+  sub_v3_v3v3(edgevec, keepv->co, oldv->co);
+
+  e = oldv->edge;
+  do {
+    float a1, a2, a3;
+    float *co1 = e->next->vert->co;
+    float *co2 = e->next->next->vert->co;
+
+    if (!ELEM(e->face, oldf1, oldf2)) {
+      float tetrav2[3], tetrav3[3];
+
+      /* tetrahedron volume = (1/3!)*|a.(b x c)| */
+      sub_v3_v3v3(tetrav2, co1, oldv->co);
+      sub_v3_v3v3(tetrav3, co2, oldv->co);
+      volumecost += fabsf(volume_tri_tetrahedron_signed_v3(tetrav2, tetrav3, edgevec));
+
+#  if 0
+      shapecost += dot_v3v3(co1, keepv->co);
+
+      if (p_wheel_edge_next(e) == NULL) {
+        shapecost += dot_v3v3(co2, keepv->co);
+      }
+#  endif
+
+      p_triangle_angles(oldv->co, co1, co2, &a1, &a2, &a3);
+      a1 = a1 - M_PI / 3.0;
+      a2 = a2 - M_PI / 3.0;
+      a3 = a3 - M_PI / 3.0;
+      shapeold = (a1 * a1 + a2 * a2 + a3 * a3) / (M_PI_2 * M_PI_2);
+
+      nshapeold++;
+    }
+    else {
+      p_triangle_angles(keepv->co, co1, co2, &a1, &a2, &a3);
+      a1 = a1 - M_PI / 3.0;
+      a2 = a2 - M_PI / 3.0;
+      a3 = a3 - M_PI / 3.0;
+      shapenew = (a1 * a1 + a2 * a2 + a3 * a3) / (M_PI_2 * M_PI_2);
+
+      nshapenew++;
+    }
+
+    e = p_wheel_edge_next(e);
+  } while (e && (e != oldv->edge));
+
+  if (!p_vert_interior(oldv)) {
+    PVert *v1 = p_boundary_edge_prev(oldv->edge)->vert;
+    PVert *v2 = p_boundary_edge_next(oldv->edge)->vert;
+
+    areacost = area_tri_v3(oldv->co, v1->co, v2->co);
+  }
+
+  elen = len_v3(edgevec);
+  weight = 1.0f; /* 0.2f */
+  cost = weight * volumecost * volumecost + elen * elen * areacost * areacost;
+#  if 0
+  cost += shapecost;
+#  else
+  shapeold /= nshapeold;
+  shapenew /= nshapenew;
+  shapecost = (shapeold + 0.00001) / (shapenew + 0.00001);
+
+  cost *= shapecost;
+#  endif
+
+  return cost;
+}
+
+static void p_collapse_cost_vertex(PVert *vert, float *r_mincost, PEdge **r_mine)
+{
+  PEdge *e, *enext, *pair;
+
+  *r_mine = NULL;
+  *r_mincost = 0.0f;
+  e = vert->edge;
+  do {
+    if (p_collapse_allowed(e, e->pair)) {
+      float cost = p_collapse_cost(e, e->pair);
+
+      if ((*r_mine == NULL) || (cost < *r_mincost)) {
+        *r_mincost = cost;
+        *r_mine = e;
+      }
+    }
+
+    enext = p_wheel_edge_next(e);
+
+    if (enext == NULL) {
+      /* The other boundary edge, where we only have the pair half-edge. */
+      pair = e->next->next;
+
+      if (p_collapse_allowed(NULL, pair)) {
+        float cost = p_collapse_cost(NULL, pair);
+
+        if ((*r_mine == NULL) || (cost < *r_mincost)) {
+          *r_mincost = cost;
+          *r_mine = pair;
+        }
+      }
+
+      break;
+    }
+
+    e = enext;
+  } while (e != vert->edge);
+}
+
+static void p_chart_post_collapse_flush(PChart *chart, PEdge *collapsed)
+{
+  /* Move to `collapsed_*`. */
+
+  PVert *v, *nextv = NULL, *verts = chart->verts;
+  PEdge *e, *nexte = NULL, *edges = chart->edges, *laste = NULL;
+  PFace *f, *nextf = NULL, *faces = chart->faces;
+
+  chart->verts = chart->collapsed_verts = NULL;
+  chart->edges = chart->collapsed_edges = NULL;
+  chart->faces = chart->collapsed_faces = NULL;
+
+  chart->nverts = chart->nedges = chart->nfaces = 0;
+
+  for (v = verts; v; v = nextv) {
+    nextv = v->nextlink;
+
+    if (v->flag & PVERT_COLLAPSE) {
+      v->nextlink = chart->collapsed_verts;
+      chart->collapsed_verts = v;
+    }
+    else {
+      v->nextlink = chart->verts;
+      chart->verts = v;
+      chart->nverts++;
+    }
+  }
+
+  for (e = edges; e; e = nexte) {
+    nexte = e->nextlink;
+
+    if (!collapsed || !(e->flag & PEDGE_COLLAPSE_EDGE)) {
+      if (e->flag & PEDGE_COLLAPSE) {
+        e->nextlink = chart->collapsed_edges;
+        chart->collapsed_edges = e;
+      }
+      else {
+        e->nextlink = chart->edges;
+        chart->edges = e;
+        chart->nedges++;
+      }
+    }
+  }
+
+  /* these are added last so they can be popped of in the right order
+   * for splitting */
+  for (e = collapsed; e; e = e->nextlink) {
+    e->nextlink = e->u.nextcollapse;
+    laste = e;
+  }
+  if (laste) {
+    laste->nextlink = chart->collapsed_edges;
+    chart->collapsed_edges = collapsed;
+  }
+
+  for (f = faces; f; f = nextf) {
+    nextf = f->nextlink;
+
+    if (f->flag & PFACE_COLLAPSE) {
+      f->nextlink = chart->collapsed_faces;
+      chart->collapsed_faces = f;
+    }
+    else {
+      f->nextlink = chart->faces;
+      chart->faces = f;
+      chart->nfaces++;
+    }
+  }
+}
+
+static void p_chart_post_split_flush(PChart *chart)
+{
+  /* Move from `collapsed_*`. */
+
+  PVert *v, *nextv = NULL;
+  PEdge *e, *nexte = NULL;
+  PFace *f, *nextf = NULL;
+
+  for (v = chart->collapsed_verts; v; v = nextv) {
+    nextv = v->nextlink;
+    v->nextlink = chart->verts;
+    chart->verts = v;
+    chart->nverts++;
+  }
+
+  for (e = chart->collapsed_edges; e; e = nexte) {
+    nexte = e->nextlink;
+    e->nextlink = chart->edges;
+    chart->edges = e;
+    chart->nedges++;
+  }
+
+  for (f = chart->collapsed_faces; f; f = nextf) {
+    nextf = f->nextlink;
+    f->nextlink = chart->faces;
+    chart->faces = f;
+    chart->nfaces++;
+  }
+
+  chart->collapsed_verts = NULL;
+  chart->collapsed_edges = NULL;
+  chart->collapsed_faces = NULL;
+}
+
+static void p_chart_simplify_compute(PChart *chart)
+{
+  /* Computes a list of edge collapses / vertex splits. The collapsed
+   * simplices go in the `chart->collapsed_*` lists, The original and
+   * collapsed may then be view as stacks, where the next collapse/split
+   * is at the top of the respective lists. */
+
+  Heap *heap = BLI_heap_new();
+  PVert *v, **wheelverts;
+  PEdge *collapsededges = NULL, *e;
+  int nwheelverts, i, ncollapsed = 0;
+
+  wheelverts = MEM_mallocN(sizeof(PVert *) * chart->nverts, "PChartWheelVerts");
+
+  /* insert all potential collapses into heap */
+  for (v = chart->verts; v; v = v->nextlink) {
+    float cost;
+    PEdge *e = NULL;
+
+    p_collapse_cost_vertex(v, &cost, &e);
+
+    if (e) {
+      v->u.heaplink = BLI_heap_insert(heap, cost, e);
+    }
+    else {
+      v->u.heaplink = NULL;
+    }
+  }
+
+  for (e = chart->edges; e; e = e->nextlink) {
+    e->u.nextcollapse = NULL;
+  }
+
+  /* pop edge collapse out of heap one by one */
+  while (!BLI_heap_is_empty(heap)) {
+    if (ncollapsed == NCOLLAPSE) {
+      break;
+    }
+
+    HeapNode *link = BLI_heap_top(heap);
+    PEdge *edge = (PEdge *)BLI_heap_pop_min(heap), *pair = edge->pair;
+    PVert *oldv, *keepv;
+    PEdge *wheele, *nexte;
+
+    /* remember the edges we collapsed */
+    edge->u.nextcollapse = collapsededges;
+    collapsededges = edge;
+
+    if (edge->vert->u.heaplink != link) {
+      edge->flag |= (PEDGE_COLLAPSE_EDGE | PEDGE_COLLAPSE_PAIR);
+      edge->next->vert->u.heaplink = NULL;
+      SWAP(PEdge *, edge, pair);
+    }
+    else {
+      edge->flag |= PEDGE_COLLAPSE_EDGE;
+      edge->vert->u.heaplink = NULL;
+    }
+
+    p_collapsing_verts(edge, pair, &oldv, &keepv);
+
+    /* gather all wheel verts and remember them before collapse */
+    nwheelverts = 0;
+    wheele = oldv->edge;
+
+    do {
+      wheelverts[nwheelverts++] = wheele->next->vert;
+      nexte = p_wheel_edge_next(wheele);
+
+      if (nexte == NULL) {
+        wheelverts[nwheelverts++] = wheele->next->next->vert;
+      }
+
+      wheele = nexte;
+    } while (wheele && (wheele != oldv->edge));
+
+    /* collapse */
+    p_collapse_edge(edge, pair);
+
+    for (i = 0; i < nwheelverts; i++) {
+      float cost;
+      PEdge *collapse = NULL;
+
+      v = wheelverts[i];
+
+      if (v->u.heaplink) {
+        BLI_heap_remove(heap, v->u.heaplink);
+        v->u.heaplink = NULL;
+      }
+
+      p_collapse_cost_vertex(v, &cost, &collapse);
+
+      if (collapse) {
+        v->u.heaplink = BLI_heap_insert(heap, cost, collapse);
+      }
+    }
+
+    ncollapsed++;
+  }
+
+  MEM_freeN(wheelverts);
+  BLI_heap_free(heap, NULL);
+
+  p_chart_post_collapse_flush(chart, collapsededges);
+}
+
+static void p_chart_complexify(PChart *chart)
+{
+  PEdge *e, *pair, *edge;
+  PVert *newv, *keepv;
+  int x = 0;
+
+  for (e = chart->collapsed_edges; e; e = e->nextlink) {
+    if (!(e->flag & PEDGE_COLLAPSE_EDGE)) {
+      break;
+    }
+
+    edge = e;
+    pair = e->pair;
+
+    if (edge->flag & PEDGE_COLLAPSE_PAIR) {
+      SWAP(PEdge *, edge, pair);
+    }
+
+    p_split_vertex(edge, pair);
