Computational Geometry Architecture
A technical deep-dive into the mathematical and systems foundations of Locus: exact analytical B-Rep solids, non-uniform rational B-spline topology, implicit minimal surface metamaterials, and bounded process computation.
Core Mathematical & Systems Pillars
1. Exact Analytical B-Rep Solids & Boundary Healing
Solid validation targets watertight boundaries, consistent winding, nondegenerate faces, and positive signed volume. Coverage depends on the modeling path and parameter domain; representative checks do not certify every possible model.
- Exact zero-radius apexes and explicit triangle fans for revolve singularities
- Native STEP ISO-10303 solid entity emission (MANIFOLD_SOLID_BREP)
- Elimination of zero-area faces and polar coordinate offsets
2. True Rational Cubic NURBS Evaluation
Sketched profiles extruded or revolved preserve true cubic (`degree = [3, 3]`) outer B-spline hull control nets rather than being degraded to uniform polygonal cages. Control nets can be pushed and pulled in real-time with preserved knot vectors and rational weights.
- Closed-seam pole welding via evaluated sculpt engines
- Analytic B_SPLINE_SURFACE_WITH_KNOTS representation in STEP
- Non-destructive transformation and sculpted history stacks
3. Bounded-Worker Multiprocessing Pools
Cloud CAD services face denial-of-service risks from expensive geometric operations. Locus routes compute-intensive workloads through a bounded multiprocessing worker pool with strict AST preflights, CPU time limits, and memory isolation.
- AST-sandboxed math evaluation with zero unsafe eval
- Bounded worker execution with deadlines and resource limits
- Validated inputs and reusable geometry results where applicable
4. Model Context Protocol for Physical Hardware
Locus implements a native Model Context Protocol (MCP) server that empowers autonomous AI agents to interact directly with the CAD kernel through validated geometric schemas rather than hallucinated code.
- Typed JSON-RPC tool contracts with strict validation gates
- Multi-body interference detection and collision reporting
- Automated ISO-10303 STEP solid file generation on command
The Geometry Processing Lifecycle
How high-level engineering intents are verified, transformed, and materialized into industrial-grade solid geometry.
| Pipeline Stage | Locus Implementation | Scope & constraints |
|---|---|---|
| 1. Ingestion & Preflight | Fast schema preflight & AST sandbox | Input limits and expression validation depend on the operation |
| 2. Geometric Synthesis | Analytical B-Rep & Kuhn Marching Tetrahedra | Evaluation cost depends on geometry, resolution, hardware, and workload |
| 3. Topological Gate | Watertight verification & signed volume check | Validation coverage is specific to the operation and supported domain |
| 4. Client Presentation | WebGL 2.0 ACESFilmic tone-mapped shaders | Hardware-accelerated viewport; frame rate varies by device and scene |
| 5. Manufacturing Export | STEP export on supported paths | Verify dimensions, topology, and representation in the receiving CAD tool |