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godot/thirdparty/misc/polypartition.cpp
reduz 746dddc067 Replace most uses of Map by HashMap 
* Map is unnecessary and inefficient in almost every case.
* Replaced by the new HashMap.
* Renamed Map to RBMap and Set to RBSet for cases that still make sense
  (order matters) but use is discouraged.

There were very few cases where replacing by HashMap was undesired because
keeping the key order was intended.
I tried to keep those (as RBMap) as much as possible, but might have missed
some. Review appreciated!
2022-05-16 10:37:48 +02:00

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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 <math.h>
#include <string.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 = 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 = iter->next()) {
numvertices += iter->get().GetNumPoints();
}
maxnumvertices = numvertices * 3;
vertices = new MonotoneVertex[maxnumvertices];
newnumvertices = numvertices;
polystartindex = 0;
for (iter = inpolys->front(); iter; iter = iter->next()) {
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.
RBSet<ScanLineEdge> edgeTree;
// Store iterators to the edge tree elements.
// This makes deleting existing edges much faster.
RBSet<ScanLineEdge>::Element **edgeTreeIterators, *edgeIter;
edgeTreeIterators = new RBSet<ScanLineEdge>::Element *[maxnumvertices];
//Pair<RBSet<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 == nullptr || 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 == nullptr || 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 == nullptr || 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, RBSet<ScanLineEdge>::Element **edgeTreeIterators,
RBSet<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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