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edge-coloring.cpp
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edge-coloring.cpp
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#include "edge-coloring.h"
#include <cstdlib>
#include <cmath>
#include <cstring>
#include <cfloat>
#include <vector>
#include <queue>
#include "arithmetics.hpp"
namespace msdfgen {
/**
* For each position < n, this function will return -1, 0, or 1,
* depending on whether the position is closer to the beginning, middle, or end, respectively.
* It is guaranteed that the output will be balanced in that the total for positions 0 through n-1 will be zero.
*/
static int symmetricalTrichotomy(int position, int n) {
return int(3+2.875*position/(n-1)-1.4375+.5)-3;
}
static bool isCorner(const Vector2 &aDir, const Vector2 &bDir, double crossThreshold) {
return dotProduct(aDir, bDir) <= 0 || fabs(crossProduct(aDir, bDir)) > crossThreshold;
}
static double estimateEdgeLength(const EdgeSegment *edge) {
double len = 0;
Point2 prev = edge->point(0);
for (int i = 1; i <= MSDFGEN_EDGE_LENGTH_PRECISION; ++i) {
Point2 cur = edge->point(1./MSDFGEN_EDGE_LENGTH_PRECISION*i);
len += (cur-prev).length();
prev = cur;
}
return len;
}
static int seedExtract2(unsigned long long &seed) {
int v = int(seed)&1;
seed >>= 1;
return v;
}
static int seedExtract3(unsigned long long &seed) {
int v = int(seed%3);
seed /= 3;
return v;
}
static EdgeColor initColor(unsigned long long &seed) {
static const EdgeColor colors[3] = { CYAN, MAGENTA, YELLOW };
return colors[seedExtract3(seed)];
}
static void switchColor(EdgeColor &color, unsigned long long &seed) {
int shifted = color<<(1+seedExtract2(seed));
color = EdgeColor((shifted|shifted>>3)&WHITE);
}
static void switchColor(EdgeColor &color, unsigned long long &seed, EdgeColor banned) {
EdgeColor combined = EdgeColor(color&banned);
if (combined == RED || combined == GREEN || combined == BLUE)
color = EdgeColor(combined^WHITE);
else
switchColor(color, seed);
}
void edgeColoringSimple(Shape &shape, double angleThreshold, unsigned long long seed) {
double crossThreshold = sin(angleThreshold);
EdgeColor color = initColor(seed);
std::vector<int> corners;
for (std::vector<Contour>::iterator contour = shape.contours.begin(); contour != shape.contours.end(); ++contour) {
if (contour->edges.empty())
continue;
{ // Identify corners
corners.clear();
Vector2 prevDirection = contour->edges.back()->direction(1);
int index = 0;
for (std::vector<EdgeHolder>::const_iterator edge = contour->edges.begin(); edge != contour->edges.end(); ++edge, ++index) {
if (isCorner(prevDirection.normalize(), (*edge)->direction(0).normalize(), crossThreshold))
corners.push_back(index);
prevDirection = (*edge)->direction(1);
}
}
// Smooth contour
if (corners.empty()) {
switchColor(color, seed);
for (std::vector<EdgeHolder>::iterator edge = contour->edges.begin(); edge != contour->edges.end(); ++edge)
(*edge)->color = color;
}
// "Teardrop" case
else if (corners.size() == 1) {
EdgeColor colors[3];
switchColor(color, seed);
colors[0] = color;
colors[1] = WHITE;
switchColor(color, seed);
colors[2] = color;
int corner = corners[0];
if (contour->edges.size() >= 3) {
int m = (int) contour->edges.size();
for (int i = 0; i < m; ++i)
contour->edges[(corner+i)%m]->color = colors[1+symmetricalTrichotomy(i, m)];
} else if (contour->edges.size() >= 1) {
