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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.c
* \ingroup bli
*
* A simple implementation of the ear cutting algorithm
* to triangulate simple polygons without holes.
*
* \note
*
* Changes made for Blender.
*
* - loop the array to clip last verts first (less array resizing)
*
* - advance the ear to clip each iteration
* to avoid fan-filling convex shapes (USE_CLIP_EVEN).
*
* - avoid intersection tests when there are no convex points (USE_CONVEX_SKIP).
*
* \note
*
* No globals - keep threadsafe.
*/
#include "BLI_utildefines.h"
#include "BLI_math.h"
#include "BLI_memarena.h"
#include "BLI_alloca.h"
#include "BLI_polyfill2d.h" /* own include */
#include "BLI_strict_flags.h"
/* avoid fan-fill topology */
#define USE_CLIP_EVEN
#define USE_CONVEX_SKIP
/* sweep back-and-forth about convex ears (avoids lop-sided fans) */
#define USE_CLIP_SWEEP
// #define USE_CONVEX_SKIP_TEST
// #define DEBUG_TIME
#ifdef DEBUG_TIME
# include "PIL_time_utildefines.h"
#endif
typedef signed char eSign;
enum {
CONCAVE = -1,
TANGENTIAL = 0,
CONVEX = 1,
};
typedef struct PolyFill {
struct PolyIndex *indices; /* vertex aligned */
const float (*coords)[2];
unsigned int coords_tot;
#ifdef USE_CONVEX_SKIP
unsigned int coords_tot_concave;
#endif
/* A polygon with n vertices has a triangulation of n-2 triangles. */
unsigned int (*tris)[3];
unsigned int tris_tot;
} PolyFill;
/* circular linklist */
typedef struct PolyIndex {
struct PolyIndex *next, *prev;
unsigned int index;
eSign sign;
} PolyIndex;
/* based on libgdx 2013-11-28, apache 2.0 licensed */
static void pf_coord_sign_calc(PolyFill *pf, PolyIndex *pi);
static PolyIndex *pf_ear_tip_find(
PolyFill *pf
#ifdef USE_CLIP_EVEN
, PolyIndex *pi_ear_init
#endif
#ifdef USE_CLIP_SWEEP
, bool reverse
#endif
);
static bool pf_ear_tip_check(PolyFill *pf, PolyIndex *pi_ear_tip);
static void pf_ear_tip_cut(PolyFill *pf, PolyIndex *pi_ear_tip);
BLI_INLINE eSign signum_i(float a)
{
if (UNLIKELY(a == 0.0f))
return 0;
else if (a > 0.0f)
return 1;
else
return -1;
}
/**
* alternative version of #area_tri_signed_v2
* needed because of float precision issues
*
* \note removes / 2 since its not needed since we only need ths sign.
*/
BLI_INLINE float area_tri_signed_v2_alt_2x(const float v1[2], const float v2[2], const float v3[2])
{
return ((v1[0] * (v2[1] - v3[1])) +
(v2[0] * (v3[1] - v1[1])) +
(v3[0] * (v1[1] - v2[1])));
}
static eSign span_tri_v2_sign(const float v1[2], const float v2[2], const float v3[2])
{
return signum_i(area_tri_signed_v2_alt_2x(v3, v2, v1));
}
static unsigned int *pf_tri_add(PolyFill *pf)
{
return pf->tris[pf->tris_tot++];
}
static void pf_coord_remove(PolyFill *pf, PolyIndex *pi)
{
pi->next->prev = pi->prev;
pi->prev->next = pi->next;
if (UNLIKELY(pf->indices == pi)) {
pf->indices = pi->next;
}
#ifdef DEBUG
pi->index = (unsigned int)-1;
pi->next = pi->prev = NULL;
#endif
pf->coords_tot -= 1;
}
static void pf_triangulate(PolyFill *pf)
{
/* localize */
PolyIndex *pi_ear;
#ifdef USE_CLIP_EVEN
PolyIndex *pi_ear_init = pf->indices;
#endif
#ifdef USE_CLIP_SWEEP
bool reverse = false;
#endif
while (pf->coords_tot > 3) {
PolyIndex *pi_prev, *pi_next;
eSign sign_orig_prev, sign_orig_next;
pi_ear = pf_ear_tip_find(
pf
#ifdef USE_CLIP_EVEN
, pi_ear_init
#endif
#ifdef USE_CLIP_SWEEP
, reverse
#endif
);
#ifdef USE_CLIP_SWEEP
#ifdef USE_CLIP_EVEN
if (pi_ear != pi_ear_init) {
reverse = !reverse;
}
#else
if (pi_ear != pf->indices) {
reverse = !reverse;
}
#endif
#endif