+    p_collapsing_verts(edge, pair, &newv, &keepv);
+
+    if (x >= NCOLLAPSEX) {
+      newv->uv[0] = keepv->uv[0];
+      newv->uv[1] = keepv->uv[1];
+    }
+    else {
+      p_vert_harmonic_insert(newv);
+      x++;
+    }
+  }
+
+  p_chart_post_split_flush(chart);
+}
+
+#  if 0
+static void p_chart_simplify(PChart *chart)
+{
+  /* Not implemented, needs proper reordering in split_flush. */
+}
+#  endif
+#endif
+
+/* ABF */
+
+#define ABF_MAX_ITER 20
+
+typedef struct PAbfSystem {
+  int ninterior, nfaces, nangles;
+  float *alpha, *beta, *sine, *cosine, *weight;
+  float *bAlpha, *bTriangle, *bInterior;
+  float *lambdaTriangle, *lambdaPlanar, *lambdaLength;
+  float (*J2dt)[3], *bstar, *dstar;
+  float minangle, maxangle;
+} PAbfSystem;
+
+static void p_abf_setup_system(PAbfSystem *sys)
+{
+  int i;
+
+  sys->alpha = (float *)MEM_mallocN(sizeof(float) * sys->nangles, "ABFalpha");
+  sys->beta = (float *)MEM_mallocN(sizeof(float) * sys->nangles, "ABFbeta");
+  sys->sine = (float *)MEM_mallocN(sizeof(float) * sys->nangles, "ABFsine");
+  sys->cosine = (float *)MEM_mallocN(sizeof(float) * sys->nangles, "ABFcosine");
+  sys->weight = (float *)MEM_mallocN(sizeof(float) * sys->nangles, "ABFweight");
+
+  sys->bAlpha = (float *)MEM_mallocN(sizeof(float) * sys->nangles, "ABFbalpha");
+  sys->bTriangle = (float *)MEM_mallocN(sizeof(float) * sys->nfaces, "ABFbtriangle");
+  sys->bInterior = (float *)MEM_mallocN(sizeof(float[2]) * sys->ninterior, "ABFbinterior");
+
+  sys->lambdaTriangle = (float *)MEM_callocN(sizeof(float) * sys->nfaces, "ABFlambdatri");
+  sys->lambdaPlanar = (float *)MEM_callocN(sizeof(float) * sys->ninterior, "ABFlamdaplane");
+  sys->lambdaLength = (float *)MEM_mallocN(sizeof(float) * sys->ninterior, "ABFlambdalen");
+
+  sys->J2dt = static_cast<float(*)[3]>(MEM_mallocN(sizeof(float) * sys->nangles * 3, "ABFj2dt"));
+  sys->bstar = (float *)MEM_mallocN(sizeof(float) * sys->nfaces, "ABFbstar");
+  sys->dstar = (float *)MEM_mallocN(sizeof(float) * sys->nfaces, "ABFdstar");
+
+  for (i = 0; i < sys->ninterior; i++) {
+    sys->lambdaLength[i] = 1.0;
+  }
+
+  sys->minangle = 1.0 * M_PI / 180.0;
+  sys->maxangle = (float)M_PI - sys->minangle;
+}
+
+static void p_abf_free_system(PAbfSystem *sys)
+{
+  MEM_freeN(sys->alpha);
+  MEM_freeN(sys->beta);
+  MEM_freeN(sys->sine);
+  MEM_freeN(sys->cosine);
+  MEM_freeN(sys->weight);
+  MEM_freeN(sys->bAlpha);
+  MEM_freeN(sys->bTriangle);
+  MEM_freeN(sys->bInterior);
+  MEM_freeN(sys->lambdaTriangle);
+  MEM_freeN(sys->lambdaPlanar);
+  MEM_freeN(sys->lambdaLength);
+  MEM_freeN(sys->J2dt);
+  MEM_freeN(sys->bstar);
+  MEM_freeN(sys->dstar);
+}
+
+static void p_abf_compute_sines(PAbfSystem *sys)
+{
+  int i;
+  float *sine = sys->sine, *cosine = sys->cosine, *alpha = sys->alpha;
+
+  for (i = 0; i < sys->nangles; i++, sine++, cosine++, alpha++) {
+    *sine = sinf(*alpha);
+    *cosine = cosf(*alpha);
+  }
+}
+
+static float p_abf_compute_sin_product(PAbfSystem *sys, PVert *v, int aid)
+{
+  PEdge *e, *e1, *e2;
+  float sin1, sin2;
+
+  sin1 = sin2 = 1.0;
+
+  e = v->edge;
+  do {
+    e1 = e->next;
+    e2 = e->next->next;
+
+    if (aid == e1->u.id) {
+      /* we are computing a derivative for this angle,
+       * so we use cos and drop the other part */
+      sin1 *= sys->cosine[e1->u.id];
+      sin2 = 0.0;
+    }
+    else {
+      sin1 *= sys->sine[e1->u.id];
+    }
+
+    if (aid == e2->u.id) {
+      /* see above */
+      sin1 = 0.0;
+      sin2 *= sys->cosine[e2->u.id];
+    }
+    else {
+      sin2 *= sys->sine[e2->u.id];
+    }
+
+    e = e->next->next->pair;
+  } while (e && (e != v->edge));
+
+  return (sin1 - sin2);
+}
+
+static float p_abf_compute_grad_alpha(PAbfSystem *sys, PFace *f, PEdge *e)
+{
+  PVert *v = e->vert, *v1 = e->next->vert, *v2 = e->next->next->vert;
+  float deriv;
+
+  deriv = (sys->alpha[e->u.id] - sys->beta[e->u.id]) * sys->weight[e->u.id];
+  deriv += sys->lambdaTriangle[f->u.id];
+
+  if (v->flag & PVERT_INTERIOR) {
+    deriv += sys->lambdaPlanar[v->u.id];
+  }
+
+  if (v1->flag & PVERT_INTERIOR) {
+    float product = p_abf_compute_sin_product(sys, v1, e->u.id);
+    deriv += sys->lambdaLength[v1->u.id] * product;
+  }
+
+  if (v2->flag & PVERT_INTERIOR) {
+    float product = p_abf_compute_sin_product(sys, v2, e->u.id);
+    deriv += sys->lambdaLength[v2->u.id] * product;
+  }
+
+  return deriv;
+}
+
+static float p_abf_compute_gradient(PAbfSystem *sys, PChart *chart)
+{
+  PFace *f;
+  PEdge *e;
+  PVert *v;
+  float norm = 0.0;
+
+  for (f = chart->faces; f; f = f->nextlink) {
+    PEdge *e1 = f->edge, *e2 = e1->next, *e3 = e2->next;
+    float gtriangle, galpha1, galpha2, galpha3;
+
+    galpha1 = p_abf_compute_grad_alpha(sys, f, e1);
+    galpha2 = p_abf_compute_grad_alpha(sys, f, e2);
+    galpha3 = p_abf_compute_grad_alpha(sys, f, e3);
+
+    sys->bAlpha[e1->u.id] = -galpha1;
+    sys->bAlpha[e2->u.id] = -galpha2;
+    sys->bAlpha[e3->u.id] = -galpha3;
+
+    norm += galpha1 * galpha1 + galpha2 * galpha2 + galpha3 * galpha3;
+
+    gtriangle = sys->alpha[e1->u.id] + sys->alpha[e2->u.id] + sys->alpha[e3->u.id] - (float)M_PI;
+    sys->bTriangle[f->u.id] = -gtriangle;
+    norm += gtriangle * gtriangle;
+  }
+
+  for (v = chart->verts; v; v = v->nextlink) {
+    if (v->flag & PVERT_INTERIOR) {
+      float gplanar = -2 * M_PI, glength;
+
+      e = v->edge;
+      do {
+        gplanar += sys->alpha[e->u.id];
+        e = e->next->next->pair;
+      } while (e && (e != v->edge));
+
+      sys->bInterior[v->u.id] = -gplanar;
+      norm += gplanar * gplanar;
+
+      glength = p_abf_compute_sin_product(sys, v, -1);
+      sys->bInterior[sys->ninterior + v->u.id] = -glength;
+      norm += glength * glength;
+    }
+  }
+
+  return norm;
+}
+
+static bool p_abf_matrix_invert(PAbfSystem *sys, PChart *chart)
+{
+  int ninterior = sys->ninterior;
+  int nvar = 2 * ninterior;
+  LinearSolver *context = EIG_linear_solver_new(0, nvar, 1);
+
+  for (int i = 0; i < nvar; i++) {
+    EIG_linear_solver_right_hand_side_add(context, 0, i, sys->bInterior[i]);
+  }
+
+  for (PFace *f = chart->faces; f; f = f->nextlink) {
+    float wi1, wi2, wi3, b, si, beta[3], j2[3][3], W[3][3];
+    float row1[6], row2[6], row3[6];
+    int vid[6];
+    PEdge *e1 = f->edge, *e2 = e1->next, *e3 = e2->next;
+    PVert *v1 = e1->vert, *v2 = e2->vert, *v3 = e3->vert;
+
+    wi1 = 1.0f / sys->weight[e1->u.id];
+    wi2 = 1.0f / sys->weight[e2->u.id];
+    wi3 = 1.0f / sys->weight[e3->u.id];
+
+    /* bstar1 = (J1*dInv*bAlpha - bTriangle) */
+    b = sys->bAlpha[e1->u.id] * wi1;
+    b += sys->bAlpha[e2->u.id] * wi2;
+    b += sys->bAlpha[e3->u.id] * wi3;
+    b -= sys->bTriangle[f->u.id];
+
+    /* si = J1*d*J1t */
+    si = 1.0f / (wi1 + wi2 + wi3);
+
+    /* J1t*si*bstar1 - bAlpha */
+    beta[0] = b * si - sys->bAlpha[e1->u.id];
+    beta[1] = b * si - sys->bAlpha[e2->u.id];
+    beta[2] = b * si - sys->bAlpha[e3->u.id];
+
+    /* use this later for computing other lambda's */
+    sys->bstar[f->u.id] = b;
+    sys->dstar[f->u.id] = si;
+
+    /* set matrix */
+    W[0][0] = si - sys->weight[e1->u.id];
+    W[0][1] = si;
+    W[0][2] = si;
+    W[1][0] = si;
+    W[1][1] = si - sys->weight[e2->u.id];
+    W[1][2] = si;
+    W[2][0] = si;
+    W[2][1] = si;
+    W[2][2] = si - sys->weight[e3->u.id];
+
+    vid[0] = vid[1] = vid[2] = vid[3] = vid[4] = vid[5] = -1;
+
+    if (v1->flag & PVERT_INTERIOR) {
+      vid[0] = v1->u.id;
+      vid[3] = ninterior + v1->u.id;
+
+      sys->J2dt[e1->u.id][0] = j2[0][0] = 1.0f * wi1;
+      sys->J2dt[e2->u.id][0] = j2[1][0] = p_abf_compute_sin_product(sys, v1, e2->u.id) * wi2;
+      sys->J2dt[e3->u.id][0] = j2[2][0] = p_abf_compute_sin_product(sys, v1, e3->u.id) * wi3;
+
+      EIG_linear_solver_right_hand_side_add(context, 0, v1->u.id, j2[0][0] * beta[0]);
+      EIG_linear_solver_right_hand_side_add(
+          context, 0, ninterior + v1->u.id, j2[1][0] * beta[1] + j2[2][0] * beta[2]);
+
+      row1[0] = j2[0][0] * W[0][0];
+      row2[0] = j2[0][0] * W[1][0];
+      row3[0] = j2[0][0] * W[2][0];
+
+      row1[3] = j2[1][0] * W[0][1] + j2[2][0] * W[0][2];
+      row2[3] = j2[1][0] * W[1][1] + j2[2][0] * W[1][2];
+      row3[3] = j2[1][0] * W[2][1] + j2[2][0] * W[2][2];
+    }
+
+    if (v2->flag & PVERT_INTERIOR) {
+      vid[1] = v2->u.id;
+      vid[4] = ninterior + v2->u.id;
