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godot/thirdparty/misc/polypartition.cpp
Aaron Franke ddd6fb37e8
Update PolyPartition / Triangulator library
2021-01-12 13:46:16 -05:00

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/*************************************************************************/
/* Copyright (c) 2011-2021 Ivan Fratric and contributors. */
/* */
/* Permission is hereby granted, free of charge, to any person obtaining */
/* a copy of this software and associated documentation files (the */
/* "Software"), to deal in the Software without restriction, including */
/* without limitation the rights to use, copy, modify, merge, publish, */
/* distribute, sublicense, and/or sell copies of the Software, and to */
/* permit persons to whom the Software is furnished to do so, subject to */
/* the following conditions: */
/* */
/* The above copyright notice and this permission notice shall be */
/* included in all copies or substantial portions of the Software. */
/* */
/* THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, */
/* EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF */
/* MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT.*/
/* IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY */
/* CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, */
/* TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE */
/* SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE. */
/*************************************************************************/
#include "polypartition.h"
#include <algorithm>
TPPLPoly::TPPLPoly() {
hole = false;
numpoints = 0;
points = NULL;
}
TPPLPoly::~TPPLPoly() {
if (points) {
delete[] points;
}
}
void TPPLPoly::Clear() {
if (points) {
delete[] points;
}
hole = false;
numpoints = 0;
points = NULL;
}
void TPPLPoly::Init(long numpoints) {
Clear();
this->numpoints = numpoints;
points = new TPPLPoint[numpoints];
}
void TPPLPoly::Triangle(TPPLPoint &p1, TPPLPoint &p2, TPPLPoint &p3) {
Init(3);
points[0] = p1;
points[1] = p2;
points[2] = p3;
}
TPPLPoly::TPPLPoly(const TPPLPoly &src) :
TPPLPoly() {
hole = src.hole;
numpoints = src.numpoints;
if (numpoints > 0) {
points = new TPPLPoint[numpoints];
memcpy(points, src.points, numpoints * sizeof(TPPLPoint));
}
}
TPPLPoly &TPPLPoly::operator=(const TPPLPoly &src) {
Clear();
hole = src.hole;
numpoints = src.numpoints;
if (numpoints > 0) {
points = new TPPLPoint[numpoints];
memcpy(points, src.points, numpoints * sizeof(TPPLPoint));
}
return *this;
}
TPPLOrientation TPPLPoly::GetOrientation() const {
long i1, i2;
tppl_float area = 0;
for (i1 = 0; i1 < numpoints; i1++) {
i2 = i1 + 1;
if (i2 == numpoints) {
i2 = 0;
}
area += points[i1].x * points[i2].y - points[i1].y * points[i2].x;
}
if (area > 0) {
return TPPL_ORIENTATION_CCW;
}
if (area < 0) {
return TPPL_ORIENTATION_CW;
}
return TPPL_ORIENTATION_NONE;
}
void TPPLPoly::SetOrientation(TPPLOrientation orientation) {
TPPLOrientation polyorientation = GetOrientation();
if (polyorientation != TPPL_ORIENTATION_NONE && polyorientation != orientation) {
Invert();
}
}
void TPPLPoly::Invert() {
std::reverse(points, points + numpoints);
}
TPPLPartition::PartitionVertex::PartitionVertex() :
previous(NULL), next(NULL) {
}
TPPLPoint TPPLPartition::Normalize(const TPPLPoint &p) {
TPPLPoint r;
tppl_float n = sqrt(p.x * p.x + p.y * p.y);
if (n != 0) {
r = p / n;
} else {
r.x = 0;
r.y = 0;
}
return r;
}
tppl_float TPPLPartition::Distance(const TPPLPoint &p1, const TPPLPoint &p2) {
tppl_float dx, dy;
dx = p2.x - p1.x;
dy = p2.y - p1.y;
return (sqrt(dx * dx + dy * dy));
}
// Checks if two lines intersect.
int TPPLPartition::Intersects(TPPLPoint &p11, TPPLPoint &p12, TPPLPoint &p21, TPPLPoint &p22) {
if ((p11.x == p21.x) && (p11.y == p21.y)) {
return 0;
}
if ((p11.x == p22.x) && (p11.y == p22.y)) {
return 0;
}
if ((p12.x == p21.x) && (p12.y == p21.y)) {
return 0;
}
if ((p12.x == p22.x) && (p12.y == p22.y)) {
return 0;
}
TPPLPoint v1ort, v2ort, v;
tppl_float dot11, dot12, dot21, dot22;
v1ort.x = p12.y - p11.y;
v1ort.y = p11.x - p12.x;
v2ort.x = p22.y - p21.y;
v2ort.y = p21.x - p22.x;
v = p21 - p11;
dot21 = v.x * v1ort.x + v.y * v1ort.y;
v = p22 - p11;
dot22 = v.x * v1ort.x + v.y * v1ort.y;
v = p11 - p21;
dot11 = v.x * v2ort.x + v.y * v2ort.y;
v = p12 - p21;
dot12 = v.x * v2ort.x + v.y * v2ort.y;
if (dot11 * dot12 > 0) {
return 0;
}
if (dot21 * dot22 > 0) {
return 0;
}
return 1;
}
// Removes holes from inpolys by merging them with non-holes.
int TPPLPartition::RemoveHoles(TPPLPolyList *inpolys, TPPLPolyList *outpolys) {
TPPLPolyList polys;
TPPLPolyList::Element *holeiter, *polyiter, *iter, *iter2;
long i, i2, holepointindex, polypointindex;
TPPLPoint holepoint, polypoint, bestpolypoint;
TPPLPoint linep1, linep2;
TPPLPoint v1, v2;
TPPLPoly newpoly;
bool hasholes;
bool pointvisible;
bool pointfound;
// Check for the trivial case of no holes.
hasholes = false;
for (iter = inpolys->front(); iter; iter = iter->next()) {
if (iter->get().IsHole()) {
hasholes = true;
break;
}
}
if (!hasholes) {
for (iter = inpolys->front(); iter; iter = iter->next()) {
outpolys->push_back(iter->get());
}
return 1;
}
polys = *inpolys;
while (1) {
// Find the hole point with the largest x.
