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ACM Transactions on Graphics (TOG), Volume 17 Issue 1, Jan. 1998

Rational parametrizations of nonsingular real cubic surfaces
Chandrajit L. Bajaj, Robert L. Holt, Arun N. Netravali
Pages: 1-31
DOI: 10.1145/269799.269800
Real cubic algebraic surfaces may be described by either implicit or parametric equations. One particularly useful representation is the rational parametrization, where the three spatial coordinates are given by rational functions of two...

The bisector surface of rational space curves
Gershon Elber, Myung-So Kim
Pages: 32-49
DOI: 10.1145/269799.269801
Given a point and a rational curve in the plane, their bisector curve is rational [Farouki and Johnston 1994a]. However, in general, the bisector of two rational curves in the plane is not rational [Farouki and Johnstone 1994b]. Given a point...

The directional parameter plane transform of a height field
David W. Paglieroni
Pages: 50-70
DOI: 10.1145/269799.269802
The linear Parameter Plane Transform (PPT) of a height field attributes an inverted cone of empty space to each height field cell. In is known that height field ray-tracing efficiency can be improved by traversing rays in steps...