A Complete Quadrilateral in Rectangular Coordinates

Quadrilateral-Octagon Coordinates for Almost Normal Surfaces

Normal and almost normal surfaces are essential tools for algorithmic 3-manifold topology, but to use them requires exponentially slow enumeration algorithms in a high-dimensional vector space. The quadrilateral coordinates of Tollefson alleviate this problem considerably for normal surfaces, by reducing the dimension of this vector space from 7n to 3n (where n is the complexity of the underlyi...

Ray-Triangle and Ray-Quadrilateral Intersections in Homogeneous Coordinates

Recent articles in Ray Tracing News have discussed solutions to the problem of intersecting a ray with a triangle using the triangle’s barycentric coordinates. This article shows yet another way to think about the ray-triangle intersection problem. The idea is to think of the barycentric coordinates of the intersection point, not as the ratio of areas, but rather as the as ratios of the volume ...

Complete wetting near an edge of a rectangular-shaped substrate.

We consider fluid adsorption near a rectangular edge of a solid substrate that interacts with the fluid atoms via long range (dispersion) forces. The curved geometry of the liquid-vapour interface dictates that the local height of the interface above the edge ℓ(E) must remain finite at any subcritical temperature, even when a macroscopically thick film is formed far from the edge. Using an inte...

A 400-MHz Processor for the Conversion of Rectangular to Polar Coordinates in 0.25- m CMOS

This paper describes the architecture and IC implementation of a rectangular-to-polar coordinate converter for digital communication applications. The architecture core uses small lookup ROMs, fast multipliers, and a single angle-rotation stage. Area and latency are reduced in comparison with traditional methods. The processor, implemented in 0.25m five-metal CMOS, has 14-b in-phase and quadrat...

A Comparison of the Optimal Multiplier in Polar and Rectangular Coordinates by Joseph Euzebe Tate