In this paper we present a new method for detecting and determining characteristic points on the surface/surface intersection while marching along the intersections. The initial interval which contains a potential characteristic point is first determined by certain criteria, then a numeric solution of the significant point is obtained by the binary subdivision method. Based on these ideas, a new marching algorithm is constructed, and it has been implemented in a surface modelling system (SurfCADM V1.0). Examples are also presented for illustrating the capability of our algorithm.

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