diff options
Diffstat (limited to 'source/blender/geometry/intern/uv_parametrizer.cc')
-rw-r--r-- | source/blender/geometry/intern/uv_parametrizer.cc | 4453 |
1 files changed, 4453 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..b15c8b6e319 --- /dev/null +++ b/source/blender/geometry/intern/uv_parametrizer.cc @@ -0,0 +1,4453 @@ +/* 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 uintptr_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 */ + +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; +}; + +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; +}; + +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; + uint flag; +}; + +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 */ + +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; +}; + +enum PHandleState { + PHANDLE_STATE_ALLOCATED, + PHANDLE_STATE_CONSTRUCTED, + PHANDLE_STATE_LSCM, + PHANDLE_STATE_STRETCH, +}; + +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; +}; + +/* 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_freeN(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 == nullptr) { + /* 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 = nullptr, *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) = nullptr; + + 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 nullptr; + } + } + + 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 nullptr; + } + } + + 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); +} + +/* Angles close to 0 or 180 degrees cause rows filled with zeros in the linear_solver. + * The matrix will then be rank deficient and / or have poor conditioning. + * => Reduce the maximum angle to 179 degrees, and spread the remainder to the other angles. + */ +static void fix_large_angle(const float v_fix[3], + const float v1[3], + const float v2[3], + float *r_fix, + float *r_a1, + float *r_a2) +{ + const float max_angle = (float)M_PI * (179.0f / 180.0f); + const float fix_amount = *r_fix - max_angle; + if (fix_amount < 0.0f) { + return; /* angle is reasonable, i.e. less than 179 degrees. */ + } + + /* The triangle is probably degenerate, or close to it. + * Without loss of generality, transform the triangle such that + * v_fix == { 0, s}, *r_fix = 180 degrees + * v1 == {-x1, 0}, *r_a1 = 0 + * v2 == { x2, 0}, *r_a2 = 0 + * + * With `s = 0`, `x1 > 0`, `x2 > 0` + * + * Now make `s` a small number and do some math: + * tan(*r_a1) = s / x1 + * tan(*r_a2) = s / x2 + * + * Remember that `tan = sin / cos`, `sin(s) ~= s` and `cos(s) = 1` + * + * Rearrange to obtain: + * *r_a1 = fix_amount * x2 / (x1 + x2) + * *r_a2 = fix_amount * x1 / (x1 + x2) + */ + + const float dist_v1 = len_v3v3(v_fix, v1); + const float dist_v2 = len_v3v3(v_fix, v2); + const float sum = dist_v1 + dist_v2; + const float weight = (sum > 1e-20f) ? dist_v2 / sum : 0.5f; + + /* Ensure sum of angles in triangle is unchanged. */ + *r_fix -= fix_amount; + *r_a1 += fix_amount * weight; + *r_a2 += fix_amount * (1.0f - weight); +} + +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 = p_vec_angle(v2, v3, v1); + + /* Fix for degenerate geometry e.g. v1 = sum(v2 + v3). See T100874 */ + fix_large_angle(v1, v2, v3, r_a1, r_a2, r_a3); + fix_large_angle(v2, v3, v1, r_a2, r_a3, r_a1); + fix_large_angle(v3, v1, v2, r_a3, r_a1, r_a2); + + /* Workaround for degenerate geometry, e.g. v1 == v2 == v3. */ + *r_a1 = max_ff(*r_a1, 0.001f); + *r_a2 = max_ff(*r_a2, 0.001f); + *r_a3 = max_ff(*r_a3, 0.001f); +} + +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 : nullptr; +} + +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 nullptr; +} + +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 = nullptr; + + 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 = nullptr; + 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 = nullptr; + return false; + } + } + + return (*r_pair != nullptr); +} + +static bool p_edge_connect_pair(ParamHandle *handle, + PEdge *e, + bool topology_from_uvs, + PEdge ***stack) +{ + PEdge *pair = nullptr; + + 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 != nullptr); +} + +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_freeN(stackbase); + + return ncharts; +} + +static void p_split_vert(ParamHandle *handle, PChart *chart, PEdge *e) +{ + PEdge *we, *lastwe = nullptr; + 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 = nullptr; + e2->pair = nullptr; + e3->pair = nullptr; + + 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 = nullptr; + + 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 = nullptr; + } + + 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 = nullptr; + + 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, nullptr); +} + +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 == nullptr) { + 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 == nullptr) { + 