1851 lines
49 KiB
C++
1851 lines
49 KiB
C++
/*************************************************************************/
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/* Copyright (c) 2011-2021 Ivan Fratric and contributors. */
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/* */
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/* Permission is hereby granted, free of charge, to any person obtaining */
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/* a copy of this software and associated documentation files (the */
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/* "Software"), to deal in the Software without restriction, including */
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/* without limitation the rights to use, copy, modify, merge, publish, */
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/* distribute, sublicense, and/or sell copies of the Software, and to */
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/* permit persons to whom the Software is furnished to do so, subject to */
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/* the following conditions: */
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/* */
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/* The above copyright notice and this permission notice shall be */
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/* included in all copies or substantial portions of the Software. */
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/* */
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/* THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, */
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/* EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF */
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/* MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT.*/
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/* IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY */
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/* CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, */
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/* TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE */
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/* SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE. */
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/*************************************************************************/
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#include "polypartition.h"
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#include <math.h>
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#include <string.h>
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#include <algorithm>
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TPPLPoly::TPPLPoly() {
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hole = false;
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numpoints = 0;
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points = NULL;
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}
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TPPLPoly::~TPPLPoly() {
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if (points) {
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delete[] points;
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}
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}
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void TPPLPoly::Clear() {
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if (points) {
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delete[] points;
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}
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hole = false;
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numpoints = 0;
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points = NULL;
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}
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void TPPLPoly::Init(long numpoints) {
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Clear();
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this->numpoints = numpoints;
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points = new TPPLPoint[numpoints];
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}
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void TPPLPoly::Triangle(TPPLPoint &p1, TPPLPoint &p2, TPPLPoint &p3) {
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Init(3);
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points[0] = p1;
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points[1] = p2;
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points[2] = p3;
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}
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TPPLPoly::TPPLPoly(const TPPLPoly &src) :
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TPPLPoly() {
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hole = src.hole;
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numpoints = src.numpoints;
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if (numpoints > 0) {
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points = new TPPLPoint[numpoints];
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memcpy(points, src.points, numpoints * sizeof(TPPLPoint));
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}
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}
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TPPLPoly &TPPLPoly::operator=(const TPPLPoly &src) {
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Clear();
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hole = src.hole;
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numpoints = src.numpoints;
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if (numpoints > 0) {
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points = new TPPLPoint[numpoints];
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memcpy(points, src.points, numpoints * sizeof(TPPLPoint));
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}
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return *this;
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}
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TPPLOrientation TPPLPoly::GetOrientation() const {
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long i1, i2;
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tppl_float area = 0;
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for (i1 = 0; i1 < numpoints; i1++) {
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i2 = i1 + 1;
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if (i2 == numpoints) {
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i2 = 0;
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}
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area += points[i1].x * points[i2].y - points[i1].y * points[i2].x;
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}
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if (area > 0) {
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return TPPL_ORIENTATION_CCW;
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}
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if (area < 0) {
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return TPPL_ORIENTATION_CW;
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}
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return TPPL_ORIENTATION_NONE;
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}
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void TPPLPoly::SetOrientation(TPPLOrientation orientation) {
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TPPLOrientation polyorientation = GetOrientation();
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if (polyorientation != TPPL_ORIENTATION_NONE && polyorientation != orientation) {
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Invert();
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}
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}
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void TPPLPoly::Invert() {
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std::reverse(points, points + numpoints);
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}
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TPPLPartition::PartitionVertex::PartitionVertex() :
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previous(NULL), next(NULL) {
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}
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TPPLPoint TPPLPartition::Normalize(const TPPLPoint &p) {
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TPPLPoint r;
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tppl_float n = sqrt(p.x * p.x + p.y * p.y);
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if (n != 0) {
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r = p / n;
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} else {
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r.x = 0;
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r.y = 0;
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}
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return r;
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}
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tppl_float TPPLPartition::Distance(const TPPLPoint &p1, const TPPLPoint &p2) {
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tppl_float dx, dy;
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dx = p2.x - p1.x;
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dy = p2.y - p1.y;
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return (sqrt(dx * dx + dy * dy));
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}
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// Checks if two lines intersect.
