In solid modeling, which method defines the topology of faces, edges, and vertices and also stores the surface geometry on which each face lies?

Introduction / Context:
Solid modeling techniques represent 3D objects for CAD/CAM/CAE workflows. Two foundational paradigms are constructive solid geometry (CSG) and boundary representation (B-rep). B-rep models a solid by explicitly storing its boundary elements and how they connect, enabling precise topology and geometry management for downstream operations such as meshing and manufacturing.

Given Data / Assumptions:

• We need a method that captures both topology (connectivity) and geometry (surfaces).
• Faces are bounded by edges; edges meet at vertices.
• Each face lies on a mathematical surface (for example, plane, cylinder, NURBS patch).

Concept / Approach:
Boundary representation (B-rep) stores the set of faces, edges, and vertices along with adjacency relations. Each face references its underlying surface definition and trimming curves. This dual recording of “what is connected to what” (topology) and “what exact shape it lies on” (geometry) is essential for accurate intersection, filleting, and tolerance control. By contrast, CSG builds solids via Boolean combinations of primitives without explicit face-level topology.

Step-by-Step Solution:

Verification / Alternative check:
Most modern CAD kernels (e.g., Parasolid-like architectures conceptually) employ B-rep to support advanced operations that need local topological and geometric detail.

Why Other Options Are Wrong:

Common Pitfalls:
Assuming CSG alone can substitute for detailed manufacturing models; without explicit B-rep topology, local edits and fillets are difficult to manage.

Final Answer:
Boundary representation.