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Geometric constraint solving with conics

机译:用锥体解决几何约束

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摘要

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: conics. we proved that the calss 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 conics 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.
机译:大多数机械CAD系统使用线路和圆圈(尺子和罗盘)作为基本绘图工具。在本文中,我们介绍了一类新的绘图工具:Conics。我们证明,这种新工具的绘图范围内的图表的图表大于可以用线和圆的绘制。实际上,我们证明了如果且才有且仅当该图可以用小于或等于四个的三角形方程序列来描述该图,则可以用Conics绘制图。这使我们能够用尺子和指南针保持几何约束求解的优雅,因为立方和四方程可以明确写入。

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