โญโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโฎ
โ โ ยท F = โFโ/โx + โFแตง/โy + โFแตค/โz โ
โ โ
โ โโโโโโโโโโโฆโโโโโโฆโโฆโโโฆ โฆ โฆ โฆโโโโโโโฆโโโโโ โ
โ โ โฆโโฃ โ โโโโโโฃ โ โ โฆโโโฆโ โ โโฃโ โโฃโ โ โฉโโโโ โ
โ โโโโโโโโโโฉ โฉโโโ โฉ โฉโโ โฉ โฉ โฉโฉ โฉโโโโฉ โฉโโโ โ
โฐโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโฏ
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 โ Camera projection โ Geometric inference โ Resolution-independent output
Traditional modeling manipulates vertices directly. My systems interpret 2D strokes as constraints on 3D formโprojecting through the camera plane to infer depth, curvature, and surface.
Traditional: Sketch โ Trace โ Extrude โ Edit vertices
This System: Sketch โ Project โ Solve โ Generate
โโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโ
โ โ
โ โ Gradient โยท Divergence โร Curl ฮ Laplacian โ
โ โ
โ โโโโโโโโโโโโโโโ โโโโโโโโโโโโโโโ โโโโโโโโโโโโโโโ โ
โ โ AFFINE โโโโ CONFORMAL โโโบโ SPECTRAL โ โ
โ โ GL(4,โ) โ โ PSL(2,โ) โ โ Lยฒ(โยณ) โ โ
โ โโโโโโโโโโโโโโโ โโโโโโโโโโโโโโโ โโโโโโโโโโโโโโโ โ
โ โ
โ Mรถbius: f(z) = (az+b)/(cz+d) Circles โ Circles โ
โ Fourier: fฬ(k) = โซ f(x) e^(-2ฯikยทx) dx โ
โ Curvature: ฮบ = dฮธ/ds โ
โ โ
โโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโ
| Project | Description |
|---|---|
| Geometric Synthesis Framework | Mathematical compiler: Lift โ Operate โ 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 โx โ yโโ
Level 1: Mahalanobis (xโy)แตฮฃโปยน(xโy)
Level 2: Riemannian Geodesic distance with g(x)
Level 3: Fisher-Rao Information geometry on shape distributions
Level 4: Learned d_L(x,y) = โฮฆ_ฮธ(x) โ ฮฆ_ฮธ(y)โ_{g(ฮธ)}
Subdivision follows spectral energy density E = ฮฃ ฮฑแตขยฒฮปแตข โ 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 โ 234 procedures (conformal PSL(2,โ))
- Linear algebra โ 240 procedures (affine GL(4,โ))
- Camera projection โ 218 procedures (sketch-to-3D mapping)
- Array batch processing โ 565 procedures (data infrastructure)
Explore the Math Repository โ
"The octree isn't just a spatial indexโit's a discretization of a distance function. Every node boundary is a level set. Swap the metric kernel, and behavior changes accordingly."