CAREER: Algebraic and Geometric Techniques for Interface Detection in Static and Dynamic Enviroments

干涉检测问题是计算几何、实体建模、机器人、制造、计算机图形学和计算机模拟环境中的基础问题。这些包括几何模型之间的碰撞检测运动，线性和曲面之间的表面相交，碰撞避免机器人运动规划，可见性计算，隐藏表面去除和边界计算。 本研究采用代数、数值和几何技术对这些问题进行了三方面的研究： 1.为静态和动态环境中的几何模型之间的干涉检测开发快速和鲁棒的算法。这组模型包括多面体、样条、代数曲面和可变形对象。 2.将这些算法专门用于交互式碰撞检测、隐藏曲面去除、曲面求交和边界计算，并特别强调鲁棒性。 3.开发高效的软件库，用于移动多面体对象之间的干涉检测，使用代数曲面和边界评估定义的实体模型。 由此产生的库将作为公共领域代码分发，并在不同的应用程序上演示。 研究工作将与以下教育目标相辅相成： 1.开发几何、符号和科学计算的本科生和研究生课程。 2. 利用万维网（WWW）技术开发新的教学方法和电子课程笔记。 3. 使用图形，几何和动画工具，开发一个算法动画和编程实验室的本科课程。 4.作为高中生和本科生的导师，在我们的实验室从事图形和建模相关的项目。 ***

The problems of interference detection are fundamental in computational geometry, solid modeling, robotics, manufacturing, computer graphics and computer-simulated environments. These include collision detection between geometric models undergoing motion, surface intersection between linear and curved surfaces, collision avoidance for robot motion planning, visibility computations, hidden surface removal and boundary computations. This research takes a three-fold approach to these problems using algebraic, numeric and geometric techniques: 1. Develop fast and robust algorithms for interference detection between geometric models in static and dynamic environments. The set of models include polyhedra, splines, algebraic surfaces and deformable objects. 2. Specialize these algorithms to interactive collision detection, hidden surface removal, surface intersection and boundary computation with special emphasis on robustness. 3. Develop efficient software libraries for interference detection between moving polyhedral objects, solid models defined using algebraic surfaces and boundary evaluation. The resulting libraries will be distributed as public domain code and demonstrated on different applications. The research efforts will be complemented with the following educational goals: 1. Development of undergraduate and graduate courses on geometric, symbolic and scientific computing. 2. Develop novel teaching methods and electronic course notes using the World-Wide Web (WWW) technology. 3. Use of graphics, geometry and animation tools to develop an algorithm animation and programming laboratory for undergraduate courses. 4. Serving as a mentor to high school and undergraduate students to work on graphics and modeling related projects in our laboratory. ***