hasholes = false;
for (iter = polys.front(); iter; iter = iter->next()) {
if (!iter->get().IsHole()) {
continue;
}
if (!hasholes) {
hasholes = true;
holeiter = iter;
holepointindex = 0;
}
for (i = 0; i < iter->get().GetNumPoints(); i++) {
if (iter->get().GetPoint(i).x > holeiter->get().GetPoint(holepointindex).x) {
holeiter = iter;
holepointindex = i;
}
}
}
if (!hasholes) {
break;
}
holepoint = holeiter->get().GetPoint(holepointindex);
pointfound = false;
for (iter = polys.front(); iter; iter = iter->next()) {
if (iter->get().IsHole()) {
continue;
}
for (i = 0; i < iter->get().GetNumPoints(); i++) {
if (iter->get().GetPoint(i).x <= holepoint.x) {
continue;
}
if (!InCone(iter->get().GetPoint((i + iter->get().GetNumPoints() - 1) % (iter->get().GetNumPoints())),
iter->get().GetPoint(i),
iter->get().GetPoint((i + 1) % (iter->get().GetNumPoints())),
holepoint)) {
continue;
}
polypoint = iter->get().GetPoint(i);
if (pointfound) {
v1 = Normalize(polypoint - holepoint);
v2 = Normalize(bestpolypoint - holepoint);
if (v2.x > v1.x) {
continue;
}
}
pointvisible = true;
for (iter2 = polys.front(); iter2; iter2->next()) {
if (iter2->get().IsHole()) {
continue;
}
for (i2 = 0; i2 < iter2->get().GetNumPoints(); i2++) {
linep1 = iter2->get().GetPoint(i2);
linep2 = iter2->get().GetPoint((i2 + 1) % (iter2->get().GetNumPoints()));
if (Intersects(holepoint, polypoint, linep1, linep2)) {
pointvisible = false;
break;
}
}
if (!pointvisible) {
break;
}
}
if (pointvisible) {
pointfound = true;
bestpolypoint = polypoint;
polyiter = iter;
polypointindex = i;
}
}
}
if (!pointfound) {
return 0;
}
newpoly.Init(holeiter->get().GetNumPoints() + polyiter->get().GetNumPoints() + 2);
i2 = 0;
for (i = 0; i <= polypointindex; i++) {
newpoly[i2] = polyiter->get().GetPoint(i);
i2++;
}
for (i = 0; i <= holeiter->get().GetNumPoints(); i++) {
newpoly[i2] = holeiter->get().GetPoint((i + holepointindex) % holeiter->get().GetNumPoints());
i2++;
}
for (i = polypointindex; i < polyiter->get().GetNumPoints(); i++) {
newpoly[i2] = polyiter->get().GetPoint(i);
i2++;
}
polys.erase(holeiter);
polys.erase(polyiter);
polys.push_back(newpoly);
}
for (iter = polys.front(); iter; iter = iter->next()) {
outpolys->push_back(iter->get());
}
return 1;
}
bool TPPLPartition::IsConvex(TPPLPoint &p1, TPPLPoint &p2, TPPLPoint &p3) {
tppl_float tmp;
tmp = (p3.y - p1.y) * (p2.x - p1.x) - (p3.x - p1.x) * (p2.y - p1.y);
if (tmp > 0) {
return 1;
} else {
return 0;
}
}
bool TPPLPartition::IsReflex(TPPLPoint &p1, TPPLPoint &p2, TPPLPoint &p3) {
tppl_float tmp;
tmp = (p3.y - p1.y) * (p2.x - p1.x) - (p3.x - p1.x) * (p2.y - p1.y);
if (tmp < 0) {
return 1;
} else {
return 0;
}
}
bool TPPLPartition::IsInside(TPPLPoint &p1, TPPLPoint &p2, TPPLPoint &p3, TPPLPoint &p) {
if (IsConvex(p1, p, p2)) {
return false;
}
if (IsConvex(p2, p, p3)) {
return false;
}
if (IsConvex(p3, p, p1)) {
return false;
}
return true;
}
bool TPPLPartition::InCone(TPPLPoint &p1, TPPLPoint &p2, TPPLPoint &p3, TPPLPoint &p) {
bool convex;
convex = IsConvex(p1, p2, p3);
if (convex) {
if (!IsConvex(p1, p2, p)) {
return false;
}
if (!IsConvex(p2, p3, p)) {
return false;
}
return true;
} else {
if (IsConvex(p1, p2, p)) {
return true;
}
if (IsConvex(p2, p3, p)) {
return true;
}
return false;
}
}
bool TPPLPartition::InCone(PartitionVertex *v, TPPLPoint &p) {
TPPLPoint p1, p2, p3;
p1 = v->previous->p;
p2 = v->p;
p3 = v->next->p;
return InCone(p1, p2, p3, p);
}
void TPPLPartition::UpdateVertexReflexity(PartitionVertex *v) {
PartitionVertex *v1 = NULL, *v3 = NULL;
v1 = v->previous;
v3 = v->next;
v->isConvex = !IsReflex(v1->p, v->p, v3->p);
}
void TPPLPartition::UpdateVertex(PartitionVertex *v, PartitionVertex *vertices, long numvertices) {
long i;
PartitionVertex *v1 = NULL, *v3 = NULL;
TPPLPoint vec1, vec3;
v1 = v->previous;
v3 = v->next;
v->isConvex = IsConvex(v1->p, v->p, v3->p);
vec1 = Normalize(v1->p - v->p);
vec3 = Normalize(v3->p - v->p);
v->angle = vec1.x * vec3.x + vec1.y * vec3.y;
if (v->isConvex) {
v->isEar = true;
for (i = 0; i < numvertices; i++) {
if ((vertices[i].p.x == v->p.x) && (vertices[i].p.y == v->p.y)) {
continue;
}
if ((vertices[i].p.x == v1->p.x) && (vertices[i].p.y == v1->p.y)) {
continue;
}
if ((vertices[i].p.x == v3->p.x) && (vertices[i].p.y == v3->p.y)) {
continue;
}
if (IsInside(v1->p, v->p, v3->p, vertices[i].p)) {
v->isEar = false;
break;
}
}
} else {
v->isEar = false;
}
}
// Triangulation by ear removal.
int TPPLPartition::Triangulate_EC(TPPLPoly *poly, TPPLPolyList *triangles) {
if (!poly->Valid()) {
return 0;
}
long numvertices;
PartitionVertex *vertices = NULL;
PartitionVertex *ear = NULL;
TPPLPoly triangle;
long i, j;
bool earfound;
if (poly->GetNumPoints() < 3) {
return 0;
}
if (poly->GetNumPoints() == 3) {
triangles->push_back(*poly);
return 1;
}
numvertices = poly->GetNumPoints();
vertices = new PartitionVertex[numvertices];
for (i = 0; i < numvertices; i++) {
vertices[i].isActive = true;
vertices[i].p = poly->GetPoint(i);
if (i == (numvertices - 1)) {
vertices[i].next = &(vertices[0]);
} else {
vertices[i].next = &(vertices[i + 1]);
}
if (i == 0) {
vertices[i].previous = &(vertices[numvertices - 1]);
} else {
vertices[i].previous = &(vertices[i - 1]);
}
}
for (i = 0; i < numvertices; i++) {
UpdateVertex(&vertices[i], vertices, numvertices);
}
for (i = 0; i < numvertices - 3; i++) {
earfound = false;
// Find the most extruded ear.
