CTAN sync 202003040302

1 files changed, 26 insertions, 6 deletions

diff --git a/graphics/asymptote/beziercurve.cc b/graphics/asymptote/beziercurve.cc
index 23f5fc6779..9a5eee79f2 100644
--- a/graphics/asymptote/beziercurve.cc
+++ b/graphics/asymptote/beziercurve.cc
@@ -20,11 +20,30 @@ void BezierCurve::init(double res)
   MaterialIndex=materialIndex;
 }
 
+inline triple normal(triple bP, triple bPP)
+{
+  return dot(bP,bP)*bPP-dot(bP,bPP)*bP;
+}
+
 void BezierCurve::render(const triple *p, bool straight) 
 {
-  GLuint i0=data.vertex1(p[0]);
-  GLuint i3=data.vertex1(p[3]);
-    
+  triple p0=p[0];
+  triple p3=p[3];
+  triple n0,n1;
+
+  if(straight) {
+    n0=n1=triple(0.0,0.0,1.0);
+  } else {
+    triple p1=p[1];
+    triple p2=p[2];
+
+    n0=normal(p1-p0,p0+p2-2.0*p1);
+    n1=normal(p3-p2,p3+p1-2.0*p2);
+  }
+
+  GLuint i0=data.vertex(p0,n0);
+  GLuint i3=data.vertex(p3,n1);
+
   if(straight) {
     std::vector<GLuint> &q=data.indices;
     q.push_back(i0);
@@ -34,9 +53,9 @@ void BezierCurve::render(const triple *p, bool straight)
   append();
 }
   
-// Use a uniform partition to draw a Bezier patch.
+// Use a uniform partition to draw a Bezier curve.
 // p is an array of 4 triples representing the control points.
-// Ii are the vertices indices.
+// Ii are the vertex indices.
 void BezierCurve::render(const triple *p, GLuint I0, GLuint I1)
 {
   triple p0=p[0];
@@ -62,7 +81,8 @@ void BezierCurve::render(const triple *p, GLuint I0, GLuint I1)
     triple s0[]={p0,m0,m3,m5};
     triple s1[]={m5,m4,m2,p3};
       
-    GLuint i0=data.vertex1(m5);
+    triple n0=normal(bezierPh(p0,p1,p2,p3),bezierPPh(p0,p1,p2,p3));
+    GLuint i0=data.vertex(m5,n0);
       
     render(s0,I0,i0);
     render(s1,i0,I1);