+
+      sys->J2dt[e1->u.id][1] = j2[0][1] = p_abf_compute_sin_product(sys, v2, e1->u.id) * wi1;
+      sys->J2dt[e2->u.id][1] = j2[1][1] = 1.0f * wi2;
+      sys->J2dt[e3->u.id][1] = j2[2][1] = p_abf_compute_sin_product(sys, v2, e3->u.id) * wi3;
+
+      EIG_linear_solver_right_hand_side_add(context, 0, v2->u.id, j2[1][1] * beta[1]);
+      EIG_linear_solver_right_hand_side_add(
+          context, 0, ninterior + v2->u.id, j2[0][1] * beta[0] + j2[2][1] * beta[2]);
+
+      row1[1] = j2[1][1] * W[0][1];
+      row2[1] = j2[1][1] * W[1][1];
+      row3[1] = j2[1][1] * W[2][1];
+
+      row1[4] = j2[0][1] * W[0][0] + j2[2][1] * W[0][2];
+      row2[4] = j2[0][1] * W[1][0] + j2[2][1] * W[1][2];
+      row3[4] = j2[0][1] * W[2][0] + j2[2][1] * W[2][2];
+    }
+
+    if (v3->flag & PVERT_INTERIOR) {
+      vid[2] = v3->u.id;
+      vid[5] = ninterior + v3->u.id;
+
+      sys->J2dt[e1->u.id][2] = j2[0][2] = p_abf_compute_sin_product(sys, v3, e1->u.id) * wi1;
+      sys->J2dt[e2->u.id][2] = j2[1][2] = p_abf_compute_sin_product(sys, v3, e2->u.id) * wi2;
+      sys->J2dt[e3->u.id][2] = j2[2][2] = 1.0f * wi3;
+
+      EIG_linear_solver_right_hand_side_add(context, 0, v3->u.id, j2[2][2] * beta[2]);
+      EIG_linear_solver_right_hand_side_add(
+          context, 0, ninterior + v3->u.id, j2[0][2] * beta[0] + j2[1][2] * beta[1]);
+
+      row1[2] = j2[2][2] * W[0][2];
+      row2[2] = j2[2][2] * W[1][2];
+      row3[2] = j2[2][2] * W[2][2];
+
+      row1[5] = j2[0][2] * W[0][0] + j2[1][2] * W[0][1];
+      row2[5] = j2[0][2] * W[1][0] + j2[1][2] * W[1][1];
+      row3[5] = j2[0][2] * W[2][0] + j2[1][2] * W[2][1];
+    }
+
+    for (int i = 0; i < 3; i++) {
+      int r = vid[i];
+
+      if (r == -1) {
+        continue;
+      }
+
+      for (int j = 0; j < 6; j++) {
+        int c = vid[j];
+
+        if (c == -1) {
+          continue;
+        }
+
+        if (i == 0) {
+          EIG_linear_solver_matrix_add(context, r, c, j2[0][i] * row1[j]);
+        }
+        else {
+          EIG_linear_solver_matrix_add(context, r + ninterior, c, j2[0][i] * row1[j]);
+        }
+
+        if (i == 1) {
+          EIG_linear_solver_matrix_add(context, r, c, j2[1][i] * row2[j]);
+        }
+        else {
+          EIG_linear_solver_matrix_add(context, r + ninterior, c, j2[1][i] * row2[j]);
+        }
+
+        if (i == 2) {
+          EIG_linear_solver_matrix_add(context, r, c, j2[2][i] * row3[j]);
+        }
+        else {
+          EIG_linear_solver_matrix_add(context, r + ninterior, c, j2[2][i] * row3[j]);
+        }
+      }
+    }
+  }
+
+  bool success = EIG_linear_solver_solve(context);
+
+  if (success) {
+    for (PFace *f = chart->faces; f; f = f->nextlink) {
+      float dlambda1, pre[3], dalpha;
+      PEdge *e1 = f->edge, *e2 = e1->next, *e3 = e2->next;
+      PVert *v1 = e1->vert, *v2 = e2->vert, *v3 = e3->vert;
+
+      pre[0] = pre[1] = pre[2] = 0.0;
+
+      if (v1->flag & PVERT_INTERIOR) {
+        float x = EIG_linear_solver_variable_get(context, 0, v1->u.id);
+        float x2 = EIG_linear_solver_variable_get(context, 0, ninterior + v1->u.id);
+        pre[0] += sys->J2dt[e1->u.id][0] * x;
+        pre[1] += sys->J2dt[e2->u.id][0] * x2;
+        pre[2] += sys->J2dt[e3->u.id][0] * x2;
+      }
+
+      if (v2->flag & PVERT_INTERIOR) {
+        float x = EIG_linear_solver_variable_get(context, 0, v2->u.id);
+        float x2 = EIG_linear_solver_variable_get(context, 0, ninterior + v2->u.id);
+        pre[0] += sys->J2dt[e1->u.id][1] * x2;
+        pre[1] += sys->J2dt[e2->u.id][1] * x;
+        pre[2] += sys->J2dt[e3->u.id][1] * x2;
+      }
+
+      if (v3->flag & PVERT_INTERIOR) {
+        float x = EIG_linear_solver_variable_get(context, 0, v3->u.id);
+        float x2 = EIG_linear_solver_variable_get(context, 0, ninterior + v3->u.id);
+        pre[0] += sys->J2dt[e1->u.id][2] * x2;
+        pre[1] += sys->J2dt[e2->u.id][2] * x2;
+        pre[2] += sys->J2dt[e3->u.id][2] * x;
+      }
+
+      dlambda1 = pre[0] + pre[1] + pre[2];
+      dlambda1 = sys->dstar[f->u.id] * (sys->bstar[f->u.id] - dlambda1);
+
+      sys->lambdaTriangle[f->u.id] += dlambda1;
+
+      dalpha = (sys->bAlpha[e1->u.id] - dlambda1);
+      sys->alpha[e1->u.id] += dalpha / sys->weight[e1->u.id] - pre[0];
+
+      dalpha = (sys->bAlpha[e2->u.id] - dlambda1);
+      sys->alpha[e2->u.id] += dalpha / sys->weight[e2->u.id] - pre[1];
+
+      dalpha = (sys->bAlpha[e3->u.id] - dlambda1);
+      sys->alpha[e3->u.id] += dalpha / sys->weight[e3->u.id] - pre[2];
+
+      /* clamp */
+      PEdge *e = f->edge;
+      do {
+        if (sys->alpha[e->u.id] > (float)M_PI) {
+          sys->alpha[e->u.id] = (float)M_PI;
+        }
+        else if (sys->alpha[e->u.id] < 0.0f) {
+          sys->alpha[e->u.id] = 0.0f;
+        }
+      } while (e != f->edge);
+    }
+
+    for (int i = 0; i < ninterior; i++) {
+      sys->lambdaPlanar[i] += (float)EIG_linear_solver_variable_get(context, 0, i);
+      sys->lambdaLength[i] += (float)EIG_linear_solver_variable_get(context, 0, ninterior + i);
+    }
+  }
+
+  EIG_linear_solver_delete(context);
+
+  return success;
+}
+
+static bool p_chart_abf_solve(PChart *chart)
+{
+  PVert *v;
+  PFace *f;
+  PEdge *e, *e1, *e2, *e3;
+  PAbfSystem sys;
+  int i;
+  float /* lastnorm, */ /* UNUSED */ limit = (chart->nfaces > 100) ? 1.0f : 0.001f;
+
+  /* setup id's */
+  sys.ninterior = sys.nfaces = sys.nangles = 0;
+
+  for (v = chart->verts; v; v = v->nextlink) {
+    if (p_vert_interior(v)) {
+      v->flag |= PVERT_INTERIOR;
+      v->u.id = sys.ninterior++;
+    }
+    else {
+      v->flag &= ~PVERT_INTERIOR;
+    }
+  }
+
+  for (f = chart->faces; f; f = f->nextlink) {
+    e1 = f->edge;
+    e2 = e1->next;
+    e3 = e2->next;
+    f->u.id = sys.nfaces++;
+
+    /* angle id's are conveniently stored in half edges */
+    e1->u.id = sys.nangles++;
+    e2->u.id = sys.nangles++;
+    e3->u.id = sys.nangles++;
+  }
+
+  p_abf_setup_system(&sys);
+
+  /* compute initial angles */
+  for (f = chart->faces; f; f = f->nextlink) {
+    float a1, a2, a3;
+
+    e1 = f->edge;
+    e2 = e1->next;
+    e3 = e2->next;
+    p_face_angles(f, &a1, &a2, &a3);
+
+    if (a1 < sys.minangle) {
+      a1 = sys.minangle;
+    }
+    else if (a1 > sys.maxangle) {
+      a1 = sys.maxangle;
+    }
+    if (a2 < sys.minangle) {
+      a2 = sys.minangle;
+    }
+    else if (a2 > sys.maxangle) {
+      a2 = sys.maxangle;
+    }
+    if (a3 < sys.minangle) {
+      a3 = sys.minangle;
+    }
+    else if (a3 > sys.maxangle) {
+      a3 = sys.maxangle;
+    }
+
+    sys.alpha[e1->u.id] = sys.beta[e1->u.id] = a1;
+    sys.alpha[e2->u.id] = sys.beta[e2->u.id] = a2;
+    sys.alpha[e3->u.id] = sys.beta[e3->u.id] = a3;
+
+    sys.weight[e1->u.id] = 2.0f / (a1 * a1);
+    sys.weight[e2->u.id] = 2.0f / (a2 * a2);
+    sys.weight[e3->u.id] = 2.0f / (a3 * a3);
+  }
+
+  for (v = chart->verts; v; v = v->nextlink) {
+    if (v->flag & PVERT_INTERIOR) {
+      float anglesum = 0.0, scale;
+
+      e = v->edge;
+      do {
+        anglesum += sys.beta[e->u.id];
+        e = e->next->next->pair;
+      } while (e && (e != v->edge));
+
+      scale = (anglesum == 0.0f) ? 0.0f : 2.0f * (float)M_PI / anglesum;
+
+      e = v->edge;
+      do {
+        sys.beta[e->u.id] = sys.alpha[e->u.id] = sys.beta[e->u.id] * scale;
+        e = e->next->next->pair;
+      } while (e && (e != v->edge));
+    }
+  }
+
+  if (sys.ninterior > 0) {
+    p_abf_compute_sines(&sys);
+
+    /* iteration */
+    /* lastnorm = 1e10; */ /* UNUSED */
+
+    for (i = 0; i < ABF_MAX_ITER; i++) {
+      float norm = p_abf_compute_gradient(&sys, chart);
+
+      /* lastnorm = norm; */ /* UNUSED */
+
+      if (norm < limit) {
+        break;
+      }
+
+      if (!p_abf_matrix_invert(&sys, chart)) {
+        param_warning("ABF failed to invert matrix");
+        p_abf_free_system(&sys);
+        return false;
+      }
+
+      p_abf_compute_sines(&sys);
+    }
+
+    if (i == ABF_MAX_ITER) {
+      param_warning("ABF maximum iterations reached");
+      p_abf_free_system(&sys);
+      return false;
+    }
+  }
+
+  chart->u.lscm.abf_alpha = (float *)MEM_dupallocN(sys.alpha);
+  p_abf_free_system(&sys);
+
+  return true;
+}
+
+/* Least Squares Conformal Maps */
+
+static void p_chart_pin_positions(PChart *chart, PVert **pin1, PVert **pin2)
+{
