A slicing algorithm for rapid prototyping and manufacturing

This paper first reviews the existing techniques of surface-plane intersection in computer-aided geometric design (CAGD). The vector fields are introduced for the detection of closed intersection loops. A distance function is defined from a surface patch to an intersecting plane and the gradient of the function defines a plane vector field. The Poincare index theorem is inconclusive in detecting critical points of plane vector field. The modified Poincare theorem is developed by extending the plane vector fields into three dimensions for the conclusive test of critical points. The initial points are obtained based on loop detection and subdivision. The resulting intersections are represented using biarc spline fitting scheme. The algorithm presented in the paper requires only the surface be parametrically defined and C ² continuous