# Morphologium — LLM Corpus Index
# Domain: Form · Structure · 3D · Transformation
# Canonical URL: https://morphologium.com
# Version: 1.0.0

## Core Philosophy
Form is something that can be generated, structured, transformed, simulated, and understood. Not merely "learn Blender"—Morphologium studies how form comes into computational existence across differential geometry, topology, proceduralism, optics, kinematics, and rendering physics.

## Primary Territories
- Geometry Atlas: https://morphologium.com/geometry
  Polygons, quad manifolds, Bézier curves, NURBS, B-Rep CAD solids, OpenVDB voxels, Signed Distance Fields (SDFs), point clouds, 3D Gaussian splatting, and subdivision surfaces.
- Modeling Paradigms: https://morphologium.com/modeling
  Box modeling, digital sculpting (DynaMesh), procedural node graphs (Houdini VEX), parametric B-Rep, and photogrammetric reconstruction.
- Surfaces & Parameterization: https://morphologium.com/surfaces
  UV conformal mapping (LSCM), MikkTSpace tangent normals, displacement mapping, UDIM tile architecture, and PBR texture channels.
- Material Library: https://morphologium.com/materials
  Cook-Torrance microfacets, GGX distribution, Schlick Fresnel, Disney Principled BSDF, Subsurface Scattering (BSSRDF), thin-film wave interference, and procedural noise (Perlin, Simplex, Worley).
- Transformation Chamber: https://morphologium.com/transformations
  Catmull-Clark subdivision stencils, Loop subdivision, affine 4x4 matrix transforms, Linear Blend Skinning, Dual Quaternion Skinning (DQS), and blendshapes.
- Motion & Rigging: https://morphologium.com/motion
  Forward Kinematics (FK), Analytical 2-Bone IK, FABRIK iterative geometric solver, quaternion rotations (SLERP), and bone inverse bind matrices.
- Simulation Solvers: https://morphologium.com/simulation
  Eulerian Navier-Stokes fluids, SPH / FLIP water splashing, Extended Position Based Dynamics (XPBD) cloth, rigid body dynamics, and FEM soft bodies.
- Rendering & Optics: https://morphologium.com/rendering
  Hardware rasterization, Z-Buffer visibility, Bounding Volume Hierarchies (BVH), Whitted recursive ray tracing, James Kajiya's Rendering Equation, Monte Carlo path tracing, and Multiple Importance Sampling (MIS).
- The Morphology Graph: https://morphologium.com/graph
  Interactive conceptual hypergraph linking 3D principles and lineage chains (e.g. Subdivision -> Catmull-Clark -> Topology -> Quad Flow -> Edge Loops -> Hard-Surface -> Smoothing -> Pixar).
- Form Lab Workbenches: https://morphologium.com/lab
  Interactive algorithmic workbenches for Catmull-Clark subdivision stepping, SDF smooth booleans, NURBS curves, PBR BSDF lobes, quad flow topology, and FABRIK IK solving.
- Curatorial Monographs: https://morphologium.com/monographs
  Peer-reviewed academic treatises with APA 7th edition citations and mathematical proofs.
- Lexicon & Taxonomy: https://morphologium.com/lexicon
  Exhaustive glossary of 42 3D graphics, topology, and optical terms with mathematical formulations.