+  if (!*pin1 || !*pin2 || *pin1 == *pin2) {
+    /* degenerate case */
+    PFace *f = chart->faces;
+    *pin1 = f->edge->vert;
+    *pin2 = f->edge->next->vert;
+
+    (*pin1)->uv[0] = 0.0f;
+    (*pin1)->uv[1] = 0.5f;
+    (*pin2)->uv[0] = 1.0f;
+    (*pin2)->uv[1] = 0.5f;
+  }
+  else {
+    int diru, dirv, dirx, diry;
+    float sub[3];
+
+    sub_v3_v3v3(sub, (*pin1)->co, (*pin2)->co);
+    sub[0] = fabsf(sub[0]);
+    sub[1] = fabsf(sub[1]);
+    sub[2] = fabsf(sub[2]);
+
+    if ((sub[0] > sub[1]) && (sub[0] > sub[2])) {
+      dirx = 0;
+      diry = (sub[1] > sub[2]) ? 1 : 2;
+    }
+    else if ((sub[1] > sub[0]) && (sub[1] > sub[2])) {
+      dirx = 1;
+      diry = (sub[0] > sub[2]) ? 0 : 2;
+    }
+    else {
+      dirx = 2;
+      diry = (sub[0] > sub[1]) ? 0 : 1;
+    }
+
+    if (dirx == 2) {
+      diru = 1;
+      dirv = 0;
+    }
+    else {
+      diru = 0;
+      dirv = 1;
+    }
+
+    (*pin1)->uv[diru] = (*pin1)->co[dirx];
+    (*pin1)->uv[dirv] = (*pin1)->co[diry];
+    (*pin2)->uv[diru] = (*pin2)->co[dirx];
+    (*pin2)->uv[dirv] = (*pin2)->co[diry];
+  }
+}
+
+static bool p_chart_symmetry_pins(PChart *chart, PEdge *outer, PVert **pin1, PVert **pin2)
+{
+  PEdge *be, *lastbe = NULL, *maxe1 = NULL, *maxe2 = NULL, *be1, *be2;
+  PEdge *cure = NULL, *firste1 = NULL, *firste2 = NULL, *nextbe;
+  float maxlen = 0.0f, curlen = 0.0f, totlen = 0.0f, firstlen = 0.0f;
+  float len1, len2;
+
+  /* find longest series of verts split in the chart itself, these are
+   * marked during construction */
+  be = outer;
+  lastbe = p_boundary_edge_prev(be);
+  do {
+    float len = p_edge_length(be);
+    totlen += len;
+
+    nextbe = p_boundary_edge_next(be);
+
+    if ((be->vert->flag & PVERT_SPLIT) ||
+        (lastbe->vert->flag & nextbe->vert->flag & PVERT_SPLIT)) {
+      if (!cure) {
+        if (be == outer) {
+          firste1 = be;
+        }
+        cure = be;
+      }
+      else {
+        curlen += p_edge_length(lastbe);
+      }
+    }
+    else if (cure) {
+      if (curlen > maxlen) {
+        maxlen = curlen;
+        maxe1 = cure;
+        maxe2 = lastbe;
+      }
+
+      if (firste1 == cure) {
+        firstlen = curlen;
+        firste2 = lastbe;
+      }
+
+      curlen = 0.0f;
+      cure = NULL;
+    }
+
+    lastbe = be;
+    be = nextbe;
+  } while (be != outer);
+
+  /* make sure we also count a series of splits over the starting point */
+  if (cure && (cure != outer)) {
+    firstlen += curlen + p_edge_length(be);
+
+    if (firstlen > maxlen) {
+      maxlen = firstlen;
+      maxe1 = cure;
+      maxe2 = firste2;
+    }
+  }
+
+  if (!maxe1 || !maxe2 || (maxlen < 0.5f * totlen)) {
+    return false;
+  }
+
+  /* find pin1 in the split vertices */
+  be1 = maxe1;
+  be2 = maxe2;
+  len1 = 0.0f;
+  len2 = 0.0f;
+
+  do {
+    if (len1 < len2) {
+      len1 += p_edge_length(be1);
+      be1 = p_boundary_edge_next(be1);
+    }
+    else {
+      be2 = p_boundary_edge_prev(be2);
+      len2 += p_edge_length(be2);
+    }
+  } while (be1 != be2);
+
+  *pin1 = be1->vert;
+
+  /* find pin2 outside the split vertices */
+  be1 = maxe1;
+  be2 = maxe2;
+  len1 = 0.0f;
+  len2 = 0.0f;
+
+  do {
+    if (len1 < len2) {
+      be1 = p_boundary_edge_prev(be1);
+      len1 += p_edge_length(be1);
+    }
+    else {
+      len2 += p_edge_length(be2);
+      be2 = p_boundary_edge_next(be2);
+    }
+  } while (be1 != be2);
+
+  *pin2 = be1->vert;
+
+  p_chart_pin_positions(chart, pin1, pin2);
+
+  return !equals_v3v3((*pin1)->co, (*pin2)->co);
+}
+
+static void p_chart_extrema_verts(PChart *chart, PVert **pin1, PVert **pin2)
+{
+  float minv[3], maxv[3], dirlen;
+  PVert *v, *minvert[3], *maxvert[3];
+  int i, dir;
+
+  /* find minimum and maximum verts over x/y/z axes */
+  minv[0] = minv[1] = minv[2] = 1e20;
+  maxv[0] = maxv[1] = maxv[2] = -1e20;
+
+  minvert[0] = minvert[1] = minvert[2] = NULL;
+  maxvert[0] = maxvert[1] = maxvert[2] = NULL;
+
+  for (v = chart->verts; v; v = v->nextlink) {
+    for (i = 0; i < 3; i++) {
+      if (v->co[i] < minv[i]) {
+        minv[i] = v->co[i];
+        minvert[i] = v;
+      }
+      if (v->co[i] > maxv[i]) {
+        maxv[i] = v->co[i];
+        maxvert[i] = v;
+      }
+    }
+  }
+
+  /* find axes with longest distance */
+  dir = 0;
+  dirlen = -1.0;
+
+  for (i = 0; i < 3; i++) {
+    if (maxv[i] - minv[i] > dirlen) {
+      dir = i;
+      dirlen = maxv[i] - minv[i];
+    }
+  }
+
+  *pin1 = minvert[dir];
+  *pin2 = maxvert[dir];
+
+  p_chart_pin_positions(chart, pin1, pin2);
+}
+
+static void p_chart_lscm_load_solution(PChart *chart)
+{
+  LinearSolver *context = chart->u.lscm.context;
+  PVert *v;
+
+  for (v = chart->verts; v; v = v->nextlink) {
+    v->uv[0] = EIG_linear_solver_variable_get(context, 0, 2 * v->u.id);
+    v->uv[1] = EIG_linear_solver_variable_get(context, 0, 2 * v->u.id + 1);
+  }
+}
+
+static void p_chart_lscm_begin(PChart *chart, bool live, bool abf)
+{
+  PVert *v, *pin1, *pin2;
+  bool select = false, deselect = false;
+  int npins = 0, id = 0;
+
+  /* give vertices matrix indices and count pins */
+  for (v = chart->verts; v; v = v->nextlink) {
+    if (v->flag & PVERT_PIN) {
+      npins++;
+      if (v->flag & PVERT_SELECT) {
+        select = true;
+      }
+    }
+
+    if (!(v->flag & PVERT_SELECT)) {
+      deselect = true;
+    }
+  }
+
+  if ((live && (!select || !deselect))) {
+    chart->u.lscm.context = NULL;
+  }
+  else {
+#if 0
+    p_chart_simplify_compute(chart);
+    p_chart_topological_sanity_check(chart);
+#endif
+
+    if (npins == 1) {
+      chart->u.lscm.single_pin_area = p_chart_uv_area(chart);
+      for (v = chart->verts; v; v = v->nextlink) {
+        if (v->flag & PVERT_PIN) {
+          chart->u.lscm.single_pin = v;
+          break;
+        }
+      }
+    }
+
+    if (abf) {
+      if (!p_chart_abf_solve(chart)) {
+        param_warning("ABF solving failed: falling back to LSCM.\n");
+      }
+    }
+
+    if (npins <= 1) {
+      /* No pins, let's find some ourself. */
+      PEdge *outer;
+
+      p_chart_boundaries(chart, &outer);
+
+      /* Outer can be NULL with non-finite coords. */
+      if (!(outer && p_chart_symmetry_pins(chart, outer, &pin1, &pin2))) {
+        p_chart_extrema_verts(chart, &pin1, &pin2);
+      }
+
+      chart->u.lscm.pin1 = pin1;
+      chart->u.lscm.pin2 = pin2;
+    }
+
+    for (v = chart->verts; v; v = v->nextlink) {
+      v->u.id = id++;
+    }
+
+    chart->u.lscm.context = EIG_linear_least_squares_solver_new(
+        2 * chart->nfaces, 2 * chart->nverts, 1);
+  }
+}
+
+static bool p_chart_lscm_solve(ParamHandle *handle, PChart *chart)
+{
+  LinearSolver *context = chart->u.lscm.context;
+  PVert *v, *pin1 = chart->u.lscm.pin1, *pin2 = chart->u.lscm.pin2;
+  PFace *f;
+  const float *alpha = chart->u.lscm.abf_alpha;
+  float area_pinned_up, area_pinned_down;
+  bool flip_faces;
+  int row;
+
+#if 0
+  /* TODO: make loading pins work for simplify/complexify. */
+#endif
+
+  for (v = chart->verts; v; v = v->nextlink) {
+    if (v->flag & PVERT_PIN) {
+      p_vert_load_pin_select_uvs(handle, v); /* reload for live */
+    }
+  }
+
+  if (chart->u.lscm.single_pin) {
+    /* If only one pin, save area and pin for transform later. */
+    copy_v2_v2(chart->u.lscm.single_pin_uv, chart->u.lscm.single_pin->uv);
+  }
+
+  if (chart->u.lscm.pin1) {
+    EIG_linear_solver_variable_lock(context, 2 * pin1->u.id);
+    EIG_linear_solver_variable_lock(context, 2 * pin1->u.id + 1);
+    EIG_linear_solver_variable_lock(context, 2 * pin2->u.id);
+    EIG_linear_solver_variable_lock(context, 2 * pin2->u.id + 1);
+
+    EIG_linear_solver_variable_set(context, 0, 2 * pin1->u.id, pin1->uv[0]);
+    EIG_linear_solver_variable_set(context, 0, 2 * pin1->u.id + 1, pin1->uv[1]);
+    EIG_linear_solver_variable_set(context, 0, 2 * pin2->u.id, pin2->uv[0]);
+    EIG_linear_solver_variable_set(context, 0, 2 * pin2->u.id + 1, pin2->uv[1]);
+  }
+  else {
+    /* set and lock the pins */
+    for (v = chart->verts; v; v = v->nextlink) {
+      if (v->flag & PVERT_PIN) {
+        EIG_linear_solver_variable_lock(context, 2 * v->u.id);
+        EIG_linear_solver_variable_lock(context, 2 * v->u.id + 1);
+
+        EIG_linear_solver_variable_set(context, 0, 2 * v->u.id, v->uv[0]);
+        EIG_linear_solver_variable_set(context, 0, 2 * v->u.id + 1, v->uv[1]);
+      }
+    }