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 : nullptr; + oldf2 = (pair) ? pair->face : nullptr; + + 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) == nullptr) { + 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 = nullptr; + *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 == nullptr) || (cost < *r_mincost)) { + *r_mincost = cost; + *r_mine = e; + } + } + + enext = p_wheel_edge_next(e); + + if (enext == nullptr) { + /* The other boundary edge, where we only have the pair half-edge. */ + pair = e->next->next; + + if (p_collapse_allowed(nullptr, pair)) { + float cost = p_collapse_cost(nullptr, pair); + + if ((*r_mine == nullptr) || (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 = nullptr, *verts = chart->verts; + PEdge *e, *nexte = nullptr, *edges = chart->edges, *laste = nullptr; + PFace *f, *nextf = nullptr, *faces = chart->faces; + + chart->verts = chart->collapsed_verts = nullptr; + chart->edges = chart->collapsed_edges = nullptr; + chart->faces = chart->collapsed_faces = nullptr; + + 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 = nullptr; + PEdge *e, *nexte = nullptr; + PFace *f, *nextf = nullptr; + + 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 = nullptr; + chart->collapsed_edges = nullptr; + chart->collapsed_faces = nullptr; +} + +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 = nullptr, *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 = nullptr; + + p_collapse_cost_vertex(v, &cost, &e); + + if (e) { + v->u.heaplink = BLI_heap_insert(heap, cost, e); + } + else { + v->u.heaplink = nullptr; + } + } + + for (e = chart->edges; e; e = e->nextlink) { + e->u.nextcollapse = nullptr; + } + + /* 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 = nullptr; + SWAP(PEdge *, edge, pair); + } + else { + edge->flag |= PEDGE_COLLAPSE_EDGE; + edge->vert->u.heaplink = nullptr; + } + + 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 == nullptr) { + 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 = nullptr; + + v = wheelverts[i]; + + if (v->u.heaplink) { + BLI_heap_remove(heap, v->u.heaplink); + v->u.heaplink = nullptr; + } + + 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, nullptr); + + 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 + +using PAbfSystem = 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; +}; + +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; + } +} + +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); + + 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 = nullptr, *maxe1 = nullptr, *maxe2 = nullptr, *be1, *be2; + PEdge *cure = nullptr, *firste1 = nullptr, *firste2 = nullptr, *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 = nullptr; + } + + 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] = nullptr; + maxvert[0] = maxvert[1] = maxvert[2] = nullptr; + + 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 = nullptr; + } + 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 = nullptr; + + MEM_SAFE_FREE(chart->u.lscm.abf_alpha); + + chart->u.lscm.pin1 = nullptr; + chart->u.lscm.pin2 = nullptr; + chart->u.lscm.single_pin = nullptr; + 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 == nullptr) { + 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_freeN(U); + MEM_freeN(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_freeN(angles); + MEM_freeN(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() +{ + ParamHandle *handle = new 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) +{ + if (!phandle) { + return; + } + 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, nullptr, nullptr); + phandle->pin_hash = nullptr; + } + + 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, nullptr); + + if (phandle->rng) { + BLI_rng_free(phandle->rng); + phandle->rng = nullptr; + } + + delete phandle; +} + +using GeoUVPinIndex = struct GeoUVPinIndex { + struct GeoUVPinIndex *next; + float uv[2]; + ParamKey reindex; +}; + +/* 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 = nullptr; + 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 (uint 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) == nullptr); + 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_freeN(phandle->construction_chart); + phandle->construction_chart = nullptr; + + phash_delete(phandle->hash_verts); + phash_delete(phandle->hash_edges); + phash_delete(phandle->hash_faces); + phandle->hash_verts = phandle->hash_edges = phandle->hash_faces = nullptr; + + 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_freeN(chart); + if (count_fail != nullptr) { + *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 != nullptr) { + *count_changed += 1; + } + } + else { + if (count_failed != nullptr) { + *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_freeN(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); + } + } +} |