Geometric Constraint Solving with Conics and Linkages (2002)
| Venue: | Computer Aided Design, Vol |
| Citations: | 2 - 1 self |
BibTeX
@ARTICLE{Gao02geometricconstraint,
author = {Xiao-shan Gao and Kun Jiang},
title = {Geometric Constraint Solving with Conics and Linkages},
journal = {Computer Aided Design, Vol},
year = {2002},
volume = {34},
pages = {421--433}
}
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Abstract
Abstract. Most mechanical CAD systems use line and circle(ruler and compass) as basic drawing tools. In this paper we introduce a class of new drawing tools: the conic. We proved that the class of diagrams within the drawing scope of this new tool is larger than that can be drawn with line and circle. Actually, we proved that a diagram can be drawn with conic if and only if this diagram can be described with a sequence of triangularised equations of degree less than or equal to four. This allows us to maintain the elegance of geometric constraint solving with ruler and compass, because the solutions of cubic and quartic equations can be written explicitly. 1.
