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Ar1 twf030 lecture2.2

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Pirouz Nourian

Lecture notes of the course Future Models I (AR1TWF030), The Why Factory, Directed by Prof. Winy Mass, TU Delft, Faculty of Architecture and Built Environment

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11 On Graphs and Fields in Computational Design Dr.ir. Pirouz Nourian Assistant Professor of Design Informatics Department of Architectural Engineering & Technology Faculty of Architecture and Built Environment
22 https://www.123rf.com/photo_6317298_airline-passengers-walking-in-the-airport-terminal.html Motivation Manifolds Continuous/Discrete Poincare Duality Graphs Fields Spatial Distance Spatial Potential Spatial Dynamics Manifold 2 Field Field 2 Manifold Configurative Design
33 https://www.allnursingschools.com/articles/acute-care-nursing/ Motivation Manifolds Continuous/Discrete Poincare Duality Graphs Fields Spatial Distance Spatial Potential Spatial Dynamics Manifold 2 Field Field 2 Manifold Configurative Design
44 not making the right inner network at the right location on an outer network Motivation Manifolds Continuous/Discrete Poincare Duality Graphs Fields Spatial Distance Spatial Potential Spatial Dynamics Manifold 2 Field Field 2 Manifold Configurative Design
55 0D: Point (the space therein everywhere resembles a 0-dimensional Euclidean Space) 1D: Curve (the space therein everywhere resembles a 1-dimensional Euclidean Space) 2D: Surface (the space therein everywhere resembles a 2-dimensional Euclidean Space) 3D: Solid (the space therein everywhere resembles a 3-dimensional Euclidean Space) Motivation Manifolds Continuous/Discrete Poincare Duality Graphs Fields Spatial Distance Spatial Potential Spatial Dynamics Manifold 2 Field Field 2 Manifold Configurative Design
66 Manifold Graph Field Motivation Manifolds Continuous/Discrete Poincare Duality Graphs Fields Spatial Distance Spatial Potential Spatial Dynamics Manifold 2 Field Field 2 Manifold Configurative Design
77 terminology • Geometry: Point (0D), Curve(1D), Surface(2D), Solid (3D) [free-form] • Geometry: Point (0D), Line(1D), Polygon(2D), Polyhedron (3D) [piecewise linear] • Topology: Vertex(0D), Edge(1D), Face(2D), Body(3D) • Graph Theory: Object, Link, (and n-Cliques) • Fields: Pixel, Voxel, Raster2D, Raster 3D Motivation Manifolds Continuous/Discrete Poincare Duality Graphs Fields Spatial Distance Spatial Potential Spatial Dynamics Manifold 2 Field Field 2 Manifold Configurative Design
88 Poincare Duality a pairing between k-dimensional features and dual features of dimension n-k in ℝ 𝑛 PRIMAL DUAL 0D vertex (e.g. as a point) 1D edge 1D edge (e.g. as a line segment) 0D vertex PRIMAL DUAL 0D vertex (e.g. a point) 2D face 1D edge (e.g. a line segment) 1D edge 2D face (e.g. a triangle or a pixel) 0D vertex PRIMAL DUAL 0D vertex (e.g. a point) 3D body 1D edge (e.g. a line segment) 2D face 2D face (e.g. a triangle or a pixel) 1D edge 3D body (e.g. a tetrahedron or a voxel) 0D vertex ℝ ℝ3 ℝ2 Configraphics: Graph Theoretical Methods of Design and Analysis of Spatial Configurations, Nourian, P, 2016 Motivation Manifolds Continuous/Discrete Poincare Duality Graphs Fields Spatial Distance Spatial Potential Spatial Dynamics Manifold 2 Field Field 2 Manifold Configurative Design
99 Poincare Duality a pairing between k-dimensional features and dual features of dimension n-k in ℝ 𝑛 PRIMAL DUAL 0D vertex (e.g. as a point) 1D edge 1D edge (e.g. as a line segment) 0D vertex ℝ A hypothetical street network (a), a Junction-to-Junction adjacency graph (b) versus a Street-to-Street adjacency graph (c), both ‘undirected’, after Batty (Batty, 2004): red dots represent graph nodes, and blue arcs represent graph links. Batty, M., 2004. A New Theory of Space Syntax. CASA Working Paper Series, March. Motivation Manifolds Continuous/Discrete Poincare Duality Graphs Fields Spatial Distance Spatial Potential Spatial Dynamics Manifold 2 Field Field 2 Manifold Configurative Design
1010 Poincare Duality a pairing between k-dimensional features and dual features of dimension n-k in ℝ 𝑛 PRIMAL DUAL 0D vertex (e.g. a point) 2D face 1D edge (e.g. a line segment) 1D edge 2D face (e.g. a triangle or a pixel) 0D vertex ℝ2 A Voronoi tessellation of 2D space and its dual that is a Delaunay triangulation Motivation Manifolds Continuous/Discrete Poincare Duality Graphs Fields Spatial Distance Spatial Potential Spatial Dynamics Manifold 2 Field Field 2 Manifold Configurative Design
1111 Poincare Duality a pairing between k-dimensional features and dual features of dimension n-k in ℝ 𝑛 PRIMAL DUAL 0D vertex (e.g. a point) 3D body 1D edge (e.g. a line segment) 2D face 2D face (e.g. a triangle or a pixel) 1D edge 3D body (e.g. a tetrahedron or a voxel) 0D vertex ℝ3 representing adjacencies between 3D cells or bodies via their dual vertices (Lee, 2001) Motivation Manifolds Continuous/Discrete Poincare Duality Graphs Fields Spatial Distance Spatial Potential Spatial Dynamics Manifold 2 Field Field 2 Manifold Configurative Design
1212 https://medium.com/basecs/k%C3%B6nigsberg-seven-small-bridges-one-giant-graph-problem-2275d1670a12 The glorious beginning of Graph Theroy Motivation Manifolds Continuous/Discrete Poincare Duality Graphs Fields Spatial Distance Spatial Potential Spatial Dynamics Manifold 2 Field Field 2 Manifold Configurative Design
1313 locus topos graph Leonhard Euler in 1736, the Seven Bridges of Königsberg Motivation Manifolds Continuous/Discrete Poincare Duality Graphs Fields Spatial Distance Spatial Potential Spatial Dynamics Manifold 2 Field Field 2 Manifold Configurative Design
1414 Geometry Topology Graph Theory locus topos graph Image Credit: Bill Hillier, Space is the machine, 1997 Motivation Manifolds Continuous/Discrete Poincare Duality Graphs Fields Spatial Distance Spatial Potential Spatial Dynamics Manifold 2 Field Field 2 Manifold Configurative Design
1515Bonds: Similarity, Intimacy, Influence, Collaboration, etc. We live in (social) bubbles! Social Networks Motivation Manifolds Continuous/Discrete Poincare Duality Graphs Fields Spatial Distance Spatial Potential Spatial Dynamics Manifold 2 Field Field 2 Manifold Configurative Design
1616 Left: The underground rail network of London, the geographical version; Right: The Tube Map by Harry Beck, the First Topological Metro Map for the London Underground Network in 1931 “everything is related to everything else, but near things are more related than distant things." Waldo Tobler Bonds: Proximity, Connectivity, Adjacency, Spatial Networks Motivation Manifolds Continuous/Discrete Poincare Duality Graphs Fields Spatial Distance Spatial Potential Spatial Dynamics Manifold 2 Field Field 2 Manifold Configurative Design
1717 Etymology of the term Rasterization Rastrum Pens Rastrum Roller Plotters Image Credits: https://nl.pinterest.com/pin/387731849143362464/ https://nl.pinterest.com/pin/71494712814015023/ Image Credits: https://en.wikipedia.org/wiki/Rastrum http://www.ebay.ie/itm/311372013714 Motivation Manifolds Continuous/Discrete Poincare Duality Graphs Fields Spatial Distance Spatial Potential Spatial Dynamics Manifold 2 Field Field 2 Manifold Configurative Design
1818 https://www.simscale.com/blog/2014/06/server-room-cooling-hvac-simulation/ Raster Space models: Scalar Fields: • Noise • Moisture • Temperature • Soil Composition • Noise Analyses Motivation Manifolds Continuous/Discrete Poincare Duality Graphs Fields Spatial Distance Spatial Potential Spatial Dynamics Manifold 2 Field Field 2 Manifold Configurative Design
1919 https://www.comsol.com/cfd-module Raster Space models: Scalar Fields: • Noise • Moisture • Temperature • Soil Composition: e.g. in geological analyses • • Noise Analyses: noise pollution levels… Vector Fields: • Computational Fluid Dynamics (CFD): e.g. ventilation and wind simulations • Egress Simulation Motivation Manifolds Continuous/Discrete Poincare Duality Graphs Fields Spatial Distance Spatial Potential Spatial Dynamics Manifold 2 Field Field 2 Manifold Configurative Design
