Avoid zero tangnet vectors on degenerate NURBS edges. Fixes #652

phkahler · phkahler · commit 408128a138df · 2020-10-18T14:54:00.000-04:00
diff --git a/src/srf/ratpoly.cpp b/src/srf/ratpoly.cpp
@@ -332,7 +332,7 @@ Vector SSurface::PointAt(double u, double v) const {
     return num;
 }
 
-void SSurface::TangentsAt(double u, double v, Vector *tu, Vector *tv) const {
+void SSurface::TangentsAt(double u, double v, Vector *tu, Vector *tv, bool retry) const {
     Vector num   = Vector::From(0, 0, 0),
            num_u = Vector::From(0, 0, 0),
            num_v = Vector::From(0, 0, 0);
@@ -364,6 +364,12 @@ void SSurface::TangentsAt(double u, double v, Vector *tu, Vector *tv) const {
 
     *tv = ((num_v.ScaledBy(den)).Minus(num.ScaledBy(den_v)));
     *tv = tv->ScaledBy(1.0/(den*den));
+    
+    // Tangent is zero at sungularities like the north pole. Move away a bit and retry. 
+    if(tv->Equals(Vector::From(0,0,0)) && retry)
+        TangentsAt(u+(0.5-u)*0.00001, v, tu, tv, false);
+    if(tu->Equals(Vector::From(0,0,0)) && retry)
+        TangentsAt(u, v+(0.5-v)*0.00001, tu, tv, false);
 }
 
 Vector SSurface::NormalAt(Point2d puv) const {
diff --git a/src/srf/surface.h b/src/srf/surface.h
@@ -335,7 +335,7 @@ class SSurface {
     void PointOnCurve(const SBezier *curve, double *up, double *vp);
     Vector PointAt(double u, double v) const;
     Vector PointAt(Point2d puv) const;
-    void TangentsAt(double u, double v, Vector *tu, Vector *tv) const;
+    void TangentsAt(double u, double v, Vector *tu, Vector *tv, bool retry=true) const;
     Vector NormalAt(Point2d puv) const;
     Vector NormalAt(double u, double v) const;
     bool LineEntirelyOutsideBbox(Vector a, Vector b, bool asSegment) const;
