Simultaneous Precise Solutions to the Visibility Problem of Sculptured Models

Abstract. We present an efficient and robust algorithm for computing continuous visibility for two- or three-dimensional shapes whose boundaries are NURBS curves or surfaces by lifting the problem into a higher dimensional parameter space. This higher dimensional formulation enables solving for the visible regions over all view directions in the domain simultaneously, therefore providing a reliable and fast computation of the visibility chart, a structure which simultaneously encodes the visible part of the shape’s boundary from every view in the domain. In this framework, visible parts of planar curves are computed by solving two polynomial equations in three variables (t and r for curve parameters and θ for a view direction). Since one of the two equations is an inequality constraint, this formulation yields two-manifold surfaces as a zero-set in a 3-D parameter space. Considering a projection of the two-manifolds onto the tθ-plane, a curve’s location is invisible if its corre...

• Type: Conference
• Year: 2006
• Where: GMP
• Authors: Joon-Kyung Seong, Gershon Elber, Elaine Cohen
• Keywords: GMP 2006, Hidden Curve Removal, Parameter Space, View Direction