2020 Spatial Geodesics and Spatial Distances • Indoor Navigation • Emergency Response Planning • Location-Based Services (indoor-outdoor) • Robot/Drone Motion Planning 3D Spatial Network & 3D Path Finding http://urban-scene.blogspot.nl/2014/02/network-analysis-in- cityengine.html Modelling Pedestrian Evacuation http://www.jigsaw24.com/news/news/2712-massmotion-advanced-3d-pedestrian-simulations-for-evacuation-plans/ Motivation Manifolds Continuous/Discrete Poincare Duality Graphs Fields Spatial Distance Spatial Potential Spatial Dynamics Manifold 2 Field Field 2 Manifold Configurative Design
2121 Different Spatial Structures Affords Different Social Structures One Decision-Maker Hub & Spokes Hierarchy Full Mesh Clique Several Decision Makers All Decision Makers Motivation Manifolds Continuous/Discrete Poincare Duality Graphs Fields Spatial Distance Spatial Potential Spatial Dynamics Manifold 2 Field Field 2 Manifold Configurative Design
2222 why is spatial arrangement important? different spatial arrangements enable different social networks Motivation Manifolds Continuous/Discrete Poincare Duality Graphs Fields Spatial Distance Spatial Potential Spatial Dynamics Manifold 2 Field Field 2 Manifold Configurative Design
2323 a spectrum of socio-spatial configurations different spatial arrangements enable different social networks Motivation Manifolds Continuous/Discrete Poincare Duality Graphs Fields Spatial Distance Spatial Potential Spatial Dynamics Manifold 2 Field Field 2 Manifold Configurative Design
2424 Importance of Network Structure position in a network strongly influences performance Close to many people Introduction In between many people Linkage Connected to many people Spread Connected to important people Influence Typical Examples of Centrality Indexes Motivation Manifolds Continuous/Discrete Poincare Duality Graphs Fields Spatial Distance Spatial Potential Spatial Dynamics Manifold 2 Field Field 2 Manifold Configurative Design
2525 Functional Structural Fit Shops Service Areas Cafes/Restaurants Operational Centre In an exemplary airport logical locations for: Close to many people In between many peopleConnected to many people Connected to important people Motivation Manifolds Continuous/Discrete Poincare Duality Graphs Fields Spatial Distance Spatial Potential Spatial Dynamics Manifold 2 Field Field 2 Manifold Configurative Design
2626 Can you make an ordered list of spaces as to their intended privacy/community level? Something like: entrance-toilet-living-kitchen-bedrooms-bathroom A Spectrum of Privacy to Community How would you connect them to one another to achieve this (as in a bubble diagram)? You can distinguish between (wanted/unwanted) spatial connectivity and adjacency links. Motivation Manifolds Continuous/Discrete Poincare Duality Graphs Fields Spatial Distance Spatial Potential Spatial Dynamics Manifold 2 Field Field 2 Manifold Configurative Design
2727 TWO INDICATORS OF PRIVACY AND COMMUNITY ▪ Integration (Closeness Centrality) ▪ Choice (Betweenness Centrality) Choice (Originally introduced as Betweenness by Freeman (Freeman, 1977)) Choice or Betweenness is a measure of centrality for nodes within a configuration as to its role in shortest paths. Intuitively shows how likely it is for people to move through a space. That literally tells how many times a node happens to be in the shortest paths between all other nodes. It can also be computed for the links connecting the nodes in a similar way. Integration (Hillier and Hanson, 1984) is a measure of centrality that indicates how likely it is for a space to be private or communal. The more integrated a space, the shallower it is to all other nodes in a configuration. Intuitively shows how likely it is for people to move to a space. Integration is calculated by computing the total depth of a node when the depths of all other nodes are projected on it. Motivation Manifolds Continuous/Discrete Poincare Duality Graphs Fields Spatial Distance Spatial Potential Spatial Dynamics Manifold 2 Field Field 2 Manifold Configurative Design
2828 For a function u(x,y,z,t) of three spatial variables (x,y,z) (see Cartesian coordinate system) and the time variable t, the heat equation is More generally in any coordinate system: https://en.wikipedia.org/wiki/Heat_equation Motivation Manifolds Continuous/Discrete Poincare Duality Graphs Fields Spatial Distance Spatial Potential Spatial Dynamics Manifold 2 Field Field 2 Manifold Configurative Design https://nl.mathworks.com/matlabcentral/fileexchange/42604-finite-difference-method-to-solve-heat-diffusion-equation-in-two-dimensions
2929 Motivation Manifolds Continuous/Discrete Poincare Duality Graphs Fields Spatial Distance Spatial Potential Spatial Dynamics Manifold 2 Field Field 2 Manifold Configurative Design http://www.clker.com/clipart-drunk-man.html Sketches by Boz, George Cruikshank, Wiki Commons The Walking Drunkard
3030 Motivation Manifolds Continuous/Discrete Poincare Duality Graphs Fields Spatial Distance Spatial Potential Spatial Dynamics Manifold 2 Field Field 2 Manifold Configurative Design Stationary Probability Distribution of Random Walkers
3131 Geographical  Geometrical  Topological  Graphical  Spectral
3232 Culprit on the Run!
3333 Where is the best place for a souvenir shop? Wanderers end up in the same areas!
3434 Pixel & Voxel Adjacencies • Sharing Edges: 4 Neighbours • Sharing Vertices: 8 Neighbours • Sharing Faces: 6 Neighbours • Sharing Edges: 18 Neighbours • Sharing Vertices: 26 Neighbours Jian Huang, Roni Yagel, Vassily Filippov, and Yair Kurzion Why do we need connectivity information? For relative positioning and topology information Motivation Manifolds Continuous/Discrete Poincare Duality Graphs Fields Spatial Distance Spatial Potential Spatial Dynamics Manifold 2 Field Field 2 Manifold Configurative Design
3535 Voxel Models: N-Adjacency & N-Paths • Separability: What could be a closure? • For defining 3D recognizable “objects” Representing closures Motivation Manifolds Continuous/Discrete Poincare Duality Graphs Fields Spatial Distance Spatial Potential Spatial Dynamics Manifold 2 Field Field 2 Manifold Configurative Design
3636 Voxel Models: N-Adjacency & N-Paths • Separability: What could be a closure? • For defining 3D recognizable “objects” Representing closures Images courtesy of Samuli Laine, NVIDIA, 2013 Motivation Manifolds Continuous/Discrete Poincare Duality Graphs Fields Spatial Distance Spatial Potential Spatial Dynamics Manifold 2 Field Field 2 Manifold Configurative Design
3737 Voxel Models: N-Adjacency & N-Paths • Separability: What could be a closure? • For defining 3D recognizable “objects” Representing closures 4-connected, 8-separating 8-connected, 4-separating Motivation Manifolds Continuous/Discrete Poincare Duality Graphs Fields Spatial Distance Spatial Potential Spatial Dynamics Manifold 2 Field Field 2 Manifold Configurative Design
3838 Voxel Models: N-Adjacency & N-Paths • Connectivity: how to represent a curve in pixels or voxels • Thinness: how do we ensure the minimality of a raster representation Representing closures for defining 3D recognizable “objects” Voxelization algorithms for geospatial applications: http://www.sciencedirect.com/science/article/pii/S2215016116000029 Motivation Manifolds Continuous/Discrete Poincare Duality Graphs Fields Spatial Distance Spatial Potential Spatial Dynamics Manifold 2 Field Field 2 Manifold Configurative Design
3939 Voxel Models: N-Adjacency & N-Paths • Connectivity: how to represent a curve in pixels or voxels • Thinness: how do we ensure the minimality of a raster representation Representing closures for defining 3D recognizable “objects” Voxelization algorithms for geospatial applications: http://www.sciencedirect.com/science/article/pii/S2215016116000029 Motivation Manifolds Continuous/Discrete Poincare Duality Graphs Fields Spatial Distance Spatial Potential Spatial Dynamics Manifold 2 Field Field 2 Manifold Configurative Design
4040 Point Cloud Rasterization [Topological] Voxelization algorithms for geospatial applications: http://www.sciencedirect.com/science/article/pii/S2215016116000029 Motivation Manifolds Continuous/Discrete Poincare Duality Graphs Fields Spatial Distance Spatial Potential Spatial Dynamics Manifold 2 Field Field 2 Manifold Configurative Design
