Solid modeling in 计算机辅助设计 represents objects as unambiguous, voluminous 3D shapes. Two primary techniques dominate: Boundary Representation (B-rep), which defines a solid by its bounding surfaces (faces, edges, vertices), and Constructive Solid Geometry (CSG), which builds complex shapes by applying Boolean operations (union, subtract, intersect) to simpler primitive solids like cubes, spheres, and cylinders.
边界表示法 (B-rep) 和构造性实体几何 (CSG) 是计算机中表示实体对象的两种基本方法。B-rep 可以说是现代 CAD 系统中用于详细设计更常见的方法。它通过明确定义实体拓扑元素的层次结构（面、边和顶点）以及每个元素的几何信息（例如，面的曲面方程、边的曲线方程）来描述实体。这种明确的边界定义使其非常适合生成逼真的渲染图和计算表面属性，这对于 CNC 加工等制造工艺至关重要。
Constructive Solid Geometry, on the other hand, takes a more procedural approach. It represents a complex object as a tree structure where the leaf nodes are simple geometric primitives (e.g., block, cylinder, sphere, cone) and the internal nodes are Boolean set operators (union, intersection, difference). For example, a hollow pipe could be created by subtracting a smaller cylinder from a larger, concentric one. CSG models are typically very compact and guarantee that the resulting object is a valid solid. However, retrieving boundary information like specific faces or edges can be computationally expensive, as it requires ‘evaluating’ the entire CSG tree. Many modern CAD systems use a hybrid approach, allowing users to build models using CSG-like operations, but storing the final result as a B-rep model for efficient manipulation and analysis.
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