Algebraic pruning: a fast technique for curve and surface intersection

Computing the intersection of parametric and algebraic curves and surfaces is a fun damental problem in computer graphics and geometric modeling This problem has been extensively studied in the literature and di erent techniques based on subdivision interval analysis and algebraic formulation are known For low degree curves and surfaces algebraic methods are considered to be the fastest whereas techniques based on subdivision and B ezier clipping perform better for higher degree intersections In this paper we introduce a new technique of algebraic pruning based on the algebraic approaches and eigenvalue formulation of the problem The resulting algorithm corre sponds to only computing the selected eigenvalues in the domain of intersection This is based on matrix formulation of the intersection problem power iterations and geometric properties of B ezier curves and surfaces The algorithm prunes the domain and converges to the solutions rapidly It has been applied to intersection of parametric and algebraic curves ray tracing and curve surface inter sections The resulting algorithm compares favorably with earlier methods in terms of performance and accuracy