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int TPPLPartition::Intersects(TPPLPoint &p11, TPPLPoint &p12, TPPLPoint &p21, TPPLPoint &p22) {
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if ((p11.x == p21.x) && (p11.y == p21.y)) {
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return 0;
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}
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if ((p11.x == p22.x) && (p11.y == p22.y)) {
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return 0;
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}
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if ((p12.x == p21.x) && (p12.y == p21.y)) {
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return 0;
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}
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if ((p12.x == p22.x) && (p12.y == p22.y)) {
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return 0;
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}
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TPPLPoint v1ort, v2ort, v;
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tppl_float dot11, dot12, dot21, dot22;
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v1ort.x = p12.y - p11.y;
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v1ort.y = p11.x - p12.x;
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v2ort.x = p22.y - p21.y;
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v2ort.y = p21.x - p22.x;
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v = p21 - p11;
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dot21 = v.x * v1ort.x + v.y * v1ort.y;
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v = p22 - p11;
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dot22 = v.x * v1ort.x + v.y * v1ort.y;
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v = p11 - p21;
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dot11 = v.x * v2ort.x + v.y * v2ort.y;
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v = p12 - p21;
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dot12 = v.x * v2ort.x + v.y * v2ort.y;
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if (dot11 * dot12 > 0) {
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return 0;
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}
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if (dot21 * dot22 > 0) {
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return 0;
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}
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return 1;
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}
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// Removes holes from inpolys by merging them with non-holes.
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int TPPLPartition::RemoveHoles(TPPLPolyList *inpolys, TPPLPolyList *outpolys) {
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TPPLPolyList polys;
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TPPLPolyList::Element *holeiter, *polyiter, *iter, *iter2;
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long i, i2, holepointindex, polypointindex;
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TPPLPoint holepoint, polypoint, bestpolypoint;
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TPPLPoint linep1, linep2;
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TPPLPoint v1, v2;
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TPPLPoly newpoly;
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bool hasholes;
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bool pointvisible;
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bool pointfound;
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// Check for the trivial case of no holes.
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hasholes = false;
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for (iter = inpolys->front(); iter; iter = iter->next()) {
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if (iter->get().IsHole()) {
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hasholes = true;
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break;
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}
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}
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if (!hasholes) {
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for (iter = inpolys->front(); iter; iter = iter->next()) {
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outpolys->push_back(iter->get());
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}
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return 1;
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}
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polys = *inpolys;
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while (1) {
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// Find the hole point with the largest x.
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hasholes = false;
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for (iter = polys.front(); iter; iter = iter->next()) {
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if (!iter->get().IsHole()) {
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continue;
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}
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if (!hasholes) {
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hasholes = true;
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holeiter = iter;
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holepointindex = 0;
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}
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for (i = 0; i < iter->get().GetNumPoints(); i++) {
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if (iter->get().GetPoint(i).x > holeiter->get().GetPoint(holepointindex).x) {
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holeiter = iter;
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holepointindex = i;
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}
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}
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}
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if (!hasholes) {
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break;
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}
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holepoint = holeiter->get().GetPoint(holepointindex);
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pointfound = false;
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for (iter = polys.front(); iter; iter = iter->next()) {
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if (iter->get().IsHole()) {
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continue;
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}
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for (i = 0; i < iter->get().GetNumPoints(); i++) {
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if (iter->get().GetPoint(i).x <= holepoint.x) {
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continue;
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}
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if (!InCone(iter->get().GetPoint((i + iter->get().GetNumPoints() - 1) % (iter->get().GetNumPoints())),
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iter->get().GetPoint(i),
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iter->get().GetPoint((i + 1) % (iter->get().GetNumPoints())),
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holepoint)) {
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continue;
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}
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polypoint = iter->get().GetPoint(i);
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if (pointfound) {
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v1 = Normalize(polypoint - holepoint);
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v2 = Normalize(bestpolypoint - holepoint);
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if (v2.x > v1.x) {
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continue;
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}
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}
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pointvisible = true;
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for (iter2 = polys.front(); iter2; iter2->next()) {
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if (iter2->get().IsHole()) {
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continue;
