SURFACE-SURFACE INTERSECTION WITH CRITICAL POINT DETECTION BASED ON , BEZIER NORMAL VECTOR SURFACES Yasushi Yamaguchi Department of Graphics and Computer Science, The University of Tokyo 3-8-1, Komaba, Meguro-ku, Tokyo 153-8902, Japan yama@graco.c.u-tokyo.ac.jp Ryuji Kamiyama NTT Telecommunications Software Headquarters 1-6, Nakase, Mihama-ku, Chiba-city, Chiba, Japan kamiyama@nwp.tsh.cae.ntt.jp F\nnihiko Kimura Department of Precision Machinery Engineering, The University of Tokyo 7-3-1, Hongo, Bunkyo-ku, Tokyo 113-8654, Japan kimura@cim.pe.u-tokyo.ac.jp Abstract Surface-surface intersection is one of essential techniques in geometric modeling. A relatively robust algorithm to calculate intersections of parametric surfaces is a marching method which repeatedly calculates consecutive points on an intersection curve starting with a certain point. However, it is difficult to find starting points of all branches of intersec- tions especially when the branches form small loops. It is also difficult to trace a curve near singular points. Critical points which have par- allel normals on both surfaces are key points to solve those problems. We will, first, propose a Bezier normal vector surface which can exactly represent normal vectors on a Bezier surface. Then we will explain a new algorithm to find all critical points by using Bezier normal vector surfaces. All starting points of intersection curves are obtained with the algorithm. Furthermore, intersection curves can be robustly traced by using the critical points. Keywords: Surface-surface intersection, Critical point, Normal vector F. Kimura (ed.), Geometric Modelling © Springer Science+Business Media New York 2001