Tracking Method for Reparametrized Geometrical Constraint Systems

2011 13th International Symposium on Symbolic and Numeric Algorithms for Scientific Computing Pub Date : 2011-09-26 DOI:10.1109/SYNASC.2011.26

Rémi Imbach, P. Mathis, P. Schreck

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引用次数: 10

Abstract

In CAD, constraint solvers allow a user to describe a figure or an object with a set of constraints like distances, angles, tangencies, incidences and so on. Geometric solvers proceed in two stages. First, a symbolic construction plan is provided from the set of constraints. Then, the dimensions of constraints are used in a numerical stage to evaluate the construction plan. However, construction plans can not be easily provided for many problems in 3D. A classic idea consists in removing and adding some constraints in order to make the problem solvable by a geometric method. This leads to a numerical problem in which numerical values for the added constraints have to be computed in order to find the values of the added dimensions that validate the removed dimensions. Finding these values is usually done by sampling which is very time-consuming when there are more than 2 variables to sample. In this paper we address the numerical stage by adapting a path-tracking method. This allows to find several solutions and this method is efficient when the number of values is greater than 2.

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重参数化几何约束系统的跟踪方法

在CAD中，约束求解器允许用户用一组约束(如距离、角度、切线、夹角等)来描述图形或对象。几何求解分两个阶段进行。首先，从约束条件出发，给出了象征性的建筑方案。然后，在数值阶段使用约束的尺寸来评估施工方案。然而，在三维环境中，由于存在许多问题，施工方案不容易提供。一个经典的想法是去除或增加一些约束，以便用几何方法解决问题。这导致了一个数值问题，在这个问题中，必须计算添加约束的数值，以便找到验证已删除维度的添加维度的值。找到这些值通常是通过抽样来完成的，当有两个以上的变量要抽样时，这是非常耗时的。在本文中，我们通过采用路径跟踪方法来解决数值阶段。这允许找到多个解，当值的数量大于2时，这种方法是有效的。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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2011 13th International Symposium on Symbolic and Numeric Algorithms for Scientific Computing

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