Parametric Surfaces and Ray Tracing

A new method for ray tracing polynomial and rational parametric surfaces is presented. The algorithm we describ is based on algebraic tools (implicitization and inversion) and does not proceed by a previous approximation of the surface. Each surface can be associated with numerical matrices in such a way that operations to be done on surfaces can be translated into operations on the corresponding matrices and treated by numerical matrix techniques. These matrices are an implicit version of a given parametric surface and contain all algebraic and topological informations about it.

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