Study on Physically-Based Methods for Assisting Interactive object Layout

大多数机械产品可以被认为是在三维空间中适当配置的刚性物体的集合。它们通过组件对象之间的接触关系传递力和运动来实现其功能。我们的研究目的是开发快速计算算法来分析这些动态相互作用及其对产品力学行为的影响。公差分析任何机械零件因其生产而产生的几何偏差。它们会给机械产品带来各种功能不确定性。设计人员通过在零件上指定适当的公差来控制偏差的影响。我们开发了一个代数算法来分析装配中两个零件的位置不确定性，如果单个零件的形状变化在公差允许的情况下。有效的碰撞检测机械设计和制造活动中的许多任务可以表示为在空间区域中对实体进行布局。精密机械产品的零部件非常紧密地放置在一个很小的空间区域，因此可以接触的零件对通常是有限的。基于机械产品的这一特点，提出了一些有效的零件碰撞检测和避免算法。稳健的几何计算描述立体几何的数值数据通常使用浮点数给出。由于浮点数基本上是近似值，因此可能存在不精确的情况，从而导致所表示的对象不一致。利用机械设计领域的公差思想可以避免某些类型的不一致。基于这一概念，提出了几种基于公差的稳定几何处理算法。

Most mechanical products can be considered as a collection of rigid objects properly configured in a three dimensional space. They realize their function by transferring forces and motions through contact relations between the component objects. The purpose of our study is to develop fast computation algorithms for analyzing these dynamic interactions and their effects on the mechanical behavior of the product.The following three results are obtained in our study.1. Tolerance analysis Any machine parts have geometric deviations due to their production. They cause various functional uncertainties of mechanical products. Designers control the effect of the deviations by specifying proper tolerances on the parts. We develop an algebraic algorithm for analyzing position uncertainties of two parts in an assembly if certain shape variations of individual parts are allowed by tolerances.2. Efficient collision detection Many tasks in machine design and manufacturing activities can be formulated as layouting of solid objects in a spatial region. Component parts of a precise mechanical product are very tightly placed in a small spatial region, therefore possible pairs of parts to contact are usually limited. Based on this characteristic of mechanical products, we develop some efficient algorithms for detecting and avoiding collisions between the parts.3. Robust geometric computation Numerical data describing the solid geometry are usually given using floating point numbers. Since floating point numbers are basically approximations, there may be imprecision that leads to inconsistencies about the represented object. Some types of the inconsistencies can be avoided by using tolerance ideas of the mechanical design field. Based on this concept, several tolerance based algorithms for stable geometric processing are developed.