// Less than three edge segments for three colors => edges must be split
EdgeSegment *parts[7] = { };
contour->edges[0]->splitInThirds(parts[0+3*corner], parts[1+3*corner], parts[2+3*corner]);
if (contour->edges.size() >= 2) {
contour->edges[1]->splitInThirds(parts[3-3*corner], parts[4-3*corner], parts[5-3*corner]);
parts[0]->color = parts[1]->color = colors[0];
parts[2]->color = parts[3]->color = colors[1];
parts[4]->color = parts[5]->color = colors[2];
} else {
parts[0]->color = colors[0];
parts[1]->color = colors[1];
parts[2]->color = colors[2];
}
contour->edges.clear();
for (int i = 0; parts[i]; ++i)
contour->edges.push_back(EdgeHolder(parts[i]));
}
}
// Multiple corners
else {
int cornerCount = (int) corners.size();
int spline = 0;
int start = corners[0];
int m = (int) contour->edges.size();
switchColor(color, seed);
EdgeColor initialColor = color;
for (int i = 0; i < m; ++i) {
int index = (start+i)%m;
if (spline+1 < cornerCount && corners[spline+1] == index) {
++spline;
switchColor(color, seed, EdgeColor((spline == cornerCount-1)*initialColor));
}
contour->edges[index]->color = color;
}
}
}
}
struct EdgeColoringInkTrapCorner {
int index;
double prevEdgeLengthEstimate;
bool minor;
EdgeColor color;
};
void edgeColoringInkTrap(Shape &shape, double angleThreshold, unsigned long long seed) {
typedef EdgeColoringInkTrapCorner Corner;
double crossThreshold = sin(angleThreshold);
EdgeColor color = initColor(seed);
std::vector<Corner> corners;
for (std::vector<Contour>::iterator contour = shape.contours.begin(); contour != shape.contours.end(); ++contour) {
if (contour->edges.empty())
continue;
double splineLength = 0;
{ // Identify corners
corners.clear();
Vector2 prevDirection = contour->edges.back()->direction(1);
int index = 0;
for (std::vector<EdgeHolder>::const_iterator edge = contour->edges.begin(); edge != contour->edges.end(); ++edge, ++index) {
if (isCorner(prevDirection.normalize(), (*edge)->direction(0).normalize(), crossThreshold)) {
Corner corner = { index, splineLength };
corners.push_back(corner);
splineLength = 0;
}
splineLength += estimateEdgeLength(*edge);
prevDirection = (*edge)->direction(1);
}
}
// Smooth contour
if (corners.empty()) {
switchColor(color, seed);
for (std::vector<EdgeHolder>::iterator edge = contour->edges.begin(); edge != contour->edges.end(); ++edge)
(*edge)->color = color;
}
// "Teardrop" case
else if (corners.size() == 1) {
EdgeColor colors[3];
switchColor(color, seed);
colors[0] = color;
colors[1] = WHITE;
switchColor(color, seed);
colors[2] = color;
int corner = corners[0].index;
if (contour->edges.size() >= 3) {
int m = (int) contour->edges.size();
for (int i = 0; i < m; ++i)
contour->edges[(corner+i)%m]->color = colors[1+symmetricalTrichotomy(i, m)];
} else if (contour->edges.size() >= 1) {
// Less than three edge segments for three colors => edges must be split
EdgeSegment *parts[7] = { };
contour->edges[0]->splitInThirds(parts[0+3*corner], parts[1+3*corner], parts[2+3*corner]);
if (contour->edges.size() >= 2) {
contour->edges[1]->splitInThirds(parts[3-3*corner], parts[4-3*corner], parts[5-3*corner]);
parts[0]->color = parts[1]->color = colors[0];
parts[2]->color = parts[3]->color = colors[1];
parts[4]->color = parts[5]->color = colors[2];
} else {
parts[0]->color = colors[0];
parts[1]->color = colors[1];
parts[2]->color = colors[2];
}
contour->edges.clear();
for (int i = 0; parts[i]; ++i)
contour->edges.push_back(EdgeHolder(parts[i]));
