#### 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...