Ray Tracing of Steiner Patches
Thomas W. Sederberg, David C. Anderson
Computer Graphics (Proceedings of SIGGRAPH 84), July 1984, pp. 159--164.
Abstract: implicitization of Steiner patch, solution of resulting quartic Steiner patches are triangular surface patches for which the Cartesian coordinates of points on the patch are defined parametrically by quadratic polynomial functions of two variables. It has recently been shown that it is possible to express a Steiner patch in an implicit equation which is a degree four polynomial in $<$i$>$x, y, z$<$/i$>$. Furthermore,the parameters of a point known to be on the surface can be computed as rational polynomial functions of $<$i$>$x, y, z$<$/i$>$. These findings lead to a straightforward algorithm for ray tracing Steiner patches in which the ray intersection equation is a degree four polynomial in the parameter of the ray. The algorithm presented represents a major simplification over existing techniques for ray tracing free-form surface patches.
Keyword(s): patch, root finding
@inproceedings{Sederberg:1984:RTO,
author = {Thomas W. Sederberg and David C. Anderson},
title = {Ray Tracing of Steiner Patches},
booktitle = {Computer Graphics (Proceedings of SIGGRAPH 84)},
pages = {159--164},
month = jul,
year = {1984},
}
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