@willsunagency/cad-brep-validator

Boundary Representation (B-Rep) topological manifold validator and Euler-Poincaré invariant checker for 3D computational geometry kernels.

Part of the open-source manufacturing infrastructure maintained by CADGuide.tools.

Theoretical Mathematical Foundation

In solid modeling systems (such as ACIS, Parasolid, Open CASCADE, and CGAL), 3D solids are bounded by orientable manifolds consisting of vertices, edges, loops, and faces. A watertight, non-self-intersecting solid with internal voids and through-holes must satisfy the extended Euler-Poincaré equation:

$$\text{Euler} = V - E + F - (L - F) - 2(S - G) = 0$$

Where:

• V: Number of vertices
• E: Number of edges
• F: Number of faces
• L: Total number of face-bounding loops (including inner void loops)
• S: Number of disconnected shells
• G: Genus (topological handles / through-holes)

Failure to satisfy this topological invariant results in failed boolean operations, non-manifold geometry, and slicing crashes in CAM and 3D printing software.

Installation

npm install @willsunagency/cad-brep-validator

Usage Example

const { validateBRepManifold } = require('@willsunagency/cad-brep-validator');

// Validating a simple cube: 8 vertices, 12 edges, 6 faces
const cubeTopology = {
  vertices: 8,
  edges: 12,
  faces: 6,
  loops: 6,
  shells: 1,
  genus: 0
};

const result = validateBRepManifold(cubeTopology);
console.log('Is Watertight Manifold:', result.valid); // true
console.log('Euler Characteristic:', result.eulerCharacteristic); // 0

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License

MIT © CADGuide.tools Team