Abstract:
Homotopy is a method for finding the roots of one equation by slowly transforming an equation to which the roots are known into the equation of interest, keeping track of how the roots change as the equation does. Homotopy has been considered in the past for surface-surface intersections in computer-aided geometric design, but rejected out of concern for speed or numerical accuracy. However, recent developments in the field as well as faster computers make this algorithm a viable candidate. Particularly, homotopy should be useful in finding starting points for tracing the intersection curve of two implicit surfaces. 1
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