Breps

Breps, short for boundary representation, is a data structure used in solid modeling to represent three-dimensional objects. Instead of storing an object as a collection of points or voxels, a brep defines it by its bounding surfaces. This approach focuses on the object's boundary, which consists of faces, edges, and vertices. Faces are the planar or curved surfaces that enclose the object. Edges are the curves or line segments where two faces meet. Vertices are the points where edges intersect.

The brep data structure is hierarchical and topological. It stores the relationships between these geometric entities. For example, it explicitly defines which edges belong to which faces, and which vertices belong to which edges. This topological information is crucial for performing valid geometric operations such as Boolean operations (union, intersection, difference), shelling, and filleting.

One of the primary advantages of brep is its ability to represent complex shapes with high precision. Unlike mesh-based representations, breps can store exact mathematical definitions of curves and surfaces, leading to more accurate representations. This makes brep a cornerstone of many CAD (Computer-Aided Design) and CAM (Computer-Aided Manufacturing) systems. The computational complexity of operations can be higher than with simpler representations, but the precision and robustness offered by breps are often essential for engineering and design applications.