Graph Layout. Last Time: Conveying Structure. Framework for conveying structure. Photographs and illustrations. What is a good view?

Transcription

1 Graph Layout Maneesh Agrawala Last Time: Conveying Structure CS : Visualization Spring 2011 Photographs and illustrations Framework for conveying structure Goal: Expose important internal features Requirements Internal features Viewpoint Blockers Procedure Transform blockers so internal features visible Reveal external shape, do not expose internal structure Canonical Views [Blanz, Tarr Bulthoff 99] What is a good view? Canonical views Oblique views from above Avoid accidental views In our case to reveal internal structure Separation of internal features in image plane 1

2 Transparency Blocker completely transparent Cutaways: Example Blocker semi-transparent Location of battery in army radio [Feiner & Seligmann 92] Midget submarine [from Holmes 93] Showing cut location Leonardo Da Vinci [French & Vierck 60] Ratchet device Sections and exploded view IBM building plan [from Holmes 93] 2

3 Exploded view Understanding 3D maps Floorplans Axonometric View Locating landmarks fastest with axonometric view [Fontaine 01] Concept design for museum guide [Tufte 97] Floorplans + Front View Generating an exploded view Works with existing 3D applications Soda Hall model from Funkhouser, Séquin, Teller Quake III Arena by Id Software 1. Geometric analysis - Find downward facing ceiling polygons 2. Place sectioning planes below ceilings 3. Multi-pass render each story separately Intercept and modify OpenGL stream Future: Enhanced spectator mode Real-world buildings Mock-up design Non-invasive [Mohr 01] Apply to existing OpenGL application without modification Seattle Public Library [from Seattle Times 04] 3

4 Authoring Pipeline Segmentation Input Segment Stack Fragment Assign ordering Annotate Stacking Fragmentation and depth assignment 4

5 Annotation Interactive viewing Interactive deformation Summary Choosing important internal features is challenging Requires semantic knowledge Are there domain-independent principles? Choosing good views Avoid accidental views Use canonical views if possible Finding blockers Visibility analysis Using deformation for browsing volume data [McGuffin 03] Transforming blockers Few basic choices (cull, move, transparency, modify drawing style) Final project Design new visualization method Pose problem, Implement creative solution Announcements Deliverables Implementation of solution 8-12 page paper in format of conference paper submission 2 design discussion presentations Schedule Project proposal: 3/14 Project presentation: 4/4 Final paper and presentation: 5/3 1:30-3pm 6 th floor Soda Grading Groups of up to 3 people, graded individually Clearly report responsibilities of each member 5

6 Topics Graph Layout Graph and Tree Visualization Tree Layout Graph Layout Goals Overview of layout approaches strengths and weaknesses Insight into implementation techniques Graphs and Trees Graphs Model relations among data Nodes and edges Trees Graphs with hierarchical structure Connected graph with N-1 edges Nodes as parents and children Spatial Layout Primary concern layout of nodes and edges Often (but not always) goal is to depict structure Connectivity, path-following Network distance Clustering Ordering (e.g., hierarchy level) Applications Tournaments Organization Charts Genealogy Diagramming (e.g., Visio) Biological Interactions (Genes, Proteins) Computer Networks Social Networks Simulation and Modeling Integrated Circuit Design 6

7 Tree Visualization Indentation Linear list, indentation encodes depth Node-Link diagrams Nodes connected by lines/curves Enclosure diagrams Represent hierarchy by enclosure Layering Layering and alignment Indentation Items along vertically spaced rows Indentation shows parent/child relationships Often used in interfaces Breadth/depth contend for space Often requires scrolling Tree layout is fast: O(n) or O(n log n), enabling real-time layout for interaction. Node-Link Diagrams Nodes distributed in space, connected by straight/curved lines Use 2D space to break apart breadth and depth Space used to communicate hierarchical orientation (typically towards authority or generality) Basic Recursive Approach Repeatedly divide space for subtrees by leaf count Breadth of tree along one dimension Depth along the other dimension Problem: exponential growth of breadth Reingold & Tilford s Tidier Layout Goal: maximize density and symmetry. Originally for binary trees, extended by Walker to cover general case. This extension was corrected by Buchheim et al to achieve a linear time algorithm. Reingold-Tilford Layout Design concerns Clearly encode depth level No edge crossings Isomorphic subtrees drawn identically Ordering and symmetry preserved Compact layout (don t waste space) 7

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12 Linear algorithm starts with bottom-up pass of the tree Y-coord by depth, arbitrary starting X-coord Merge left and right subtrees Shift right as close as possible to left Computed efficiently by maintaining subtree contours Shifts in position saved for each node as visited Parent nodes are centered above their children Top-down pass for assignment of final positions Sum of initial layout and aggregated shifts 12

13 Radial Layout Node-link diagram in polar coords Radius encodes depth, root at center Angular sectors assigned to subtrees (recursive approach) Reingold-Tilford approach can also be applied here 13