20151017_attractive planar panelization using dynamic relaxation principles_00

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


Content I_PQ Mesh ApproximationII_PQ Mesh AttractionIII_Case Study


Steps

• Computation of Lines of Principle Curvature (LPC)

• Topology Mesh• Subdivision Mesh (Catmull Clarke)• Planar Relax

I_PQ Mesh Approximation


Principle Curvature Vector Field

Integrated Vector Field

Revolving Normal Planes

Max/Min Directions

Lines of Principle Curvature (LPC)


Discrete Computation of Indvidual LPC


Discrete Computation of LPC


Umbilic Point

LPC Map


Adaptive Quad Tree DecompositionUmbilic Point Condition

Umbilic Point Extraction

Umbilic Point Condition with tolerance


Starting Candidates

Final Canidates

Quad Tree Quadrants

Refinement

Umbilic Point Extraction


Umbilic Points – Principal Types

Star

Lemon Star

Mon Star


Crude Start Mesh

1 2

34

56


Subdivided Mesh (2 Steps)


Subdivided Mesh (3 Steps)


Integrated Vector Field

Dynamic Relaxation Equation

Planar Relax

Planar Pulling forces

fp


Before Optimization

Planar Relax Optimization

After Optimization (1644 cycles)


Steps

• Computation of Attractors• Deformation of Starting Mesh• Smoothing of Deformed Mesh• Planarization of Deformed Mesh• Repetitive Execution

II_PQ Mesh Attraction


Computation of Attractors

Scale Modifier

Attracting vectors

fa

fa mod


III_Case Study

Westfield Shopping Centre / London, UK © Seele


LPC Graph


Topology Mesh

Guide LPC


Subdivided Mesh

Mesh on design surface


Planar Relaxation

Non – planarity: 11.4% Non – planarity: 5%, iteration = 124

Non – planarity: 3%, iterations = 566 Non – planarity: 1%, iterations = 1556


Deviation from Design Surface


Planar Attraction

Attracting Vectors


Deformed Mesh

Scale modifier: 0.3 – planarity: 7,1%


Attraction Cycles

Loop 5 Non-Planar : 1%


Attraction Cycles



Mesh Distortions


Thank you very much for your attention!

20151017_attractive planar panelization using dynamic relaxation principles_00

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