+  }
+
+  /* detect up direction based on pinned vertices */
+  area_pinned_up = 0.0f;
+  area_pinned_down = 0.0f;
+
+  for (f = chart->faces; f; f = f->nextlink) {
+    PEdge *e1 = f->edge, *e2 = e1->next, *e3 = e2->next;
+    PVert *v1 = e1->vert, *v2 = e2->vert, *v3 = e3->vert;
+
+    if ((v1->flag & PVERT_PIN) && (v2->flag & PVERT_PIN) && (v3->flag & PVERT_PIN)) {
+      float area = p_face_uv_area_signed(f);
+
+      if (area > 0.0f) {
+        area_pinned_up += area;
+      }
+      else {
+        area_pinned_down -= area;
+      }
+    }
+  }
+
+  flip_faces = (area_pinned_down > area_pinned_up);
+
+  /* construct matrix */
+
+  row = 0;
+  for (f = chart->faces; f; f = f->nextlink) {
+    PEdge *e1 = f->edge, *e2 = e1->next, *e3 = e2->next;
+    PVert *v1 = e1->vert, *v2 = e2->vert, *v3 = e3->vert;
+    float a1, a2, a3, ratio, cosine, sine;
+    float sina1, sina2, sina3, sinmax;
+
+    if (alpha) {
+      /* use abf angles if passed on */
+      a1 = *(alpha++);
+      a2 = *(alpha++);
+      a3 = *(alpha++);
+    }
+    else {
+      p_face_angles(f, &a1, &a2, &a3);
+    }
+
+    if (flip_faces) {
+      SWAP(float, a2, a3);
+      SWAP(PEdge *, e2, e3);
+      SWAP(PVert *, v2, v3);
+    }
+
+    sina1 = sinf(a1);
+    sina2 = sinf(a2);
+    sina3 = sinf(a3);
+
+    sinmax = max_fff(sina1, sina2, sina3);
+
+    /* shift vertices to find most stable order */
+    if (sina3 != sinmax) {
+      SHIFT3(PVert *, v1, v2, v3);
+      SHIFT3(float, a1, a2, a3);
+      SHIFT3(float, sina1, sina2, sina3);
+
+      if (sina2 == sinmax) {
+        SHIFT3(PVert *, v1, v2, v3);
+        SHIFT3(float, a1, a2, a3);
+        SHIFT3(float, sina1, sina2, sina3);
+      }
+    }
+
+    /* angle based lscm formulation */
+    ratio = (sina3 == 0.0f) ? 1.0f : sina2 / sina3;
+    cosine = cosf(a1) * ratio;
+    sine = sina1 * ratio;
+
+    EIG_linear_solver_matrix_add(context, row, 2 * v1->u.id, cosine - 1.0f);
+    EIG_linear_solver_matrix_add(context, row, 2 * v1->u.id + 1, -sine);
+    EIG_linear_solver_matrix_add(context, row, 2 * v2->u.id, -cosine);
+    EIG_linear_solver_matrix_add(context, row, 2 * v2->u.id + 1, sine);
+    EIG_linear_solver_matrix_add(context, row, 2 * v3->u.id, 1.0);
+    row++;
+
+    EIG_linear_solver_matrix_add(context, row, 2 * v1->u.id, sine);
+    EIG_linear_solver_matrix_add(context, row, 2 * v1->u.id + 1, cosine - 1.0f);
+    EIG_linear_solver_matrix_add(context, row, 2 * v2->u.id, -sine);
+    EIG_linear_solver_matrix_add(context, row, 2 * v2->u.id + 1, -cosine);
+    EIG_linear_solver_matrix_add(context, row, 2 * v3->u.id + 1, 1.0);
+    row++;
+  }
+
+  if (EIG_linear_solver_solve(context)) {
+    p_chart_lscm_load_solution(chart);
+    return true;
+  }
+
+  for (v = chart->verts; v; v = v->nextlink) {
+    v->uv[0] = 0.0f;
+    v->uv[1] = 0.0f;
+  }
+
+  return false;
+}
+
+static void p_chart_lscm_transform_single_pin(PChart *chart)
+{
+  PVert *pin = chart->u.lscm.single_pin;
+
+  /* If only one pin, keep UV area the same. */
+  const float new_area = p_chart_uv_area(chart);
+  if (new_area > 0.0f) {
+    const float scale = chart->u.lscm.single_pin_area / new_area;
+    if (scale > 0.0f) {
+      p_chart_uv_scale(chart, sqrtf(scale));
+    }
+  }
+
+  /* Translate to keep the pinned vertex in place. */
+  float offset[2];
+  sub_v2_v2v2(offset, chart->u.lscm.single_pin_uv, pin->uv);
+  p_chart_uv_translate(chart, offset);
+}
+
+static void p_chart_lscm_end(PChart *chart)
+{
+  EIG_linear_solver_delete(chart->u.lscm.context);
+  chart->u.lscm.context = NULL;
+
+  MEM_SAFE_FREE(chart->u.lscm.abf_alpha);
+
+  chart->u.lscm.pin1 = NULL;
+  chart->u.lscm.pin2 = NULL;
+  chart->u.lscm.single_pin = NULL;
+  chart->u.lscm.single_pin_area = 0.0f;
+}
+
+/* Stretch */
+
+#define P_STRETCH_ITER 20
+
+static void p_stretch_pin_boundary(PChart *chart)
+{
+  PVert *v;
+
+  for (v = chart->verts; v; v = v->nextlink) {
+    if (v->edge->pair == NULL) {
+      v->flag |= PVERT_PIN;
+    }
+    else {
+      v->flag &= ~PVERT_PIN;
+    }
+  }
+}
+
+static float p_face_stretch(PFace *f)
+{
+  float T, w, tmp[3];
+  float Ps[3], Pt[3];
+  float a, c, area;
+  PEdge *e1 = f->edge, *e2 = e1->next, *e3 = e2->next;
+  PVert *v1 = e1->vert, *v2 = e2->vert, *v3 = e3->vert;
+
+  area = p_face_uv_area_signed(f);
+
+  if (area <= 0.0f) {
+    /* When a face is flipped, provide a large penalty.
+     * Add on a slight gradient to unflip the face, see also: T99781. */
+    return 1e8f * (1.0f + p_edge_uv_length(e1) + p_edge_uv_length(e2) + p_edge_uv_length(e3));
+  }
+
+  w = 1.0f / (2.0f * area);
+
+  /* compute derivatives */
+  copy_v3_v3(Ps, v1->co);
+  mul_v3_fl(Ps, (v2->uv[1] - v3->uv[1]));
+
+  copy_v3_v3(tmp, v2->co);
+  mul_v3_fl(tmp, (v3->uv[1] - v1->uv[1]));
+  add_v3_v3(Ps, tmp);
+
+  copy_v3_v3(tmp, v3->co);
+  mul_v3_fl(tmp, (v1->uv[1] - v2->uv[1]));
+  add_v3_v3(Ps, tmp);
+
+  mul_v3_fl(Ps, w);
+
+  copy_v3_v3(Pt, v1->co);
+  mul_v3_fl(Pt, (v3->uv[0] - v2->uv[0]));
+
+  copy_v3_v3(tmp, v2->co);
+  mul_v3_fl(tmp, (v1->uv[0] - v3->uv[0]));
+  add_v3_v3(Pt, tmp);
+
+  copy_v3_v3(tmp, v3->co);
+  mul_v3_fl(tmp, (v2->uv[0] - v1->uv[0]));
+  add_v3_v3(Pt, tmp);
+
+  mul_v3_fl(Pt, w);
+
+  /* Sander Tensor */
+  a = dot_v3v3(Ps, Ps);
+  c = dot_v3v3(Pt, Pt);
+
+  T = sqrtf(0.5f * (a + c));
+  if (f->flag & PFACE_FILLED) {
+    T *= 0.2f;
+  }
+
+  return T;
+}
+
+static float p_stretch_compute_vertex(PVert *v)
+{
+  PEdge *e = v->edge;
+  float sum = 0.0f;
+
+  do {
+    sum += p_face_stretch(e->face);
+    e = p_wheel_edge_next(e);
+  } while (e && e != (v->edge));
+
+  return sum;
+}
+
+static void p_chart_stretch_minimize(PChart *chart, RNG *rng)
+{
+  PVert *v;
+  PEdge *e;
+  int j, nedges;
+  float orig_stretch, low, stretch_low, high, stretch_high, mid, stretch;
+  float orig_uv[2], dir[2], random_angle, trusted_radius;
+
+  for (v = chart->verts; v; v = v->nextlink) {
+    if ((v->flag & PVERT_PIN) || !(v->flag & PVERT_SELECT)) {
+      continue;
+    }
+
+    orig_stretch = p_stretch_compute_vertex(v);
+    orig_uv[0] = v->uv[0];
+    orig_uv[1] = v->uv[1];
+
+    /* move vertex in a random direction */
+    trusted_radius = 0.0f;
+    nedges = 0;
+    e = v->edge;
+
+    do {
+      trusted_radius += p_edge_uv_length(e);
+      nedges++;
+
+      e = p_wheel_edge_next(e);
+    } while (e && e != (v->edge));
+
+    trusted_radius /= 2 * nedges;
+
+    random_angle = BLI_rng_get_float(rng) * 2.0f * (float)M_PI;
+    dir[0] = trusted_radius * cosf(random_angle);
+    dir[1] = trusted_radius * sinf(random_angle);
+
+    /* calculate old and new stretch */
+    low = 0;
+    stretch_low = orig_stretch;
+
+    add_v2_v2v2(v->uv, orig_uv, dir);
+    high = 1;
+    stretch = stretch_high = p_stretch_compute_vertex(v);
+
+    /* binary search for lowest stretch position */
+    for (j = 0; j < P_STRETCH_ITER; j++) {
+      mid = 0.5f * (low + high);
+      v->uv[0] = orig_uv[0] + mid * dir[0];
+      v->uv[1] = orig_uv[1] + mid * dir[1];
+      stretch = p_stretch_compute_vertex(v);
+
+      if (stretch_low < stretch_high) {
+        high = mid;
+        stretch_high = stretch;
+      }
+      else {
+        low = mid;
+        stretch_low = stretch;
+      }
+    }
+
+    /* no luck, stretch has increased, reset to old values */
+    if (stretch >= orig_stretch) {
+      copy_v2_v2(v->uv, orig_uv);
+    }
+  }
+}
+
+/* Minimum area enclosing rectangle for packing */
+
+static int p_compare_geometric_uv(const void *a, const void *b)
+{
+  const PVert *v1 = *(const PVert *const *)a;
+  const PVert *v2 = *(const PVert *const *)b;
+
+  if (v1->uv[0] < v2->uv[0]) {
+    return -1;
+  }
+  if (v1->uv[0] == v2->uv[0]) {
+    if (v1->uv[1] < v2->uv[1]) {
+      return -1;
+    }
+    if (v1->uv[1] == v2->uv[1]) {
+      return 0;
+    }
+    return 1;
+  }
+  return 1;
+}
+
+static bool p_chart_convex_hull(PChart *chart, PVert ***r_verts, int *r_nverts, int *r_right)
+{
+  /* Graham algorithm, taken from:
+   * http://aspn.activestate.com/ASPN/Cookbook/Python/Recipe/117225 */
+
+  PEdge *be, *e;
+  int npoints = 0, i, ulen, llen;
+  PVert **U, **L, **points, **p;
+
+  p_chart_boundaries(chart, &be);
+
+  if (!be) {
+    return false;
+  }
+
+  e = be;
+  do {
+    npoints++;
+    e = p_boundary_edge_next(e);
+  } while (e != be);
+
+  p = points = (PVert **)MEM_mallocN(sizeof(PVert *) * npoints * 2, "PCHullpoints");
