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/*
* ***** BEGIN GPL LICENSE BLOCK *****
*
* This program is free software; you can redistribute it and/or
* modify it under the terms of the GNU General Public License
* as published by the Free Software Foundation; either version 2
* of the License, or (at your option) any later version.
*
* This program is distributed in the hope that it will be useful,
* but WITHOUT ANY WARRANTY; without even the implied warranty of
* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
* GNU General Public License for more details.
*
* You should have received a copy of the GNU General Public License
* along with this program; if not, write to the Free Software Foundation,
* Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301, USA.
*
* ***** END GPL LICENSE BLOCK *****
*/
/** \file blender/blenlib/intern/polyfill2d_beautify.c
* \ingroup bli
*
* This function is to improve the tessellation resulting from polyfill2d,
* creating optimal topology.
*
* The functionality here matches #BM_mesh_beautify_fill,
* but its far simpler to perform this operation in 2d,
* on a simple polygon representation where we _know_:
*
* - The polygon is primitive with no holes with a continuous boundary.
* - Tris have consistent winding.
* - 2d (saves some hassles projecting face pairs on an axis for every edge-rotation)
* also saves us having to store all previous edge-states (see #EdRotState in bmesh_beautify.c)
*
* \note
*
* No globals - keep threadsafe.
*/
#include "BLI_utildefines.h"
#include "BLI_math.h"
#include "BLI_memarena.h"
#include "BLI_heap.h"
#include "BLI_polyfill2d_beautify.h" /* own include */
#include "BLI_strict_flags.h"
/* Used to find matching edges. */
struct OrderEdge {
uint verts[2];
uint e_half;
};
/* Half edge used for rotating in-place. */
struct HalfEdge {
uint v;
uint e_next;
uint e_radial;
uint base_index;
};
static int oedge_cmp(const void *a1, const void *a2)
{
const struct OrderEdge *x1 = a1, *x2 = a2;
if (x1->verts[0] > x2->verts[0]) {
return 1;
}
else if (x1->verts[0] < x2->verts[0]) {
return -1;
}
if (x1->verts[1] > x2->verts[1]) {
return 1;
}
else if (x1->verts[1] < x2->verts[1]) {
return -1;
}
/* only for pradictability */
if (x1->e_half > x2->e_half) {
return 1;
}
else if (x1->e_half < x2->e_half) {
return -1;
}
/* Should never get here, no two edges should be the same. */
BLI_assert(false);
return 0;
}
BLI_INLINE bool is_boundary_edge(uint i_a, uint i_b, const uint coord_last)
{
BLI_assert(i_a < i_b);
return ((i_a + 1 == i_b) || UNLIKELY((i_a == 0) && (i_b == coord_last)));
}
/**
* Assuming we have 2 triangles sharing an edge (2 - 4),
* check if the edge running from (1 - 3) gives better results.
*
* \param lock_degenerate: Use to avoid rotating out of a degenerate state.
* - When true, an existing zero area face on either side of the (2 - 4) split will return a positive value.
* - When false, the check must be non-biased towards either split direction.
*
* \return (negative number means the edge can be rotated, lager == better).
*/
float BLI_polyfill_beautify_quad_rotate_calc_ex(
const float v1[2], const float v2[2], const float v3[2], const float v4[2],
const bool lock_degenerate)
{
/* not a loop (only to be able to break out) */
do {
/* Allow very small faces to be considered non-zero. */
const float eps_zero_area = 1e-12f;
const float area_2x_234 = cross_tri_v2(v2, v3, v4);
const float area_2x_241 = cross_tri_v2(v2, v4, v1);
const float area_2x_123 = cross_tri_v2(v1, v2, v3);
const float area_2x_134 = cross_tri_v2(v1, v3, v4);
BLI_assert((ELEM(v1, v2, v3, v4) == false) &&
(ELEM(v2, v1, v3, v4) == false) &&
(ELEM(v3, v1, v2, v4) == false) &&
(ELEM(v4, v1, v2, v3) == false));
/*
* Test for unusable (1-3) state.
* - Area sign flipping to check faces aren't going to point in opposite directions.
* - Area epsilon check that the one of the faces won't be zero area.
