工业自动化系统与集成 产品数据表示与交换 第42部分：集成通用资源：几何与拓扑表示

[中文适用范围]： 本文件规定了用于几何和拓扑表示的集成通用资源构造。以下内容属于本文件的范围： **几何模式的范围包括以下内容**：点、向量、参数曲线和参数曲面的定义；具有内部参数化的有限体积的定义；变换算子的定义；直接通过坐标值定义的点，或通过现有曲线或曲面的参数定义的点；圆锥曲线和基本曲面的定义；在参数曲面上定义的曲线；一般参数样条曲线、曲面和体积的定义；局部细化的样条曲线、曲面和体积的定义；点、曲线和曲面副本的定义；偏移曲线和曲面的定义；交线的定义。 **拓扑模式的范围包括以下内容**：顶点、边和面的基本拓扑实体的定义，每种实体都有专门的子类型，以便与点、曲线或曲面的几何分别相关联；通过基本实体的集合形成路径、回路和壳体等拓扑结构，并对这些结构的完整性进行约束；面与几何体积的关联；拓扑实体的方向。 **几何模型模式的范围包括以下内容**：描述三维实体物体精确几何形式的数据；构造实体几何（CSG）模型；二维空间中的CSG模型；CSG基本体和半空间的定义；通过扫掠操作创建实体模型；流形边界表示（B-rep）模型；确保B-rep模型完整性的约束；曲面模型；线框模型；几何集合；在新位置创建实体模型的副本；网格几何；将网格几何与精确几何相关联。 **扫描数据三维形状模型模式的范围包括以下内容**：将形状表示为由扫描过程生成的点云。 **以下内容不在本文件的范围内**：所有其他通过程序定义的曲线和曲面形式；没有参数表示形式的曲线和曲面；任何以显式形式表示的直纹曲面。 **注**：直纹曲面的几何形状在很大程度上依赖于边界曲线的参数化和将两条曲线上点对关联的方法。然而，具有B样条边界曲线的直纹曲面可以通过B样条曲面实体进行精确表示。 此外，以下内容也不在本文件的范围内：实体模型的空间占用形式（如八叉树模型）；几何公差；以特征形式表示的隐式表示；装配体和机构。 [外文原描述]： This document specifies the integrated generic resource constructs for geometric and topological representation. The following are within the scope of this document: The following are in the scope of the geometry schema: definition of points, vectors, parametric curves and parametric surfaces; definition of finite volumes with internal parametrisation; definition of transformation operators; points defined directly by their coordinate values or in terms of the parameters of an existing curve or surface; definition of conic curves and elementary surfaces; definition of curves defined on a parametric surface; definition of general parametric spline curves, surfaces and volumes; definition of locally refined spline curves, surfaces and volumes; definition of point, curve and surface replicas; definition of offset curves and surfaces; definition of intersection curves. The following are in the scope of the topology schema: definition of the fundamental topological entities vertex, edge, and face, each with a specialised subtype to enable it to be associated with the geometry of a point, curve, or surface, respectively; collections of the basic entities to form topological structures of path, loop and shell and constraints to ensure the integrity of these structures; the association of faces with geometric volumes; orientation of topological entities. The following are in the scope of the geometric model schema: data describing the precise geometric form of three-dimensional solid objects; constructive solid geometry (CSG) models; CSG models in two-dimensional space; definition of CSG primitives and half-spaces; creation of solid models by sweeping operations; manifold boundary representation (B-rep) models; constraints to ensure the integrity of B-rep models; surface models; wireframe models; geometric sets; creation of a replica of a solid model in a new location; tessellated geometry; the association of tessellated geometry with exact geometry. The following are in the scope of the scan data 3d shape model schema: representation of a shape as a cloud of points produced by a scanning process. The following are outside the scope of this document: all other forms of procedurally defined curves and surfaces; curves and surfaces which do not have a parametric form of representation; any form of explicit representation of a ruled surface. NOTE For a ruled surface the geometry is critically dependent upon the parametrisation of the boundary curves and the method of associating pairs of points on the two curves. A ruled surface with B-spline boundary curves can however be exactly represented by the B-spline surface entity. spatial occupancy forms of solid models (such as octree models); geometric tolerances; implicit forms of representation in terms of features; assemblies and mechanisms.