20151017_attractive planar panelization using dynamic relaxation principles_00
TRANSCRIPT
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Structural Membranes 2015 19.10.2015 Barcelona / Spain Dipl. Ing. Florian Gauss
Attractive planar panelization using Dynamic Relaxation
Principles 19.October 2015 Barcelona Structural Membranes 2015
F. Gauss* P. Teuffel
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Structural Membranes 2015 19.10.2015 Barcelona / Spain Dipl. Ing. Florian Gauss
Content I_PQ Mesh ApproximationII_PQ Mesh AttractionIII_Case Study
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Structural Membranes 2015 19.10.2015 Barcelona / Spain Dipl. Ing. Florian Gauss
Steps
• Computation of Lines of Principle Curvature (LPC)
• Topology Mesh• Subdivision Mesh (Catmull Clarke)• Planar Relax
I_PQ Mesh Approximation
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Structural Membranes 2015 19.10.2015 Barcelona / Spain Dipl. Ing. Florian Gauss
Principle Curvature Vector Field
Integrated Vector Field
Revolving Normal Planes
Max/Min Directions
Lines of Principle Curvature (LPC)
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Structural Membranes 2015 19.10.2015 Barcelona / Spain Dipl. Ing. Florian Gauss
Discrete Computation of Indvidual LPC
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Structural Membranes 2015 19.10.2015 Barcelona / Spain Dipl. Ing. Florian Gauss
Discrete Computation of LPC
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Structural Membranes 2015 19.10.2015 Barcelona / Spain Dipl. Ing. Florian Gauss
Discrete Computation of LPC
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Structural Membranes 2015 19.10.2015 Barcelona / Spain Dipl. Ing. Florian Gauss
Discrete Computation of LPC
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Structural Membranes 2015 19.10.2015 Barcelona / Spain Dipl. Ing. Florian Gauss
Discrete Computation of LPC
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Structural Membranes 2015 19.10.2015 Barcelona / Spain Dipl. Ing. Florian Gauss
Discrete Computation of LPC
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Structural Membranes 2015 19.10.2015 Barcelona / Spain Dipl. Ing. Florian Gauss
Discrete Computation of LPC
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Structural Membranes 2015 19.10.2015 Barcelona / Spain Dipl. Ing. Florian Gauss
Discrete Computation of LPC
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Structural Membranes 2015 19.10.2015 Barcelona / Spain Dipl. Ing. Florian Gauss
Umbilic Point
LPC Map
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Structural Membranes 2015 19.10.2015 Barcelona / Spain Dipl. Ing. Florian Gauss
Adaptive Quad Tree DecompositionUmbilic Point Condition
Umbilic Point Extraction
Umbilic Point Condition with tolerance
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Structural Membranes 2015 19.10.2015 Barcelona / Spain Dipl. Ing. Florian Gauss
Starting Candidates
Final Canidates
Quad Tree Quadrants
Refinement
Umbilic Point Extraction
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Structural Membranes 2015 19.10.2015 Barcelona / Spain Dipl. Ing. Florian Gauss
Umbilic Points – Principal Types
Star
Lemon Star
Mon Star
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Structural Membranes 2015 19.10.2015 Barcelona / Spain Dipl. Ing. Florian Gauss
Crude Start Mesh
1 2
34
56
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Structural Membranes 2015 19.10.2015 Barcelona / Spain Dipl. Ing. Florian Gauss
Subdivided Mesh (2 Steps)
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Structural Membranes 2015 19.10.2015 Barcelona / Spain Dipl. Ing. Florian Gauss
Subdivided Mesh (3 Steps)
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Structural Membranes 2015 19.10.2015 Barcelona / Spain Dipl. Ing. Florian Gauss
Integrated Vector Field
Dynamic Relaxation Equation
Planar Relax
Planar Pulling forces
fp
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Structural Membranes 2015 19.10.2015 Barcelona / Spain Dipl. Ing. Florian Gauss
Before Optimization
Planar Relax Optimization
After Optimization (1644 cycles)
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Structural Membranes 2015 19.10.2015 Barcelona / Spain Dipl. Ing. Florian Gauss
Steps
• Computation of Attractors• Deformation of Starting Mesh• Smoothing of Deformed Mesh• Planarization of Deformed Mesh• Repetitive Execution
II_PQ Mesh Attraction
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Structural Membranes 2015 19.10.2015 Barcelona / Spain Dipl. Ing. Florian Gauss
Computation of Attractors
Scale Modifier
Attracting vectors
fa
fa mod
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Structural Membranes 2015 19.10.2015 Barcelona / Spain Dipl. Ing. Florian Gauss
III_Case Study
Westfield Shopping Centre / London, UK © Seele
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Structural Membranes 2015 19.10.2015 Barcelona / Spain Dipl. Ing. Florian Gauss
LPC Graph
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Structural Membranes 2015 19.10.2015 Barcelona / Spain Dipl. Ing. Florian Gauss
Topology Mesh
Guide LPC
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Structural Membranes 2015 19.10.2015 Barcelona / Spain Dipl. Ing. Florian Gauss
Subdivided Mesh
Mesh on design surface
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Structural Membranes 2015 19.10.2015 Barcelona / Spain Dipl. Ing. Florian Gauss
Planar Relaxation
Non – planarity: 11.4% Non – planarity: 5%, iteration = 124
Non – planarity: 3%, iterations = 566 Non – planarity: 1%, iterations = 1556
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Structural Membranes 2015 19.10.2015 Barcelona / Spain Dipl. Ing. Florian Gauss
Deviation from Design Surface
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Structural Membranes 2015 19.10.2015 Barcelona / Spain Dipl. Ing. Florian Gauss
Planar Attraction
Attracting Vectors
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Structural Membranes 2015 19.10.2015 Barcelona / Spain Dipl. Ing. Florian Gauss
Deformed Mesh
Scale modifier: 0.3 – planarity: 7,1%
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Structural Membranes 2015 19.10.2015 Barcelona / Spain Dipl. Ing. Florian Gauss
Attraction Cycles
Loop 5 Non-Planar : 1%
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Structural Membranes 2015 19.10.2015 Barcelona / Spain Dipl. Ing. Florian Gauss
Attraction Cycles
Loop 10 Non-Planar : 1%
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Structural Membranes 2015 19.10.2015 Barcelona / Spain Dipl. Ing. Florian Gauss
Attraction Cycles
Loop 15 Non-Planar : 1%
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Structural Membranes 2015 19.10.2015 Barcelona / Spain Dipl. Ing. Florian Gauss
Attraction Cycles
Loop 20 Non-Planar : 1%
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Structural Membranes 2015 19.10.2015 Barcelona / Spain Dipl. Ing. Florian Gauss
Attraction Cycles
Loop 25 Non-Planar : 1%
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Structural Membranes 2015 19.10.2015 Barcelona / Spain Dipl. Ing. Florian Gauss
Attraction Cycles
Loop 30 Non-Planar : 1%
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Structural Membranes 2015 19.10.2015 Barcelona / Spain Dipl. Ing. Florian Gauss
Mesh Distortions
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Structural Membranes 2015 19.10.2015 Barcelona / Spain Dipl. Ing. Florian Gauss
Thank you very much for your attention!