论文标题
几何约束解决的综述
A review on geometric constraint solving
论文作者
论文摘要
本文对参数计算机辅助设计（CAD）的几何约束解决方案进行了全面综述，重点是在过去15年中的进步。几何约束求解可以追溯到1960年代的第一个CAD原型Sketchpad，但是仅在1980年代后期引入参数CAD之后才进行了认真的研究。在接下来的30年历史中，可以确定两个发展阶段：（1）最初的15年（1980年代末至2000年代中期）主要致力于对良好约束的系统或仅具有结构性约束依赖关系的系统的几何约束分解； （2）第二个15年（2000年代末 - 现在）已经看到研究工作转向了一般约束系统的分类标准和分解算法（具有和没有非结构性约束依赖性）。大多数现有评论都集中在头15年。但是，考虑到手动指定的约束系统通常包含不受约束和过度约束的部分，并且必须在数值求解可以正确检测并解决此类部分。在这方面，本综述论文涵盖了两个阶段，并将讨论处理通用约束系统已经成为可能的事情，在不久的将来可以期望哪些发展以及哪些领域仍然有问题。
This paper presents a comprehensive review of geometric constraint solving in parametric computer-aided design (CAD), with the major focus on its advances in the last 15 years. Geometric constraint solving can date back to the very first CAD prototype, Sketchpad, in the 1960s, but serious research studies were carried out only after parametric CAD was introduced in the late 1980s. In the following 30-year history of GCS research, two development stages may be identified: (1) the first 15 years (late 1980s - mid 2000s) were primarily devoted to geometric constraint decomposition for well-constrained systems or those with only structural constraint dependencies; and (2) the second 15 years (late 2000s - now) have seen research efforts shifted towards classification criteria and decomposition algorithms for general constraint systems (with and without non-structural constraint dependencies). Most existing reviews focused on the first 15 years. The problem researched in the second 15 years is, however, equally important, considering that a manually specified constraint system usually contains under- and over-constrained parts, and that such parts must be correctly detected and resolved before numerical solving can work. In this regard, this review paper covers both stages and will discusses what has already been made possible for handling general constraint systems, what developments can be expected in the near future, and which areas remain problematic.
