Edge coloring by edge to edge distance - experimental version

Author: Chlumsky

core/edge-coloring.cpp

@@ -1,6 +1,12 @@
 
 #include "edge-coloring.h"
 
+#include <cstdlib>
+#include <cmath>
+#include <cstring>
+#include <queue>
+#include "arithmetics.hpp"
+
 namespace msdfgen {
 
 static bool isCorner(const Vector2 &aDir, const Vector2 &bDir, double crossThreshold) {
@@ -215,4 +221,279 @@ void edgeColoringInkTrap(Shape &shape, double angleThreshold, unsigned long long
     }
 }
 
+// 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 = fabs(SignedDistance::INFINITE.distance);
+    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 = (int) seed&1;
+                seed >>= 1;
+                break;
+            case 4:
+                color = 2;
+                break;
+            case 5:
+                color = ((int) seed+1&1)<<1;
+                seed >>= 1;
+                break;
+            case 6:
+                color = ((int) seed&1)+1;
+                seed >>= 1;
+                break;
+            case 7:
+                color = int((seed+i)%3);
+                seed /= 3;
+                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 (int(3+2.875*i/(m-1)-1.4375+.5)-3)
+                            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 = 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 = 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]];
+    }
+}
+
 }

core/edge-coloring.h

@@ -20,4 +20,10 @@ void edgeColoringSimple(Shape &shape, double angleThreshold, unsigned long long
  */
 void edgeColoringInkTrap(Shape &shape, double angleThreshold, unsigned long long seed = 0);
 
+/** The alternative coloring by distance tries to use different colors for edges that are close together.
+ *  This should theoretically be the best strategy on average. However, since it needs to compute the distance
+ *  between all pairs of edges, and perform a graph optimization task, it is much slower than the rest.
+ */
+void edgeColoringByDistance(Shape &shape, double angleThreshold, unsigned long long seed = 0);
+
 }

main.cpp

@@ -304,7 +304,7 @@ static const char *helpText =
         "\tSets the scale used to convert shape units to pixels asymmetrically.\n"
     "  -autoframe\n"
         "\tAutomatically scales (unless specified) and translates the shape to fit.\n"
-    "  -coloringstrategy <simple / inktrap>\n"
+    "  -coloringstrategy <simple / inktrap / distance>\n"
         "\tSelects the strategy of the edge coloring heuristic.\n"
     "  -distanceshift <shift>\n"
         "\tShifts all normalized distances in the output distance field by this value.\n"
@@ -715,6 +715,7 @@ int main(int argc, const char * const *argv) {
         ARG_CASE("-coloringstrategy", 1) {
             if (!strcmp(argv[argPos+1], "simple")) edgeColoring = edgeColoringSimple;
             else if (!strcmp(argv[argPos+1], "inktrap")) edgeColoring = edgeColoringInkTrap;
+            else if (!strcmp(argv[argPos+1], "distance")) edgeColoring = edgeColoringByDistance;
             else
                 puts("Unknown coloring strategy specified.");
             argPos += 2;