#### Filter Results:

#### Publication Year

1991

2011

#### Co-author

#### Key Phrase

#### Publication Venue

Learn More

An inversion equation takes the Cartesian coordinates of a point on a parametric curve or surface and returns the parameter value(s) of that point. A 2-D curve inversion equation has the form t = f (x, y)/g(x, y). This paper shows that practical insight into inversion can be obtained by studying the geometry of the implicit curves f (x, y) = 0 and g(x, y) =… (More)

We identify a class of monomial supports that are inherently improper because any surface rational parametrization defined on them is improper. A surface support is inherently improper if and only if the gcd of the normalized areas of the triangular sub-supports is non-unity. The constructive proof of this claim can be used to detect all and correct almost… (More)

Macaulay's concise but explicit expression for nmltivariate resultants has many potential applications in computer-aided geometric design. Here we describe its use in solid modeling for finding the intersections of three implicit quadric surfaces. By B6zout's theorem, three quadric surfaces have either at most eight or intlnitely many intersections. Our… (More)

EEcient algorithms are derived for computing the entries of the Bezout resultant matrix for two univariate polynomials of degree n and for calculating the entries of the Dixon-Cayley resultant matrix for three bivariate polynomials of bidegree (m; n). Standard methods based on explicit formulas require O(n 3) additions and multiplications to compute all the… (More)

The method of moving curves and moving surfaces is a new, eeective tool for implicitizing rational curves and surfaces. Here we investigate a relationship between the moving line coeecient matrix and the moving conic coeecient matrix for rational curves. Based on this relationship, we present a new proof that the method of moving conics always produces the… (More)