+  U = (PVert **)MEM_mallocN(sizeof(PVert *) * npoints, "PCHullU");
+  L = (PVert **)MEM_mallocN(sizeof(PVert *) * npoints, "PCHullL");
+
+  e = be;
+  do {
+    *p = e->vert;
+    p++;
+    e = p_boundary_edge_next(e);
+  } while (e != be);
+
+  qsort(points, npoints, sizeof(PVert *), p_compare_geometric_uv);
+
+  ulen = llen = 0;
+  for (p = points, i = 0; i < npoints; i++, p++) {
+    while ((ulen > 1) && (p_area_signed(U[ulen - 2]->uv, (*p)->uv, U[ulen - 1]->uv) <= 0)) {
+      ulen--;
+    }
+    while ((llen > 1) && (p_area_signed(L[llen - 2]->uv, (*p)->uv, L[llen - 1]->uv) >= 0)) {
+      llen--;
+    }
+
+    U[ulen] = *p;
+    ulen++;
+    L[llen] = *p;
+    llen++;
+  }
+
+  npoints = 0;
+  for (p = points, i = 0; i < ulen; i++, p++, npoints++) {
+    *p = U[i];
+  }
+
+  /* the first and last point in L are left out, since they are also in U */
+  for (i = llen - 2; i > 0; i--, p++, npoints++) {
+    *p = L[i];
+  }
+
+  *r_verts = points;
+  *r_nverts = npoints;
+  *r_right = ulen - 1;
+
+  MEM_SAFE_FREE(U);
+  MEM_SAFE_FREE(L);
+
+  return true;
+}
+
+static float p_rectangle_area(float *p1, float *dir, float *p2, float *p3, float *p4)
+{
+  /* given 4 points on the rectangle edges and the direction of on edge,
+   * compute the area of the rectangle */
+
+  float orthodir[2], corner1[2], corner2[2], corner3[2];
+
+  orthodir[0] = dir[1];
+  orthodir[1] = -dir[0];
+
+  if (!p_intersect_line_2d_dir(p1, dir, p2, orthodir, corner1)) {
+    return 1e10;
+  }
+
+  if (!p_intersect_line_2d_dir(p1, dir, p4, orthodir, corner2)) {
+    return 1e10;
+  }
+
+  if (!p_intersect_line_2d_dir(p3, dir, p4, orthodir, corner3)) {
+    return 1e10;
+  }
+
+  return len_v2v2(corner1, corner2) * len_v2v2(corner2, corner3);
+}
+
+static float p_chart_minimum_area_angle(PChart *chart)
+{
+  /* minimum area enclosing rectangle with rotating calipers, info:
+   * http://cgm.cs.mcgill.ca/~orm/maer.html */
+
+  float rotated, minarea, minangle, area, len;
+  float *angles, miny, maxy, v[2], a[4], mina;
+  int npoints, right, i_min, i_max, i, idx[4], nextidx;
+  PVert **points, *p1, *p2, *p3, *p4, *p1n;
+
+  /* compute convex hull */
+  if (!p_chart_convex_hull(chart, &points, &npoints, &right)) {
+    return 0.0;
+  }
+
+  /* find left/top/right/bottom points, and compute angle for each point */
+  angles = (float *)MEM_mallocN(sizeof(float) * npoints, "PMinAreaAngles");
+
+  i_min = i_max = 0;
+  miny = 1e10;
+  maxy = -1e10;
+
+  for (i = 0; i < npoints; i++) {
+    p1 = (i == 0) ? points[npoints - 1] : points[i - 1];
+    p2 = points[i];
+    p3 = (i == npoints - 1) ? points[0] : points[i + 1];
+
+    angles[i] = (float)M_PI - p_vec2_angle(p1->uv, p2->uv, p3->uv);
+
+    if (points[i]->uv[1] < miny) {
+      miny = points[i]->uv[1];
+      i_min = i;
+    }
+    if (points[i]->uv[1] > maxy) {
+      maxy = points[i]->uv[1];
+      i_max = i;
+    }
+  }
+
+  /* left, top, right, bottom */
+  idx[0] = 0;
+  idx[1] = i_max;
+  idx[2] = right;
+  idx[3] = i_min;
+
+  v[0] = points[idx[0]]->uv[0];
+  v[1] = points[idx[0]]->uv[1] + 1.0f;
+  a[0] = p_vec2_angle(points[(idx[0] + 1) % npoints]->uv, points[idx[0]]->uv, v);
+
+  v[0] = points[idx[1]]->uv[0] + 1.0f;
+  v[1] = points[idx[1]]->uv[1];
+  a[1] = p_vec2_angle(points[(idx[1] + 1) % npoints]->uv, points[idx[1]]->uv, v);
+
+  v[0] = points[idx[2]]->uv[0];
+  v[1] = points[idx[2]]->uv[1] - 1.0f;
+  a[2] = p_vec2_angle(points[(idx[2] + 1) % npoints]->uv, points[idx[2]]->uv, v);
+
+  v[0] = points[idx[3]]->uv[0] - 1.0f;
+  v[1] = points[idx[3]]->uv[1];
+  a[3] = p_vec2_angle(points[(idx[3] + 1) % npoints]->uv, points[idx[3]]->uv, v);
+
+  /* 4 rotating calipers */
+
+  rotated = 0.0;
+  minarea = 1e10;
+  minangle = 0.0;
+
+  while (rotated <= (float)M_PI_2) { /* INVESTIGATE: how far to rotate? */
+    /* rotate with the smallest angle */
+    i_min = 0;
+    mina = 1e10;
+
+    for (i = 0; i < 4; i++) {
+      if (a[i] < mina) {
+        mina = a[i];
+        i_min = i;
+      }
+    }
+
+    rotated += mina;
+    nextidx = (idx[i_min] + 1) % npoints;
+
+    a[i_min] = angles[nextidx];
+    a[(i_min + 1) % 4] = a[(i_min + 1) % 4] - mina;
+    a[(i_min + 2) % 4] = a[(i_min + 2) % 4] - mina;
+    a[(i_min + 3) % 4] = a[(i_min + 3) % 4] - mina;
+
+    /* compute area */
+    p1 = points[idx[i_min]];
+    p1n = points[nextidx];
+    p2 = points[idx[(i_min + 1) % 4]];
+    p3 = points[idx[(i_min + 2) % 4]];
+    p4 = points[idx[(i_min + 3) % 4]];
+
+    len = len_v2v2(p1->uv, p1n->uv);
+
+    if (len > 0.0f) {
+      len = 1.0f / len;
+      v[0] = (p1n->uv[0] - p1->uv[0]) * len;
+      v[1] = (p1n->uv[1] - p1->uv[1]) * len;
+
+      area = p_rectangle_area(p1->uv, v, p2->uv, p3->uv, p4->uv);
+
+      /* remember smallest area */
+      if (area < minarea) {
+        minarea = area;
+        minangle = rotated;
+      }
+    }
+
+    idx[i_min] = nextidx;
+  }
+
+  /* try keeping rotation as small as possible */
+  if (minangle > (float)M_PI_4) {
+    minangle -= (float)M_PI_2;
+  }
+
+  MEM_SAFE_FREE(angles);
+  MEM_SAFE_FREE(points);
+
+  return minangle;
+}
+
+static void p_chart_rotate_minimum_area(PChart *chart)
+{
+  float angle = p_chart_minimum_area_angle(chart);
+  float sine = sinf(angle);
+  float cosine = cosf(angle);
+  PVert *v;
+
+  for (v = chart->verts; v; v = v->nextlink) {
+    float oldu = v->uv[0], oldv = v->uv[1];
+    v->uv[0] = cosine * oldu - sine * oldv;
+    v->uv[1] = sine * oldu + cosine * oldv;
+  }
+}
+
+static void p_chart_rotate_fit_aabb(PChart *chart)
+{
+  float(*points)[2] = static_cast<float(*)[2]>(MEM_mallocN(sizeof(*points) * chart->nverts, __func__));
+
+  p_chart_uv_to_array(chart, points);
+
+  float angle = BLI_convexhull_aabb_fit_points_2d(points, chart->nverts);
+
+  MEM_freeN(points);
+
+  if (angle != 0.0f) {
+    float mat[2][2];
+    angle_to_mat2(mat, angle);
+    p_chart_uv_transform(chart, mat);
+  }
+}
+
+/* Exported */
+
+ParamHandle *GEO_uv_parametrizer_construct_begin(void)
+{
+  ParamHandle *handle = (ParamHandle *)MEM_callocN(sizeof(*handle), "ParamHandle");
+  handle->construction_chart = (PChart *)MEM_callocN(sizeof(PChart), "PChart");
+  handle->state = PHANDLE_STATE_ALLOCATED;
+  handle->arena = BLI_memarena_new(MEM_SIZE_OPTIMAL(1 << 16), "param construct arena");
+  handle->polyfill_arena = BLI_memarena_new(BLI_MEMARENA_STD_BUFSIZE, "param polyfill arena");
+  handle->polyfill_heap = BLI_heap_new_ex(BLI_POLYFILL_ALLOC_NGON_RESERVE);
+  handle->aspx = 1.0f;
+  handle->aspy = 1.0f;
+
+  handle->hash_verts = phash_new((PHashLink **)&handle->construction_chart->verts, 1);
+  handle->hash_edges = phash_new((PHashLink **)&handle->construction_chart->edges, 1);
+  handle->hash_faces = phash_new((PHashLink **)&handle->construction_chart->faces, 1);
+
+  return handle;
+}
+
+void GEO_uv_parametrizer_aspect_ratio(ParamHandle *phandle, float aspx, float aspy)
+{
+  phandle->aspx = aspx;
+  phandle->aspy = aspy;
+}
+
+void GEO_uv_parametrizer_delete(ParamHandle *phandle)
+{
+  param_assert(ELEM(phandle->state, PHANDLE_STATE_ALLOCATED, PHANDLE_STATE_CONSTRUCTED));
+
+  for (int i = 0; i < phandle->ncharts; i++) {
+    MEM_SAFE_FREE(phandle->charts[i]);
+  }
+
+  MEM_SAFE_FREE(phandle->charts);
+
+  if (phandle->pin_hash) {
+    BLI_ghash_free(phandle->pin_hash, NULL, NULL);
+    phandle->pin_hash = NULL;
+  }
+
+  MEM_SAFE_FREE(phandle->construction_chart);
+
+  phash_delete(phandle->hash_verts);
+  phash_delete(phandle->hash_edges);
+  phash_delete(phandle->hash_faces);
+
+  BLI_memarena_free(phandle->arena);
+  BLI_memarena_free(phandle->polyfill_arena);
+  BLI_heap_free(phandle->polyfill_heap, NULL);
+
+  BLI_rng_free(phandle->rng);
+  phandle->rng = NULL;
+
+  MEM_freeN(phandle);
+}
+
+typedef struct GeoUVPinIndex {
+  struct GeoUVPinIndex *next;
+  float uv[2];
+  ParamKey reindex;
+} GeoUVPinIndex;
+
+/* Find a (mostly) unique ParamKey given a BMVert index and UV co-ordinates.
+ * For each unique pinned UVs, return a unique ParamKey, starting with
+ *  a very large number, and decreasing steadily from there.
+ * For non-pinned UVs which share a BMVert with a pinned UV,
+ *  return the index corresponding to the closest pinned UV.
+ * For everything else, just return the BMVert index.
+ * Note that ParamKeys will eventually be hashed, so they don't need to be contiguous.
