Approximating surfaces with discontinuities

Approximating polyhedral objects with deformable smooth surfaces

We propose a method to approximate a polyhedral object with a deformable smooth surface, namely the t-skin defined by Edelsbrunner for all 0 < t < 1. We guarantee that they are homeomorphic and their Hausdorff distance is at most ε > 0. This construction makes it possible for fully automatic, smooth and robust deformation between two polyhedral objects with different topologies. En route to our...

Approximating Closed Rational Surfaces

In this chapter, the problem of drawing a closed rational surface is considered. As in the case of rational curves, the key to drawing a closed rational surface is to partition the parameter domain into simple connected regions Ri such as triangles or rectangles, in such a way that there is some prespecified region R0 and some projectivities such that every other region is the image of the regi...

Approximating catmull-clark subdivision surfaces with bicubic patches

Approximating rational triangular Bézier surfaces by polynomial triangular Bézier surfaces

An attractive method for approximating rational triangular Bézier surfaces by polynomial triangular Bézier surfaces is introduced. The main result is that the arbitrary given order derived vectors of a polynomial triangular surface converge uniformly to those of the approximated rational triangular Bézier surface as the elevated degree tends to infinity. The polynomial triangular surface is con...

Approximating the Location of Integrand Discontinuities for Penumbral Illumination with Area Light Sources

The problem of computing soft shadows with area light sources has received considerable attention in computer graphics. In part, this is a difficult problem because the integral that defines the radiance at a point must take into account the visibility function. Most of the solutions proposed have been limited to polygonal environments, and require a full visibility determination preprocessing ...