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/sup 2/ continuous.

[1]  Ren C. Luo,et al.  Topological method for loop detection of surface intersection problems , 1995, Comput. Aided Des..

[2]  Michael I. Jordan,et al.  Surface/surface intersection , 1987, Comput. Aided Geom. Des..

[3]  William S. Massey,et al.  Algebraic Topology: An Introduction , 1977 .

[4]  Rida T. Farouki,et al.  The characterization of parametric surface sections , 1986, Comput. Vis. Graph. Image Process..

[5]  T. Sederberg,et al.  Improved test for closed loops in surface intersections , 1989 .

[6]  J. C. Burkill,et al.  Ordinary Differential Equations , 1964 .

[7]  David A. Fredricks,et al.  Intersection of Parametric Surfaces and a Plane , 1984, IEEE Computer Graphics and Applications.

[8]  K. Cheng.  Using plane vector fields to obtain all the intersection curves of two general surfaces , 1989 .

[9]  B. Su,et al.  Computational geometry: curve and surface modeling , 1989 .

[10]  Eric Klassen,et al.  Exploiting topological and geometric properties for selective subdivision , 1985, SCG '85.

[11]  I. Faux,et al.  Computational Geometry for Design and Manufacture , 1979 .

[12]  Nicholas M. Patrikalakis,et al.  Topological and differential-equation methods for surface intersections , 1992, Comput. Aided Des..

[13]  Thomas W. Sederberg,et al.  Loop detection in surface patch intersections , 1988, Comput. Aided Geom. Des..

[14]  Robert E. Barnhill,et al.  A marching method for parametric surface/surface intersection , 1990, Comput. Aided Geom. Des..

[15]  Ren C. Luo,et al.  Free form surface representation and machining for complex parts , 1994, Proceedings of the 1994 IEEE International Conference on Robotics and Automation.