Towards a New Generation of Robust CAD/CAM Systems

该项目的目标是利用不精确/离散的计算机算法，在稳健地表示、询问和操纵复杂物体的几何形状方面推进知识状态，并发展必要的理论和算法，这些理论和算法可以构成未来CAD/CAM系统的基础。本理论将主要涉及区间算法和数值分析中的条件作用概念，微分拓扑中的稳定性概念，代数拓扑中的简单复理论概念，微分几何的基本概念，所有应用于计算几何表示和算法。具体目标是：分析如何使用区间非均匀有理b样条曲线和表面斑块来获得复杂物体建模系统中固体灵活自由形式边界的鲁棒机器实现。开发允许稳定布尔运算的方法。研究由布尔运算产生的邻接关系的局部稳定性。研究如何将布尔运算产生的邻接关系的局部稳定性特性集成到全局拓扑广义边界表示元组结构中，从而获得与可变数值分辨率兼容的一致几何结果。在系统的结果信息不确定的情况下，以及在答案是特定的情况下，获得可靠的分类。

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.