}
}
// Multiple corners
else {
int cornerCount = (int) corners.size();
int majorCornerCount = cornerCount;
if (cornerCount > 3) {
corners.begin()->prevEdgeLengthEstimate += splineLength;
for (int i = 0; i < cornerCount; ++i) {
if (
corners[i].prevEdgeLengthEstimate > corners[(i+1)%cornerCount].prevEdgeLengthEstimate &&
corners[(i+1)%cornerCount].prevEdgeLengthEstimate < corners[(i+2)%cornerCount].prevEdgeLengthEstimate
) {
corners[i].minor = true;
--majorCornerCount;
}
}
}
EdgeColor initialColor = BLACK;
for (int i = 0; i < cornerCount; ++i) {
if (!corners[i].minor) {
--majorCornerCount;
switchColor(color, seed, EdgeColor(!majorCornerCount*initialColor));
corners[i].color = color;
if (!initialColor)
initialColor = color;
}
}
for (int i = 0; i < cornerCount; ++i) {
if (corners[i].minor) {
EdgeColor nextColor = corners[(i+1)%cornerCount].color;
corners[i].color = EdgeColor((color&nextColor)^WHITE);
} else
color = corners[i].color;
}
int spline = 0;
int start = corners[0].index;
color = corners[0].color;
int m = (int) contour->edges.size();
for (int i = 0; i < m; ++i) {
int index = (start+i)%m;
if (spline+1 < cornerCount && corners[spline+1].index == index)
color = corners[++spline].color;
contour->edges[index]->color = color;
}
}
}
}
// EDGE COLORING BY DISTANCE - EXPERIMENTAL IMPLEMENTATION - WORK IN PROGRESS
#define MAX_RECOLOR_STEPS 16
#define EDGE_DISTANCE_PRECISION 16
static double edgeToEdgeDistance(const EdgeSegment &a, const EdgeSegment &b, int precision) {
if (a.point(0) == b.point(0) || a.point(0) == b.point(1) || a.point(1) == b.point(0) || a.point(1) == b.point(1))
return 0;
double iFac = 1./precision;
double minDistance = (b.point(0)-a.point(0)).length();
for (int i = 0; i <= precision; ++i) {
double t = iFac*i;
double d = fabs(a.signedDistance(b.point(t), t).distance);
minDistance = min(minDistance, d);
}
for (int i = 0; i <= precision; ++i) {
double t = iFac*i;
double d = fabs(b.signedDistance(a.point(t), t).distance);
minDistance = min(minDistance, d);
}
return minDistance;
}
static double splineToSplineDistance(EdgeSegment *const *edgeSegments, int aStart, int aEnd, int bStart, int bEnd, int precision) {
double minDistance = DBL_MAX;
for (int ai = aStart; ai < aEnd; ++ai)
for (int bi = bStart; bi < bEnd && minDistance; ++bi) {
double d = edgeToEdgeDistance(*edgeSegments[ai], *edgeSegments[bi], precision);
minDistance = min(minDistance, d);
}
return minDistance;
}
static void colorSecondDegreeGraph(int *coloring, const int *const *edgeMatrix, int vertexCount, unsigned long long seed) {
for (int i = 0; i < vertexCount; ++i) {
int possibleColors = 7;
for (int j = 0; j < i; ++j) {
if (edgeMatrix[i][j])
possibleColors &= ~(1<<coloring[j]);
}
int color = 0;
switch (possibleColors) {
case 1:
color = 0;
break;
case 2:
color = 1;
break;
case 3:
color = seedExtract2(seed); // 0 or 1
break;
case 4:
color = 2;
break;
case 5:
color = (int) !seedExtract2(seed)<<1; // 2 or 0
break;
case 6:
color = seedExtract2(seed)+1; // 1 or 2
break;
case 7:
color = (seedExtract3(seed)+i)%3; // 0 or 1 or 2
break;
}
coloring[i] = color;
}
}
static int vertexPossibleColors(const int *coloring, const int *edgeVector, int vertexCount) {
int usedColors = 0;
for (int i = 0; i < vertexCount; ++i)
if (edgeVector[i])
usedColors |= 1<<coloring[i];
return 7&~usedColors;
}
