Geometric computations in parameter space
Proceedings of the 21st spring conference on Computer graphics
Sliding windows algorithm for B-spline multiplication
Proceedings of the 2007 ACM symposium on Solid and physical modeling
Sweeping Surface Generated by a Class of Generalized Quasi-cubic Interpolation Spline
ICCS '07 Proceedings of the 7th international conference on Computational Science, Part II
Critical point analysis using domain lifting for fast geometry queries
Computer-Aided Design
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We present an efficient and robust algorithm for computing the perspective silhouette of the boundary of a general swept volume. We also construct the topology of connected components of the silhouette. At each instant t, a three-dimensional object moving along a trajectory touches the envelope surface of its swept volume along a characteristic curve Kt. The same instance of the moving object has a silhouette curve Lt on its own boundary. The intersection Kt∩Lt contributes to the silhouette of the general swept volume. We reformulate this problem as a system of two polynomial equations in three variables. The connected components of the resulting silhouette curves are constructed by detecting the instances where the two curves Kt and Lt intersect each other tangentially on the surface of the moving object. We also consider a general case where the eye position changes while moving along a predefined path. The problem is reformulated as a system of two polynomial equations in four variables, where the zero-set is a two-manifold. By analyzing the topology of the zero-set, we achieve an efficient algorithm for generating a continuous animation of perspective silhouettes of a general swept volume.