+ */
+ParamKey GEO_uv_find_pin_index(ParamHandle *handle, const int bmvertindex, const float uv[2])
+{
+  if (!handle->pin_hash) {
+    return bmvertindex; /* No verts pinned. */
+  }
+
+  const GeoUVPinIndex *pinuvlist = (const GeoUVPinIndex *)BLI_ghash_lookup(
+      handle->pin_hash, POINTER_FROM_INT(bmvertindex));
+  if (!pinuvlist) {
+    return bmvertindex; /* Vert not pinned. */
+  }
+
+  /* At least one of the UVs associated with bmvertindex is pinned. Find the best one. */
+  float bestdistsquared = len_squared_v2v2(pinuvlist->uv, uv);
+  ParamKey bestkey = pinuvlist->reindex;
+  pinuvlist = pinuvlist->next;
+  while (pinuvlist) {
+    const float distsquared = len_squared_v2v2(pinuvlist->uv, uv);
+    if (bestdistsquared > distsquared) {
+      bestdistsquared = distsquared;
+      bestkey = pinuvlist->reindex;
+    }
+    pinuvlist = pinuvlist->next;
+  }
+  return bestkey;
+}
+
+static GeoUVPinIndex *new_geo_uv_pinindex(ParamHandle *handle, const float uv[2])
+{
+  GeoUVPinIndex *pinuv = (GeoUVPinIndex *)BLI_memarena_alloc(handle->arena, sizeof(*pinuv));
+  pinuv->next = NULL;
+  copy_v2_v2(pinuv->uv, uv);
+  pinuv->reindex = PARAM_KEY_MAX - (handle->unique_pin_count++);
+  return pinuv;
+}
+
+void GEO_uv_prepare_pin_index(ParamHandle *handle, const int bmvertindex, const float uv[2])
+{
+  if (!handle->pin_hash) {
+    handle->pin_hash = BLI_ghash_int_new("uv pin reindex");
+  }
+
+  GeoUVPinIndex *pinuvlist = (GeoUVPinIndex *)BLI_ghash_lookup(handle->pin_hash,
+                                                               POINTER_FROM_INT(bmvertindex));
+  if (!pinuvlist) {
+    BLI_ghash_insert(
+        handle->pin_hash, POINTER_FROM_INT(bmvertindex), new_geo_uv_pinindex(handle, uv));
+    return;
+  }
+
+  while (true) {
+    if (equals_v2v2(pinuvlist->uv, uv)) {
+      return;
+    }
+    if (!pinuvlist->next) {
+      pinuvlist->next = new_geo_uv_pinindex(handle, uv);
+      return;
+    }
+    pinuvlist = pinuvlist->next;
+  }
+}
+
+static void p_add_ngon(ParamHandle *handle,
+                       const ParamKey key,
+                       const int nverts,
+                       const ParamKey *vkeys,
+                       const float **co,
+                       float **uv, /* Output will eventually be written to `uv`. */
+                       const bool *pin,
+                       const bool *select)
+{
+  /* Allocate memory for polyfill. */
+  MemArena *arena = handle->polyfill_arena;
+  Heap *heap = handle->polyfill_heap;
+  uint nfilltri = nverts - 2;
+  uint(*tris)[3] = static_cast<uint(*)[3]>(BLI_memarena_alloc(arena, sizeof(*tris) * (size_t)nfilltri));
+  float(*projverts)[2] = static_cast<float(*)[2]>(BLI_memarena_alloc(arena, sizeof(*projverts) * (size_t)nverts));
+
+  /* Calc normal, flipped: to get a positive 2d cross product. */
+  float normal[3];
+  zero_v3(normal);
+
+  const float *co_curr, *co_prev = co[nverts - 1];
+  for (int j = 0; j < nverts; j++) {
+    co_curr = co[j];
+    add_newell_cross_v3_v3v3(normal, co_prev, co_curr);
+    co_prev = co_curr;
+  }
+  if (UNLIKELY(normalize_v3(normal) == 0.0f)) {
+    normal[2] = 1.0f;
+  }
+
+  /* Project verts to 2d. */
+  float axis_mat[3][3];
+  axis_dominant_v3_to_m3_negate(axis_mat, normal);
+  for (int j = 0; j < nverts; j++) {
+    mul_v2_m3v3(projverts[j], axis_mat, co[j]);
+  }
+
+  BLI_polyfill_calc_arena(projverts, nverts, 1, tris, arena);
+
+  /* Beautify helps avoid thin triangles that give numerical problems. */
+  BLI_polyfill_beautify(projverts, nverts, tris, arena, heap);
+
+  /* Add triangles. */
+  for (int j = 0; j < nfilltri; j++) {
+    uint *tri = tris[j];
+    uint v0 = tri[0];
+    uint v1 = tri[1];
+    uint v2 = tri[2];
+
+    const ParamKey tri_vkeys[3] = {vkeys[v0], vkeys[v1], vkeys[v2]};
+    const float *tri_co[3] = {co[v0], co[v1], co[v2]};
+    float *tri_uv[3] = {uv[v0], uv[v1], uv[v2]};
+    bool tri_pin[3] = {pin[v0], pin[v1], pin[v2]};
+    bool tri_select[3] = {select[v0], select[v1], select[v2]};
+
+    GEO_uv_parametrizer_face_add(handle, key, 3, tri_vkeys, tri_co, tri_uv, tri_pin, tri_select);
+  }
+
+  BLI_memarena_clear(arena);
+}
+
+void GEO_uv_parametrizer_face_add(ParamHandle *phandle,
+                                  const ParamKey key,
+                                  const int nverts,
+                                  const ParamKey *vkeys,
+                                  const float **co,
+                                  float **uv,
+                                  const bool *pin,
+                                  const bool *select)
+{
+  param_assert(phash_lookup(phandle->hash_faces, key) == NULL);
+  param_assert(phandle->state == PHANDLE_STATE_ALLOCATED);
+  param_assert(ELEM(nverts, 3, 4));
+
+  if (nverts > 4) {
+    /* ngon */
+    p_add_ngon(phandle, key, nverts, vkeys, co, uv, pin, select);
+  }
+  else if (nverts == 4) {
+    /* quad */
+    if (p_quad_split_direction(phandle, co, vkeys)) {
+      p_face_add_construct(phandle, key, vkeys, co, uv, 0, 1, 2, pin, select);
+      p_face_add_construct(phandle, key, vkeys, co, uv, 0, 2, 3, pin, select);
+    }
+    else {
+      p_face_add_construct(phandle, key, vkeys, co, uv, 0, 1, 3, pin, select);
+      p_face_add_construct(phandle, key, vkeys, co, uv, 1, 2, 3, pin, select);
+    }
+  }
+  else if (!p_face_exists(phandle, vkeys, 0, 1, 2)) {
+    /* triangle */
+    p_face_add_construct(phandle, key, vkeys, co, uv, 0, 1, 2, pin, select);
+  }
+}
+
+void GEO_uv_parametrizer_edge_set_seam(ParamHandle *phandle, ParamKey *vkeys)
+{
+  PEdge *e;
+
+  param_assert(phandle->state == PHANDLE_STATE_ALLOCATED);
+
+  e = p_edge_lookup(phandle, vkeys);
+  if (e) {
+    e->flag |= PEDGE_SEAM;
+  }
+}
+
+void GEO_uv_parametrizer_construct_end(ParamHandle *phandle,
+                                       bool fill,
+                                       bool topology_from_uvs,
+                                       int *count_fail)
+{
+  PChart *chart = phandle->construction_chart;
+  int i, j;
+  PEdge *outer;
+
+  param_assert(phandle->state == PHANDLE_STATE_ALLOCATED);
+
+  phandle->ncharts = p_connect_pairs(phandle, topology_from_uvs);
+  phandle->charts = p_split_charts(phandle, chart, phandle->ncharts);
+
+  MEM_SAFE_FREE(phandle->construction_chart);
+
+  phash_delete(phandle->hash_verts);
+  phash_delete(phandle->hash_edges);
+  phash_delete(phandle->hash_faces);
+  phandle->hash_verts = phandle->hash_edges = phandle->hash_faces = NULL;
+
+  for (i = j = 0; i < phandle->ncharts; i++) {
+    PVert *v;
+    chart = phandle->charts[i];
+
+    p_chart_boundaries(chart, &outer);
+
+    if (!topology_from_uvs && chart->nboundaries == 0) {
+      MEM_SAFE_FREE(chart);
+      if (count_fail != NULL) {
+        *count_fail += 1;
+      }
+      continue;
+    }
+
+    phandle->charts[j] = chart;
+    j++;
+
+    if (fill && (chart->nboundaries > 1)) {
+      p_chart_fill_boundaries(phandle, chart, outer);
+    }
+
+    for (v = chart->verts; v; v = v->nextlink) {
+      p_vert_load_pin_select_uvs(phandle, v);
+    }
+  }
+
+  phandle->ncharts = j;
+
+  phandle->state = PHANDLE_STATE_CONSTRUCTED;
+}
+
+void GEO_uv_parametrizer_lscm_begin(ParamHandle *phandle, bool live, bool abf)
+{
+  PFace *f;
+  int i;
+
+  param_assert(phandle->state == PHANDLE_STATE_CONSTRUCTED);
+  phandle->state = PHANDLE_STATE_LSCM;
+
+  for (i = 0; i < phandle->ncharts; i++) {
+    for (f = phandle->charts[i]->faces; f; f = f->nextlink) {
+      p_face_backup_uvs(f);
+    }
+    p_chart_lscm_begin(phandle->charts[i], live, abf);
+  }
+}
+
+void GEO_uv_parametrizer_lscm_solve(ParamHandle *phandle, int *count_changed, int *count_failed)
+{
+  PChart *chart;
+  int i;
+
+  param_assert(phandle->state == PHANDLE_STATE_LSCM);
+
+  for (i = 0; i < phandle->ncharts; i++) {
+    chart = phandle->charts[i];
+
+    if (chart->u.lscm.context) {
+      const bool result = p_chart_lscm_solve(phandle, chart);
+
+      if (result && !chart->has_pins) {
+        p_chart_rotate_minimum_area(chart);
+      }
+      else if (result && chart->u.lscm.single_pin) {
+        p_chart_rotate_fit_aabb(chart);
+        p_chart_lscm_transform_single_pin(chart);
+      }
+
+      if (!result || !chart->has_pins) {
+        p_chart_lscm_end(chart);
+      }
+
+      if (result) {
+        if (count_changed != NULL) {
+          *count_changed += 1;
+        }
+      }
+      else {
+        if (count_failed != NULL) {
+          *count_failed += 1;
+        }
+      }
+    }
+  }
+}
+
+void GEO_uv_parametrizer_lscm_end(ParamHandle *phandle)
+{
+  BLI_assert(phandle->state == PHANDLE_STATE_LSCM);
+
+  for (int i = 0; i < phandle->ncharts; i++) {
+    p_chart_lscm_end(phandle->charts[i]);
+#if 0
+    p_chart_complexify(phandle->charts[i]);
+#endif
+  }
+
+  phandle->state = PHANDLE_STATE_CONSTRUCTED;
+}
+
+void GEO_uv_parametrizer_stretch_begin(ParamHandle *phandle)
+{
+  PChart *chart;
+  PVert *v;
+  PFace *f;
+  int i;
+
+  param_assert(phandle->state == PHANDLE_STATE_CONSTRUCTED);
+  phandle->state = PHANDLE_STATE_STRETCH;
+
+  phandle->rng = BLI_rng_new(31415926);
+  phandle->blend = 0.0f;
+
+  for (i = 0; i < phandle->ncharts; i++) {
+    chart = phandle->charts[i];
+
+    for (v = chart->verts; v; v = v->nextlink) {
+      v->flag &= ~PVERT_PIN; /* don't use user-defined pins */
+    }
+
+    p_stretch_pin_boundary(chart);
+
+    for (f = chart->faces; f; f = f->nextlink) {
+      p_face_backup_uvs(f);
+      f->u.area3d = p_face_area(f);
+    }
+  }
+}
+
+void GEO_uv_parametrizer_stretch_blend(ParamHandle *phandle, float blend)
+{
+  param_assert(phandle->state == PHANDLE_STATE_STRETCH);
+  phandle->blend = blend;
+}
+
+void GEO_uv_parametrizer_stretch_iter(ParamHandle *phandle)
+{
+  PChart *chart;
+  int i;
+
+  param_assert(phandle->state == PHANDLE_STATE_STRETCH);
+
+  for (i = 0; i < phandle->ncharts; i++) {
+    chart = phandle->charts[i];
+    p_chart_stretch_minimize(chart, phandle->rng);
+  }
+}
+
+void GEO_uv_parametrizer_stretch_end(ParamHandle *phandle)
+{
+  param_assert(phandle->state == PHANDLE_STATE_STRETCH);
+  phandle->state = PHANDLE_STATE_CONSTRUCTED;
+}
+
+/* don't pack, just rotate (used for better packing) */
+static void GEO_uv_parametrizer_pack_rotate(ParamHandle *phandle, bool ignore_pinned)
+{
+  PChart *chart;
+  int i;
+
+  for (i = 0; i < phandle->ncharts; i++) {
+    chart = phandle->charts[i];
+
+    if (ignore_pinned && chart->has_pins) {
+      continue;
+    }
+
+    p_chart_rotate_fit_aabb(chart);
+  }
+}
+
+void GEO_uv_parametrizer_pack(ParamHandle *handle,
+                              float margin,
+                              bool do_rotate,
+                              bool ignore_pinned)
+{
+  /* box packing variables */
+  BoxPack *boxarray, *box;
+  float tot_width, tot_height, scale;
+
+  PChart *chart;
+  int i, unpacked = 0;
+  float trans[2];
+  double area = 0.0;
+
+  if (handle->ncharts == 0) {
+    return;
+  }
+
+  /* this could be its own function */
+  if (do_rotate) {
+    GEO_uv_parametrizer_pack_rotate(handle, ignore_pinned);
+  }
+
+  if (handle->aspx != handle->aspy) {
+    GEO_uv_parametrizer_scale(handle, 1.0f / handle->aspx, 1.0f / handle->aspy);
+  }
+
+  /* we may not use all these boxes */
+  boxarray = (BoxPack *)MEM_mallocN(handle->ncharts * sizeof(BoxPack), "BoxPack box");
+
+  for (i = 0; i < handle->ncharts; i++) {
+    chart = handle->charts[i];
+
+    if (ignore_pinned && chart->has_pins) {
+      unpacked++;
+      continue;
+    }
+
+    box = boxarray + (i - unpacked);
+
+    p_chart_uv_bbox(chart, trans, chart->u.pack.size);
+
+    trans[0] = -trans[0];
+    trans[1] = -trans[1];
+
+    p_chart_uv_translate(chart, trans);
+
+    box->w = chart->u.pack.size[0] + trans[0];
+    box->h = chart->u.pack.size[1] + trans[1];
+    box->index = i; /* Warning this index skips chart->has_pins boxes. */
+
+    if (margin > 0.0f) {
+      area += (double)sqrtf(box->w * box->h);
+    }
+  }
+
+  if (margin > 0.0f) {
+    /* multiply the margin by the area to give predictable results not dependent on UV scale,
+     * ...Without using the area running pack multiple times also gives a bad feedback loop.