for (j = 0; j < numvertices; j++) {
if (!vertices[j].isActive) {
continue;
}
if (!vertices[j].isEar) {
continue;
}
if (!earfound) {
earfound = true;
ear = &(vertices[j]);
} else {
if (vertices[j].angle > ear->angle) {
ear = &(vertices[j]);
}
}
}
if (!earfound) {
delete[] vertices;
return 0;
}
triangle.Triangle(ear->previous->p, ear->p, ear->next->p);
triangles->push_back(triangle);
ear->isActive = false;
ear->previous->next = ear->next;
ear->next->previous = ear->previous;
if (i == numvertices - 4) {
break;
}
UpdateVertex(ear->previous, vertices, numvertices);
UpdateVertex(ear->next, vertices, numvertices);
}
for (i = 0; i < numvertices; i++) {
if (vertices[i].isActive) {
triangle.Triangle(vertices[i].previous->p, vertices[i].p, vertices[i].next->p);
triangles->push_back(triangle);
break;
}
}
delete[] vertices;
return 1;
}
int TPPLPartition::Triangulate_EC(TPPLPolyList *inpolys, TPPLPolyList *triangles) {
TPPLPolyList outpolys;
TPPLPolyList::Element *iter;
if (!RemoveHoles(inpolys, &outpolys)) {
return 0;
}
for (iter = outpolys.front(); iter; iter = iter->next()) {
if (!Triangulate_EC(&(iter->get()), triangles)) {
return 0;
}
}
return 1;
}
int TPPLPartition::ConvexPartition_HM(TPPLPoly *poly, TPPLPolyList *parts) {
if (!poly->Valid()) {
return 0;
}
TPPLPolyList triangles;
TPPLPolyList::Element *iter1, *iter2;
TPPLPoly *poly1 = NULL, *poly2 = NULL;
TPPLPoly newpoly;
TPPLPoint d1, d2, p1, p2, p3;
long i11, i12, i21, i22, i13, i23, j, k;
bool isdiagonal;
long numreflex;
// Check if the poly is already convex.
numreflex = 0;
for (i11 = 0; i11 < poly->GetNumPoints(); i11++) {
if (i11 == 0) {
i12 = poly->GetNumPoints() - 1;
} else {
i12 = i11 - 1;
}
if (i11 == (poly->GetNumPoints() - 1)) {
i13 = 0;
} else {
i13 = i11 + 1;
}
if (IsReflex(poly->GetPoint(i12), poly->GetPoint(i11), poly->GetPoint(i13))) {
numreflex = 1;
break;
}
}
if (numreflex == 0) {
parts->push_back(*poly);
return 1;
}
if (!Triangulate_EC(poly, &triangles)) {
return 0;
}
for (iter1 = triangles.front(); iter1; iter1 = iter1->next()) {
poly1 = &(iter1->get());
for (i11 = 0; i11 < poly1->GetNumPoints(); i11++) {
d1 = poly1->GetPoint(i11);
i12 = (i11 + 1) % (poly1->GetNumPoints());
d2 = poly1->GetPoint(i12);
isdiagonal = false;
for (iter2 = iter1; iter2; iter2 = iter2->next()) {
if (iter1 == iter2) {
continue;
}
poly2 = &(iter2->get());
for (i21 = 0; i21 < poly2->GetNumPoints(); i21++) {
if ((d2.x != poly2->GetPoint(i21).x) || (d2.y != poly2->GetPoint(i21).y)) {
continue;
}
i22 = (i21 + 1) % (poly2->GetNumPoints());
if ((d1.x != poly2->GetPoint(i22).x) || (d1.y != poly2->GetPoint(i22).y)) {
continue;
}
isdiagonal = true;
break;
}
if (isdiagonal) {
break;
}
}
if (!isdiagonal) {
continue;
}
p2 = poly1->GetPoint(i11);
if (i11 == 0) {
i13 = poly1->GetNumPoints() - 1;
} else {
i13 = i11 - 1;
}
p1 = poly1->GetPoint(i13);
if (i22 == (poly2->GetNumPoints() - 1)) {
i23 = 0;
} else {
i23 = i22 + 1;
}
p3 = poly2->GetPoint(i23);
if (!IsConvex(p1, p2, p3)) {
continue;
}
p2 = poly1->GetPoint(i12);
if (i12 == (poly1->GetNumPoints() - 1)) {
i13 = 0;
} else {
i13 = i12 + 1;
}
p3 = poly1->GetPoint(i13);
if (i21 == 0) {
i23 = poly2->GetNumPoints() - 1;
} else {
i23 = i21 - 1;
}
p1 = poly2->GetPoint(i23);
if (!IsConvex(p1, p2, p3)) {
continue;
}
newpoly.Init(poly1->GetNumPoints() + poly2->GetNumPoints() - 2);
k = 0;
for (j = i12; j != i11; j = (j + 1) % (poly1->GetNumPoints())) {
newpoly[k] = poly1->GetPoint(j);
k++;
}
for (j = i22; j != i21; j = (j + 1) % (poly2->GetNumPoints())) {
newpoly[k] = poly2->GetPoint(j);
k++;
}
triangles.erase(iter2);
iter1->get() = newpoly;
poly1 = &(iter1->get());
i11 = -1;
continue;
}
}
for (iter1 = triangles.front(); iter1; iter1 = iter1->next()) {
parts->push_back(iter1->get());
}
return 1;
}
int TPPLPartition::ConvexPartition_HM(TPPLPolyList *inpolys, TPPLPolyList *parts) {
TPPLPolyList outpolys;
TPPLPolyList::Element *iter;
if (!RemoveHoles(inpolys, &outpolys)) {
return 0;
}
for (iter = outpolys.front(); iter; iter = iter->next()) {
if (!ConvexPartition_HM(&(iter->get()), parts)) {
return 0;
}
}
return 1;
}
// Minimum-weight polygon triangulation by dynamic programming.
// Time complexity: O(n^3)
// Space complexity: O(n^2)
int TPPLPartition::Triangulate_OPT(TPPLPoly *poly, TPPLPolyList *triangles) {
if (!poly->Valid()) {
return 0;
}
long i, j, k, gap, n;
DPState **dpstates = NULL;
TPPLPoint p1, p2, p3, p4;
long bestvertex;
tppl_float weight, minweight, d1, d2;
Diagonal diagonal, newdiagonal;
DiagonalList diagonals;
TPPLPoly triangle;
int ret = 1;
n = poly->GetNumPoints();
dpstates = new DPState *[n];
for (i = 1; i < n; i++) {
dpstates[i] = new DPState[i];
}
// Initialize states and visibility.
for (i = 0; i < (n - 1); i++) {
p1 = poly->GetPoint(i);
for (j = i + 1; j < n; j++) {
dpstates[j][i].visible = true;
dpstates[j][i].weight = 0;
dpstates[j][i].bestvertex = -1;
if (j != (i + 1)) {
p2 = poly->GetPoint(j);
// Visibility check.
