Improperly parametrized rational curves
Computer Aided Geometric Design
Curve implicitization using moving lines
Computer Aided Geometric Design
Implicitization using moving curves and surfaces
SIGGRAPH '95 Proceedings of the 22nd annual conference on Computer graphics and interactive techniques
On the validity of implicitization by moving quadrics for rational surfaces with no base points
Journal of Symbolic Computation
Elimination and Resultants - Part 1: Elimination and Bivariate Resultants
IEEE Computer Graphics and Applications
Inherently improper surface parametric supports
Computer Aided Geometric Design
Interval implicitization of parametric surfaces
ICICA'10 Proceedings of the First international conference on Information computing and applications
Implicitizing rational surfaces of revolution using µ-bases
Computer Aided Geometric Design
| Hi-index | 0.01 |
A degree n rational plane curve revolving in space around an axis in its plane yields a degree 2n rational surface. Two formulas are presented to generate 2n moving planes that follow the surface. These 2n moving planes give a 2nx2n implicitization determinant that manifests conspicuously the geometric action of revolution in two algebraic aspects. Firstly the moving planes are constructed by successively shifting terms of polynomials from one column to another of a spawning 3x3 determinant. Secondly the right half of the 2nx2n implicitization determinant is an n-row rotation of the left half with some sign flipping. Additionally, it is observed that rational parametrizations for a surface obtained as a surface of revolution with a symmetric generatrix must be improper.