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https://hdl.handle.net/2440/45343
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Type: | Conference paper |
Title: | Drawing ruled surfaces using the Dual de Boor algorithm |
Author: | Ding, Yulin (Rena) |
Citation: | Electronic Notes in Theoretical Computer Science [CATS'02, Computing: the Australasian Theory Symposium], 2002; 61: 178-190 |
Publisher: | Elsevier |
Issue Date: | 2002 |
ISSN: | 1571-0661 |
Conference Name: | Computing: The Australasian Theory Symposium (2002 : Melbourne, Australia) |
School/Discipline: | School of Computer Science |
Statement of Responsibility: | Rena Ding |
Abstract: | This paper outlines emerging methods, presently under investigation, for constructing ruled surfaces and solid-body trajectories in a Computer Aided Geometric Design (CAGD) context. The underlying principle is that of the standard De Boor Algorithm [4,2,15] for constructing B-spline curves on the plane, or in 3-dimensional space. But the coordinates of all 3-vector points including the control points to be interpolated are now taken to be dual, not real, numbers. When the six resulting number components are interpreted as Pl ű cker coordinates [12], each dual point finds interpretation as a line, and each curve as a ruled surface, in 3-dimensional space. The construction of a duplicated surface is discussed along with some new methods based on a rigid body character. The problem of drawing infinitely long lines, on a screen, as represented by Pl űcker coordinates, is touched upon. |
DOI: | 10.1016/S1571-0661(04)00312-3 |
Appears in Collections: | Computer Science publications |
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