Towards a New Generation of Robust CAD/CAM Systems

该项目的目标是促进国家的 在鲁棒地表示、询问和操纵方面的知识 使用不精确/离散计算机的复杂物体的几何形状 算法和开发必要的理论和算法， 可以成为未来CAD/CAM系统的基础。 这一理论 将主要涉及区间算术的概念， 条件从数值分析以及概念 从微分拓扑学出发，单纯复理论的稳定性 从代数拓扑学和微分学的基本概念 几何，所有这些都应用于计算几何表示， 算法 具体目标是：分析区间非均匀性 有理B样条曲线和曲面片可以用来获得 灵活的自由形式边界的鲁棒机器实现， 在复杂物体的建模系统中的实体。 发展 允许稳定的布尔运算的方法。 探讨如何 布尔邻接的局部稳定性 运营 为了研究局部稳定性 由布尔运算产生的邻接可以被集成到 全局拓扑广义边界表示单元- 元组结构，以便获得一致的几何结果， 保持与可变数字分辨率兼容。 获得 一个可靠的案件分类，其中产生的信息 是不确定的，而那些答案是 特定.

The object of this project is to advance the state of knowledge in robustly representing, interrogating and manipulating the geometry of complex objects using imprecise/discrete computer arithmetic and developing the necessary theory and algorithms which can form the basis for CAD/CAM systems of the future. This theory will involve primarily concepts of interval arithmetic and conditioning from numerical analysis as well as concepts of stability from differential topology, of simplicial complex theory from algebraic topology, and basic concepts of differential geometry, all applied in computational geometry representations and algorithms. Specific objectives are: To analyze how interval non-uniform rational B-spline curves and surface patches can be used to obtain robust machine realizations of flexible free-form boundaries for solids in a modeling system for complex objects. To develop methods which allow stable Boolean operations. To investigate how local stability properties of adjacencies resulting from Boolean operations. To investigate how local stability properties of adjacencies resulting from Boolean operations can be integrated in a global topological generalized Boundary Representation cell- tuple structure, so as to obtain consistent geometric results which remain compatible with a variable numerical resolution. To obtain a reliable classification of cases where the resulting information of the system is uncertain and those cases where the answer is specific.