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}
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for (i2 = 0; i2 < iter2->get().GetNumPoints(); i2++) {
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linep1 = iter2->get().GetPoint(i2);
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linep2 = iter2->get().GetPoint((i2 + 1) % (iter2->get().GetNumPoints()));
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if (Intersects(holepoint, polypoint, linep1, linep2)) {
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pointvisible = false;
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break;
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}
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}
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if (!pointvisible) {
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break;
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}
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}
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if (pointvisible) {
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pointfound = true;
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bestpolypoint = polypoint;
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polyiter = iter;
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polypointindex = i;
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}
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}
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}
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if (!pointfound) {
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return 0;
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}
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newpoly.Init(holeiter->get().GetNumPoints() + polyiter->get().GetNumPoints() + 2);
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i2 = 0;
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for (i = 0; i <= polypointindex; i++) {
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newpoly[i2] = polyiter->get().GetPoint(i);
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i2++;
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}
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for (i = 0; i <= holeiter->get().GetNumPoints(); i++) {
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newpoly[i2] = holeiter->get().GetPoint((i + holepointindex) % holeiter->get().GetNumPoints());
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i2++;
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}
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for (i = polypointindex; i < polyiter->get().GetNumPoints(); i++) {
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newpoly[i2] = polyiter->get().GetPoint(i);
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i2++;
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}
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polys.erase(holeiter);
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polys.erase(polyiter);
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polys.push_back(newpoly);
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}
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for (iter = polys.front(); iter; iter = iter->next()) {
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outpolys->push_back(iter->get());
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}
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return 1;
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}
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bool TPPLPartition::IsConvex(TPPLPoint &p1, TPPLPoint &p2, TPPLPoint &p3) {
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tppl_float tmp;
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tmp = (p3.y - p1.y) * (p2.x - p1.x) - (p3.x - p1.x) * (p2.y - p1.y);
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if (tmp > 0) {
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return 1;
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} else {
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return 0;
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}
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}
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bool TPPLPartition::IsReflex(TPPLPoint &p1, TPPLPoint &p2, TPPLPoint &p3) {
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tppl_float tmp;
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tmp = (p3.y - p1.y) * (p2.x - p1.x) - (p3.x - p1.x) * (p2.y - p1.y);
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if (tmp < 0) {
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return 1;
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} else {
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return 0;
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}
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}
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bool TPPLPartition::IsInside(TPPLPoint &p1, TPPLPoint &p2, TPPLPoint &p3, TPPLPoint &p) {
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if (IsConvex(p1, p, p2)) {
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return false;
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}
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if (IsConvex(p2, p, p3)) {
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return false;
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}
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if (IsConvex(p3, p, p1)) {
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return false;
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}
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return true;
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}
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bool TPPLPartition::InCone(TPPLPoint &p1, TPPLPoint &p2, TPPLPoint &p3, TPPLPoint &p) {
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bool convex;
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convex = IsConvex(p1, p2, p3);
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if (convex) {
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if (!IsConvex(p1, p2, p)) {
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return false;
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}
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if (!IsConvex(p2, p3, p)) {
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return false;
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}
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return true;
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} else {
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if (IsConvex(p1, p2, p)) {
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return true;
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}
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if (IsConvex(p2, p3, p)) {
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return true;
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}
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return false;
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}
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}
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bool TPPLPartition::InCone(PartitionVertex *v, TPPLPoint &p) {
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TPPLPoint p1, p2, p3;
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p1 = v->previous->p;
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p2 = v->p;
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p3 = v->next->p;
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return InCone(p1, p2, p3, p);
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}
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void TPPLPartition::UpdateVertexReflexity(PartitionVertex *v) {
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PartitionVertex *v1 = NULL, *v3 = NULL;
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v1 = v->previous;
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v3 = v->next;
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v->isConvex = !IsReflex(v1->p, v->p, v3->p);
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}
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void TPPLPartition::UpdateVertex(PartitionVertex *v, PartitionVertex *vertices, long numvertices) {
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long i;
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PartitionVertex *v1 = NULL, *v3 = NULL;
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TPPLPoint vec1, vec3;