if (i == 0) {
p3 = poly->GetPoint(n - 1);
} else {
p3 = poly->GetPoint(i - 1);
}
if (i == (n - 1)) {
p4 = poly->GetPoint(0);
} else {
p4 = poly->GetPoint(i + 1);
}
if (!InCone(p3, p1, p4, p2)) {
dpstates[j][i].visible = false;
continue;
}
if (j == 0) {
p3 = poly->GetPoint(n - 1);
} else {
p3 = poly->GetPoint(j - 1);
}
if (j == (n - 1)) {
p4 = poly->GetPoint(0);
} else {
p4 = poly->GetPoint(j + 1);
}
if (!InCone(p3, p2, p4, p1)) {
dpstates[j][i].visible = false;
continue;
}
for (k = 0; k < n; k++) {
p3 = poly->GetPoint(k);
if (k == (n - 1)) {
p4 = poly->GetPoint(0);
} else {
p4 = poly->GetPoint(k + 1);
}
if (Intersects(p1, p2, p3, p4)) {
dpstates[j][i].visible = false;
break;
}
}
}
}
}
dpstates[n - 1][0].visible = true;
dpstates[n - 1][0].weight = 0;
dpstates[n - 1][0].bestvertex = -1;
for (gap = 2; gap < n; gap++) {
for (i = 0; i < (n - gap); i++) {
j = i + gap;
if (!dpstates[j][i].visible) {
continue;
}
bestvertex = -1;
for (k = (i + 1); k < j; k++) {
if (!dpstates[k][i].visible) {
continue;
}
if (!dpstates[j][k].visible) {
continue;
}
if (k <= (i + 1)) {
d1 = 0;
} else {
d1 = Distance(poly->GetPoint(i), poly->GetPoint(k));
}
if (j <= (k + 1)) {
d2 = 0;
} else {
d2 = Distance(poly->GetPoint(k), poly->GetPoint(j));
}
weight = dpstates[k][i].weight + dpstates[j][k].weight + d1 + d2;
if ((bestvertex == -1) || (weight < minweight)) {
bestvertex = k;
minweight = weight;
}
}
if (bestvertex == -1) {
for (i = 1; i < n; i++) {
delete[] dpstates[i];
}
delete[] dpstates;
return 0;
}
dpstates[j][i].bestvertex = bestvertex;
dpstates[j][i].weight = minweight;
}
}
newdiagonal.index1 = 0;
newdiagonal.index2 = n - 1;
diagonals.push_back(newdiagonal);
while (!diagonals.is_empty()) {
diagonal = diagonals.front()->get();
diagonals.pop_front();
bestvertex = dpstates[diagonal.index2][diagonal.index1].bestvertex;
if (bestvertex == -1) {
ret = 0;
break;
}
triangle.Triangle(poly->GetPoint(diagonal.index1), poly->GetPoint(bestvertex), poly->GetPoint(diagonal.index2));
triangles->push_back(triangle);
if (bestvertex > (diagonal.index1 + 1)) {
newdiagonal.index1 = diagonal.index1;
newdiagonal.index2 = bestvertex;
diagonals.push_back(newdiagonal);
}
if (diagonal.index2 > (bestvertex + 1)) {
newdiagonal.index1 = bestvertex;
newdiagonal.index2 = diagonal.index2;
diagonals.push_back(newdiagonal);
}
}
for (i = 1; i < n; i++) {
delete[] dpstates[i];
}
delete[] dpstates;
return ret;
}
void TPPLPartition::UpdateState(long a, long b, long w, long i, long j, DPState2 **dpstates) {
Diagonal newdiagonal;
DiagonalList *pairs = NULL;
long w2;
w2 = dpstates[a][b].weight;
if (w > w2) {
return;
}
pairs = &(dpstates[a][b].pairs);
newdiagonal.index1 = i;
newdiagonal.index2 = j;
if (w < w2) {
pairs->clear();
pairs->push_front(newdiagonal);
dpstates[a][b].weight = w;
} else {
if ((!pairs->is_empty()) && (i <= pairs->front()->get().index1)) {
return;
}
while ((!pairs->is_empty()) && (pairs->front()->get().index2 >= j)) {
pairs->pop_front();
}
pairs->push_front(newdiagonal);
}
}
void TPPLPartition::TypeA(long i, long j, long k, PartitionVertex *vertices, DPState2 **dpstates) {
DiagonalList *pairs = NULL;
DiagonalList::Element *iter, *lastiter;
long top;
long w;
if (!dpstates[i][j].visible) {
return;
}
top = j;
w = dpstates[i][j].weight;
if (k - j > 1) {
if (!dpstates[j][k].visible) {
return;
}
w += dpstates[j][k].weight + 1;
}
if (j - i > 1) {
pairs = &(dpstates[i][j].pairs);
iter = pairs->back();
lastiter = pairs->back();
while (iter != pairs->front()) {
iter--;
if (!IsReflex(vertices[iter->get().index2].p, vertices[j].p, vertices[k].p)) {
lastiter = iter;
} else {
break;
}
}
if (lastiter == pairs->back()) {
w++;
} else {
if (IsReflex(vertices[k].p, vertices[i].p, vertices[lastiter->get().index1].p)) {
w++;
} else {
top = lastiter->get().index1;
}
}
}
UpdateState(i, k, w, top, j, dpstates);
}
void TPPLPartition::TypeB(long i, long j, long k, PartitionVertex *vertices, DPState2 **dpstates) {
DiagonalList *pairs = NULL;
DiagonalList::Element *iter, *lastiter;
long top;
long w;
if (!dpstates[j][k].visible) {
return;
}
top = j;
w = dpstates[j][k].weight;
if (j - i > 1) {
if (!dpstates[i][j].visible) {
return;
}
w += dpstates[i][j].weight + 1;
}
if (k - j > 1) {
pairs = &(dpstates[j][k].pairs);
iter = pairs->front();
if ((!pairs->is_empty()) && (!IsReflex(vertices[i].p, vertices[j].p, vertices[iter->get().index1].p))) {
lastiter = iter;
while (iter) {
if (!IsReflex(vertices[i].p, vertices[j].p, vertices[iter->get().index1].p)) {
lastiter = iter;
iter = iter->next();
} else {
break;
}
}
if (IsReflex(vertices[lastiter->get().index2].p, vertices[k].p, vertices[i].p)) {
w++;
} else {
top = lastiter->get().index2;
}
} else {
w++;
}
}
UpdateState(i, k, w, j, top, dpstates);
}
int TPPLPartition::ConvexPartition_OPT(TPPLPoly *poly, TPPLPolyList *parts) {
if (!poly->Valid()) {
return 0;
}
TPPLPoint p1, p2, p3, p4;
PartitionVertex *vertices = NULL;
DPState2 **dpstates = NULL;
long i, j, k, n, gap;
DiagonalList diagonals, diagonals2;
Diagonal diagonal, newdiagonal;
DiagonalList *pairs = NULL, *pairs2 = NULL;
DiagonalList::Element *iter, *iter2;
int ret;
TPPLPoly newpoly;
List<long> indices;
List<long>::Element *iiter;
bool ijreal, jkreal;
n = poly->GetNumPoints();
vertices = new PartitionVertex[n];
dpstates = new DPState2 *[n];
for (i = 0; i < n; i++) {
dpstates[i] = new DPState2[n];
}
// Initialize vertex information.
