Geometric conditions of non-self-intersecting NURBS surfaces

NURBS surface is very useful in geometric modeling, animation, image morphing and deformation. Constructing non-self-intersecting (injective) NURBS surfaces is an important process in surface and solid modeling. In this paper, the injective conditions of tensor product NURBS surface are studied, based on the geometric positions of control points, which are equivalent to the surface to be non-self-intersecting for all positive weights. Finally, some representative examples are provided.