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v1 = v->previous;
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v3 = v->next;
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v->isConvex = IsConvex(v1->p, v->p, v3->p);
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vec1 = Normalize(v1->p - v->p);
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vec3 = Normalize(v3->p - v->p);
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v->angle = vec1.x * vec3.x + vec1.y * vec3.y;
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if (v->isConvex) {
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v->isEar = true;
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for (i = 0; i < numvertices; i++) {
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if ((vertices[i].p.x == v->p.x) && (vertices[i].p.y == v->p.y)) {
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continue;
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}
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if ((vertices[i].p.x == v1->p.x) && (vertices[i].p.y == v1->p.y)) {
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continue;
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}
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if ((vertices[i].p.x == v3->p.x) && (vertices[i].p.y == v3->p.y)) {
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continue;
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}
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if (IsInside(v1->p, v->p, v3->p, vertices[i].p)) {
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v->isEar = false;
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break;
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}
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}
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} else {
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v->isEar = false;
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}
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}
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// Triangulation by ear removal.
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int TPPLPartition::Triangulate_EC(TPPLPoly *poly, TPPLPolyList *triangles) {
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if (!poly->Valid()) {
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return 0;
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}
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long numvertices;
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PartitionVertex *vertices = NULL;
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PartitionVertex *ear = NULL;
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TPPLPoly triangle;
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long i, j;
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bool earfound;
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if (poly->GetNumPoints() < 3) {
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return 0;
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}
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if (poly->GetNumPoints() == 3) {
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triangles->push_back(*poly);
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return 1;
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}
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numvertices = poly->GetNumPoints();
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vertices = new PartitionVertex[numvertices];
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for (i = 0; i < numvertices; i++) {
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vertices[i].isActive = true;
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vertices[i].p = poly->GetPoint(i);
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if (i == (numvertices - 1)) {
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vertices[i].next = &(vertices[0]);
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} else {
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vertices[i].next = &(vertices[i + 1]);
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}
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if (i == 0) {
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vertices[i].previous = &(vertices[numvertices - 1]);
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} else {
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vertices[i].previous = &(vertices[i - 1]);
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}
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}
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for (i = 0; i < numvertices; i++) {
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UpdateVertex(&vertices[i], vertices, numvertices);
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}
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for (i = 0; i < numvertices - 3; i++) {
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earfound = false;
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// Find the most extruded ear.
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for (j = 0; j < numvertices; j++) {
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if (!vertices[j].isActive) {
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continue;
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}
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if (!vertices[j].isEar) {
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continue;
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}
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if (!earfound) {
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earfound = true;
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ear = &(vertices[j]);
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} else {
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if (vertices[j].angle > ear->angle) {
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ear = &(vertices[j]);
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}
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}
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}
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if (!earfound) {
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delete[] vertices;
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return 0;
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}
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triangle.Triangle(ear->previous->p, ear->p, ear->next->p);
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triangles->push_back(triangle);
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ear->isActive = false;
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ear->previous->next = ear->next;
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ear->next->previous = ear->previous;
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if (i == numvertices - 4) {
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break;
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}
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UpdateVertex(ear->previous, vertices, numvertices);
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UpdateVertex(ear->next, vertices, numvertices);
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}
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for (i = 0; i < numvertices; i++) {
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if (vertices[i].isActive) {
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triangle.Triangle(vertices[i].previous->p, vertices[i].p, vertices[i].next->p);
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triangles->push_back(triangle);
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break;
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}
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}
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delete[] vertices;
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return 1;
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}
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int TPPLPartition::Triangulate_EC(TPPLPolyList *inpolys, TPPLPolyList *triangles) {
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TPPLPolyList outpolys;
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TPPLPolyList::Element *iter;
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|
|
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.
|
|
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 == 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, 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);
|
|
}
|