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的基础问题。其中包括运动几何模型之间的碰撞检测，直线和曲面之间的曲面相交，机器人运动规划的碰撞避免，可见性计算，隐藏表面去除和边界计算。本研究采用代数、数值和几何技术的三重方法来解决这些问题：为静态和动态环境中几何模型之间的干扰检测开发快速和鲁棒的算法。该模型集包括多面体、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，隐藏表面去除，表面相交和边界计算，并特别强调鲁棒性。3. 开发高效的软件库，用于移动多面体物体之间的干扰检测，使用代数曲面定义的实体模型和边界评估。生成的库将作为公共领域代码发布，并在不同的应用程序上进行演示。研究工作将与以下教育目标相辅相成：发展几何、符号和科学计算的本科和研究生课程。2. 利用万维网技术开发新颖的教学方法和电子课程笔记。3. 利用图形、几何和动画工具开发了一个算法动画和编程实验室的本科课程。4. 在我们的实验室担任高中和本科生的图形和建模相关项目的导师。＊＊＊

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. ***