Graphics (TOG)


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ACM Transactions on Graphics (TOG) - Special issue on computer-aided design, Volume 8 Issue 4, Oct. 1989

Blending algebraic surfaces
J. Warren
Pages: 263-278
DOI: 10.1145/77269.77270
A new definition of geometric continuity for implicitly defined surfaces is introduced. Under this definition, it is shown that algebraic blending surfaces (surfaces that smoothly join two or more surfaces) have a very specific...

The displacement method for implicit blending surfaces in solid models
A. P. Rockwood
Pages: 279-297
DOI: 10.1145/77269.77271
To date, methods that blend solids, that is, B-rep or CSG models, with implicit functions require successive composition of the blending functions to handle an arbitrary solid model. The shape of the resulting surfaces depends upon the algebraic...

On local implicit approximation and its applications
J. H. Chuang, C. M. Hoffmann
Pages: 298-324
DOI: 10.1145/77269.77272
A method is proposed for computing an implicit approximant at a point to a parametric curve or surface. The method works for both polynomially and rationally parameterized curves and surfaces and achieves an order of contact that can be...

Automatic parameterization of rational curves and surfaces IV: algebraic space curves
S. S. Abhyankar, C. J. Bajaj
Pages: 325-334
DOI: 10.1145/77269.77273
For an irreducible algebraic space curve C that is implicitly defined as the intersection of two algebraic surfaces, f (x, y, z) = 0 and g...

Rational continuity: parametric, geometric, and Frenet frame continuity of rational curves
M. E. Hohmeyer, B. A. Barsky
Pages: 335-359
DOI: 10.1145/77269.77274
The parametric, geometric, or Frenet frame continuity of a rational curve has often been ensured by requiring the homogeneous polynomial curve associated with the rational curve to possess either parametric, geometric, or Frenet frame...

A generalized Ball curve and its recursive algorithm
H. B. Said
Pages: 360-371
DOI: 10.1145/77269.77275
The use of Bernstein polynomials as the basis functions in Bézier's UNISURF is well known. These basis functions possess the shape-preserving properties that are required in designing free form curves and surfaces. These curves and...