Triangtular Patches under Tension

Abstract

Given a triangular surface scheme that only approximates the initial data the resulting surfaces do not reflect the shape of control vertices as much as the user would have liked. By supplying tension parameters, or what in this case might be called "shape" parameters, the user is able to force the triangular surface patch to follow the control vertices as close as desired without moving or introducing additional control point A revised radiosity method for curved surfaces is proposed, based on the Monte Carlo approach. In order to improve the accuracy of the solution, a smoothly reconstructed illumination function with selected discontinuities is used during the radiosity computation. The reconstructed function is used as a random number distribution for position sampling to overcome the constant radiosity assumption syndrome. Illumination information stored at the surface control points is used to preserve continuity of the illumination across the boundary of adjacent surfaces and to avoid Mach band effects. Implementation in Flatland is discussed.