# Discrete Urban Space and Connectivity

SA(Social Algorithms) 2020, Computational Design

**Subtitle: Partition & Relationship**

KeywordData Structure, Graph, Matrix, Pixel, Voxel, Discretization, Partition, Connection, Search

Workshop Reference1.Computational Design Thinking for Designers — link(Eng)

2. Data & Design — link(Eng) — link(KR)

## !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)/DistanceClustering 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 —linkZoningas Graph —link

Associative geometry —link

Interface —link/link

Network for ML —link

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

NJSTUDIO Presentation slide

Data structure as GraphJSON/GeoJSONas GraphMatrix(link)Pixel(link) andVoxel(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/BFSexamples —CodePen