Painter's algorithm

Abstract: Consider a collection of disjoint polygons in the plane containing a total ofn edges We show how to build, inO(n 2) time and space, a data structure from which inO(n) time we can compute the visibility polygon of a given point with respect to the polygon collection As an application of this structure, the visibility graph of the given polygons can be constructed inO(n 2) time and space This implies that the shortest path that connects two points in the plane and avoids the polygons in our collection can be computed inO(n 2) time, improving earlierO(n 2 logn) results

Abstract: Efficiently identifying polygons that are visible from a changing synthetic viewpoint is an important problem in computer graphics. Even with hardware support, simple algorithms like depth-buffering cannot achieve interactive frame rates when applied to geometric models with many polygons. However, a visibility algorithm that exploits the occlusion properties of the scene to identify a superset of visible polygons, without touching most invisible polygons, could achieve fast frame rates while viewing such models. In this paper, we present a new approach to the visibility problem. The novel aspects of our algorithm are that it is temporally coherent and conservative ; for all viewpoints the algorithm overestimates the set of visible polygons. As the synthetic viewpoint moves, the algorithm reuses visibility information computed for previous viewpoints. It does so by computing visual events at which visibility changes occur, and efficiently identifying and discarding these events as the viewpoint changes. In essence, the algorithm implicitly constructs and maintains a linearized portion of an aspect graph , a data structure for representing visual events. We demonstrate that the visibility algorithm significantly accelerates rendering of several test models.

Abstract: One of the most interesting ways of assembling small units is along one of the lattices that make up crystals. In this column I live entirely in a 2D world, so the crystals are nothing but collections of polygons in the plane. It is well known that there are only three regular polygons that can tile the plane. Here the verb tile means to cover the infinite plane with a set of polygons so that no gaps or overlaps exist among the polygons. Each polygon is called a tile and the composite pattern is called a tiling.

Abstract: A high speed hidden surface processor capable of operating in real time and suitable for interaction with a computer-generated imagery or computer graphics system, whereby a realistic three-dimensional scene can be projected on a two-dimensional video display. The scene is formed by one or more polygons that are visible from an arbitrary viewpoint. The present hidden surface processor employs a hidden surface algorithm, such that certain polygons or portions of polygons, which polygons are obscured by other polygons lying closer to the viewpoint, are removed or truncated. Ordered linked lists of scan line data corresponding to the surfaces of the visible polygons are assembled and stored, so that the complete scene may be subsequently displayed with increased speed and minimized hardware implementation costs.