A boundary representation specifies a solid through its oriented bounding faces and their edge and vertex of a polyhedron incidence. Supporting planes and coordinates supply geometry; face loops and adjacency supply topology. A valid closed manifold model requires compatible orientation, two incident faces per edge and a single local fan at each vertex of a polyhedron, together with an embedded boundary.
A mesh representation with two oppositely directed records per ordinary edge. Each record stores its origin vertex of a polyhedron, incident face, next face-boundary record and opposite record; previous records are often cached. The opposite record's origin gives the destination. This usage differs from a dangling half-edge of a graph.
An edge record stores endpoint vertices of a polyhedron, its two incident faces, and predecessor and successor edges for each face. These four boundary-neighbour references are the wings. Face and vertex of a polyhedron records also carry entry references for traversal. Local edits must preserve all reciprocal incidence references and orientations.
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Boundary representation, often abbreviated as B-rep, is a method used in computer graphics and geometric modeling to represent the shape and topology of a three-dimensional object. In B-rep, the object is defined by its boundaries, which include faces, edges, and vertices. Here are the key components of B-rep: 1. **Vertices**: The corner points of the object where edges meet. 2. **Edges**: The line segments that connect vertices.