4141 6-Connected Stanford Bunny, 1265 voxels (0.8,0.8.0.8) 26-Connected Stanford Bunny, 755 voxels (0.8, 0.8, 0.8) Control on Connectivity Level Stanford Bunny, scaled 0.1: Mesh (V:34834 F:69664) Motivation Manifolds Continuous/Discrete Poincare Duality Graphs Fields Spatial Distance Spatial Potential Spatial Dynamics Manifold 2 Field Field 2 Manifold Configurative Design
4242 26-Connected Voxels of various XYZ dimensions: 0.8x0.8x0.1 Motivation Manifolds Continuous/Discrete Poincare Duality Graphs Fields Spatial Distance Spatial Potential Spatial Dynamics Manifold 2 Field Field 2 Manifold Configurative Design
4343 6-Connected Voxels of various XYZ dimensions: 0.8x0.8x0.8 Motivation Manifolds Continuous/Discrete Poincare Duality Graphs Fields Spatial Distance Spatial Potential Spatial Dynamics Manifold 2 Field Field 2 Manifold Configurative Design
4444 Topological Rasterization with Semantics from a BIM model [original model] Motivation Manifolds Continuous/Discrete Poincare Duality Graphs Fields Spatial Distance Spatial Potential Spatial Dynamics Manifold 2 Field Field 2 Manifold Configurative Design
4545 Topological Rasterization with Semantics from a BIM model [0.5 by 0.5 by 0.5 M] Motivation Manifolds Continuous/Discrete Poincare Duality Graphs Fields Spatial Distance Spatial Potential Spatial Dynamics Manifold 2 Field Field 2 Manifold Configurative Design
4646 Topological Rasterization with Semantics from a BIM model [0.4 by 0.4 by 0.4 M] Motivation Manifolds Continuous/Discrete Poincare Duality Graphs Fields Spatial Distance Spatial Potential Spatial Dynamics Manifold 2 Field Field 2 Manifold Configurative Design
4747 Topological Rasterization with Semantics from a BIM model [0.2 by 0.2 by 0.2 M] Motivation Manifolds Continuous/Discrete Poincare Duality Graphs Fields Spatial Distance Spatial Potential Spatial Dynamics Manifold 2 Field Field 2 Manifold Configurative Design
4848 Topological Rasterization with Semantics from a BIM model [0.1 by 0.1 by 0.1 M] Motivation Manifolds Continuous/Discrete Poincare Duality Graphs Fields Spatial Distance Spatial Potential Spatial Dynamics Manifold 2 Field Field 2 Manifold Configurative Design
4949 Sparce Voxel Octree (SVO) • Make smaller voxels if needed depending on the desired LOD • the position of a voxel is inferred based upon its position relative to other voxels • Connectivity graph of a voxel model Adaptive Resolution: a more efficient way of representation Image courtesy of NVIDIA, GPU Gems 2 http://http.developer.nvidia.com/GPUGems2/gpugems2_chapter37.html Motivation Manifolds Continuous/Discrete Poincare Duality Graphs Fields Spatial Distance Spatial Potential Spatial Dynamics Manifold 2 Field Field 2 Manifold Configurative Design
5050 Octree and Quadtree representation How do they work? • 2D Quadtrees (recursive subdivision of a bounding rectangle into 4 rectangles): divide the shape to pixels small enough to represent the required ‘geometric’ LOD, wherever needed, larger elsewhere. • 3D Octrees (recursive subdivision of a bounding box into 8 boxes): divide the shape to voxels small enough to represent the required ‘geometric’ LOD, wherever needed, larger elsewhere. Images from Wiki Commons Motivation Manifolds Continuous/Discrete Poincare Duality Graphs Fields Spatial Distance Spatial Potential Spatial Dynamics Manifold 2 Field Field 2 Manifold Configurative Design
5151 3D raster vs 3D vector representation Rasterize Vectorize Manifold Model • 0D: Points • 1D: Polylines • 2D: Meshes • 3D: Solids Field Model • Raster 2D • Raster3D Motivation Manifolds Continuous/Discrete Poincare Duality Graphs Fields Spatial Distance Spatial Potential Spatial Dynamics Manifold 2 Field Field 2 Manifold Configurative Design
5252 Rasterization Algorithms How to convert vector data consistently to Raster2D or Raster 3D data Rasterize Topological Rasterization: Nourian, P., Gonçalves, R., Zlatanova, S., Ohori, K. A., & Vo, A. V. (2016). Voxelization Algorithms for Geospatial Applications: Computational Methods for Voxelating Spatial Datasets of 3D City Models Containing 3D Surface, Curve and Point Data Models. MethodsX. Manifold Model • 0D: Points • 1D: Polylines • 2D: Meshes • 3D: Solids Field Model • Raster 2D • Raster3D Motivation Manifolds Continuous/Discrete Poincare Duality Graphs Fields Spatial Distance Spatial Potential Spatial Dynamics Manifold 2 Field Field 2 Manifold Configurative Design
5353 Vectorization Algorithms How to convert raster data consistently to Vector2D or Vector3D data Vectorize Manifold Model • 0D: Points • 1D: Polylines • 2D: Meshes • 3D: Solids Field Model • Raster 2D • Raster3D • Iso-Surface Algorithms • Iso-Curve Algorithms Motivation Manifolds Continuous/Discrete Poincare Duality Graphs Fields Spatial Distance Spatial Potential Spatial Dynamics Manifold 2 Field Field 2 Manifold Configurative Design
5454 Iso-Curve Algorithms How to construct topography contour lines from elevation raster maps? • Marching Squares • Marching Triangles Note: Marching triangle does not bring about ambiguous topological situations, unlike marching squares. Therefore, curves produced by marching triangles are always manifold. Images from wiki commons Motivation Manifolds Continuous/Discrete Poincare Duality Graphs Fields Spatial Distance Spatial Potential Spatial Dynamics Manifold 2 Field Field 2 Manifold Configurative Design
5555 Iso-Surface Algorithms How to construct contour surfaces from continuous Raster 3D field/function models? • Marching Cubes (William E. Lorensen and Harvey E. Cline, 1985) • Marching Tetrahedrons (Doi and Koide, 1991)_ Prototyped Note: Marching tetrahedrons does not bring about ambiguous topological situations, unlike marching cubes. Therefore, surfaces produced by marching tetrahedrons are always manifold. • Extracting boundaries using voxel attributes https://github.com/Pirouz-Nourian/MarchingTetrahedrons Motivation Manifolds Continuous/Discrete Poincare Duality Graphs Fields Spatial Distance Spatial Potential Spatial Dynamics Manifold 2 Field Field 2 Manifold Configurative Design
5656 Extracting an Isosurface from voxel data Using the Marching Cubes algorithm Image courtesy of Paul Bourke Motivation Manifolds Continuous/Discrete Poincare Duality Graphs Fields Spatial Distance Spatial Potential Spatial Dynamics Manifold 2 Field Field 2 Manifold Configurative Design
5757 Example: Numeric Query How to construct contour meshes from continuous Raster 3D field/function models? Note: Marching tetrahedrons does not bring about ambiguous topological situations, unlike marching cubes. Therefore, surfaces produced by marching tetrahedrons are always manifold. • Extracting boundaries using voxel attributes (measures, semantic etc.) Motivation Manifolds Continuous/Discrete Poincare Duality Graphs Fields Spatial Distance Spatial Potential Spatial Dynamics Manifold 2 Field Field 2 Manifold Configurative Design
5858 Profiling Algorithms Image courtesy of Oregon State University Check out TUD Raster Works tools for examples: https://sites.google.com/site/pirouznourian/otb_3dgis https://github.com/Pirouz-Nourian OTB Building, X Section OTB Building, Y Section OTB , Z Section Motivation Manifolds Continuous/Discrete Poincare Duality Graphs Fields Spatial Distance Spatial Potential Spatial Dynamics Manifold 2 Field Field 2 Manifold Configurative Design
5959 Spatial Configuration: the particular way, in which spaces are linked to each other in a building or a built environment Design as Spatial Configuration • Any meaningful set has something more than all of its items. • A certain configuration ‘reflects and affects’ social interactions within a built environment. • How do we design a plan to embody a spatial configuration? reverse? Villa Savoye Le Corbusier & Pierre Jeanneret A bubble diagram of Villa Savoye Motivation Manifolds Continuous/Discrete Poincare Duality Graphs Fields Spatial Distance Spatial Potential Spatial Dynamics Manifold 2 Field Field 2 Manifold Configurative Design