#ifdef USE_CONVEX_SKIP
if (pi_ear->sign != CONVEX) {
pf->coords_tot_concave -= 1;
}
#endif
pi_prev = pi_ear->prev;
pi_next = pi_ear->next;
pf_ear_tip_cut(pf, pi_ear);
/* The type of the two vertices adjacent to the clipped vertex may have changed. */
sign_orig_prev = pi_prev->sign;
sign_orig_next = pi_next->sign;
/* check if any verts became convex the (else if)
* case is highly unlikely but may happen with degenerate polygons */
if (sign_orig_prev != CONVEX) {
pf_coord_sign_calc(pf, pi_prev);
#ifdef USE_CONVEX_SKIP
if (pi_prev->sign == CONVEX) {
pf->coords_tot_concave -= 1;
}
#endif
}
if (sign_orig_next != CONVEX) {
pf_coord_sign_calc(pf, pi_next);
#ifdef USE_CONVEX_SKIP
if (pi_next->sign == CONVEX) {
pf->coords_tot_concave -= 1;
}
#endif
}
#ifdef USE_CLIP_EVEN
#ifdef USE_CLIP_SWEEP
pi_ear_init = reverse ? pi_next->next : pi_prev->prev;
#else
pi_ear_init = pi_next->next;
#endif
#endif
}
if (pf->coords_tot == 3) {
unsigned int *tri = pf_tri_add(pf);
pi_ear = pf->indices;
tri[0] = pi_ear->index; pi_ear = pi_ear->next;
tri[1] = pi_ear->index; pi_ear = pi_ear->next;
tri[2] = pi_ear->index;
}
}
/**
* \return CONCAVE, TANGENTIAL or CONVEX
*/
static void pf_coord_sign_calc(PolyFill *pf, PolyIndex *pi)
{
/* localize */
const float (*coords)[2] = pf->coords;
pi->sign = span_tri_v2_sign(
coords[pi->prev->index],
coords[pi->index],
coords[pi->next->index]);
}
static PolyIndex *pf_ear_tip_find(
PolyFill *pf
#ifdef USE_CLIP_EVEN
, PolyIndex *pi_ear_init
#endif
#ifdef USE_CLIP_SWEEP
, bool reverse
#endif
)
{
/* localize */
const unsigned int coords_tot = pf->coords_tot;
PolyIndex *pi_ear;
unsigned int i;
#ifdef USE_CLIP_EVEN
pi_ear = pi_ear_init;
#else
pi_ear = pf->indices;
#endif
i = coords_tot;
while (i--) {
if (pf_ear_tip_check(pf, pi_ear)) {
return pi_ear;
}
#ifdef USE_CLIP_SWEEP
pi_ear = reverse ? pi_ear->prev : pi_ear->next;
#else
pi_ear = pi_ear->next;
#endif
}
/* Desperate mode: if no vertex is an ear tip, we are dealing with a degenerate polygon (e.g. nearly collinear).
* Note that the input was not necessarily degenerate, but we could have made it so by clipping some valid ears.
*
* Idea taken from Martin Held, "FIST: Fast industrial-strength triangulation of polygons", Algorithmica (1998),
* http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.115.291
*
* Return a convex or tangential vertex if one exists.
*/
#ifdef USE_CLIP_EVEN
pi_ear = pi_ear_init;
#else
pi_ear = pf->indices;
#endif
i = coords_tot;
while (i--) {
if (pi_ear->sign != CONCAVE) {
return pi_ear;
}
pi_ear = pi_ear->next;
}
/* If all vertices are concave, just return the last one. */
return pi_ear;
}
static bool pf_ear_tip_check(PolyFill *pf, PolyIndex *pi_ear_tip)
{
/* localize */
PolyIndex *pi_curr;
const float (*coords)[2] = pf->coords;
const float *v1, *v2, *v3;
#ifdef USE_CONVEX_SKIP
unsigned int coords_tot_concave_checked = 0;
#endif
#ifdef USE_CONVEX_SKIP
#ifdef USE_CONVEX_SKIP_TEST
/* check if counting is wrong */
{
unsigned int coords_tot_concave_test = 0;
unsigned int i = pf->coords_tot;
while (i--) {
if (pf->indices[i].sign != CONVEX) {
coords_tot_concave_test += 1;
}
}
BLI_assert(coords_tot_concave_test == pf->coords_tot_concave);
}
#endif
/* fast-path for circles */
if (pf->coords_tot_concave == 0) {
return true;
}
#endif
if (UNLIKELY(pi_ear_tip->sign == CONCAVE)) {
return false;
}
v1 = coords[pi_ear_tip->prev->index];
v2 = coords[pi_ear_tip->index];
v3 = coords[pi_ear_tip->next->index];
/* Check if any point is inside the triangle formed by previous, current and next vertices.