static void uncolorSameNeighbors(std::queue<int> &uncolored, int *coloring, const int *const *edgeMatrix, int vertex, int vertexCount) {
for (int i = vertex+1; i < vertexCount; ++i) {
if (edgeMatrix[vertex][i] && coloring[i] == coloring[vertex]) {
coloring[i] = -1;
uncolored.push(i);
}
}
for (int i = 0; i < vertex; ++i) {
if (edgeMatrix[vertex][i] && coloring[i] == coloring[vertex]) {
coloring[i] = -1;
uncolored.push(i);
}
}
}
static bool tryAddEdge(int *coloring, int *const *edgeMatrix, int vertexCount, int vertexA, int vertexB, int *coloringBuffer) {
static const int FIRST_POSSIBLE_COLOR[8] = { -1, 0, 1, 0, 2, 2, 1, 0 };
edgeMatrix[vertexA][vertexB] = 1;
edgeMatrix[vertexB][vertexA] = 1;
if (coloring[vertexA] != coloring[vertexB])
return true;
int bPossibleColors = vertexPossibleColors(coloring, edgeMatrix[vertexB], vertexCount);
if (bPossibleColors) {
coloring[vertexB] = FIRST_POSSIBLE_COLOR[bPossibleColors];
return true;
}
memcpy(coloringBuffer, coloring, sizeof(int)*vertexCount);
std::queue<int> uncolored;
{
int *coloring = coloringBuffer;
coloring[vertexB] = FIRST_POSSIBLE_COLOR[7&~(1<<coloring[vertexA])];
uncolorSameNeighbors(uncolored, coloring, edgeMatrix, vertexB, vertexCount);
int step = 0;
while (!uncolored.empty() && step < MAX_RECOLOR_STEPS) {
int i = uncolored.front();
uncolored.pop();
int possibleColors = vertexPossibleColors(coloring, edgeMatrix[i], vertexCount);
if (possibleColors) {
coloring[i] = FIRST_POSSIBLE_COLOR[possibleColors];
continue;
}
do {
coloring[i] = step++%3;
} while (edgeMatrix[i][vertexA] && coloring[i] == coloring[vertexA]);
uncolorSameNeighbors(uncolored, coloring, edgeMatrix, i, vertexCount);
}
}
if (!uncolored.empty()) {
edgeMatrix[vertexA][vertexB] = 0;
edgeMatrix[vertexB][vertexA] = 0;
return false;
}
memcpy(coloring, coloringBuffer, sizeof(int)*vertexCount);
return true;
}
static int cmpDoublePtr(const void *a, const void *b) {
return sign(**reinterpret_cast<const double *const *>(a)-**reinterpret_cast<const double *const *>(b));
}
void edgeColoringByDistance(Shape &shape, double angleThreshold, unsigned long long seed) {
std::vector<EdgeSegment *> edgeSegments;
std::vector<int> splineStarts;
double crossThreshold = sin(angleThreshold);
std::vector<int> corners;
for (std::vector<Contour>::iterator contour = shape.contours.begin(); contour != shape.contours.end(); ++contour)
if (!contour->edges.empty()) {
// Identify corners
corners.clear();
Vector2 prevDirection = contour->edges.back()->direction(1);
int index = 0;
for (std::vector<EdgeHolder>::const_iterator edge = contour->edges.begin(); edge != contour->edges.end(); ++edge, ++index) {
if (isCorner(prevDirection.normalize(), (*edge)->direction(0).normalize(), crossThreshold))
corners.push_back(index);
prevDirection = (*edge)->direction(1);
}
splineStarts.push_back((int) edgeSegments.size());
// Smooth contour
if (corners.empty())
for (std::vector<EdgeHolder>::iterator edge = contour->edges.begin(); edge != contour->edges.end(); ++edge)
edgeSegments.push_back(&**edge);
// "Teardrop" case
else if (corners.size() == 1) {
int corner = corners[0];
if (contour->edges.size() >= 3) {
int m = (int) contour->edges.size();
for (int i = 0; i < m; ++i) {
if (i == m/2)
splineStarts.push_back((int) edgeSegments.size());
if (symmetricalTrichotomy(i, m))
edgeSegments.push_back(&*contour->edges[(corner+i)%m]);
else
contour->edges[(corner+i)%m]->color = WHITE;
}
} else if (contour->edges.size() >= 1) {