6060 How to design a plan with a particular spatial configuration? A Syntactic Design Process • An abstract graph may correspond to many concrete plan layouts! • A spatial configuration can be analyzed in terms of its social implications • Configurations are in-between the abstract domain of functions and the concrete domain of forms Design Process FormFunction Configuration Abstract Concrete Configurational Analysis An Interactive Process Motivation Manifolds Continuous/Discrete Poincare Duality Graphs Fields Spatial Distance Spatial Potential Spatial Dynamics Manifold 2 Field Field 2 Manifold Configurative Design
6161 How to design a plan with a particular spatial configuration? A Syntactic Design Process More specifically: An Interactive Process Design Process FormFunction Configuration Abstract Concrete Configurational Analysis Bubble Diagram (Graph) Plan Diagrams (Bubble Packing) Topological Embedding (Map) Motivation Manifolds Continuous/Discrete Poincare Duality Graphs Fields Spatial Distance Spatial Potential Spatial Dynamics Manifold 2 Field Field 2 Manifold Configurative Design
6262 Implicit modelling as level sets A strategy for design modeling/3D sketching Model a Scalar Field Get Iso-surfaces Motivation Manifolds Continuous/Discrete Poincare Duality Graphs Fields Spatial Distance Spatial Potential Spatial Dynamics Manifold 2 Field Field 2 Manifold Configurative Design
6363 From Graph to Field to Space a continuous approach to spatial configuration!? Say each space is defined in simplest form as a node, then in the absence of external influences it becomes a circle or hemisphere then… Motivation Manifolds Continuous/Discrete Poincare Duality Graphs Fields Spatial Distance Spatial Potential Spatial Dynamics Manifold 2 Field Field 2 Manifold Configurative Design
6464 From Graph to Field to Space ISOSURFACE: a scalar field of values is evaluated at every point of a 3D grid; then layers of the field can be found as ‘iso-surfaces’. An isosurface is the border between those points whose attribute values are above the iso value and the ones below. Raster3D methods are based on OTB_3DGIS.DLL https://sites.google.com/site/pirouznourian/otb_3dgis ▪ voxel representation of big spatial data ▪ converting 3D vector data to 3D raster data and vice versa ▪ using voxel representation in spatial analysis ▪ voxel operations for spatial planning Motivation Manifolds Continuous/Discrete Poincare Duality Graphs Fields Spatial Distance Spatial Potential Spatial Dynamics Manifold 2 Field Field 2 Manifold Configurative Design
6565 From Graph to Field to Space What does (might) it all have to do with architecture? Imagine a 3D configuration composed of nodes and links (vertices and edges) as in the top picture. We can think of a field around this configuration, which looks in 2D like the slice shown at the bottom. Controlling the field we can create the boundaries of spaces as isosurfaces! From Inside Out!? Try it out! bubble diagram-to-field-to-space!? Motivation Manifolds Continuous/Discrete Poincare Duality Graphs Fields Spatial Distance Spatial Potential Spatial Dynamics Manifold 2 Field Field 2 Manifold Configurative Design
6666 Questions: p.nourian@tudelft.nl
CONFIGURBANISTSYNTACTIC Space Syntax For Architectural Configuration Network Analysis For Urban Configuration For 3D Reconstruction from Point Clouds rasterworks.dll Library of Raster3D & Voxel Tools Introduction Networks Fields (regular, irregular)
SYNTACTIC Space Syntax for Generative Design A Plugin for Grasshopper 3D, Written in VB.NET & C# ▪ Real-Time Space Syntax Analyses for Parametric Design ▪ Interactive Bubble Diagrams ▪ Automated Graph Drawing Algorithms ▪ Enumeration of Plan Configuration Topologies ▪ Measuring the Socio-Spatial/Programmatic Performance ▪ Topological Layout Download: https://sites.google.com/site/pirouznourian/syntactic-design User Group: www.grasshopper3d.com/group/space-syntax Publications: ▪ Nourian, P. Rezvani, S., Sariyildiz, S. (2013). Designing with Space Syntax. Proceedings of eCAADe 2013, (pp. 357-366). Delft. ▪ Nourian, P., Rezvani, S., Sariyildiz, S. (2013). A Syntactic Design Methodology. Proceedings of 9th Space Syntax Symposium. Seoul. Introduction
SYNTACTIC Space Syntax for Generative Design Schemas and Screenshots Introduction
SYNTACTIC Space Syntax for Generative Design Schemas and Screenshots Introduction
CONFIGURBANIST Urban Configuration Analysis A Plugin for Grasshopper 3D, Written in C# & VB.NET ▪ Easiest Paths for Walking and Cycling ▪ Network Centrality Analysis ▪ Fuzzy Accessibility Analysis of POI ▪ Polycentric Distributions ▪ Spatial Network Analysis ▪ Zoning for Facility Location Planning Download: https://sites.google.com/site/pirouznourian/configurbanist User Group: www.grasshopper3d.com/group/cheetah Publications: ▪ Nourian, P, van der Hoeven, F, Sariyildiz, S, Rezvani, S, (2016) Spectral Modelling of Spatial Networks, SimAUD, UCL, London, ACM press, Accepted. ▪ Nourian, P, van der Hoeven, F, Rezvani, S, Sariyildiz, S, (2016) Supporting Bipedalism: Computational Analysis of Walking and Cycling Accessibility for Geodesign Workflows, RIUS Research in Urbanism Series, GEODESIGN, TU Delft, Accepted. ▪ Nourian, P., Rezvani, S., Sariyildiz, S, van der Hoeven, F. (2015). CONFIGURBANIST - Urban Configuration Analysis for Walking and Cycling via Easiest Paths, proceedings of the 33rd eCAADe ▪ Nourian, P., van der Hoeven, F, Rezvani, S., Sariyildiz, S. (2015). Easiest paths for walking and cycling: Combining syntactic and geographic analyses in studying walking and cycling mobility, proceedings of the 10th Space Syntax Symposium, UCL, London [URL] Introduction
CONFIGURBANIST Urban Configuration Analysis Schemas and Screenshots Introduction “Easiest Paths” for walking and cycling, which are as short, flat and straightforward as possible
CONFIGURBANIST Urban Configuration Analysis Schemas and Screenshots Introduction Closeness Zoning Betweenness
TOIDAR 3D Building Reconstruction from LIDAR Point Clouds A Plugin for Grasshopper 3D, Written in C#, VB.NET, and Python ▪ made for (and further developed by) MSc Geomatics students ▪ point cloud classifications: height, aspect, slope ▪ point cloud segmentation ▪ surface and solid reconstruction out of point clouds Download: https://github.com/Pirouz-Nourian/TOIDAR https://sites.google.com/site/pirouznourian/toidar Contributors: Dr. Sisi Zlatanova, Tom Broersen, Jiale Chen, Martin Dennemark, Florian Fichtner, Martijn Koopman, Ivo de Liefde, Marco Lam, Maarten Pronk, Stella Psomadaki, Rusne Sileryte, Dimitris Zervakis, Kaixuan Zhou Publication(s): ▪ Chen, J, Sileryte, R, Zhou, K, Nourian, P & Zlatanova, S (2014). Automated 3D reconstruction of buildings out of point clouds obtained from panoramic images. Walnut Creek, USA: CycloMedia. (TUD) Funding: Partially supported by Cyclomedia B.V. (3K €) Introduction
TOIDAR 3D Building Reconstruction from LIDAR Point Clouds Schemas and Screenshots Introduction
TOIDAR 3D Building Reconstruction from LIDAR Point Clouds Schemas and Screenshots Introduction Images by students: Jiale Chen, Rusne Sileryte, Kaixuan Zhou
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RASTERWORKS.DLL 3D Raster Modelling and Iso-Surfaces Schemas and Screenshots Introduction Iso surfaces Level Sets Voxelated OTB building 3D Fields
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Ar1 twf030 lecture2.2

  • 1. 11 On Graphs and Fields in Computational Design Dr.ir. Pirouz Nourian Assistant Professor of Design Informatics Department of Architectural Engineering & Technology Faculty of Architecture and Built Environment
  • 4. 44 not making the right inner network at the right location on an outer network Motivation Manifolds Continuous/Discrete Poincare Duality Graphs Fields Spatial Distance Spatial Potential Spatial Dynamics Manifold 2 Field Field 2 Manifold Configurative Design
  • 5. 55 0D: Point (the space therein everywhere resembles a 0-dimensional Euclidean Space) 1D: Curve (the space therein everywhere resembles a 1-dimensional Euclidean Space) 2D: Surface (the space therein everywhere resembles a 2-dimensional Euclidean Space) 3D: Solid (the space therein everywhere resembles a 3-dimensional Euclidean Space) Motivation Manifolds Continuous/Discrete Poincare Duality Graphs Fields Spatial Distance Spatial Potential Spatial Dynamics Manifold 2 Field Field 2 Manifold Configurative Design
