When clipping ears to triangulate a curved surface, clip the ear

that minimizes the chord tolerance.

[git-p4: depot-paths = "//depot/solvespace/": change = 1921]

polygon.h

@@ -61,7 +61,7 @@ public:
     bool IsEar(int bp);
     bool BridgeToContour(SContour *sc, SEdgeList *el, List<Vector> *vl);
     void ClipEarInto(SMesh *m, int bp);
-    void UvTriangulateInto(SMesh *m);
+    void UvTriangulateInto(SMesh *m, SSurface *srf);
 };
 
 typedef struct {
@@ -88,7 +88,7 @@ public:
     bool IsEmpty(void);
     Vector AnyPoint(void);
     void OffsetInto(SPolygon *dest, double r);
-    void UvTriangulateInto(SMesh *m);
+    void UvTriangulateInto(SMesh *m, SSurface *srf);
 };
 
 class STriangle {

solvespace.h

@@ -141,6 +141,7 @@ void vl(void); // debug function to validate heaps
 //================
 
 
+class SSurface;
 #include "dsc.h"
 #include "polygon.h"
 #include "srf/surface.h"

srf/ratpoly.cpp

@@ -731,7 +731,9 @@ void SSurface::TriangulateInto(SShell *shell, SMesh *sm) {
     ZERO(&poly);
     if(el.AssemblePolygon(&poly, NULL, true)) {
         int i, start = sm->l.n;
-        poly.UvTriangulateInto(sm);
+        // Curved surfaces are triangulated in such a way as to minimize
+        // deviation between edges and surface; but doesn't matter for planes.
+        poly.UvTriangulateInto(sm, (degm == 1 && degn == 1) ? NULL : this);
 
         STriMeta meta = { face, color };
         for(i = start; i < sm->l.n; i++) {

srf/surface.h

@@ -211,6 +211,7 @@ public:
     void TriangulateInto(SShell *shell, SMesh *sm);
     void MakeEdgesInto(SShell *shell, SEdgeList *sel, bool asUv);
     void MakeClassifyingBsp(SShell *shell);
+    double ChordToleranceForEdge(Vector a, Vector b);
 
     void Reverse(void);
     void Clear(void);

srf/triangulate.cpp

@@ -1,6 +1,6 @@
 #include "../solvespace.h"
 
-void SPolygon::UvTriangulateInto(SMesh *m) {
+void SPolygon::UvTriangulateInto(SMesh *m, SSurface *srf) {
     if(l.n <= 0) return;
 
     SDWORD in = GetMilliseconds();
@@ -80,7 +80,7 @@ void SPolygon::UvTriangulateInto(SMesh *m) {
         }
 //        dbp("finished merging holes: %d ms", GetMilliseconds() - in);
 
-        merged.UvTriangulateInto(m);
+        merged.UvTriangulateInto(m, srf);
 //        dbp("finished ear clippping: %d ms", GetMilliseconds() - in);
         merged.l.Clear();
         el.Clear();
@@ -250,7 +250,7 @@ void SContour::ClipEarInto(SMesh *m, int bp) {
     l.RemoveTagged();
 }
 
-void SContour::UvTriangulateInto(SMesh *m) {
+void SContour::UvTriangulateInto(SMesh *m, SSurface *srf) {
     int i;
 
     // Clean the original contour by removing any zero-length edges.
@@ -276,24 +276,57 @@ void SContour::UvTriangulateInto(SMesh *m) {
             }
         }
 
-        // And find a candidate ear; alternate the starting position so
-        // we generate strip-like triangulations instead of fan-like
-        int ear = -1;
+        int bestEar = -1;
+        double bestChordTol = VERY_POSITIVE;
+        // Alternate the starting position so we generate strip-like
+        // triangulations instead of fan-like
         toggle = !toggle;
         int offset = toggle ? -1 : 0;
         for(i = 0; i < l.n; i++) {
-            ear = WRAP(i+offset, l.n);
+            int ear = WRAP(i+offset, l.n);
             if(l.elem[ear].ear == SPoint::EAR) {
-                break;
+                if(!srf) {
+                    bestEar = ear;
+                    break;
+                }
+                // If we are triangulating a curved surface, then try to
+                // clip ears that have a small chord tolerance from the
+                // surface.
+                Vector prev = l.elem[WRAP((i+offset-1), l.n)].p,
+                       next = l.elem[WRAP((i+offset+1), l.n)].p;
+                double tol = srf->ChordToleranceForEdge(prev, next);
+                if(tol < bestChordTol - LENGTH_EPS) {
+                    bestEar = ear;
+                    bestChordTol = tol;
+                }
+                if(bestChordTol < 0.1*(SS.chordTol / SS.GW.scale)) {
+                    break;
+                }
             }
         }
-        if(ear < 0) {
+        if(bestEar < 0) {
             dbp("couldn't find an ear! fail");
             return;
         }
-        ClipEarInto(m, ear);
+        ClipEarInto(m, bestEar);
     }
 
     ClipEarInto(m, 0); // add the last triangle
 }
 
+double SSurface::ChordToleranceForEdge(Vector a, Vector b) {
+    Vector as = PointAt(a.x, a.y), bs = PointAt(b.x, b.y);
+
+    double worst = VERY_NEGATIVE;
+    int i;
+    for(i = 1; i <= 3; i++) {
+        Vector p  = a. Plus((b. Minus(a )).ScaledBy(i/4.0)),
+               ps = as.Plus((bs.Minus(as)).ScaledBy(i/4.0));
+
+        Vector pps = PointAt(p.x, p.y);
+        worst = max(worst, (pps.Minus(ps)).MagSquared());
+    }
+    return sqrt(worst);
+}
+
+