+     * multiply by 0.1 so the margin value from the UI can be from
+     * 0.0 to 1.0 but not give a massive margin */
+    margin = (margin * (float)area) * 0.1f;
+    unpacked = 0;
+    for (i = 0; i < handle->ncharts; i++) {
+      chart = handle->charts[i];
+
+      if (ignore_pinned && chart->has_pins) {
+        unpacked++;
+        continue;
+      }
+
+      box = boxarray + (i - unpacked);
+      trans[0] = margin;
+      trans[1] = margin;
+      p_chart_uv_translate(chart, trans);
+      box->w += margin * 2;
+      box->h += margin * 2;
+    }
+  }
+
+  BLI_box_pack_2d(boxarray, handle->ncharts - unpacked, &tot_width, &tot_height);
+
+  if (tot_height > tot_width) {
+    scale = tot_height != 0.0f ? (1.0f / tot_height) : 1.0f;
+  }
+  else {
+    scale = tot_width != 0.0f ? (1.0f / tot_width) : 1.0f;
+  }
+
+  for (i = 0; i < handle->ncharts - unpacked; i++) {
+    box = boxarray + i;
+    trans[0] = box->x;
+    trans[1] = box->y;
+
+    chart = handle->charts[box->index];
+    p_chart_uv_translate(chart, trans);
+    p_chart_uv_scale(chart, scale);
+  }
+  MEM_SAFE_FREE(boxarray);
+
+  if (handle->aspx != handle->aspy) {
+    GEO_uv_parametrizer_scale(handle, handle->aspx, handle->aspy);
+  }
+}
+
+void GEO_uv_parametrizer_average(ParamHandle *phandle,
+                                 bool ignore_pinned,
+                                 bool scale_uv,
+                                 bool shear)
+{
+  PChart *chart;
+  int i;
+  float tot_uvarea = 0.0f, tot_facearea = 0.0f;
+  float tot_fac, fac;
+  float minv[2], maxv[2], trans[2];
+
+  if (phandle->ncharts == 0) {
+    return;
+  }
+
+  for (i = 0; i < phandle->ncharts; i++) {
+    chart = phandle->charts[i];
+
+    if (ignore_pinned && chart->has_pins) {
+      continue;
+    }
+
+    p_chart_uv_bbox(chart, minv, maxv);
+    mid_v2_v2v2(chart->u.pack.origin, minv, maxv);
+
+    if (scale_uv || shear) {
+      /* It's possible that for some "bad" inputs, the following iteration will converge slowly or
+       * perhaps even diverge. Rather than infinite loop, we only iterate a maximum of `max_iter`
+       * times. (Also useful when making changes to the calculation.) */
+      int max_iter = 10;
+      for (int j = 0; j < max_iter; j++) {
+        /* An island could contain millions of polygons. When summing many small values, we need to
+         * use double precision in the accumulator to maintain accuracy. Note that the individual
+         * calculations only need to be at single precision.*/
+        double scale_cou = 0;
+        double scale_cov = 0;
+        double scale_cross = 0;
+        double weight_sum = 0;
+        for (PFace *f = chart->faces; f; f = f->nextlink) {
+          float m[2][2], s[2][2];
+          PVert *va = f->edge->vert;
+          PVert *vb = f->edge->next->vert;
+          PVert *vc = f->edge->next->next->vert;
+          s[0][0] = va->uv[0] - vc->uv[0];
+          s[0][1] = va->uv[1] - vc->uv[1];
+          s[1][0] = vb->uv[0] - vc->uv[0];
+          s[1][1] = vb->uv[1] - vc->uv[1];
+          /* Find the "U" axis and "V" axis in triangle co-ordinates. Normally this would require
+           * SVD, but in 2D we can use a cheaper matrix inversion instead.*/
+          if (!invert_m2_m2(m, s)) {
+            continue;
+          }
+          float cou[3], cov[3]; /* i.e. Texture "U" and texture "V" in 3D co-ordinates.*/
+          for (int k = 0; k < 3; k++) {
+            cou[k] = m[0][0] * (va->co[k] - vc->co[k]) + m[0][1] * (vb->co[k] - vc->co[k]);
+            cov[k] = m[1][0] * (va->co[k] - vc->co[k]) + m[1][1] * (vb->co[k] - vc->co[k]);
+          }
+          const float weight = p_face_area(f);
+          scale_cou += len_v3(cou) * weight;
+          scale_cov += len_v3(cov) * weight;
+          if (shear) {
+            normalize_v3(cov);
+            normalize_v3(cou);
+
+            /* Why is scale_cross called `cross` when we call `dot`? The next line calculates:
+             * `scale_cross += length(cross(cross(cou, face_normal), cov))`
+             * By construction, both `cou` and `cov` are orthogonal to the face normal.
+             * By definition, the normal vector has unit length. */
+            scale_cross += dot_v3v3(cou, cov) * weight;
+          }
+          weight_sum += weight;
+        }
+        if (scale_cou * scale_cov < 1e-10f) {
+          break;
+        }
+        const float scale_factor_u = scale_uv ? sqrtf(scale_cou / scale_cov) : 1.0f;
+
+        /* Compute correction transform. */
+        float t[2][2];
+        t[0][0] = scale_factor_u;
+        t[1][0] = clamp_f((float)(scale_cross / weight_sum), -0.5f, 0.5f);
+        t[0][1] = 0;
+        t[1][1] = 1.0f / scale_factor_u;
+
+        /* Apply the correction. */
+        p_chart_uv_transform(chart, t);
+
+        /* How far from the identity transform are we? [[1,0],[0,1]] */
+        const float err = fabsf(t[0][0] - 1.0f) + fabsf(t[1][0]) + fabsf(t[0][1]) +
+                          fabsf(t[1][1] - 1.0f);
+
+        const float tolerance = 1e-6f; /* Trade accuracy for performance. */
+        if (err < tolerance) {
+          /* Too slow? Use Richardson Extrapolation to accelerate the convergence.*/
+          break;
+        }
+      }
+    }
+
+    chart->u.pack.area = 0.0f;    /* 3d area */
+    chart->u.pack.rescale = 0.0f; /* UV area, abusing rescale for tmp storage, oh well :/ */
+
+    for (PFace *f = chart->faces; f; f = f->nextlink) {
+      chart->u.pack.area += p_face_area(f);
+      chart->u.pack.rescale += fabsf(p_face_uv_area_signed(f));
+    }
+
+    tot_facearea += chart->u.pack.area;
+    tot_uvarea += chart->u.pack.rescale;
+  }
+
+  if (tot_facearea == tot_uvarea || tot_facearea == 0.0f || tot_uvarea == 0.0f) {
+    /* nothing to do */
+    return;
+  }
+
+  tot_fac = tot_facearea / tot_uvarea;
+
+  for (i = 0; i < phandle->ncharts; i++) {
+    chart = phandle->charts[i];
+
+    if (ignore_pinned && chart->has_pins) {
+      continue;
+    }
+
+    if (chart->u.pack.area != 0.0f && chart->u.pack.rescale != 0.0f) {
+      fac = chart->u.pack.area / chart->u.pack.rescale;
+
+      /* Average scale. */
+      p_chart_uv_scale(chart, sqrtf(fac / tot_fac));
+
+      /* Get the current island center. */
+      p_chart_uv_bbox(chart, minv, maxv);
+
+      /* Move to original center. */
+      mid_v2_v2v2(trans, minv, maxv);
+      negate_v2(trans);
+      add_v2_v2(trans, chart->u.pack.origin);
+      p_chart_uv_translate(chart, trans);
+    }
+  }
+}
+
+void GEO_uv_parametrizer_scale(ParamHandle *phandle, float x, float y)
+{
+  PChart *chart;
+  int i;
+
+  for (i = 0; i < phandle->ncharts; i++) {
+    chart = phandle->charts[i];
+    p_chart_uv_scale_xy(chart, x, y);
+  }
+}
+
+void GEO_uv_parametrizer_flush(ParamHandle *phandle)
+{
+  PChart *chart;
+  int i;
+
+  for (i = 0; i < phandle->ncharts; i++) {
+    chart = phandle->charts[i];
+
+    if ((phandle->state == PHANDLE_STATE_LSCM) && !chart->u.lscm.context) {
+      continue;
+    }
+
+    if (phandle->blend == 0.0f) {
+      p_flush_uvs(phandle, chart);
+    }
+    else {
+      p_flush_uvs_blend(phandle, chart, phandle->blend);
+    }
+  }
+}
+
+void GEO_uv_parametrizer_flush_restore(ParamHandle *phandle)
+{
+  PChart *chart;
+  PFace *f;
+  int i;
+
+  for (i = 0; i < phandle->ncharts; i++) {
+    chart = phandle->charts[i];
+
+    for (f = chart->faces; f; f = f->nextlink) {
+      p_face_restore_uvs(f);
+    }
+  }
+}