* Only consider vertices that are not part of this triangle, or else we'll always find one inside. */
for (pi_curr = pi_ear_tip->next->next; pi_curr != pi_ear_tip->prev; pi_curr = pi_curr->next) {
/* Concave vertices can obviously be inside the candidate ear, but so can tangential vertices
* if they coincide with one of the triangle's vertices. */
if (pi_curr->sign != CONVEX) {
const float *v = coords[pi_curr->index];
/* Because the polygon has clockwise winding order,
* the area sign will be positive if the point is strictly inside.
* It will be 0 on the edge, which we want to include as well. */
/* note: check (v3, v1) first since it fails _far_ more often then the other 2 checks (those fail equally).
* It's logical - the chance is low that points exist on the same side as the ear we're clipping off. */
if ((span_tri_v2_sign(v3, v1, v) != CONCAVE) &&
(span_tri_v2_sign(v1, v2, v) != CONCAVE) &&
(span_tri_v2_sign(v2, v3, v) != CONCAVE))
{
return false;
}
#ifdef USE_CONVEX_SKIP
coords_tot_concave_checked += 1;
if (coords_tot_concave_checked == pf->coords_tot_concave) {
break;
}
#endif
}
}
return true;
}
static void pf_ear_tip_cut(PolyFill *pf, PolyIndex *pi_ear_tip)
{
unsigned int *tri = pf_tri_add(pf);
tri[0] = pi_ear_tip->prev->index;
tri[1] = pi_ear_tip->index;
tri[2] = pi_ear_tip->next->index;
pf_coord_remove(pf, pi_ear_tip);
}
/**
* Triangulates the given (convex or concave) simple polygon to a list of triangle vertices.
*
* \param coords pairs describing vertices of the polygon, in either clockwise or counterclockwise order.
* \return triples of triangle indices in clockwise order.
* Note the returned array is reused for later calls to the same method.
*/
static void polyfill_calc_ex(
const float (*coords)[2],
const unsigned int coords_tot,
unsigned int (*r_tris)[3],
PolyIndex *r_indices)
{
PolyFill pf;
/* localize */
PolyIndex *indices = r_indices;
unsigned int i;
/* assign all polyfill members here */
pf.indices = r_indices;
pf.coords = coords;
pf.coords_tot = coords_tot;
#ifdef USE_CONVEX_SKIP
pf.coords_tot_concave = 0;
#endif
pf.tris = r_tris;
pf.tris_tot = 0;
if ((coords_tot < 3) ||
cross_poly_v2(coords, coords_tot) > 0.0f)
{
for (i = 0; i < coords_tot; i++) {
indices[i].next = &indices[i + 1];
indices[i].prev = &indices[i - 1];
indices[i].index = i;
}
}
else {
/* reversed */
unsigned int n = coords_tot - 1;
for (i = 0; i < coords_tot; i++) {
indices[i].next = &indices[i + 1];
indices[i].prev = &indices[i - 1];
indices[i].index = (n - i);
}
}
indices[0].prev = &indices[coords_tot - 1];
indices[coords_tot - 1].next = &indices[0];
for (i = 0; i < coords_tot; i++) {
PolyIndex *pi = &indices[i];
pf_coord_sign_calc(&pf, pi);
#ifdef USE_CONVEX_SKIP
if (pi->sign != CONVEX) {
pf.coords_tot_concave += 1;
}
#endif
}
pf_triangulate(&pf);
}
void BLI_polyfill_calc_arena(
const float (*coords)[2],
const unsigned int coords_tot,
unsigned int (*r_tris)[3],
struct MemArena *arena)
{
PolyIndex *indices = BLI_memarena_alloc(arena, sizeof(*indices) * coords_tot);
#ifdef DEBUG_TIME
TIMEIT_START(polyfill2d);
#endif
polyfill_calc_ex(
coords, coords_tot,
r_tris,
/* cache */
indices);
/* indices are no longer needed,
* caller can clear arena */
#ifdef DEBUG_TIME
TIMEIT_END(polyfill2d);
#endif
}
void BLI_polyfill_calc(
const float (*coords)[2],
const unsigned int coords_tot,
unsigned int (*r_tris)[3])
{
PolyIndex *indices = BLI_array_alloca(indices, coords_tot);
#ifdef DEBUG_TIME
TIMEIT_START(polyfill2d);
#endif
polyfill_calc_ex(
coords, coords_tot,
r_tris,
/* cache */
indices);
#ifdef DEBUG_TIME
TIMEIT_END(polyfill2d);
#endif
}
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