  • 6. 66 Manifold Graph Field Motivation Manifolds Continuous/Discrete Poincare Duality Graphs Fields Spatial Distance Spatial Potential Spatial Dynamics Manifold 2 Field Field 2 Manifold Configurative Design
  • 7. 77 terminology • Geometry: Point (0D), Curve(1D), Surface(2D), Solid (3D) [free-form] • Geometry: Point (0D), Line(1D), Polygon(2D), Polyhedron (3D) [piecewise linear] • Topology: Vertex(0D), Edge(1D), Face(2D), Body(3D) • Graph Theory: Object, Link, (and n-Cliques) • Fields: Pixel, Voxel, Raster2D, Raster 3D Motivation Manifolds Continuous/Discrete Poincare Duality Graphs Fields Spatial Distance Spatial Potential Spatial Dynamics Manifold 2 Field Field 2 Manifold Configurative Design
  • 8. 88 Poincare Duality a pairing between k-dimensional features and dual features of dimension n-k in ℝ 𝑛 PRIMAL DUAL 0D vertex (e.g. as a point) 1D edge 1D edge (e.g. as a line segment) 0D vertex PRIMAL DUAL 0D vertex (e.g. a point) 2D face 1D edge (e.g. a line segment) 1D edge 2D face (e.g. a triangle or a pixel) 0D vertex PRIMAL DUAL 0D vertex (e.g. a point) 3D body 1D edge (e.g. a line segment) 2D face 2D face (e.g. a triangle or a pixel) 1D edge 3D body (e.g. a tetrahedron or a voxel) 0D vertex ℝ ℝ3 ℝ2 Configraphics: Graph Theoretical Methods of Design and Analysis of Spatial Configurations, Nourian, P, 2016 Motivation Manifolds Continuous/Discrete Poincare Duality Graphs Fields Spatial Distance Spatial Potential Spatial Dynamics Manifold 2 Field Field 2 Manifold Configurative Design
  • 9. 99 Poincare Duality a pairing between k-dimensional features and dual features of dimension n-k in ℝ 𝑛 PRIMAL DUAL 0D vertex (e.g. as a point) 1D edge 1D edge (e.g. as a line segment) 0D vertex ℝ A hypothetical street network (a), a Junction-to-Junction adjacency graph (b) versus a Street-to-Street adjacency graph (c), both ‘undirected’, after Batty (Batty, 2004): red dots represent graph nodes, and blue arcs represent graph links. Batty, M., 2004. A New Theory of Space Syntax. CASA Working Paper Series, March. Motivation Manifolds Continuous/Discrete Poincare Duality Graphs Fields Spatial Distance Spatial Potential Spatial Dynamics Manifold 2 Field Field 2 Manifold Configurative Design
  • 10. 1010 Poincare Duality a pairing between k-dimensional features and dual features of dimension n-k in ℝ 𝑛 PRIMAL DUAL 0D vertex (e.g. a point) 2D face 1D edge (e.g. a line segment) 1D edge 2D face (e.g. a triangle or a pixel) 0D vertex ℝ2 A Voronoi tessellation of 2D space and its dual that is a Delaunay triangulation Motivation Manifolds Continuous/Discrete Poincare Duality Graphs Fields Spatial Distance Spatial Potential Spatial Dynamics Manifold 2 Field Field 2 Manifold Configurative Design
  • 11. 1111 Poincare Duality a pairing between k-dimensional features and dual features of dimension n-k in ℝ 𝑛 PRIMAL DUAL 0D vertex (e.g. a point) 3D body 1D edge (e.g. a line segment) 2D face 2D face (e.g. a triangle or a pixel) 1D edge 3D body (e.g. a tetrahedron or a voxel) 0D vertex ℝ3 representing adjacencies between 3D cells or bodies via their dual vertices (Lee, 2001) Motivation Manifolds Continuous/Discrete Poincare Duality Graphs Fields Spatial Distance Spatial Potential Spatial Dynamics Manifold 2 Field Field 2 Manifold Configurative Design
  • 12. 1212 https://medium.com/basecs/k%C3%B6nigsberg-seven-small-bridges-one-giant-graph-problem-2275d1670a12 The glorious beginning of Graph Theroy Motivation Manifolds Continuous/Discrete Poincare Duality Graphs Fields Spatial Distance Spatial Potential Spatial Dynamics Manifold 2 Field Field 2 Manifold Configurative Design
  • 13. 1313 locus topos graph Leonhard Euler in 1736, the Seven Bridges of Königsberg Motivation Manifolds Continuous/Discrete Poincare Duality Graphs Fields Spatial Distance Spatial Potential Spatial Dynamics Manifold 2 Field Field 2 Manifold Configurative Design
  • 14. 1414 Geometry Topology Graph Theory locus topos graph Image Credit: Bill Hillier, Space is the machine, 1997 Motivation Manifolds Continuous/Discrete Poincare Duality Graphs Fields Spatial Distance Spatial Potential Spatial Dynamics Manifold 2 Field Field 2 Manifold Configurative Design
  • 15. 1515Bonds: Similarity, Intimacy, Influence, Collaboration, etc. We live in (social) bubbles! Social Networks Motivation Manifolds Continuous/Discrete Poincare Duality Graphs Fields Spatial Distance Spatial Potential Spatial Dynamics Manifold 2 Field Field 2 Manifold Configurative Design
  • 16. 1616 Left: The underground rail network of London, the geographical version; Right: The Tube Map by Harry Beck, the First Topological Metro Map for the London Underground Network in 1931 “everything is related to everything else, but near things are more related than distant things." Waldo Tobler Bonds: Proximity, Connectivity, Adjacency, Spatial Networks Motivation Manifolds Continuous/Discrete Poincare Duality Graphs Fields Spatial Distance Spatial Potential Spatial Dynamics Manifold 2 Field Field 2 Manifold Configurative Design
  • 17. 1717 Etymology of the term Rasterization Rastrum Pens Rastrum Roller Plotters Image Credits: https://nl.pinterest.com/pin/387731849143362464/ https://nl.pinterest.com/pin/71494712814015023/ Image Credits: https://en.wikipedia.org/wiki/Rastrum http://www.ebay.ie/itm/311372013714 Motivation Manifolds Continuous/Discrete Poincare Duality Graphs Fields Spatial Distance Spatial Potential Spatial Dynamics Manifold 2 Field Field 2 Manifold Configurative Design
  • 18. 1818 https://www.simscale.com/blog/2014/06/server-room-cooling-hvac-simulation/ Raster Space models: Scalar Fields: • Noise • Moisture • Temperature • Soil Composition • Noise Analyses Motivation Manifolds Continuous/Discrete Poincare Duality Graphs Fields Spatial Distance Spatial Potential Spatial Dynamics Manifold 2 Field Field 2 Manifold Configurative Design
  • 19. 1919 https://www.comsol.com/cfd-module Raster Space models: Scalar Fields: • Noise • Moisture • Temperature • Soil Composition: e.g. in geological analyses • • Noise Analyses: noise pollution levels… Vector Fields: • Computational Fluid Dynamics (CFD): e.g. ventilation and wind simulations • Egress Simulation Motivation Manifolds Continuous/Discrete Poincare Duality Graphs Fields Spatial Distance Spatial Potential Spatial Dynamics Manifold 2 Field Field 2 Manifold Configurative Design
  • 20. 2020 Spatial Geodesics and Spatial Distances • Indoor Navigation • Emergency Response Planning • Location-Based Services (indoor-outdoor) • Robot/Drone Motion Planning 3D Spatial Network & 3D Path Finding http://urban-scene.blogspot.nl/2014/02/network-analysis-in- cityengine.html Modelling Pedestrian Evacuation http://www.jigsaw24.com/news/news/2712-massmotion-advanced-3d-pedestrian-simulations-for-evacuation-plans/ Motivation Manifolds Continuous/Discrete Poincare Duality Graphs Fields Spatial Distance Spatial Potential Spatial Dynamics Manifold 2 Field Field 2 Manifold Configurative Design
  • 21. 2121 Different Spatial Structures Affords Different Social Structures One Decision-Maker Hub & Spokes Hierarchy Full Mesh Clique Several Decision Makers All Decision Makers Motivation Manifolds Continuous/Discrete Poincare Duality Graphs Fields Spatial Distance Spatial Potential Spatial Dynamics Manifold 2 Field Field 2 Manifold Configurative Design
  • 22. 2222 why is spatial arrangement important? different spatial arrangements enable different social networks Motivation Manifolds Continuous/Discrete Poincare Duality Graphs Fields Spatial Distance Spatial Potential Spatial Dynamics Manifold 2 Field Field 2 Manifold Configurative Design
  • 23. 2323 a spectrum of socio-spatial configurations different spatial arrangements enable different social networks Motivation Manifolds Continuous/Discrete Poincare Duality Graphs Fields Spatial Distance Spatial Potential Spatial Dynamics Manifold 2 Field Field 2 Manifold Configurative Design