*/
if ((area_2x_123 >= 0.0f) != (area_2x_134 >= 0.0f)) {
break;
}
else if ((fabsf(area_2x_123) <= eps_zero_area) || (fabsf(area_2x_134) <= eps_zero_area)) {
break;
}
/* Test for unusable (2-4) state (same as above). */
if ((area_2x_234 >= 0.0f) != (area_2x_241 >= 0.0f)) {
if (lock_degenerate) {
break;
}
else {
return -FLT_MAX; /* always rotate */
}
}
else if ((fabsf(area_2x_234) <= eps_zero_area) || (fabsf(area_2x_241) <= eps_zero_area)) {
return -FLT_MAX; /* always rotate */
}
{
/* testing rule: the area divided by the perimeter,
* check if (1-3) beats the existing (2-4) edge rotation */
float area_a, area_b;
float prim_a, prim_b;
float fac_24, fac_13;
float len_12, len_23, len_34, len_41, len_24, len_13;
/* edges around the quad */
len_12 = len_v2v2(v1, v2);
len_23 = len_v2v2(v2, v3);
len_34 = len_v2v2(v3, v4);
len_41 = len_v2v2(v4, v1);
/* edges crossing the quad interior */
len_13 = len_v2v2(v1, v3);
len_24 = len_v2v2(v2, v4);
/* note, area is in fact (area * 2),
* but in this case its OK, since we're comparing ratios */
/* edge (2-4), current state */
area_a = fabsf(area_2x_234);
area_b = fabsf(area_2x_241);
prim_a = len_23 + len_34 + len_24;
prim_b = len_41 + len_12 + len_24;
fac_24 = (area_a / prim_a) + (area_b / prim_b);
/* edge (1-3), new state */
area_a = fabsf(area_2x_123);
area_b = fabsf(area_2x_134);
prim_a = len_12 + len_23 + len_13;
prim_b = len_34 + len_41 + len_13;
fac_13 = (area_a / prim_a) + (area_b / prim_b);
/* negative number if (1-3) is an improved state */
return fac_24 - fac_13;
}
} while (false);
return FLT_MAX;
}
static float polyedge_rotate_beauty_calc(
const float (*coords)[2],
const struct HalfEdge *edges,
const struct HalfEdge *e_a)
{
const struct HalfEdge *e_b = &edges[e_a->e_radial];
const struct HalfEdge *e_a_other = &edges[edges[e_a->e_next].e_next];
const struct HalfEdge *e_b_other = &edges[edges[e_b->e_next].e_next];
const float *v1, *v2, *v3, *v4;
v1 = coords[e_a_other->v];
v2 = coords[e_a->v];
v3 = coords[e_b_other->v];
v4 = coords[e_b->v];
return BLI_polyfill_beautify_quad_rotate_calc(v1, v2, v3, v4);
}
static void polyedge_beauty_cost_update_single(
const float (*coords)[2],
const struct HalfEdge *edges,
struct HalfEdge *e,
Heap *eheap, HeapNode **eheap_table)
{
const uint i = e->base_index;
/* recalculate edge */
const float cost = polyedge_rotate_beauty_calc(coords, edges, e);
/* We can get cases where both choices generate very small negative costs, which leads to infinite loop.
* Anyway, costs above that are not worth recomputing, maybe we could even optimize it to a smaller limit?
* Actually, FLT_EPSILON is too small in some cases, 1e-6f seems to work OK hopefully?
* See T43578, T49478. */
if (cost < -1e-6f) {
BLI_heap_insert_or_update(eheap, &eheap_table[i], cost, e);
}
else {
if (eheap_table[i]) {
BLI_heap_remove(eheap, eheap_table[i]);
eheap_table[i] = NULL;
}
}
}
static void polyedge_beauty_cost_update(
const float (*coords)[2],
struct HalfEdge *edges,
struct HalfEdge *e,
Heap *eheap, HeapNode **eheap_table)
{
struct HalfEdge *e_arr[4];
e_arr[0] = &edges[e->e_next];
e_arr[1] = &edges[e_arr[0]->e_next];
e = &edges[e->e_radial];
e_arr[2] = &edges[e->e_next];
e_arr[3] = &edges[e_arr[2]->e_next];
for (uint i = 0; i < 4; i++) {
if (e_arr[i] && e_arr[i]->base_index != UINT_MAX) {
polyedge_beauty_cost_update_single(
coords, edges,
e_arr[i],
eheap, eheap_table);
}
}
}
static void polyedge_rotate(
struct HalfEdge *edges,
struct HalfEdge *e)
{
/** CCW winding, rotate internal edge to new vertical state.
* <pre>
* Before After
* X X
* / \ /|\
* e4/ \e5 e4/ | \e5
* / e3 \ / | \
* X ------- X -> X e0|e3 X
* \ e0 / \ | /
* e2\ /e1 e2\ | /e1
* \ / \|/
* X X
* </pre>
*/
struct HalfEdge *ed[6];
uint ed_index[6];
ed_index[0] = (uint)(e - edges);
ed[0] = &edges[ed_index[0]];
ed_index[1] = ed[0]->e_next;
ed[1] = &edges[ed_index[1]];
ed_index[2] = ed[1]->e_next;
ed[2] = &edges[ed_index[2]];
ed_index[3] = e->e_radial;
ed[3] = &edges[ed_index[3]];
ed_index[4] = ed[3]->e_next;
ed[4] = &edges[ed_index[4]];
ed_index[5] = ed[4]->e_next;
ed[5] = &edges[ed_index[5]];
ed[0]->e_next = ed_index[2];
ed[1]->e_next = ed_index[3];
ed[2]->e_next = ed_index[4];
ed[3]->e_next = ed_index[5];
ed[4]->e_next = ed_index[0];
ed[5]->e_next = ed_index[1];
ed[0]->v = ed[5]->v;
ed[3]->v = ed[2]->v;
}
/**
* The intention is that this calculates the output of #BLI_polyfill_calc
*
*
* \note assumes the \a coords form a boundary,
* so any edges running along contiguous (wrapped) indices,
* are ignored since the edges wont share 2 faces.
