Perspective silhouette of a general swept volume

Joon Kyung Seong, Ku Jin Kim, Myung Soo Kim, Gershon Elber

Research output: Contribution to journalArticle

7 Citations (Scopus)

Abstract

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 K t. The same instance of the moving object has a silhouette curve L t on its own boundary. The intersection K t ∩ L t 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 K t and L t 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.

Original languageEnglish
Pages (from-to)109-116
Number of pages8
JournalVisual Computer
Volume22
Issue number2
DOIs
Publication statusPublished - 2006 Feb

Keywords

  • Perspective silhouette
  • Sweep surface
  • Time varying silhouette
  • Topology
  • Zero-set computation

ASJC Scopus subject areas

  • Software
  • Computer Vision and Pattern Recognition
  • Computer Graphics and Computer-Aided Design

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