通用网格模型的等距曲面快速造型方法

项目名称： 通用网格模型的等距曲面快速造型方法

项目编号： No.61003125

项目类型： 青年科学基金项目

立项/批准年度： 2011

项目学科： 轻工业、手工业

项目作者： 刘圣军

作者单位： 中南大学

项目金额： 7万元

中文摘要： 等距曲面广泛使用于设计与制造各个应用领域，如快速成型、基于公差带的误差分析、刀具路径规划和机器人碰撞检测与处理等。现有的生成等距曲面的方法通常是先沿模型的曲面法向方向等距偏移所有的面，然后修剪或者延伸这些偏移面以重构出一个封闭的三维模型。然而，由于求交裁剪数值运算复杂且不稳定，这些方法难以应用于通用网格模型。在本项目中，我们提出了一个可行的方案，它能快速构造出通用网格模型的等距曲面，并使该曲面无自相交且具有尖锐特征。首先，根据等距曲面的本质属性使用距离函数隐式地定义给定模型的等距曲面，这种基于体表示的定义能保证曲面无自相交；然后，将模型及其等距曲面嵌入一个均匀的体网格中，等距曲面则处于体网格中的一个窄带内。我们采用有效算法减少大量的冗余计算实现了快速构造由隐式函数定义的窄带内的局部距离场。我们设计了四个过滤器以加速计算过程，分别是球扫成体层次结构过滤器，包围盒过滤器，内/外过滤器和八叉树过滤器；最后，我们构造出一个保证无自相交的曲面多边形化方法抽取出等距曲面的网格曲面，并重构出等距曲面上的尖锐特征。

中文关键词： 等距曲面；通用网格模型；尖锐特征；无自相交；距离场

英文摘要： Offset surface is widely used in fields for designing and manufacture, such as rapid phrototype, error analysis based on the tolerance zone, cutter path planning, robotic collision detection and processing, etc. Generally, for the existed offset surface generation methods, offsets of 3D models are achieved by first offsetting the all surfaces of the model along their normal directions and then trimming or extending these offset surfaces to reconstruct a closed 3D model. However, it is difficult to apply these methods to general mesh models because the trimming is numerically complex and unstable. In this projection, we proposed a practical scheme to fast construct intersection-free offset surfaces, which preserve sharp features from freefrom triangular mesh surfaces. Firstly, an offset surface is implicitly defined with a distance function according to its intrinsic property. This volumetric definition makes the offset surface immune from self-intersections. Then, we embed the given model and its offset surface into a uniform grid where the offset surface is located in a narrow band. By designing efficient algorithms, it can alleviate the computation redundancies for fast constructing the local distance field defined by the implicit function in the narrow band. Four filters conducted to speed the computation are a swept sphere volume hierarchy filter, a bounding box filter, a inside/outside filter, and an octree filter. At last, our modified intersection-free dual contouring algorithm is presented to extract the offset surface and reconstruct the sharp features on the offsets.

英文关键词： Offset surface; General mesh model; Sharp feature; Intersection-free; Distance field