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ACM Transactions on Graphics (TOG), Volume 9 Issue 2, April 1990

Improper intersection of algebraic curves
Shreeram S. Abhyankar, Srinivasan Chandrasekar, Vijaya Chandru
Pages: 147-159
DOI: 10.1145/78956.78957
Bezout's theorem gives an upper bound on the degree of the intersection of properly intersecting algebraic varieties. In spaces of dimension higher than two, however, intersections between many algebraic varieties such as curves are improper....

A butterfly subdivision scheme for surface interpolation with tension control
Nira Dyn, David Levine, John A. Gregory
Pages: 160-169
DOI: 10.1145/78956.78958
A new interpolatory subdivision scheme for surface design is presented. The new scheme is designed for a general triangulation of control points and has a tension parameter that provides design flexibility. The resulting limit surface is...

Solid representation and operation using extended octrees
Pere Brunet, Isabel Navazo
Pages: 170-197
DOI: 10.1145/78956.78959
Solid modelers must be based on reliable and fast algorithms for Boolean operations. The octree model, as well as several generalizations (polytrees, integrated polytrees, extended octrees), is specially well suited for these algorithms and can...

Two remarks on Tau-splines
Dieter Lasser
Pages: 198-211
DOI: 10.1145/78956.78960
We present a Bézier representation of &tgr;-splines, curvature and torsion-continuous quintics, which were introduced in CAGD by Hagen in 1985 [32]. Explicit formulas are given for the conversion from Bézier representation to...

On the construction of surfaces interpolating curves. I. A method for handling nonconstant parameter curves
David R. Ferguson, Thomas A. Grandine
Pages: 212-225
DOI: 10.1145/78956.78961
In industrial design, the tool of choice for constructing surfaces that interpolate curves is the Boolean sum surface technique. However, if curves do not lie on constant parameter lines, reparametrizations will be needed, and this may introduce...

The RGYB color geometry
Colin Ware, William Cowan
Pages: 226-232
DOI: 10.1145/78956.78962
Background:The gamut of a color CRT is defined by its three primary colors, each produced by a phosphor/electron gun combination. Light from the primaries combines additively, so the color gamut is a subset of a three dimensional vector...