for (i = 0; i < n; i++) {
vertices[i].p = poly->GetPoint(i);
vertices[i].isActive = true;
if (i == 0) {
vertices[i].previous = &(vertices[n - 1]);
} else {
vertices[i].previous = &(vertices[i - 1]);
}
if (i == (poly->GetNumPoints() - 1)) {
vertices[i].next = &(vertices[0]);
} else {
vertices[i].next = &(vertices[i + 1]);
}
}
for (i = 1; i < n; i++) {
UpdateVertexReflexity(&(vertices[i]));
}
// Initialize states and visibility.
for (i = 0; i < (n - 1); i++) {
p1 = poly->GetPoint(i);
for (j = i + 1; j < n; j++) {
dpstates[i][j].visible = true;
if (j == i + 1) {
dpstates[i][j].weight = 0;
} else {
dpstates[i][j].weight = 2147483647;
}
if (j != (i + 1)) {
p2 = poly->GetPoint(j);
// Visibility check.
if (!InCone(&vertices[i], p2)) {
dpstates[i][j].visible = false;
continue;
}
if (!InCone(&vertices[j], p1)) {
dpstates[i][j].visible = false;
continue;
}
for (k = 0; k < n; k++) {
p3 = poly->GetPoint(k);
if (k == (n - 1)) {
p4 = poly->GetPoint(0);
} else {
p4 = poly->GetPoint(k + 1);
}
if (Intersects(p1, p2, p3, p4)) {
dpstates[i][j].visible = false;
break;
}
}
}
}
}
for (i = 0; i < (n - 2); i++) {
j = i + 2;
if (dpstates[i][j].visible) {
dpstates[i][j].weight = 0;
newdiagonal.index1 = i + 1;
newdiagonal.index2 = i + 1;
dpstates[i][j].pairs.push_back(newdiagonal);
}
}
dpstates[0][n - 1].visible = true;
vertices[0].isConvex = false; // By convention.
for (gap = 3; gap < n; gap++) {
for (i = 0; i < n - gap; i++) {
if (vertices[i].isConvex) {
continue;
}
k = i + gap;
if (dpstates[i][k].visible) {
if (!vertices[k].isConvex) {
for (j = i + 1; j < k; j++) {
TypeA(i, j, k, vertices, dpstates);
}
} else {
for (j = i + 1; j < (k - 1); j++) {
if (vertices[j].isConvex) {
continue;
}
TypeA(i, j, k, vertices, dpstates);
}
TypeA(i, k - 1, k, vertices, dpstates);
}
}
}
for (k = gap; k < n; k++) {
if (vertices[k].isConvex) {
continue;
}
i = k - gap;
if ((vertices[i].isConvex) && (dpstates[i][k].visible)) {
TypeB(i, i + 1, k, vertices, dpstates);
for (j = i + 2; j < k; j++) {
if (vertices[j].isConvex) {
continue;
}
TypeB(i, j, k, vertices, dpstates);
}
}
}
}
// Recover solution.
ret = 1;
newdiagonal.index1 = 0;
newdiagonal.index2 = n - 1;
diagonals.push_front(newdiagonal);
while (!diagonals.is_empty()) {
diagonal = diagonals.front()->get();
diagonals.pop_front();
if ((diagonal.index2 - diagonal.index1) <= 1) {
continue;
}
pairs = &(dpstates[diagonal.index1][diagonal.index2].pairs);
if (pairs->is_empty()) {
ret = 0;
break;
}
if (!vertices[diagonal.index1].isConvex) {
iter = pairs->back();
iter--;
j = iter->get().index2;
newdiagonal.index1 = j;
newdiagonal.index2 = diagonal.index2;
diagonals.push_front(newdiagonal);
if ((j - diagonal.index1) > 1) {
if (iter->get().index1 != iter->get().index2) {
pairs2 = &(dpstates[diagonal.index1][j].pairs);
while (1) {
if (pairs2->is_empty()) {
ret = 0;
break;
}
iter2 = pairs2->back();
iter2--;
if (iter->get().index1 != iter2->get().index1) {
pairs2->pop_back();
} else {
break;
}
}
if (ret == 0) {
break;
}
}
newdiagonal.index1 = diagonal.index1;
newdiagonal.index2 = j;
diagonals.push_front(newdiagonal);
}
} else {
iter = pairs->front();
j = iter->get().index1;
newdiagonal.index1 = diagonal.index1;
newdiagonal.index2 = j;
diagonals.push_front(newdiagonal);
if ((diagonal.index2 - j) > 1) {
if (iter->get().index1 != iter->get().index2) {
pairs2 = &(dpstates[j][diagonal.index2].pairs);
while (1) {
if (pairs2->is_empty()) {
ret = 0;
break;
}
iter2 = pairs2->front();
if (iter->get().index2 != iter2->get().index2) {
pairs2->pop_front();
} else {
break;
}
}
if (ret == 0) {
break;
}
}
newdiagonal.index1 = j;
newdiagonal.index2 = diagonal.index2;
diagonals.push_front(newdiagonal);
}
}
}
if (ret == 0) {
for (i = 0; i < n; i++) {
delete[] dpstates[i];
}
delete[] dpstates;
delete[] vertices;
return ret;
}
newdiagonal.index1 = 0;
newdiagonal.index2 = n - 1;
diagonals.push_front(newdiagonal);
while (!diagonals.is_empty()) {
diagonal = diagonals.front()->get();
diagonals.pop_front();
if ((diagonal.index2 - diagonal.index1) <= 1) {
continue;
}
indices.clear();
diagonals2.clear();
indices.push_back(diagonal.index1);
indices.push_back(diagonal.index2);
diagonals2.push_front(diagonal);
while (!diagonals2.is_empty()) {
diagonal = diagonals2.front()->get();
diagonals2.pop_front();
if ((diagonal.index2 - diagonal.index1) <= 1) {
continue;
}
ijreal = true;
jkreal = true;
pairs = &(dpstates[diagonal.index1][diagonal.index2].pairs);
if (!vertices[diagonal.index1].isConvex) {
iter = pairs->back();
iter--;
j = iter->get().index2;
if (iter->get().index1 != iter->get().index2) {
ijreal = false;
}
} else {
iter = pairs->front();
j = iter->get().index1;
if (iter->get().index1 != iter->get().index2) {
jkreal = false;
}
}
newdiagonal.index1 = diagonal.index1;
newdiagonal.index2 = j;
if (ijreal) {
diagonals.push_back(newdiagonal);
} else {
diagonals2.push_back(newdiagonal);
}
newdiagonal.index1 = j;
newdiagonal.index2 = diagonal.index2;
if (jkreal) {
diagonals.push_back(newdiagonal);
} else {
diagonals2.push_back(newdiagonal);
}
indices.push_back(j);
}
//std::sort(indices.begin(), indices.end());
indices.sort();
newpoly.Init((long)indices.size());
k = 0;
for (iiter = indices.front(); iiter != indices.back(); iiter = iiter->next()) {
newpoly[k] = vertices[iiter->get()].p;
k++;
}
parts->push_back(newpoly);
}
for (i = 0; i < n; i++) {
delete[] dpstates[i];
}
delete[] dpstates;
delete[] vertices;
return ret;
}
// Creates a monotone partition of a list of polygons that
// can contain holes. Triangulates a set of polygons by
// first partitioning them into monotone polygons.
