A Differential Method for Parametric Surface Intersection

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Abstract

In this paper, a new method for computing the intersection of parametric surfaces is proposed. In our approach, this issue is formulated in terms of an initial value problem of first-order ordinary differential equations (ODEs), which are to be numerically integrated. In order to determine the initial value for this system, a simple procedure based on the vector field associated with the gradient of the distance function between points lying on each of the parametric surfaces is described. Such a procedure yields a starting point on the nearest branch of the intersection curve. The performance of the presented method is analyzed by means of some illustrative examples that contain many of the most common features found in parametric surface intersection problems.