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- Ming Zhang, Ron Goldman
- ISSAC
- 2000

We present a way to construct the Sylvester <italic>A</italic>-resultant matrix for three bi-degree (<italic>m, n</italic>) polynomials whose Newton polygon is modified by cutting off rectangles at the corners. We also show that the determinant of this matrix is generically non-singular, so this determinant is indeed the resultant of the three originalâ€¦ (More)

- Phillip J. Barry, Ron Goldman
- SIGGRAPH
- 1988

It is known that certain Catmull-Rom splines [7] interpolate their control vertices and share many properties such as affine invariance, global smoothness, and local control with B-spline curves; they are therefore of possible interest to computer aided design. It is shown here that another property a class of Catmull-Rom splines shares with B-spline curvesâ€¦ (More)

- Ron Goldman
- Computer Aided Geometric Design
- 2005

Curvature formulas for implicit curves and surfaces are derived from the classical curvature formulas in Differential Geometry for parametric curves and surfaces. These closed formulas include curvature for implicit planar curves, curvature and torsion for implicit space curves, and mean and Gaussian curvature for implicit surfaces. Some extensions of theseâ€¦ (More)

- Tony DeRose, Ron Goldman, Hans Hagen, Stephen Mann
- ACM Trans. Graph.
- 1993

In view of the fundamental role that functional composition plays in mathematics, it is not surprising that a variety of problems in geometric modeling can be viewed as instances of the following composition problem: given representations for two functions <italic>F</italic> and <italic>G</italic>, compute a representation of the function <italic>H</italic>â€¦ (More)

- Ron Goldman, Thomas W. Sederberg, David C. Anderson
- Computer Aided Geometric Design
- 1984

- Ning Song, Ron Goldman
- Computer Aided Geometric Design
- 2009

- Thomas W. Sederberg, David C. Anderson, Ron Goldman
- Computer Vision, Graphics, and Image Processing
- 1984

- David A. Cox, Ron Goldman, Ming Zhang
- J. Symb. Comput.
- 2000

Techniques from algebraic geometry and commutative algebra are adopted to establish suucient polynomial conditions for the validity of implicitization by the method of moving quadrics both for rectangular tensor product surfaces of bi-degree (m; n) and for triangular surfaces of total degree n in the absence of base points.

- Thomas W. Sederberg, Ron Goldman, Hang Du
- J. Symb. Comput.
- 1997

- Eng-Wee Chionh, Ron Goldman
- The Visual Computer
- 1992