On ray tracing parametric surfaces
- 1 July 1985
- journal article
- Published by Association for Computing Machinery (ACM) in ACM SIGGRAPH Computer Graphics
- Vol. 19 (3) , 171-179
- https://doi.org/10.1145/325165.325233
Abstract
A new method for ray tracing parametric surfaces is presented. The new algorithm solves the ray surface intersection directly using multivariate Newton iteration. This provides enough generality to render surfaces which could not be ray traced using existing methods. To overcome the problem of finding a starting point for the Newton algorithm, techniques from Interval Analysis are employed. The results are presented in terms of solving a general nonlinear system of equations f(x)= 0, and thus can be extended to a large class of problems which arise in computer graphics.Keywords
This publication has 11 references indexed in Scilit:
- Distributed ray tracingACM SIGGRAPH Computer Graphics, 1984
- Ray tracing of Steiner patchesACM SIGGRAPH Computer Graphics, 1984
- Ray tracing algebraic surfacesACM SIGGRAPH Computer Graphics, 1983
- A Generalization of Algebraic Surface DrawingACM Transactions on Graphics, 1982
- Ray tracing parametric patchesACM SIGGRAPH Computer Graphics, 1982
- An improved illumination model for shaded displayCommunications of the ACM, 1980
- A Theoretical Development for the Computer Generation and Display of Piecewise Polynomial SurfacesPublished by Institute of Electrical and Electronics Engineers (IEEE) ,1980
- Safe Starting Regions for Iterative MethodsSIAM Journal on Numerical Analysis, 1977
- A Test for Existence of Solutions to Nonlinear SystemsSIAM Journal on Numerical Analysis, 1977
- Newton-Algorithmen zur Bestimmung von Nullstellen mit FehlerschrankenComputing, 1969