A scanline algorithm for displaying trimmed surfaces by using Bézier clipping

Abstract

Displaying objects with high accuracy is necessary for CAGD (computer-aided geometric design) and for the synthesis of photo-realistic images. Traditionally, polygonal approximation methods have been employed to display free-form surfaces. They bring on low accuracy of display not only in shape, but also in intensity of objects. In this paper, a scanline algorithm to directly display parametric surface patches, expressed by trimmed B6zier surfaces, without polygonal approximation is proposed. In the method proposed here, curved surfaces are subdivided into subpatches with curved edges intersecting with a scanline, and the intersections of every subpatch and the scanline are calculated. This method is extremely robust for calculating the intersections, which can be obtained with only a few iterations; the B6zier clipping method is used for the iteration. Anti-aliased images with shadows and texture mapping are given to show the effectiveness of the method proposed.

A New Radiosity Approach Using Area Sampling for Parametric Patches

“…For the scanning algorithm, we employ the author's scanline algorithm [17]using Bézier Clipping [16] because of the following advantages: Bézier Clipping is an iterative method which takes advantage of the convex hull property of Bézier curves, provides more robust convergence to the solution than Newton's method, and can be used to find a solution for curve/plane, surface/plane, and ray/surface intersections.…”

“…As mentioned in section 3, hidden-surface removal is done by scan-line algorithm [17]. Patches are subdivided into almost flat sub-patches, the intersections between scanlines and the edges of sub-patches are calculated.…”

Shadow Volume Generation from Free Form Surfaces

“…All images in this paper were created using this renderer. Methods to render free form surfaces directly, without the need for a polygonal approximations, are under active research, and shadow volumes could easily t into these approaches Elber 1992b, Lane 1980, Nishita 1991, Schantz 1988. I n the derivation presented here, light sources are assumed to be point sources at either nite or in nite distances.…”

“…This allows one to render scenes from any viewpoint without the need to redetermine the underlying shadow representation, possibly exploiting the use of a hardware renderer. Di erent approaches for the direct rendering of free from surfaces with shadows, that do not use raytracing, have been examined elsewhere Nishita 1991, Reeves 1987, Williams 1978.…”