  • 24. 2424 Importance of Network Structure position in a network strongly influences performance Close to many people Introduction In between many people Linkage Connected to many people Spread Connected to important people Influence Typical Examples of Centrality Indexes Motivation Manifolds Continuous/Discrete Poincare Duality Graphs Fields Spatial Distance Spatial Potential Spatial Dynamics Manifold 2 Field Field 2 Manifold Configurative Design
  • 25. 2525 Functional Structural Fit Shops Service Areas Cafes/Restaurants Operational Centre In an exemplary airport logical locations for: Close to many people In between many peopleConnected to many people Connected to important people Motivation Manifolds Continuous/Discrete Poincare Duality Graphs Fields Spatial Distance Spatial Potential Spatial Dynamics Manifold 2 Field Field 2 Manifold Configurative Design
  • 26. 2626 Can you make an ordered list of spaces as to their intended privacy/community level? Something like: entrance-toilet-living-kitchen-bedrooms-bathroom A Spectrum of Privacy to Community How would you connect them to one another to achieve this (as in a bubble diagram)? You can distinguish between (wanted/unwanted) spatial connectivity and adjacency links. Motivation Manifolds Continuous/Discrete Poincare Duality Graphs Fields Spatial Distance Spatial Potential Spatial Dynamics Manifold 2 Field Field 2 Manifold Configurative Design
  • 27. 2727 TWO INDICATORS OF PRIVACY AND COMMUNITY ▪ Integration (Closeness Centrality) ▪ Choice (Betweenness Centrality) Choice (Originally introduced as Betweenness by Freeman (Freeman, 1977)) Choice or Betweenness is a measure of centrality for nodes within a configuration as to its role in shortest paths. Intuitively shows how likely it is for people to move through a space. That literally tells how many times a node happens to be in the shortest paths between all other nodes. It can also be computed for the links connecting the nodes in a similar way. Integration (Hillier and Hanson, 1984) is a measure of centrality that indicates how likely it is for a space to be private or communal. The more integrated a space, the shallower it is to all other nodes in a configuration. Intuitively shows how likely it is for people to move to a space. Integration is calculated by computing the total depth of a node when the depths of all other nodes are projected on it. Motivation Manifolds Continuous/Discrete Poincare Duality Graphs Fields Spatial Distance Spatial Potential Spatial Dynamics Manifold 2 Field Field 2 Manifold Configurative Design
  • 28. 2828 For a function u(x,y,z,t) of three spatial variables (x,y,z) (see Cartesian coordinate system) and the time variable t, the heat equation is More generally in any coordinate system: https://en.wikipedia.org/wiki/Heat_equation Motivation Manifolds Continuous/Discrete Poincare Duality Graphs Fields Spatial Distance Spatial Potential Spatial Dynamics Manifold 2 Field Field 2 Manifold Configurative Design https://nl.mathworks.com/matlabcentral/fileexchange/42604-finite-difference-method-to-solve-heat-diffusion-equation-in-two-dimensions
  • 29. 2929 Motivation Manifolds Continuous/Discrete Poincare Duality Graphs Fields Spatial Distance Spatial Potential Spatial Dynamics Manifold 2 Field Field 2 Manifold Configurative Design http://www.clker.com/clipart-drunk-man.html Sketches by Boz, George Cruikshank, Wiki Commons The Walking Drunkard
  • 30. 3030 Motivation Manifolds Continuous/Discrete Poincare Duality Graphs Fields Spatial Distance Spatial Potential Spatial Dynamics Manifold 2 Field Field 2 Manifold Configurative Design Stationary Probability Distribution of Random Walkers
  • 31. 3131 Geographical  Geometrical  Topological  Graphical  Spectral
  • 33. 3333 Where is the best place for a souvenir shop? Wanderers end up in the same areas!
  • 34. 3434 Pixel & Voxel Adjacencies • Sharing Edges: 4 Neighbours • Sharing Vertices: 8 Neighbours • Sharing Faces: 6 Neighbours • Sharing Edges: 18 Neighbours • Sharing Vertices: 26 Neighbours Jian Huang, Roni Yagel, Vassily Filippov, and Yair Kurzion Why do we need connectivity information? For relative positioning and topology information Motivation Manifolds Continuous/Discrete Poincare Duality Graphs Fields Spatial Distance Spatial Potential Spatial Dynamics Manifold 2 Field Field 2 Manifold Configurative Design
  • 35. 3535 Voxel Models: N-Adjacency & N-Paths • Separability: What could be a closure? • For defining 3D recognizable “objects” Representing closures Motivation Manifolds Continuous/Discrete Poincare Duality Graphs Fields Spatial Distance Spatial Potential Spatial Dynamics Manifold 2 Field Field 2 Manifold Configurative Design
  • 36. 3636 Voxel Models: N-Adjacency & N-Paths • Separability: What could be a closure? • For defining 3D recognizable “objects” Representing closures Images courtesy of Samuli Laine, NVIDIA, 2013 Motivation Manifolds Continuous/Discrete Poincare Duality Graphs Fields Spatial Distance Spatial Potential Spatial Dynamics Manifold 2 Field Field 2 Manifold Configurative Design
  • 37. 3737 Voxel Models: N-Adjacency & N-Paths • Separability: What could be a closure? • For defining 3D recognizable “objects” Representing closures 4-connected, 8-separating 8-connected, 4-separating Motivation Manifolds Continuous/Discrete Poincare Duality Graphs Fields Spatial Distance Spatial Potential Spatial Dynamics Manifold 2 Field Field 2 Manifold Configurative Design
  • 38. 3838 Voxel Models: N-Adjacency & N-Paths • Connectivity: how to represent a curve in pixels or voxels • Thinness: how do we ensure the minimality of a raster representation Representing closures for defining 3D recognizable “objects” Voxelization algorithms for geospatial applications: http://www.sciencedirect.com/science/article/pii/S2215016116000029 Motivation Manifolds Continuous/Discrete Poincare Duality Graphs Fields Spatial Distance Spatial Potential Spatial Dynamics Manifold 2 Field Field 2 Manifold Configurative Design
  • 39. 3939 Voxel Models: N-Adjacency & N-Paths • Connectivity: how to represent a curve in pixels or voxels • Thinness: how do we ensure the minimality of a raster representation Representing closures for defining 3D recognizable “objects” Voxelization algorithms for geospatial applications: http://www.sciencedirect.com/science/article/pii/S2215016116000029 Motivation Manifolds Continuous/Discrete Poincare Duality Graphs Fields Spatial Distance Spatial Potential Spatial Dynamics Manifold 2 Field Field 2 Manifold Configurative Design
  • 40. 4040 Point Cloud Rasterization [Topological] Voxelization algorithms for geospatial applications: http://www.sciencedirect.com/science/article/pii/S2215016116000029 Motivation Manifolds Continuous/Discrete Poincare Duality Graphs Fields Spatial Distance Spatial Potential Spatial Dynamics Manifold 2 Field Field 2 Manifold Configurative Design
  • 41. 4141 6-Connected Stanford Bunny, 1265 voxels (0.8,0.8.0.8) 26-Connected Stanford Bunny, 755 voxels (0.8, 0.8, 0.8) Control on Connectivity Level Stanford Bunny, scaled 0.1: Mesh (V:34834 F:69664) Motivation Manifolds Continuous/Discrete Poincare Duality Graphs Fields Spatial Distance Spatial Potential Spatial Dynamics Manifold 2 Field Field 2 Manifold Configurative Design
  • 42. 4242 26-Connected Voxels of various XYZ dimensions: 0.8x0.8x0.1 Motivation Manifolds Continuous/Discrete Poincare Duality Graphs Fields Spatial Distance Spatial Potential Spatial Dynamics Manifold 2 Field Field 2 Manifold Configurative Design
  • 43. 4343 6-Connected Voxels of various XYZ dimensions: 0.8x0.8x0.8 Motivation Manifolds Continuous/Discrete Poincare Duality Graphs Fields Spatial Distance Spatial Potential Spatial Dynamics Manifold 2 Field Field 2 Manifold Configurative Design
  • 44. 4444 Topological Rasterization with Semantics from a BIM model [original model] Motivation Manifolds Continuous/Discrete Poincare Duality Graphs Fields Spatial Distance Spatial Potential Spatial Dynamics Manifold 2 Field Field 2 Manifold Configurative Design
  • 45. 4545 Topological Rasterization with Semantics from a BIM model [0.5 by 0.5 by 0.5 M] Motivation Manifolds Continuous/Discrete Poincare Duality Graphs Fields Spatial Distance Spatial Potential Spatial Dynamics Manifold 2 Field Field 2 Manifold Configurative Design
