Added DihedralAngleRad that computes the signed dihedral angle between the normals of two adjacent faces

vcg/simplex/face/topology.h

@@ -63,6 +63,56 @@ inline bool IsBorder(FaceType const & f,  const int j )
   return true;
 }
 
+/*! \brief Compute the signed dihedral angle between the normals of two adjacent faces
+ *
+ * The angle between the normal is signed according to the concavity/convexity of the
+ * dihedral angle: negative if the edge shared between the two faces is concave, positive otherwise.
+ * The surface it is assumend to be oriented.
+ * It simply use the projection of  the opposite vertex onto the plane of the other one.
+ * It does not assume anything on face normals.
+*
+*     v0 ___________ vf1
+*       |\          |
+*       |  \i1   f1 |
+*       |    \      |
+*       |f0  i0\    |
+*       |        \  |
+*       |__________\|
+*    vf0             v1
+*/
+
+template <class FaceType>
+inline typename FaceType::ScalarType DihedralAngleRad(FaceType & f,  const int i )
+{
+  typedef typename FaceType::ScalarType ScalarType;
+  typedef typename FaceType::CoordType CoordType;
+  typedef typename FaceType::VertexType VertexType;
+
+  FaceType *f0 = &f;
+  FaceType *f1 = f.FFp(i);
+  int i0=i;
+  int i1=f.FFi(i);
+  VertexType *vf0 = f0->V2(i0);
+  VertexType *vf1 = f1->V2(i1);
+
+  CoordType n0 = NormalizedNormal(*f0);
+  CoordType n1 = NormalizedNormal(*f1);
+  ScalarType off0 = n0*vf0->P();
+  ScalarType off1 = n1*vf1->P();
+
+  ScalarType dist01 = off0 - n0*vf1->P();
+  ScalarType dist10 = off1 - n1*vf0->P();
+
+  // just to be sure use the sign of the largest in absolute value;
+  ScalarType sign;
+  if(fabs(dist01) > fabs(dist10)) sign = dist01;
+  else sign=dist10;
+
+  ScalarType angleRad=Angle(f0->N(),f1->N());
+
+  if(sign > 0 ) return angleRad;
+  else return -angleRad;
+}
 
 /// Count border edges of the face
 template <class FaceType>