// Less than three edge segments for three colors => edges must be split
EdgeSegment *parts[7] = { };
contour->edges[0]->splitInThirds(parts[0+3*corner], parts[1+3*corner], parts[2+3*corner]);
if (contour->edges.size() >= 2) {
contour->edges[1]->splitInThirds(parts[3-3*corner], parts[4-3*corner], parts[5-3*corner]);
edgeSegments.push_back(parts[0]);
edgeSegments.push_back(parts[1]);
parts[2]->color = parts[3]->color = WHITE;
splineStarts.push_back((int) edgeSegments.size());
edgeSegments.push_back(parts[4]);
edgeSegments.push_back(parts[5]);
} else {
edgeSegments.push_back(parts[0]);
parts[1]->color = WHITE;
splineStarts.push_back((int) edgeSegments.size());
edgeSegments.push_back(parts[2]);
}
contour->edges.clear();
for (int i = 0; parts[i]; ++i)
contour->edges.push_back(EdgeHolder(parts[i]));
}
}
// Multiple corners
else {
int cornerCount = (int) corners.size();
int spline = 0;
int start = corners[0];
int m = (int) contour->edges.size();
for (int i = 0; i < m; ++i) {
int index = (start+i)%m;
if (spline+1 < cornerCount && corners[spline+1] == index) {
splineStarts.push_back((int) edgeSegments.size());
++spline;
}
edgeSegments.push_back(&*contour->edges[index]);
}
}
}
splineStarts.push_back((int) edgeSegments.size());
int segmentCount = (int) edgeSegments.size();
int splineCount = (int) splineStarts.size()-1;
if (!splineCount)
return;
std::vector<double> distanceMatrixStorage(splineCount*splineCount);
std::vector<double *> distanceMatrix(splineCount);
for (int i = 0; i < splineCount; ++i)
distanceMatrix[i] = &distanceMatrixStorage[i*splineCount];
const double *distanceMatrixBase = &distanceMatrixStorage[0];
for (int i = 0; i < splineCount; ++i) {
distanceMatrix[i][i] = -1;
for (int j = i+1; j < splineCount; ++j) {
double dist = splineToSplineDistance(&edgeSegments[0], splineStarts[i], splineStarts[i+1], splineStarts[j], splineStarts[j+1], EDGE_DISTANCE_PRECISION);
distanceMatrix[i][j] = dist;
distanceMatrix[j][i] = dist;
}
}
std::vector<const double *> graphEdgeDistances;
graphEdgeDistances.reserve(splineCount*(splineCount-1)/2);
for (int i = 0; i < splineCount; ++i)
for (int j = i+1; j < splineCount; ++j)
graphEdgeDistances.push_back(&distanceMatrix[i][j]);
int graphEdgeCount = (int) graphEdgeDistances.size();
if (!graphEdgeDistances.empty())
qsort(&graphEdgeDistances[0], graphEdgeDistances.size(), sizeof(const double *), &cmpDoublePtr);
std::vector<int> edgeMatrixStorage(splineCount*splineCount);
std::vector<int *> edgeMatrix(splineCount);
for (int i = 0; i < splineCount; ++i)
edgeMatrix[i] = &edgeMatrixStorage[i*splineCount];
int nextEdge = 0;
for (; nextEdge < graphEdgeCount && !*graphEdgeDistances[nextEdge]; ++nextEdge) {
int elem = (int) (graphEdgeDistances[nextEdge]-distanceMatrixBase);
int row = elem/splineCount;
int col = elem%splineCount;
edgeMatrix[row][col] = 1;
edgeMatrix[col][row] = 1;
}
std::vector<int> coloring(2*splineCount);
colorSecondDegreeGraph(&coloring[0], &edgeMatrix[0], splineCount, seed);
for (; nextEdge < graphEdgeCount; ++nextEdge) {
int elem = (int) (graphEdgeDistances[nextEdge]-distanceMatrixBase);
tryAddEdge(&coloring[0], &edgeMatrix[0], splineCount, elem/splineCount, elem%splineCount, &coloring[splineCount]);
}
const EdgeColor colors[3] = { YELLOW, CYAN, MAGENTA };
int spline = -1;
for (int i = 0; i < segmentCount; ++i) {
if (splineStarts[spline+1] == i)
++spline;
edgeSegments[i]->color = colors[coloring[spline]];
}
}
}