// Time complexity: O(n*log(n)), n is the number of vertices.
// Space complexity: O(n)
// The algorithm used here is outlined in the book
// "Computational Geometry: Algorithms and Applications"
// by Mark de Berg, Otfried Cheong, Marc van Kreveld, and Mark Overmars.
int TPPLPartition::MonotonePartition(TPPLPolyList *inpolys, TPPLPolyList *monotonePolys) {
TPPLPolyList::Element *iter;
MonotoneVertex *vertices = NULL;
long i, numvertices, vindex, vindex2, newnumvertices, maxnumvertices;
long polystartindex, polyendindex;
TPPLPoly *poly = NULL;
MonotoneVertex *v = NULL, *v2 = NULL, *vprev = NULL, *vnext = NULL;
ScanLineEdge newedge;
bool error = false;
numvertices = 0;
for (iter = inpolys->front(); iter; iter++) {
numvertices += iter->get().GetNumPoints();
}
maxnumvertices = numvertices * 3;
vertices = new MonotoneVertex[maxnumvertices];
newnumvertices = numvertices;
polystartindex = 0;
for (iter = inpolys->front(); iter; iter++) {
poly = &(iter->get());
polyendindex = polystartindex + poly->GetNumPoints() - 1;
for (i = 0; i < poly->GetNumPoints(); i++) {
vertices[i + polystartindex].p = poly->GetPoint(i);
if (i == 0) {
vertices[i + polystartindex].previous = polyendindex;
} else {
vertices[i + polystartindex].previous = i + polystartindex - 1;
}
if (i == (poly->GetNumPoints() - 1)) {
vertices[i + polystartindex].next = polystartindex;
} else {
vertices[i + polystartindex].next = i + polystartindex + 1;
}
}
polystartindex = polyendindex + 1;
}
// Construct the priority queue.
long *priority = new long[numvertices];
for (i = 0; i < numvertices; i++) {
priority[i] = i;
}
std::sort(priority, &(priority[numvertices]), VertexSorter(vertices));
// Determine vertex types.
TPPLVertexType *vertextypes = new TPPLVertexType[maxnumvertices];
for (i = 0; i < numvertices; i++) {
v = &(vertices[i]);
vprev = &(vertices[v->previous]);
vnext = &(vertices[v->next]);
if (Below(vprev->p, v->p) && Below(vnext->p, v->p)) {
if (IsConvex(vnext->p, vprev->p, v->p)) {
vertextypes[i] = TPPL_VERTEXTYPE_START;
} else {
vertextypes[i] = TPPL_VERTEXTYPE_SPLIT;
}
} else if (Below(v->p, vprev->p) && Below(v->p, vnext->p)) {
if (IsConvex(vnext->p, vprev->p, v->p)) {
vertextypes[i] = TPPL_VERTEXTYPE_END;
} else {
vertextypes[i] = TPPL_VERTEXTYPE_MERGE;
}
} else {
vertextypes[i] = TPPL_VERTEXTYPE_REGULAR;
}
}
// Helpers.
long *helpers = new long[maxnumvertices];
// Binary search tree that holds edges intersecting the scanline.
// Note that while set doesn't actually have to be implemented as
// a tree, complexity requirements for operations are the same as
// for the balanced binary search tree.
Set<ScanLineEdge> edgeTree;
// Store iterators to the edge tree elements.
// This makes deleting existing edges much faster.
Set<ScanLineEdge>::Element **edgeTreeIterators, *edgeIter;
edgeTreeIterators = new Set<ScanLineEdge>::Element *[maxnumvertices];
//Pair<Set<ScanLineEdge>::iterator, bool> edgeTreeRet;
for (i = 0; i < numvertices; i++) {
edgeTreeIterators[i] = nullptr;
}
// For each vertex.
for (i = 0; i < numvertices; i++) {
vindex = priority[i];
v = &(vertices[vindex]);
vindex2 = vindex;
v2 = v;
// Depending on the vertex type, do the appropriate action.
// Comments in the following sections are copied from
// "Computational Geometry: Algorithms and Applications".
// Notation: e_i = e subscript i, v_i = v subscript i, etc.
switch (vertextypes[vindex]) {
case TPPL_VERTEXTYPE_START:
// Insert e_i in T and set helper(e_i) to v_i.
newedge.p1 = v->p;
newedge.p2 = vertices[v->next].p;
newedge.index = vindex;
//edgeTreeRet = edgeTree.insert(newedge);
//edgeTreeIterators[vindex] = edgeTreeRet.first;
edgeTreeIterators[vindex] = edgeTree.insert(newedge);
helpers[vindex] = vindex;
break;
case TPPL_VERTEXTYPE_END:
if (edgeTreeIterators[v->previous] == edgeTree.back()) {
error = true;
break;
}
// If helper(e_i - 1) is a merge vertex
if (vertextypes[helpers[v->previous]] == TPPL_VERTEXTYPE_MERGE) {
// Insert the diagonal connecting vi to helper(e_i - 1) in D.
AddDiagonal(vertices, &newnumvertices, vindex, helpers[v->previous],
vertextypes, edgeTreeIterators, &edgeTree, helpers);
}
// Delete e_i - 1 from T
edgeTree.erase(edgeTreeIterators[v->previous]);
break;
case TPPL_VERTEXTYPE_SPLIT:
// Search in T to find the edge e_j directly left of v_i.
newedge.p1 = v->p;
newedge.p2 = v->p;
edgeIter = edgeTree.lower_bound(newedge);
if (edgeIter == edgeTree.front()) {
error = true;
break;
}
edgeIter--;
// Insert the diagonal connecting vi to helper(e_j) in D.
