Interactive Technical Documentation • 123 Concepts

Computational Geometry & Parametric Design

A comprehensive reference wiki for 3D computational geometry, spatial data structures, mesh algorithms, and procedural modeling with live Three.js viewports.

Three.jsComputational GeometryRhino3DMReact Three FiberSpatial Partitioning

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Knowledge Base & Concept Directory

123 articles

Ch. 1: Geometry

3D geometry basic concepts

The Vector The Point The Matrix The Quaternion The Plane The Line The Polyline The Polygon The Mesh Face The Mesh The Box The Sphere The Curve The Surface The Brep

Trees & Searches Binary Trees The KD-Tree The Octree The BVH AABB Trees R-Trees Interval Trees

2D Booleans 3D Booleans Winding Rules BSP CSG

Signed Distance Fields

SDF Basics SDF Booleans SDF Blending Raymarching SDF Transformations & Curves

Robotics Kinematics

Degrees Of Freedom Forward Kinematics Inverse Kinematics

Advanced Surfacing

The Sweep The Revolve Network Surfaces The Loft & NURBS Math

Topology & Repair

Manifold Geometry Hole Filling Mesh Welding Mesh Topology & Decimation Half-Edge Data Structure Isotropic Remeshing

Computational Metrics

Area And Volume Centroid And Moments Gaussian Curvature Barycentric Coordinates The Heat Method

Convex Geometry

Convex Hull Delaunay Triangulation Voronoi Diagrams Medial Axis & Skeletons

Differential Geometry

Vectors And Tangents Normals And Binormals Principal Curvatures

Spatial Grids Marching Cubes Implicit Modeling Dual Contouring Marching Squares Mesh Isolines (3D)

Subdivision & Relaxation

Catmull Clark Laplacian Smoothing Dynamic Relaxation Loop Subdivision

Generative Algorithms

L Systems Cellular Automata Reaction Diffusion Wave Function Collapse Boids Flocking

Animation Principles

Additive Manufacturing

Planar Slicing & Layering Infill & Toolpaths Overhangs & Supports

Subtractive CAM & Nesting

CNC Offsets & Relief 2D Irregular Nesting

Fabrication & Panelization

Planar Quad (PQ) Meshes Developable Surfaces

Form-Finding & Statics

Thrust Network Analysis Minimal Surfaces & Catenaries

Environmental Geometry

Isovists & Viewshed Solar & Acoustics

Curve Engineering

Curvature Combs & Continuity Clothoids & Fairing

Collision & Contact Physics

GJK & EPA Contact Physics Continuous Collision (CCD)

Parameterization & UV

Harmonic & Conformal UV Distortion & ARAP Flattening

GPU & Neural Representations

GPU Morton Codes & LBVH NeRF & 3D Gaussian Splatting

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data + automation applied to geometry

2.1 Cloud CollaborationWIP

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Ch. 3: SustainabilityWIP

tbd

3.1 Future of DesignWIP

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Ch. 4: Data ScienceWIP

data science and machine learning techniques applied to AECO

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Ch. 5: Multi-Format AssetsWIP

working with multi-format assets, multiple representation of the same object

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Ch. 6: Visual AestheticsWIP

concepts and principles to beautify geometry

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