Cubic curve distance optimization

core/edge-segments.cpp

@@ -199,9 +199,9 @@ SignedDistance QuadraticSegment::signedDistance(Point2 origin, double &param) co
     double minDistance = nonZeroSign(crossProduct(epDir, qa))*qa.length(); // distance from A
     param = -dotProduct(qa, epDir)/dotProduct(epDir, epDir);
     {
-        epDir = direction(1);
         double distance = (p[2]-origin).length(); // distance from B
         if (distance < fabs(minDistance)) {
+            epDir = direction(1);
             minDistance = nonZeroSign(crossProduct(epDir, p[2]-origin))*distance;
             param = dotProduct(origin-p[1], epDir)/dotProduct(epDir, epDir);
         }
@@ -235,25 +235,31 @@ SignedDistance CubicSegment::signedDistance(Point2 origin, double &param) const
     double minDistance = nonZeroSign(crossProduct(epDir, qa))*qa.length(); // distance from A
     param = -dotProduct(qa, epDir)/dotProduct(epDir, epDir);
     {
-        epDir = direction(1);
         double distance = (p[3]-origin).length(); // distance from B
         if (distance < fabs(minDistance)) {
+            epDir = direction(1);
             minDistance = nonZeroSign(crossProduct(epDir, p[3]-origin))*distance;
             param = dotProduct(epDir-(p[3]-origin), epDir)/dotProduct(epDir, epDir);
         }
     }
     // Iterative minimum distance search
     for (int i = 0; i <= MSDFGEN_CUBIC_SEARCH_STARTS; ++i) {
-        double t = (double) i/MSDFGEN_CUBIC_SEARCH_STARTS;
+        double t = 1./MSDFGEN_CUBIC_SEARCH_STARTS*i;
         Vector2 qe = qa+3*t*ab+3*t*t*br+t*t*t*as;
-        for (int step = 0; step < MSDFGEN_CUBIC_SEARCH_STEPS; ++step) {
-            // Improve t
-            Vector2 d1 = 3*ab+6*t*br+3*t*t*as;
-            Vector2 d2 = 6*br+6*t*as;
-            t -= dotProduct(qe, d1)/(dotProduct(d1, d1)+dotProduct(qe, d2));
-            if (t <= 0 || t >= 1)
-                break;
-            qe = qa+3*t*ab+3*t*t*br+t*t*t*as;
+        Vector2 d1 = 3*ab+6*t*br+3*t*t*as;
+        Vector2 d2 = 6*br+6*t*as;
+        double improvedT = t-dotProduct(qe, d1)/(dotProduct(d1, d1)+dotProduct(qe, d2));
+        if (improvedT > 0 && improvedT < 1) {
+            int remainingSteps = MSDFGEN_CUBIC_SEARCH_STEPS;
+            do {
+                t = improvedT;
+                qe = qa+3*t*ab+3*t*t*br+t*t*t*as;
+                d1 = 3*ab+6*t*br+3*t*t*as;
+                if (!--remainingSteps)
+                    break;
+                d2 = 6*br+6*t*as;
+                improvedT = t-dotProduct(qe, d1)/(dotProduct(d1, d1)+dotProduct(qe, d2));
+            } while (improvedT > 0 && improvedT < 1);
             double distance = qe.length();
             if (distance < fabs(minDistance)) {
                 minDistance = nonZeroSign(crossProduct(d1, qe))*distance;