Morphological Taxonomy
The formal taxonomic hierarchy classifying three-dimensional spatial representations, transformation schemes, surface parameterizations, and radiative transfer models.
Geometric Representation & Spatial Discretization
Fundamental mathematical representations of 3D space, volume, and boundary envelopes.
Discrete Boundary Manifolds
Piecewise-linear faceted approximations.
Continuous Parametric Representations
Analytic polynomial curves and surfaces.
Implicit & Volumetric Fields
Scalar and vector fields over ℝ³.
Point-Based & Neural Representations
Unstructured spatial coordinates and neural radiance distributions.
Transformation, Skinning & Subdivision
Operators and stencils that deform, smooth, and transform geometric entities across time.
Recursive Subdivision Schemes
Iterative topological splitting and smoothing stencils.
Skeletal Deformation & Skinning
Deforming surface meshes via internal skeletal armatures.
Space Warping & Morphing
Macro-spatial deformation and topological morph targets.
Surface Parameterization & Texture Architecture
Mapping 2D pixel fields, normal perturbations, and physical properties onto 3D manifolds.
Conformal Flattening & UV Unwrapping
Bijective coordinate mappings from 3D to 2D.
Normal & Height Field Perturbation
Encoding micro-surface angles and physical displacement.
Optics, Shading & Radiative Transfer
The physics of light transport, microfacet reflection, and path integration.
Microfacet Reflectance Models
Statistical optical scattering on rough surfaces.
Subsurface & Volumetric Optics
Scattering through translucent media and atmospheric particulate fields.
Global Illumination Integration
Solving the Kajiya Rendering Equation.