  • 46. 4646 Topological Rasterization with Semantics from a BIM model [0.4 by 0.4 by 0.4 M] Motivation Manifolds Continuous/Discrete Poincare Duality Graphs Fields Spatial Distance Spatial Potential Spatial Dynamics Manifold 2 Field Field 2 Manifold Configurative Design
  • 47. 4747 Topological Rasterization with Semantics from a BIM model [0.2 by 0.2 by 0.2 M] Motivation Manifolds Continuous/Discrete Poincare Duality Graphs Fields Spatial Distance Spatial Potential Spatial Dynamics Manifold 2 Field Field 2 Manifold Configurative Design
  • 48. 4848 Topological Rasterization with Semantics from a BIM model [0.1 by 0.1 by 0.1 M] Motivation Manifolds Continuous/Discrete Poincare Duality Graphs Fields Spatial Distance Spatial Potential Spatial Dynamics Manifold 2 Field Field 2 Manifold Configurative Design
  • 49. 4949 Sparce Voxel Octree (SVO) • Make smaller voxels if needed depending on the desired LOD • the position of a voxel is inferred based upon its position relative to other voxels • Connectivity graph of a voxel model Adaptive Resolution: a more efficient way of representation Image courtesy of NVIDIA, GPU Gems 2 http://http.developer.nvidia.com/GPUGems2/gpugems2_chapter37.html Motivation Manifolds Continuous/Discrete Poincare Duality Graphs Fields Spatial Distance Spatial Potential Spatial Dynamics Manifold 2 Field Field 2 Manifold Configurative Design
  • 50. 5050 Octree and Quadtree representation How do they work? • 2D Quadtrees (recursive subdivision of a bounding rectangle into 4 rectangles): divide the shape to pixels small enough to represent the required ‘geometric’ LOD, wherever needed, larger elsewhere. • 3D Octrees (recursive subdivision of a bounding box into 8 boxes): divide the shape to voxels small enough to represent the required ‘geometric’ LOD, wherever needed, larger elsewhere. Images from Wiki Commons Motivation Manifolds Continuous/Discrete Poincare Duality Graphs Fields Spatial Distance Spatial Potential Spatial Dynamics Manifold 2 Field Field 2 Manifold Configurative Design
  • 51. 5151 3D raster vs 3D vector representation Rasterize Vectorize Manifold Model • 0D: Points • 1D: Polylines • 2D: Meshes • 3D: Solids Field Model • Raster 2D • Raster3D Motivation Manifolds Continuous/Discrete Poincare Duality Graphs Fields Spatial Distance Spatial Potential Spatial Dynamics Manifold 2 Field Field 2 Manifold Configurative Design
  • 52. 5252 Rasterization Algorithms How to convert vector data consistently to Raster2D or Raster 3D data Rasterize Topological Rasterization: Nourian, P., Gonçalves, R., Zlatanova, S., Ohori, K. A., & Vo, A. V. (2016). Voxelization Algorithms for Geospatial Applications: Computational Methods for Voxelating Spatial Datasets of 3D City Models Containing 3D Surface, Curve and Point Data Models. MethodsX. Manifold Model • 0D: Points • 1D: Polylines • 2D: Meshes • 3D: Solids Field Model • Raster 2D • Raster3D Motivation Manifolds Continuous/Discrete Poincare Duality Graphs Fields Spatial Distance Spatial Potential Spatial Dynamics Manifold 2 Field Field 2 Manifold Configurative Design
  • 53. 5353 Vectorization Algorithms How to convert raster data consistently to Vector2D or Vector3D data Vectorize Manifold Model • 0D: Points • 1D: Polylines • 2D: Meshes • 3D: Solids Field Model • Raster 2D • Raster3D • Iso-Surface Algorithms • Iso-Curve Algorithms Motivation Manifolds Continuous/Discrete Poincare Duality Graphs Fields Spatial Distance Spatial Potential Spatial Dynamics Manifold 2 Field Field 2 Manifold Configurative Design
  • 54. 5454 Iso-Curve Algorithms How to construct topography contour lines from elevation raster maps? • Marching Squares • Marching Triangles Note: Marching triangle does not bring about ambiguous topological situations, unlike marching squares. Therefore, curves produced by marching triangles are always manifold. Images from wiki commons Motivation Manifolds Continuous/Discrete Poincare Duality Graphs Fields Spatial Distance Spatial Potential Spatial Dynamics Manifold 2 Field Field 2 Manifold Configurative Design
  • 55. 5555 Iso-Surface Algorithms How to construct contour surfaces from continuous Raster 3D field/function models? • Marching Cubes (William E. Lorensen and Harvey E. Cline, 1985) • Marching Tetrahedrons (Doi and Koide, 1991)_ Prototyped Note: Marching tetrahedrons does not bring about ambiguous topological situations, unlike marching cubes. Therefore, surfaces produced by marching tetrahedrons are always manifold. • Extracting boundaries using voxel attributes https://github.com/Pirouz-Nourian/MarchingTetrahedrons Motivation Manifolds Continuous/Discrete Poincare Duality Graphs Fields Spatial Distance Spatial Potential Spatial Dynamics Manifold 2 Field Field 2 Manifold Configurative Design
  • 56. 5656 Extracting an Isosurface from voxel data Using the Marching Cubes algorithm Image courtesy of Paul Bourke Motivation Manifolds Continuous/Discrete Poincare Duality Graphs Fields Spatial Distance Spatial Potential Spatial Dynamics Manifold 2 Field Field 2 Manifold Configurative Design
  • 57. 5757 Example: Numeric Query How to construct contour meshes from continuous Raster 3D field/function models? Note: Marching tetrahedrons does not bring about ambiguous topological situations, unlike marching cubes. Therefore, surfaces produced by marching tetrahedrons are always manifold. • Extracting boundaries using voxel attributes (measures, semantic etc.) Motivation Manifolds Continuous/Discrete Poincare Duality Graphs Fields Spatial Distance Spatial Potential Spatial Dynamics Manifold 2 Field Field 2 Manifold Configurative Design
  • 58. 5858 Profiling Algorithms Image courtesy of Oregon State University Check out TUD Raster Works tools for examples: https://sites.google.com/site/pirouznourian/otb_3dgis https://github.com/Pirouz-Nourian OTB Building, X Section OTB Building, Y Section OTB , Z Section Motivation Manifolds Continuous/Discrete Poincare Duality Graphs Fields Spatial Distance Spatial Potential Spatial Dynamics Manifold 2 Field Field 2 Manifold Configurative Design
  • 59. 5959 Spatial Configuration: the particular way, in which spaces are linked to each other in a building or a built environment Design as Spatial Configuration • Any meaningful set has something more than all of its items. • A certain configuration ‘reflects and affects’ social interactions within a built environment. • How do we design a plan to embody a spatial configuration? reverse? Villa Savoye Le Corbusier & Pierre Jeanneret A bubble diagram of Villa Savoye Motivation Manifolds Continuous/Discrete Poincare Duality Graphs Fields Spatial Distance Spatial Potential Spatial Dynamics Manifold 2 Field Field 2 Manifold Configurative Design
  • 60. 6060 How to design a plan with a particular spatial configuration? A Syntactic Design Process • An abstract graph may correspond to many concrete plan layouts! • A spatial configuration can be analyzed in terms of its social implications • Configurations are in-between the abstract domain of functions and the concrete domain of forms Design Process FormFunction Configuration Abstract Concrete Configurational Analysis An Interactive Process Motivation Manifolds Continuous/Discrete Poincare Duality Graphs Fields Spatial Distance Spatial Potential Spatial Dynamics Manifold 2 Field Field 2 Manifold Configurative Design
  • 61. 6161 How to design a plan with a particular spatial configuration? A Syntactic Design Process More specifically: An Interactive Process Design Process FormFunction Configuration Abstract Concrete Configurational Analysis Bubble Diagram (Graph) Plan Diagrams (Bubble Packing) Topological Embedding (Map) Motivation Manifolds Continuous/Discrete Poincare Duality Graphs Fields Spatial Distance Spatial Potential Spatial Dynamics Manifold 2 Field Field 2 Manifold Configurative Design
  • 62. 6262 Implicit modelling as level sets A strategy for design modeling/3D sketching Model a Scalar Field Get Iso-surfaces Motivation Manifolds Continuous/Discrete Poincare Duality Graphs Fields Spatial Distance Spatial Potential Spatial Dynamics Manifold 2 Field Field 2 Manifold Configurative Design