AddDiagonal(vertices, &newnumvertices, vindex, helpers[edgeIter->get().index],
vertextypes, edgeTreeIterators, &edgeTree, helpers);
vindex2 = newnumvertices - 2;
v2 = &(vertices[vindex2]);
// helper(e_j) in v_i.
helpers[edgeIter->get().index] = vindex;
// Insert e_i in T and set helper(e_i) to v_i.
newedge.p1 = v2->p;
newedge.p2 = vertices[v2->next].p;
newedge.index = vindex2;
//edgeTreeRet = edgeTree.insert(newedge);
//edgeTreeIterators[vindex2] = edgeTreeRet.first;
edgeTreeIterators[vindex2] = edgeTree.insert(newedge);
helpers[vindex2] = vindex2;
break;
case TPPL_VERTEXTYPE_MERGE:
if (edgeTreeIterators[v->previous] == edgeTree.back()) {
error = true;
break;
}
// if helper(e_i - 1) is a merge vertex
if (vertextypes[helpers[v->previous]] == TPPL_VERTEXTYPE_MERGE) {
// Insert the diagonal connecting vi to helper(e_i - 1) in D.
AddDiagonal(vertices, &newnumvertices, vindex, helpers[v->previous],
vertextypes, edgeTreeIterators, &edgeTree, helpers);
vindex2 = newnumvertices - 2;
v2 = &(vertices[vindex2]);
}
// Delete e_i - 1 from T.
edgeTree.erase(edgeTreeIterators[v->previous]);
// Search in T to find the edge e_j directly left of v_i.
newedge.p1 = v->p;
newedge.p2 = v->p;
edgeIter = edgeTree.lower_bound(newedge);
if (edgeIter == edgeTree.front()) {
error = true;
break;
}
edgeIter--;
// If helper(e_j) is a merge vertex.
if (vertextypes[helpers[edgeIter->get().index]] == TPPL_VERTEXTYPE_MERGE) {
// Insert the diagonal connecting v_i to helper(e_j) in D.
AddDiagonal(vertices, &newnumvertices, vindex2, helpers[edgeIter->get().index],
vertextypes, edgeTreeIterators, &edgeTree, helpers);
}
// helper(e_j) <- v_i
helpers[edgeIter->get().index] = vindex2;
break;
case TPPL_VERTEXTYPE_REGULAR:
// If the interior of P lies to the right of v_i.
if (Below(v->p, vertices[v->previous].p)) {
if (edgeTreeIterators[v->previous] == edgeTree.back()) {
error = true;
break;
}
// If helper(e_i - 1) is a merge vertex.
if (vertextypes[helpers[v->previous]] == TPPL_VERTEXTYPE_MERGE) {
// Insert the diagonal connecting v_i to helper(e_i - 1) in D.
AddDiagonal(vertices, &newnumvertices, vindex, helpers[v->previous],
vertextypes, edgeTreeIterators, &edgeTree, helpers);
vindex2 = newnumvertices - 2;
v2 = &(vertices[vindex2]);
}
// Delete e_i - 1 from T.
edgeTree.erase(edgeTreeIterators[v->previous]);
// Insert e_i in T and set helper(e_i) to v_i.
newedge.p1 = v2->p;
newedge.p2 = vertices[v2->next].p;
newedge.index = vindex2;
//edgeTreeRet = edgeTree.insert(newedge);
//edgeTreeIterators[vindex2] = edgeTreeRet.first;
edgeTreeIterators[vindex2] = edgeTree.insert(newedge);
helpers[vindex2] = vindex;
} else {
// Search in T to find the edge e_j directly left of v_i.
newedge.p1 = v->p;
newedge.p2 = v->p;
edgeIter = edgeTree.lower_bound(newedge);
if (edgeIter == edgeTree.front()) {
error = true;
break;
}
edgeIter = edgeIter->prev();
// If helper(e_j) is a merge vertex.
if (vertextypes[helpers[edgeIter->get().index]] == TPPL_VERTEXTYPE_MERGE) {
// Insert the diagonal connecting v_i to helper(e_j) in D.
AddDiagonal(vertices, &newnumvertices, vindex, helpers[edgeIter->get().index],
vertextypes, edgeTreeIterators, &edgeTree, helpers);
}
// helper(e_j) <- v_i.
helpers[edgeIter->get().index] = vindex;
}
break;
}
if (error)
break;
}
char *used = new char[newnumvertices];
memset(used, 0, newnumvertices * sizeof(char));
if (!error) {
// Return result.
long size;
TPPLPoly mpoly;
for (i = 0; i < newnumvertices; i++) {
if (used[i]) {
continue;
}
v = &(vertices[i]);
vnext = &(vertices[v->next]);
size = 1;
while (vnext != v) {
vnext = &(vertices[vnext->next]);
size++;
}
mpoly.Init(size);
v = &(vertices[i]);
mpoly[0] = v->p;
vnext = &(vertices[v->next]);
size = 1;
used[i] = 1;
used[v->next] = 1;
while (vnext != v) {
mpoly[size] = vnext->p;
used[vnext->next] = 1;
vnext = &(vertices[vnext->next]);
size++;
}
monotonePolys->push_back(mpoly);
}
}
// Cleanup.
delete[] vertices;
delete[] priority;
delete[] vertextypes;
delete[] edgeTreeIterators;
delete[] helpers;
delete[] used;
if (error) {
return 0;
} else {
return 1;
}
}
// Adds a diagonal to the doubly-connected list of vertices.
void TPPLPartition::AddDiagonal(MonotoneVertex *vertices, long *numvertices, long index1, long index2,
TPPLVertexType *vertextypes, Set<ScanLineEdge>::Element **edgeTreeIterators,
Set<ScanLineEdge> *edgeTree, long *helpers) {
long newindex1, newindex2;
newindex1 = *numvertices;
(*numvertices)++;
newindex2 = *numvertices;
(*numvertices)++;
vertices[newindex1].p = vertices[index1].p;
vertices[newindex2].p = vertices[index2].p;
vertices[newindex2].next = vertices[index2].next;
vertices[newindex1].next = vertices[index1].next;
vertices[vertices[index2].next].previous = newindex2;
vertices[vertices[index1].next].previous = newindex1;
vertices[index1].next = newindex2;
vertices[newindex2].previous = index1;
vertices[index2].next = newindex1;
vertices[newindex1].previous = index2;
// Update all relevant structures.
vertextypes[newindex1] = vertextypes[index1];
edgeTreeIterators[newindex1] = edgeTreeIterators[index1];
helpers[newindex1] = helpers[index1];
if (edgeTreeIterators[newindex1] != edgeTree->back()) {
edgeTreeIterators[newindex1]->get().index = newindex1;
}
vertextypes[newindex2] = vertextypes[index2];
edgeTreeIterators[newindex2] = edgeTreeIterators[index2];
helpers[newindex2] = helpers[index2];
if (edgeTreeIterators[newindex2] != edgeTree->back()) {
edgeTreeIterators[newindex2]->get().index = newindex2;
}
}
bool TPPLPartition::Below(TPPLPoint &p1, TPPLPoint &p2) {
if (p1.y < p2.y) {
return true;
} else if (p1.y == p2.y) {
if (p1.x < p2.x) {
return true;
}
}
return false;
}
// Sorts in the falling order of y values, if y is equal, x is used instead.
