╔══════════════════════════════════════════════════════════════════════════════╗
║ ║
║ ██████╗ ███████╗ ██████╗ ███╗ ███╗███████╗████████╗██████╗ ██╗ ██████╗ ║
║ ██╔════╝ ██╔════╝██╔═══██╗████╗ ████║██╔════╝╚══██╔══╝██╔══██╗██║██╔════╝ ║
║ ██║ ███╗█████╗ ██║ ██║██╔████╔██║█████╗ ██║ ██████╔╝██║██║ ║
║ ██║ ██║██╔══╝ ██║ ██║██║╚██╔╝██║██╔══╝ ██║ ██╔══██╗██║██║ ║
║ ╚██████╔╝███████╗╚██████╔╝██║ ╚═╝ ██║███████╗ ██║ ██║ ██║██║╚██████╗ ║
║ ╚═════╝ ╚══════╝ ╚═════╝ ╚═╝ ╚═╝╚══════╝ ╚═╝ ╚═╝ ╚═╝╚═╝ ╚═════╝ ║
║ ║
║ ███████╗██╗ ██╗███╗ ██╗████████╗██╗ ██╗███████╗███████╗██╗███████╗ ║
║ ██╔════╝╚██╗ ██╔╝████╗ ██║╚══██╔══╝██║ ██║██╔════╝██╔════╝██║██╔════╝ ║
║ ███████╗ ╚████╔╝ ██╔██╗ ██║ ██║ ███████║█████╗ ███████╗██║███████╗ ║
║ ╚════██║ ╚██╔╝ ██║╚██╗██║ ██║ ██╔══██║██╔══╝ ╚════██║██║╚════██║ ║
║ ███████║ ██║ ██║ ╚████║ ██║ ██║ ██║███████╗███████║██║███████║ ║
║ ╚══════╝ ╚═╝ ╚═╝ ╚═══╝ ╚═╝ ╚═╝ ╚═╝╚══════╝╚══════╝╚═╝╚══════╝ ║
║ ║
║ A Mathematical Compiler for 3D Modeling ║
║ ║
╠══════════════════════════════════════════════════════════════════════════════╣
║ ║
║ THE TRI-SPACE ENGINE ║
║ ║
║ ┌─────────────┐ ┌─────────────┐ ┌─────────────┐ ║
║ │ AFFINE │◄──►│ CONFORMAL │◄──►│ SPECTRAL │ ║
║ │ GL(4,ℝ) │ │ PSL(2,ℂ) │ │ L²(ℝ³) │ ║
║ └─────────────┘ └─────────────┘ └─────────────┘ ║
║ │ │ │ ║
║ ▼ ▼ ▼ ║
║ ┌─────────────┐ ┌─────────────┐ ┌─────────────┐ ║
║ │ Position │ │ Angles │ │ Fields │ ║
║ │ Rotation │ │ Circles │ │ Fourier │ ║
║ │ Scale │ │ Möbius │ │ FNO │ ║
║ └─────────────┘ └─────────────┘ └─────────────┘ ║
║ ║
╚══════════════════════════════════════════════════════════════════════════════╝
Mathematical specification IS the program — geometry as algebraic expressions, not data to be processed.
Download Audio Narration (MP3) — 5 minute overview of the complete framework
This framework treats 3D modeling as mathematical compilation:
- LIFT — Convert 2D sketch input into algebraic representations
- OPERATE — Transform losslessly in the appropriate mathematical space
- COLLAPSE — Generate polygons only when rendering demands it
Traditional pipelines destroy structure at every step. Continuous curves become jagged polylines. Circles become approximated polygons. Resolution is locked at creation time. We fix all of this.
