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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 original… (More)
It is known that certain Catmull-Rom splines  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 curves… (More)
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 these… (More)
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>… (More)
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.