Topological Neighborhoods for Spline Curves: Practice & Theory

The unresolved subtleties of floating point computations in geometric modeling become considerably more difficult in animations and scientific visualizations. Some emerging solutions based upon topological considerations will be presented. A novel geometric seeding algorithm for Newton’s method was used in experiments to determine feasible support for these visualization applications. 1 Computing the pipe surface radius Parametric curves have been shown to have a particular neighborhood whose boundary is non-self-intersecting [5]. It has also been shown that specified movements of the curve within this neighborhood preserve the topology of the curve [9, 8], as is desired in visualization. This neighborhood is defined by a single value, which is the radius of a pipe surface, where that radius depends on curvature and the minimum length over those line segments which are normal to the curve at both endpoints of the line segment [5]. Since computation of curvature is a well-treated problem, the focus of this paper is efficient and accurate floating point techniques to compute the other dependeancy for that radius. ∗Department of Computer Science & Engineering, University of Connecticut, Storrs, CT 06269-2155, [email protected].