Discrete Urban Space and Connectivity

SA(Social Algorithms) 2020, Computational Design

Subtitle: Partition & Relationship

Keyword
Data Structure, Graph, Matrix, Pixel, Voxel, Discretization, Partition, Connection, Search

Workshop Reference
1. Computational Design Thinking for Designers — link(Eng)
2. Data & Design — link(Eng) — link(KR)

Data to Wisdom, The Information Factory S.A.

!We are able to answer these questions below.

how to capture and process spatial data in design

Relationship among data in a space

Discrete a space into parts

1. Graph

Graph is a mathematical object that consists of set of points and edges, dealing with discrete information.

Graph is widely used for computation, discrete mathematics or representing relational data structures, and It has explicit relationship among vertices by edges visualizing the topological aspect such as street network of urban, highway or the subway map, whose graphs closely resemble their physical form due to its characteristics.

2. Pixel / Voxel (Volumetric Element)

- Voxel could be considered as a set of image(pixel)

Voxel is a 3 dimensional grid containing pixels can have rich data set including R, G, B, A values. It is frequently utilized for visualization of scientific or medical data which is needed for volumetric representation.

Voxel for geometry in space is a discretized space of geometry where it has a beam or node are connecting but as a continuous map in space. This is basically an idea that an object become a 3 dimensional map.

3. Partition

Linear regression, KNN , Support vector machine, Random Forest, CNN, Tensorflow Playground

Delaunay triangulation / Voronoi diagram

Discrete space — Space Partitioning

Quad Tree / Octree / Bin System

Axis(AABB) / Distance

Clustering Points: Collision-Based Dynamic Graph method — link

4. Connectivity

GRAPH — link
Graph Data Structure for Spatial data — link(KR)

Social network as Graph — link
Transportation as Graph (Street, freeway(highway), subway, sky way…)
Folder structure as Graph — link
Programming executions as Graph — link
Zoning as Graph — link
Associative geometry — link
Interface — link / link
Network for ML — link

Structure — link, link
Mesh(Polygon) as Graph — link
Mesh from Rhino3d: link

NJSTUDIO Presentation slide

Data structure as Graph
JSON /GeoJSON as Graph
Matrix (link) Pixel(link) and Voxel(link) as Graph

TYPE

Directed Graph / Undirected Graph / Mixed Graph / Weighted Graph
… Multigraph / Bipartite Graph / DAG(Directed Acyclic Graph)

SEARCH / TRAVERSAL — link

Graph Data Structure And Algorithms — link
DFS / BFS examples — CodePen

3. Example

By NJSTUDIO

By NJSTUDIO

Rigid body: link
Agent Boids System A: link
Agent Boids System B: link
Rect Pos Optimizer: link
Graph system: link

Volumetric Representations and Machine Learning, NJ Namju Lee

Three, Terrain, pixel map(matrix): link
Rhino Grasshopper, Terrain, pixel map(matrix): link
Three, Voxel map: link