  • 63. 6363 From Graph to Field to Space a continuous approach to spatial configuration!? Say each space is defined in simplest form as a node, then in the absence of external influences it becomes a circle or hemisphere then… Motivation Manifolds Continuous/Discrete Poincare Duality Graphs Fields Spatial Distance Spatial Potential Spatial Dynamics Manifold 2 Field Field 2 Manifold Configurative Design
  • 64. 6464 From Graph to Field to Space ISOSURFACE: a scalar field of values is evaluated at every point of a 3D grid; then layers of the field can be found as ‘iso-surfaces’. An isosurface is the border between those points whose attribute values are above the iso value and the ones below. Raster3D methods are based on OTB_3DGIS.DLL https://sites.google.com/site/pirouznourian/otb_3dgis ▪ voxel representation of big spatial data ▪ converting 3D vector data to 3D raster data and vice versa ▪ using voxel representation in spatial analysis ▪ voxel operations for spatial planning Motivation Manifolds Continuous/Discrete Poincare Duality Graphs Fields Spatial Distance Spatial Potential Spatial Dynamics Manifold 2 Field Field 2 Manifold Configurative Design
  • 65. 6565 From Graph to Field to Space What does (might) it all have to do with architecture? Imagine a 3D configuration composed of nodes and links (vertices and edges) as in the top picture. We can think of a field around this configuration, which looks in 2D like the slice shown at the bottom. Controlling the field we can create the boundaries of spaces as isosurfaces! From Inside Out!? Try it out! bubble diagram-to-field-to-space!? Motivation Manifolds Continuous/Discrete Poincare Duality Graphs Fields Spatial Distance Spatial Potential Spatial Dynamics Manifold 2 Field Field 2 Manifold Configurative Design
  • 67. CONFIGURBANISTSYNTACTIC Space Syntax For Architectural Configuration Network Analysis For Urban Configuration For 3D Reconstruction from Point Clouds rasterworks.dll Library of Raster3D & Voxel Tools Introduction Networks Fields (regular, irregular)
  • 68. SYNTACTIC Space Syntax for Generative Design A Plugin for Grasshopper 3D, Written in VB.NET & C# ▪ Real-Time Space Syntax Analyses for Parametric Design ▪ Interactive Bubble Diagrams ▪ Automated Graph Drawing Algorithms ▪ Enumeration of Plan Configuration Topologies ▪ Measuring the Socio-Spatial/Programmatic Performance ▪ Topological Layout Download: https://sites.google.com/site/pirouznourian/syntactic-design User Group: www.grasshopper3d.com/group/space-syntax Publications: ▪ Nourian, P. Rezvani, S., Sariyildiz, S. (2013). Designing with Space Syntax. Proceedings of eCAADe 2013, (pp. 357-366). Delft. ▪ Nourian, P., Rezvani, S., Sariyildiz, S. (2013). A Syntactic Design Methodology. Proceedings of 9th Space Syntax Symposium. Seoul. Introduction
  • 69. SYNTACTIC Space Syntax for Generative Design Schemas and Screenshots Introduction
  • 70. SYNTACTIC Space Syntax for Generative Design Schemas and Screenshots Introduction
  • 71. CONFIGURBANIST Urban Configuration Analysis A Plugin for Grasshopper 3D, Written in C# & VB.NET ▪ Easiest Paths for Walking and Cycling ▪ Network Centrality Analysis ▪ Fuzzy Accessibility Analysis of POI ▪ Polycentric Distributions ▪ Spatial Network Analysis ▪ Zoning for Facility Location Planning Download: https://sites.google.com/site/pirouznourian/configurbanist User Group: www.grasshopper3d.com/group/cheetah Publications: ▪ Nourian, P, van der Hoeven, F, Sariyildiz, S, Rezvani, S, (2016) Spectral Modelling of Spatial Networks, SimAUD, UCL, London, ACM press, Accepted. ▪ Nourian, P, van der Hoeven, F, Rezvani, S, Sariyildiz, S, (2016) Supporting Bipedalism: Computational Analysis of Walking and Cycling Accessibility for Geodesign Workflows, RIUS Research in Urbanism Series, GEODESIGN, TU Delft, Accepted. ▪ Nourian, P., Rezvani, S., Sariyildiz, S, van der Hoeven, F. (2015). CONFIGURBANIST - Urban Configuration Analysis for Walking and Cycling via Easiest Paths, proceedings of the 33rd eCAADe ▪ Nourian, P., van der Hoeven, F, Rezvani, S., Sariyildiz, S. (2015). Easiest paths for walking and cycling: Combining syntactic and geographic analyses in studying walking and cycling mobility, proceedings of the 10th Space Syntax Symposium, UCL, London [URL] Introduction
  • 72. CONFIGURBANIST Urban Configuration Analysis Schemas and Screenshots Introduction “Easiest Paths” for walking and cycling, which are as short, flat and straightforward as possible
  • 73. CONFIGURBANIST Urban Configuration Analysis Schemas and Screenshots Introduction Closeness Zoning Betweenness
  • 74. TOIDAR 3D Building Reconstruction from LIDAR Point Clouds A Plugin for Grasshopper 3D, Written in C#, VB.NET, and Python ▪ made for (and further developed by) MSc Geomatics students ▪ point cloud classifications: height, aspect, slope ▪ point cloud segmentation ▪ surface and solid reconstruction out of point clouds Download: https://github.com/Pirouz-Nourian/TOIDAR https://sites.google.com/site/pirouznourian/toidar Contributors: Dr. Sisi Zlatanova, Tom Broersen, Jiale Chen, Martin Dennemark, Florian Fichtner, Martijn Koopman, Ivo de Liefde, Marco Lam, Maarten Pronk, Stella Psomadaki, Rusne Sileryte, Dimitris Zervakis, Kaixuan Zhou Publication(s): ▪ Chen, J, Sileryte, R, Zhou, K, Nourian, P & Zlatanova, S (2014). Automated 3D reconstruction of buildings out of point clouds obtained from panoramic images. Walnut Creek, USA: CycloMedia. (TUD) Funding: Partially supported by Cyclomedia B.V. (3K €) Introduction
  • 75. TOIDAR 3D Building Reconstruction from LIDAR Point Clouds Schemas and Screenshots Introduction
  • 76. TOIDAR 3D Building Reconstruction from LIDAR Point Clouds Schemas and Screenshots Introduction Images by students: Jiale Chen, Rusne Sileryte, Kaixuan Zhou
  • 77. RASTERWORKS.DLL 3D Raster Modelling and Iso-Surfaces A Library for Grasshopper 3D & MonetDB, written in C#, C++, C ▪ Topological Voxelation Tools ▪ Vector3D to Raster3D Operations & Raster specific queries ▪ Raster3D to Vector3D Operations (Level-Sets & Iso-Surfaces) Download: https://github.com/NLeSC/geospatial-voxels https://github.com/Pirouz-Nourian/MarchingTetrahedrons https://github.com/Pirouz-Nourian/Topological_Voxelizer_CSharp Contributors: Dr. Sisi Zlatanova, Dr. Romulo Goncalves, Dr. Ken Arroyo Ahori, Ir. Anh Vu Vo Publications: ▪ Nourian, P, Goncalves, R, Zlatanova, S, Arroyo Ahori, Vo, A.V., (2016) Voxelization Algorithms for Geospatial Applications, MethodsX, Elsevier [URL] ▪ Zlatanova, S, Nourian, P, Goncalves, R, Vo, A.V., (2016) TOWARDS 3D RASTER GIS: ON DEVELOPING A RASTER ENGINE FOR SPATIAL DBMS, proceedings of ISPRS WG IV/2 Workshop “Global Geospatial Information and High Resolution Global Land Cover/Land Use Mapping”, April 21, 2016, Novosibirsk, Russian Federation, [URL] ▪ Goncalves, R, Ivanova, M, Kersten, M, Scholten, H, Zlatanova, S , Alvanaki, F, Nourian, P & Dias, E (2014, November 3). Big Data analytics in the Geo-Spatial Domain. Groningen, Big Data Across Disciplines: In Search of Symbiosis, conference 3-5 November 2014. [URL] Funding: Grant number 027.013.703 from NLeSC Introduction
  • 78. RASTERWORKS.DLL 3D Raster Modelling and Iso-Surfaces Schemas and Screenshots Introduction Iso surfaces Level Sets Voxelated OTB building 3D Fields
  • 79. RASTERWORKS.DLL 3D Raster Modelling and Iso-Surfaces Schemas and Screenshots Introduction MonetDB: a geospatial database to support 3D GIS operations Rhino-GH: a parametric CAD environment working as a computational geometry lab & visualization environment ODBC connection Interface between MonetDB & Grasshopper RASTERWORKS.DLL an analytic engine for voxel/raster 3D operations Laboratory Software Architecture
  • 80. RASTERWORKS.DLL 3D Raster Modelling and Iso-Surfaces Schemas and Screenshots Introduction MonetDB: a geospatial database to support 3D GIS operations RASTERWORKS.DLL an analytic engine for voxel/raster 3D operations Rhino-GH: a parametric CAD environment working as a computational geometry lab & visualization environment Voxelizer code in C#Voxelizer code in C resolving dependencies • Avoid reading vector data from different file formats • Avoid querying vector data only for the purpose of voxelization • Transformation between vector and raster on a database level