Intrinsic Mesh Swarm Computer-Aided Design (IMS-CAD)
Abstract
This white paper presents the complete technical specification, mathematical foundations, system architecture, and prior art disclosure for Intrinsic Mesh Swarm Computer-Aided Design (IMS-CAD)—a novel, deterministic, coordinate-passive CAD engine designed to replace continuous Non-Uniform Rational B-Splines (NURBS) and Boundary Representation (B-Rep) kernels. By discarding continuous parametric surface trimming and global Cartesian coordinate origins, IMS-CAD solves the foundational limitations of legacy CAD engines, including trimming failures, floating-point coordinate drift, non-manifold topological crashes, and lossy CAM/FEA tessellation conversions. Key Theoretical Pillars and Technical Innovations: Discrete Differential Geometry Core: Replaces continuous differential calculus with exact discrete invariants defined directly on discrete polygonal complexes, using discrete turn vectors, discrete torsion, and discrete parallel transport. 1D Active Edge Agents and 0D Topological Frame Junctions: Establishes an agentic, data-oriented architecture where 1D curvilinear edges act as autonomous computational units that minimize local strain energy, while 0D vertices function as non-autonomous Topological Frame Junctions (lock-free message routers and 1 nanometer integer lattice anchors). Critically Damped Wavefront Relaxation: A dynamic physical update rule applied across active edge agents to dissipate perturbation energy rapidly without oscillatory ringing, ensuring convergence within 5 to 10 lock-step interaction rounds. Bounded k-Hop Wave Propagation: Limits parameter update waves to a localized topological neighborhood of depth h_max, maintaining O(k) local editing performance (50 to 500 active agents) rather than triggering global feature tree re-evaluations. Sub-Mesh Cell Universes and Port-Adjacency Hypergraphs: Models complex multi-part assemblies as a hypergraph of independent 3D intrinsic universes connected via Boundary Ports (SE(3) rigid transformations) without requiring a shared global origin. Dual-Grid Integer Lattice and Exact Snap-Rounding: Anchors discrete calculation points to an internal 1 nanometer fixed-point integer grid with a 10 nanometer base manufacturing resolution, evaluating 3x3 and 4x4 integer determinants to eliminate floating-point ambiguity and guarantee 100% watertight CSG Boolean operations. Direct CAM and Additive Toolpath Compilation: Eliminates the lossy STL/tessellation conversion step by compiling CNC cutter location paths and additive slicing contours directly from ground-truth discrete geometry using WebGPU compute pipelines. Document Contents: Introduction and Motivation: Historical failure modes of NURBS/B-Rep and the shift to discrete intrinsic geometry. Key Theoretical Concepts: Detailed specifications and functional justifications for core architectural abstractions. Discrete Mathematics Matrix: Mapping Discrete Differential Geometry, Discrete Exterior Calculus, Discrete Elastic Rods, Algebraic Topology, and Rational Quaternions to Rust system runtime requirements. IMS-CAD Rust Engine Architecture: Data-Oriented Design Structure-of-Arrays memory layouts, parallel Rayon lock-step relaxation engines, zero-copy wgpu buffer bindings, and Topological Junction Storage routing. NURBS vs. IMS-CAD Feature Comparison: Comprehensive side-by-side performance and precision analysis matrix. CSG Boolean Pipeline and Design Workflow: Deterministic 4-stage intersection and seam relaxation procedures. Assembly and Manufacturing Grounding: Port-Adjacency Hypergraph evaluation, Zero-Holonomy cycle consistency solvers, Root Anchor Node machine grounding, and direct G-code compilation. Technical Glossary: Standardized definitions for 26 key domain terms. Exhaustive References: 33 peer-reviewed journal articles/conference papers and 32 textbooks covering computational geometry, multi-agent consensus, and systems architecture. Appendices: Production-grade Rust implementation code modules and a rigorous mathematical Q&A addressing 15 foundational theoretical questions. This document and its underlying disclosures are dual-licensed under the following terms:* Creative Commons Attribution 4.0 International (CC BY 4.0): The text, prose, structure, figures, andformatting of this paper are licensed under CC BY 4.0. You are free to share and adapt the materialfor any purpose, provided appropriate credit is given. Full license text:https://creativecommons.org/licenses/by/4.0/.* Apache License, Version 2.0 (Apache-2.0): The mathematical formulations, pseudocode, algorith-mic specifications, data structures, software paradigms, and computational methods describedherein constitute the ”Work” and are licensed under Apache 2.0. Full license text:https://www.apache.org/licenses/LICENSE-2.0.