Shifting planes to follow a surface of revolution

Authors:
Eng-Wee Chionh
Affiliations:
School of Computing, National University of Singapore, Law Link, Singapore
Venue:
GMP'08 Proceedings of the 5th international conference on Advances in geometric modeling and processing
Year:
2008

Citing 4
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Abstract

A degree n rational plane curve rotating about an axis in the plane creates a degree 2n rational surface. Two formulas are given to generate 2n moving planes that follow the surface. These 2n moving planes lead to a 2n × 2n implicitization determinant that manifests the geometric revolution algebraically in two aspects. Firstly the moving planes are constructed by successively shifting terms of polynomials from one column to another of a spawning 3 × 3 determinant. Secondly the right half of the 2n × 2n implicitization determinant is almost an n-row rotation of the left half. As an aside, it is observed that rational parametrizations of a surface of revolution due to a symmetric rational generatrix must be improper.