论文信息 - On the Validity of Implicitization by Moving Quadrics for Rational Surfaces with No Base Points

On the Validity of Implicitization by Moving Quadrics for Rational Surfaces with No Base Points

Techniques from algebraic geometry and commutative algebra are adopted to establish sufficient 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.

Ron Goldman | Ming Zhang | David A. Cox | R. Goldman | Ming Zhang

[1] Joe W. Harris,et al. Principles of Algebraic Geometry , 1978 .

[2] A. L. Dixon. The Eliminant of Three Quantics in two Independent Variables , 1909 .

[3] T. Willmore. Algebraic Geometry , 1973, Nature.

[4] Falai Chen,et al. The moving line ideal basis of planar rational curves , 1998, Comput. Aided Geom. Des..

[5] Ron Goldman,et al. On a relationship between the moving line and moving conic coefficient matrices , 1999, Comput. Aided Geom. Des..

[6] Dinesh Manocha,et al. Implicitizing Rational Parametric Surfaces , 1990 .

[7] Falai Chen,et al. Implicitization using moving curves and surfaces , 1995, SIGGRAPH.

[8] Ron Goldman,et al. Implicitizing Rational Curves by the Method of Moving Algebraic Curves , 1997, J. Symb. Comput..

[9] David A. Cox,et al. Using Algebraic Geometry , 1998 .

[10] Miles Reid,et al. Commutative Ring Theory , 1989 .