*/
void BLI_polyfill_beautify(
const float (*coords)[2],
const uint coords_tot,
uint (*tris)[3],
/* structs for reuse */
MemArena *arena, Heap *eheap)
{
const uint coord_last = coords_tot - 1;
const uint tris_len = coords_tot - 2;
/* internal edges only (between 2 tris) */
const uint edges_len = tris_len - 1;
HeapNode **eheap_table;
const uint half_edges_len = 3 * tris_len;
struct HalfEdge *half_edges = BLI_memarena_alloc(arena, sizeof(*half_edges) * half_edges_len);
struct OrderEdge *order_edges = BLI_memarena_alloc(arena, sizeof(struct OrderEdge) * 2 * edges_len);
uint order_edges_len = 0;
/* first build edges */
for (uint i = 0; i < tris_len; i++) {
for (uint j_curr = 0, j_prev = 2; j_curr < 3; j_prev = j_curr++) {
const uint e_index_prev = (i * 3) + j_prev;
const uint e_index_curr = (i * 3) + j_curr;
half_edges[e_index_prev].v = tris[i][j_prev];
half_edges[e_index_prev].e_next = e_index_curr;
half_edges[e_index_prev].e_radial = UINT_MAX;
half_edges[e_index_prev].base_index = UINT_MAX;
uint e_pair[2] = {tris[i][j_prev], tris[i][j_curr]};
if (e_pair[0] > e_pair[1]) {
SWAP(uint, e_pair[0], e_pair[1]);
}
/* ensure internal edges. */
if (!is_boundary_edge(e_pair[0], e_pair[1], coord_last)) {
order_edges[order_edges_len].verts[0] = e_pair[0];
order_edges[order_edges_len].verts[1] = e_pair[1];
order_edges[order_edges_len].e_half = e_index_prev;
order_edges_len += 1;
}
}
}
BLI_assert(edges_len * 2 == order_edges_len);
qsort(order_edges, order_edges_len, sizeof(struct OrderEdge), oedge_cmp);
for (uint i = 0, base_index = 0; i < order_edges_len; base_index++) {
const struct OrderEdge *oe_a = &order_edges[i++];
const struct OrderEdge *oe_b = &order_edges[i++];
BLI_assert(oe_a->verts[0] == oe_a->verts[0] && oe_a->verts[1] == oe_a->verts[1]);
half_edges[oe_a->e_half].e_radial = oe_b->e_half;
half_edges[oe_b->e_half].e_radial = oe_a->e_half;
half_edges[oe_a->e_half].base_index = base_index;
half_edges[oe_b->e_half].base_index = base_index;
}
/* order_edges could be freed now. */
/* Now perform iterative rotations. */
#if 0
eheap_table = BLI_memarena_alloc(arena, sizeof(HeapNode *) * (size_t)edges_len);
#else
/* We can re-use this since its big enough. */
eheap_table = (void *)order_edges;
order_edges = NULL;
#endif
/* Build heap. */
{
struct HalfEdge *e = half_edges;
for (uint i = 0; i < half_edges_len; i++, e++) {
/* Accounts for boundary edged too (UINT_MAX). */
if (e->e_radial < i) {
const float cost = polyedge_rotate_beauty_calc(coords, half_edges, e);
if (cost < 0.0f) {
eheap_table[e->base_index] = BLI_heap_insert(eheap, cost, e);
}
else {
eheap_table[e->base_index] = NULL;
}
}
}
}
while (BLI_heap_is_empty(eheap) == false) {
struct HalfEdge *e = BLI_heap_popmin(eheap);
eheap_table[e->base_index] = NULL;
polyedge_rotate(half_edges, e);
/* recalculate faces connected on the heap */
polyedge_beauty_cost_update(
coords, half_edges,
e,
eheap, eheap_table);
}
BLI_heap_clear(eheap, NULL);
/* MEM_freeN(eheap_table); */ /* arena */
/* get tris from half edge. */
uint tri_index = 0;
for (uint i = 0; i < half_edges_len; i++) {
struct HalfEdge *e = &half_edges[i];
if (e->v != UINT_MAX) {
uint *tri = tris[tri_index++];
tri[0] = e->v;
e->v = UINT_MAX;
e = &half_edges[e->e_next];
tri[1] = e->v;
e->v = UINT_MAX;
e = &half_edges[e->e_next];
tri[2] = e->v;
e->v = UINT_MAX;
}
}
}
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