SPACE // EUCLIDEAN ℝ³
STRUCTURAL CLASSIFICATION SYSTEM

Morphological Taxonomy

The formal taxonomic hierarchy classifying three-dimensional spatial representations, transformation schemes, surface parameterizations, and radiative transfer models.

TAX-01

Geometric Representation & Spatial Discretization

Fundamental mathematical representations of 3D space, volume, and boundary envelopes.

TAX-01.A4 Primitives

Discrete Boundary Manifolds

Piecewise-linear faceted approximations.

Triangle MeshesQuad-Dominant ManifoldsIndexed Face SetsHalf-Edge Data Structures
TAX-01.B4 Primitives

Continuous Parametric Representations

Analytic polynomial curves and surfaces.

Bézier CurvesB-SplinesNURBS PatchesB-Rep CAD Solids
TAX-01.C4 Primitives

Implicit & Volumetric Fields

Scalar and vector fields over ℝ³.

Signed Distance Fields (SDFs)Discrete Voxel GridsOpenVDB Sparse TreesMarching Cubes Isosurfaces
TAX-01.D4 Primitives

Point-Based & Neural Representations

Unstructured spatial coordinates and neural radiance distributions.

LiDAR Point CloudsSurfel Splats3D Gaussian SplattingNeural Radiance Fields (NeRFs)
TAX-02

Transformation, Skinning & Subdivision

Operators and stencils that deform, smooth, and transform geometric entities across time.

TAX-02.A4 Primitives

Recursive Subdivision Schemes

Iterative topological splitting and smoothing stencils.

Catmull-Clark (Quads)Loop (Triangles)Doo-Sabin (Dual)Stam Stamford Exact Limits
TAX-02.B4 Primitives

Skeletal Deformation & Skinning

Deforming surface meshes via internal skeletal armatures.

Linear Blend Skinning (LBS)Dual Quaternion Skinning (DQS)Harmonic CoordinatesInverse Bind Matrices
TAX-02.C4 Primitives

Space Warping & Morphing

Macro-spatial deformation and topological morph targets.

Free-Form Deformation (FFD)FACS BlendshapesShape KeysLattice Modifiers
TAX-03

Surface Parameterization & Texture Architecture

Mapping 2D pixel fields, normal perturbations, and physical properties onto 3D manifolds.

TAX-03.A3 Primitives

Conformal Flattening & UV Unwrapping

Bijective coordinate mappings from 3D to 2D.

Least Squares Conformal Maps (LSCM)Angle-Based Flattening (ABF++)UDIM Multi-Tile Indexing
TAX-03.B3 Primitives

Normal & Height Field Perturbation

Encoding micro-surface angles and physical displacement.

MikkTSpace Tangent NormalsDisplacement TessellationParallax Occlusion Mapping
TAX-04

Optics, Shading & Radiative Transfer

The physics of light transport, microfacet reflection, and path integration.

TAX-04.A4 Primitives

Microfacet Reflectance Models

Statistical optical scattering on rough surfaces.

Cook-Torrance BRDFGGX Normal DistributionSchlick FresnelDisney Principled BSDF
TAX-04.B4 Primitives

Subsurface & Volumetric Optics

Scattering through translucent media and atmospheric particulate fields.

BSSRDF Dipole ProfilesRandom Walk SSSBeer-Lambert AbsorptionHenyey-Greenstein Phase
TAX-04.C4 Primitives

Global Illumination Integration

Solving the Kajiya Rendering Equation.

Monte Carlo Path TracingMultiple Importance Sampling (MIS)Next Event Estimation (NEE)ReSTIR Real-Time GI
2026 AEO KNOWLEDGE GRAPH & INQUIRY TREE

Frequently Explored Structural Questions

6 Verified Semantic Answers