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ACM Transactions on Graphics (TOG), Volume 8 Issue 3, July 1989

A geometric characterization of parametric cubic curves
Maureen C. Stone, Tony D. DeRose
Pages: 147-163
DOI: 10.1145/77055.77056
In this paper, we analyze planar parametric cubic curves to determine conditions for loops, cusps, or inflection points. By expressing the curve to be analyzed as a linear combination of control points, it can be transformed such that three of...

Blending parametric surfaces
Daniel J. Filip
Pages: 164-173
DOI: 10.1145/77055.77057
A blending surface is a surface that smoothly connects two given surfaces along two arbitrary curves, one on each surface. This is particularly useful in the modeling operations of filleting a sharp edge between joining surfaces or connecting...

Automatic parsing of degenerate quadric-surface intersections
R. T. Farouki, C. Neff, M. A. O'Conner
Pages: 174-203
DOI: 10.1145/77055.77058
In general, two quadric surfaces intersect in a nonsingular quartic space curve. Under special circumstances, however, this intersection may “degenerate” into a quartic with a double point, or a composite of lines, conics, and...

A multisided generalization of Bézier surfaces
Charles T. Loop, Tony D. DeRose
Pages: 204-234
DOI: 10.1145/77055.77059
In this paper we introduce a class of surface patch representations, called S-patches, that unify and generalize triangular and tensor product Bézier surfaces by allowing patches to be defined over any convex polygonal domain; hence,...

Local generalized Hermite interpolation by quartic C2 space curves
Jörg Peters
Pages: 235-242
DOI: 10.1145/77055.77060
This paper develops and explains the construction of a piecewise quartic space curve that interpolates positional, tangent, and curvature data. The construction is local and explicit; that is, it does not involve the solution of equations. If...

A round trip to B-splines via de Casteljau
Hartmut Prautzsch
Pages: 243-254
DOI: 10.1145/77055.77061
B-splines are constructed from Bézier curves solely using de Casteljau's construction. Divided differences are not being used, nor is Mansfield's recurrence formula presupposed. Yet, it is shown how to differentiate, subdivide, and...