bool TPPLPartition::VertexSorter::operator()(long index1, long index2) {
if (vertices[index1].p.y > vertices[index2].p.y) {
return true;
} else if (vertices[index1].p.y == vertices[index2].p.y) {
if (vertices[index1].p.x > vertices[index2].p.x) {
return true;
}
}
return false;
}
bool TPPLPartition::ScanLineEdge::IsConvex(const TPPLPoint &p1, const TPPLPoint &p2, const TPPLPoint &p3) const {
tppl_float tmp;
tmp = (p3.y - p1.y) * (p2.x - p1.x) - (p3.x - p1.x) * (p2.y - p1.y);
if (tmp > 0) {
return 1;
}
return 0;
}
bool TPPLPartition::ScanLineEdge::operator<(const ScanLineEdge &other) const {
if (other.p1.y == other.p2.y) {
if (p1.y == p2.y) {
return (p1.y < other.p1.y);
}
return IsConvex(p1, p2, other.p1);
} else if (p1.y == p2.y) {
return !IsConvex(other.p1, other.p2, p1);
} else if (p1.y < other.p1.y) {
return !IsConvex(other.p1, other.p2, p1);
} else {
return IsConvex(p1, p2, other.p1);
}
}
// Triangulates monotone polygon.
// Time complexity: O(n)
// Space complexity: O(n)
int TPPLPartition::TriangulateMonotone(TPPLPoly *inPoly, TPPLPolyList *triangles) {
if (!inPoly->Valid()) {
return 0;
}
long i, i2, j, topindex, bottomindex, leftindex, rightindex, vindex;
TPPLPoint *points = NULL;
long numpoints;
TPPLPoly triangle;
numpoints = inPoly->GetNumPoints();
points = inPoly->GetPoints();
// Trivial case.
if (numpoints == 3) {
triangles->push_back(*inPoly);
return 1;
}
topindex = 0;
bottomindex = 0;
for (i = 1; i < numpoints; i++) {
if (Below(points[i], points[bottomindex])) {
bottomindex = i;
}
if (Below(points[topindex], points[i])) {
topindex = i;
}
}
// Check if the poly is really monotone.
i = topindex;
while (i != bottomindex) {
i2 = i + 1;
if (i2 >= numpoints) {
i2 = 0;
}
if (!Below(points[i2], points[i])) {
return 0;
}
i = i2;
}
i = bottomindex;
while (i != topindex) {
i2 = i + 1;
if (i2 >= numpoints) {
i2 = 0;
}
if (!Below(points[i], points[i2])) {
return 0;
}
i = i2;
}
char *vertextypes = new char[numpoints];
long *priority = new long[numpoints];
// Merge left and right vertex chains.
priority[0] = topindex;
vertextypes[topindex] = 0;
leftindex = topindex + 1;
if (leftindex >= numpoints) {
leftindex = 0;
}
rightindex = topindex - 1;
if (rightindex < 0) {
rightindex = numpoints - 1;
}
for (i = 1; i < (numpoints - 1); i++) {
if (leftindex == bottomindex) {
priority[i] = rightindex;
rightindex--;
if (rightindex < 0) {
rightindex = numpoints - 1;
}
vertextypes[priority[i]] = -1;
} else if (rightindex == bottomindex) {
priority[i] = leftindex;
leftindex++;
if (leftindex >= numpoints) {
leftindex = 0;
}
vertextypes[priority[i]] = 1;
} else {
if (Below(points[leftindex], points[rightindex])) {
priority[i] = rightindex;
rightindex--;
if (rightindex < 0) {
rightindex = numpoints - 1;
}
vertextypes[priority[i]] = -1;
} else {
priority[i] = leftindex;
leftindex++;
if (leftindex >= numpoints) {
leftindex = 0;
}
vertextypes[priority[i]] = 1;
}
}
}
priority[i] = bottomindex;
vertextypes[bottomindex] = 0;
long *stack = new long[numpoints];
long stackptr = 0;
stack[0] = priority[0];
stack[1] = priority[1];
stackptr = 2;
// For each vertex from top to bottom trim as many triangles as possible.
for (i = 2; i < (numpoints - 1); i++) {
vindex = priority[i];
if (vertextypes[vindex] != vertextypes[stack[stackptr - 1]]) {
for (j = 0; j < (stackptr - 1); j++) {
if (vertextypes[vindex] == 1) {
triangle.Triangle(points[stack[j + 1]], points[stack[j]], points[vindex]);
} else {
triangle.Triangle(points[stack[j]], points[stack[j + 1]], points[vindex]);
}
triangles->push_back(triangle);
}
stack[0] = priority[i - 1];
stack[1] = priority[i];
stackptr = 2;
} else {
stackptr--;
while (stackptr > 0) {
if (vertextypes[vindex] == 1) {
if (IsConvex(points[vindex], points[stack[stackptr - 1]], points[stack[stackptr]])) {
triangle.Triangle(points[vindex], points[stack[stackptr - 1]], points[stack[stackptr]]);
triangles->push_back(triangle);
stackptr--;
} else {
break;
}
} else {
if (IsConvex(points[vindex], points[stack[stackptr]], points[stack[stackptr - 1]])) {
triangle.Triangle(points[vindex], points[stack[stackptr]], points[stack[stackptr - 1]]);
triangles->push_back(triangle);
stackptr--;
} else {
break;
}
}
}
stackptr++;
stack[stackptr] = vindex;
stackptr++;
}
}
vindex = priority[i];
for (j = 0; j < (stackptr - 1); j++) {
if (vertextypes[stack[j + 1]] == 1) {
triangle.Triangle(points[stack[j]], points[stack[j + 1]], points[vindex]);
} else {
triangle.Triangle(points[stack[j + 1]], points[stack[j]], points[vindex]);
}
triangles->push_back(triangle);
}
delete[] priority;
delete[] vertextypes;
delete[] stack;
return 1;
}
int TPPLPartition::Triangulate_MONO(TPPLPolyList *inpolys, TPPLPolyList *triangles) {
TPPLPolyList monotone;
TPPLPolyList::Element *iter;
if (!MonotonePartition(inpolys, &monotone)) {
return 0;
}
for (iter = monotone.front(); iter; iter = iter->next()) {
if (!TriangulateMonotone(&(iter->get()), triangles)) {
return 0;
}
}
return 1;
}
int TPPLPartition::Triangulate_MONO(TPPLPoly *poly, TPPLPolyList *triangles) {
TPPLPolyList polys;
polys.push_back(*poly);
return Triangulate_MONO(&polys, triangles);
}
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