╭────────────────────────────────────────────────────────────────╮
│ ∇ · F = ∂Fₓ/∂x + ∂Fᵧ/∂y + ∂Fᵤ/∂z │
│ │
│ ╔═╗╔═╗╔═╗╔╦╗╔═╗╔╦╗╦═╗╦ ╦ ╦ ╦╔═╗╔═╗╦╔═╔═╗ │
│ ║ ╦║╣ ║ ║║║║║╣ ║ ╠╦╝╚╦╝ ╠═╣╠═╣║ ╠╩╗╚═╗ │
│ ╚═╝╚═╝╚═╝╩ ╩╚═╝ ╩ ╩╚═ ╩ ╩ ╩╩ ╩╚═╝╩ ╩╚═╝ │
╰────────────────────────────────────────────────────────────────╯
Computational Geometry & Algorithmic 3D Tool Developer
Camera-centric sketch-based modeling | Conformal geometry | Spectral methods
I build tools where mathematical specification IS the execution. The algebra IS the geometry. The tree IS the program.
Camera-Centric Sketch-Based 3D Modeling
2D input → Camera projection → Geometric inference → Resolution-independent output
Traditional modeling manipulates vertices directly. My systems interpret 2D strokes as constraints on 3D form—projecting through the camera plane to infer depth, curvature, and surface.
Traditional: Sketch → Trace → Extrude → Edit vertices
This System: Sketch → Project → Solve → Generate
┌────────────────────────────────────────────────────────────────┐
│ │
│ ∇ Gradient ∇· Divergence ∇× Curl Δ Laplacian │
│ │
│ ┌─────────────┐ ┌─────────────┐ ┌─────────────┐ │
│ │ AFFINE │◄─│ CONFORMAL │─►│ SPECTRAL │ │
│ │ GL(4,ℝ) │ │ PSL(2,ℂ) │ │ L²(ℝ³) │ │
│ └─────────────┘ └─────────────┘ └─────────────┘ │
│ │
│ Möbius: f(z) = (az+b)/(cz+d) Circles → Circles │
│ Fourier: f̂(k) = ∫ f(x) e^(-2πik·x) dx │
│ Curvature: κ = dθ/ds │
│ │
└────────────────────────────────────────────────────────────────┘
| Project | Description |
|---|---|
| Geometric Synthesis Framework | Mathematical compiler: Lift → Operate → Collapse |
| Skeletal Singleton Tree (SST) | Functional L-system separating state from mutation |
| Neural Sketch Field | FNO-based surface anticipation from boundary curves |
| Curvature-Aware Octree | Riemannian metric hierarchy for spectral subdivision |
Extending classical octree indexing into learned Riemannian manifolds:
Level 0: Euclidean ‖x − y‖₂
Level 1: Mahalanobis (x−y)ᵀΣ⁻¹(x−y)
Level 2: Riemannian Geodesic distance with g(x)
Level 3: Fisher-Rao Information geometry on shape distributions
Level 4: Learned d_L(x,y) = ‖Φ_θ(x) − Φ_θ(y)‖_{g(θ)}
Subdivision follows spectral energy density E = Σ αᵢ²λᵢ — refining where geometry is rich, staying coarse where smooth.
Executive Summary Audio (5 min)
Geometry: Computational geometry, conformal maps, spectral methods, Frenet-Serret frames
3D Platforms: Maya (MEL/Python), Blender, Unreal Engine 5
Mathematics: Linear algebra, differential geometry, Riemannian manifolds, L-systems
ML Integration: Fourier Neural Operators, geometric deep learning, spectral regularization
Analyzed and organized:
- Circle/tangent geometry — 234 procedures (conformal PSL(2,ℂ))
- Linear algebra — 240 procedures (affine GL(4,ℝ))
- Camera projection — 218 procedures (sketch-to-3D mapping)
- Array batch processing — 565 procedures (data infrastructure)
"The octree isn't just a spatial index—it's a discretization of a distance function. Every node boundary is a level set. Swap the metric kernel, and behavior changes accordingly."