| Document | Description |
|---|---|
| EXECUTIVE_SUMMARY.md | Complete overview with diagrams and mathematics |
| MATHEMATICAL_COMPILER.md | Tri-Space Engine architecture |
| SKELETAL_SINGLETON_TREE.md | State/Mutation separation |
| NEURAL_SKETCH_FIELD.md | Generative anticipation system |
| SUPERNODE_ABSTRACT.md | Unified architectural unit |
Three synchronized mathematical contexts, each preserving different invariants:
| Layer | Algebra | Preserves | Operations |
|---|---|---|---|
| Affine | GL(4,ℝ) | Position, orientation, scale | Translate, Rotate, Scale |
| Conformal | PSL(2,ℂ) | Angles, circles, cross-ratios | Möbius transforms, tangent constructions |
| Spectral | L²(ℝ³) | Frequency content, smoothness | Fourier Neural Operators |
// Circle through three points
string $circle = Circle3Point(<<0,0,0>>, <<1,0,0>>, <<0,1,0>>);
// Tangent from point to circle
string $tangents[] = PointToCircleTangents(1.0, <<0,0,0>>, <<2,0,0>>);
// Project to camera plane
vector $projected = ProjectToCameraPlane(<<1,2,3>>, "persp");
circle_procedures.mel— 184 conformal geometry procedureslinear_algebra.mel— 240 matrix operationssketch_modeling.mel— 218 camera-centric tools
from math_core import Vec3, Mat4, align_to_surface
from sst_nodes import Translate, Rotate, Box, Boolean
# Build SST
scene = Translate(0, 1, 0) >> Box(1, 1, 1)
scene = scene | (Rotate(45, Vec3.Y) >> Sphere(0.5))
# Collapse to mesh
mesh = scene.collapse(resolution=1024)maya-math/
├── EXECUTIVE_SUMMARY.md # Complete framework overview
├── media/
│ └── executive_summary_narration.mp3 # Audio narration
│
├── docs/ # Framework documentation
│ ├── ABSTRACT.md # Vision and philosophy
│ ├── MATHEMATICAL_COMPILER.md # Tri-Space Engine
│ ├── SKELETAL_SINGLETON_TREE.md
│ ├── NEURAL_SKETCH_FIELD.md
│ ├── SUPERNODE_ABSTRACT.md
│ └── core/ # Core module specs
│ ├── math_foundations.md
│ ├── state_schema.md
│ ├── mutation_schema.md
│ └── ...
│
├── cleaned/ # Annotated MEL procedures
│ ├── circle_procedures.mel # 184 procedures
│ ├── linear_algebra.mel # 240 procedures
│ ├── sketch_modeling.mel # 218 procedures
│ ├── tangent_procedures.mel # 71 procedures
│ ├── polygon_ops.mel # 135 procedures
│ └── utility.mel # 253 procedures
│
└── implementations/
└── python/
├── math_core.py # Vec3, Mat4, align_to_surface
└── sst_nodes.py # SST Node System
┌──────────────────────────────────────────────────────────────────────────────┐
│ FUNDAMENTAL STRUCTURES │
├──────────────────────────────────────────────────────────────────────────────┤
│ │
│ AFFINE MATRIX MÖBIUS TRANSFORM │
│ │
│ ┌ ┐ az + b │
│ │ R₁₁ R₁₂ R₁₃ Tₓ │ f(z) = ───────── │
│ │ R₂₁ R₂₂ R₂₃ Tᵧ │ cz + d │
│ │ R₃₁ R₃₂ R₃₃ Tᵤ │ │
│ │ 0 0 0 1 │ where ad - bc ≠ 0 │
│ └ ┘ │
│ │
│ FOURIER TRANSFORM CURVATURE │
│ │
│ f̂(k) = ∫ f(x) e^(-2πik·x) dx dθ │
│ κ = ──── │
│ ds │
└──────────────────────────────────────────────────────────────────────────────┘
- Resolution Independence — Geometry stored as algebraic expressions, not fixed-resolution meshes
- Lossless Operations — Boolean, extrude, bevel without destroying structure
- Neural Anticipation — Predict surfaces from boundary curves in real-time
- Cross-Platform — SST transpiles to any target (Maya, Blender, WebGL, etc.)
- Camera-Centric — 2D sketch input naturally projects to 3D
- 2,308 MEL procedures across 68 files
- 1,055 cleaned and annotated procedures
- 5 core mathematical frameworks
- 3 synchronized algebraic layers
Part of the 3D Tools ML Hybrid framework — bridging legacy Maya tools with modern mathematical architecture