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

Structural Membranes 2015 19.10.2015 Barcelona / Spain Dipl. Ing. Florian Gauss

Content I_PQ Mesh ApproximationII_PQ Mesh AttractionIII_Case Study

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

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)

Structural Membranes 2015 19.10.2015 Barcelona / Spain Dipl. Ing. Florian Gauss

Discrete Computation of Indvidual LPC

Structural Membranes 2015 19.10.2015 Barcelona / Spain Dipl. Ing. Florian Gauss

Discrete Computation of LPC

Structural Membranes 2015 19.10.2015 Barcelona / Spain Dipl. Ing. Florian Gauss

Discrete Computation of LPC

Structural Membranes 2015 19.10.2015 Barcelona / Spain Dipl. Ing. Florian Gauss

Discrete Computation of LPC

Structural Membranes 2015 19.10.2015 Barcelona / Spain Dipl. Ing. Florian Gauss

Discrete Computation of LPC

Structural Membranes 2015 19.10.2015 Barcelona / Spain Dipl. Ing. Florian Gauss

Discrete Computation of LPC

Structural Membranes 2015 19.10.2015 Barcelona / Spain Dipl. Ing. Florian Gauss

Discrete Computation of LPC

Structural Membranes 2015 19.10.2015 Barcelona / Spain Dipl. Ing. Florian Gauss

Discrete Computation of LPC

Structural Membranes 2015 19.10.2015 Barcelona / Spain Dipl. Ing. Florian Gauss

Umbilic Point

LPC Map

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

Structural Membranes 2015 19.10.2015 Barcelona / Spain Dipl. Ing. Florian Gauss

Starting Candidates

Final Canidates

Quad Tree Quadrants

Refinement

Umbilic Point Extraction

Structural Membranes 2015 19.10.2015 Barcelona / Spain Dipl. Ing. Florian Gauss

Umbilic Points – Principal Types

Star

Lemon Star

Mon Star

Structural Membranes 2015 19.10.2015 Barcelona / Spain Dipl. Ing. Florian Gauss

Crude Start Mesh

1 2

34

56

Structural Membranes 2015 19.10.2015 Barcelona / Spain Dipl. Ing. Florian Gauss

Subdivided Mesh (2 Steps)

Structural Membranes 2015 19.10.2015 Barcelona / Spain Dipl. Ing. Florian Gauss

Subdivided Mesh (3 Steps)

Structural Membranes 2015 19.10.2015 Barcelona / Spain Dipl. Ing. Florian Gauss

Integrated Vector Field

Dynamic Relaxation Equation

Planar Relax

Planar Pulling forces

fp

Structural Membranes 2015 19.10.2015 Barcelona / Spain Dipl. Ing. Florian Gauss

Before Optimization

Planar Relax Optimization

After Optimization (1644 cycles)

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

Structural Membranes 2015 19.10.2015 Barcelona / Spain Dipl. Ing. Florian Gauss

Computation of Attractors

Scale Modifier

Attracting vectors

fa

fa mod

Structural Membranes 2015 19.10.2015 Barcelona / Spain Dipl. Ing. Florian Gauss

III_Case Study

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Structural Membranes 2015 19.10.2015 Barcelona / Spain Dipl. Ing. Florian Gauss

LPC Graph

Structural Membranes 2015 19.10.2015 Barcelona / Spain Dipl. Ing. Florian Gauss

Topology Mesh

Guide LPC

Structural Membranes 2015 19.10.2015 Barcelona / Spain Dipl. Ing. Florian Gauss

Subdivided Mesh

Mesh on design surface

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

Structural Membranes 2015 19.10.2015 Barcelona / Spain Dipl. Ing. Florian Gauss

Deviation from Design Surface

Structural Membranes 2015 19.10.2015 Barcelona / Spain Dipl. Ing. Florian Gauss

Planar Attraction

Attracting Vectors

Structural Membranes 2015 19.10.2015 Barcelona / Spain Dipl. Ing. Florian Gauss

Deformed Mesh

Scale modifier: 0.3 – planarity: 7,1%

Structural Membranes 2015 19.10.2015 Barcelona / Spain Dipl. Ing. Florian Gauss

Attraction Cycles

Loop 5 Non-Planar : 1%

Structural Membranes 2015 19.10.2015 Barcelona / Spain Dipl. Ing. Florian Gauss

Attraction Cycles

Loop 10 Non-Planar : 1%

Structural Membranes 2015 19.10.2015 Barcelona / Spain Dipl. Ing. Florian Gauss

Attraction Cycles

Loop 15 Non-Planar : 1%

Structural Membranes 2015 19.10.2015 Barcelona / Spain Dipl. Ing. Florian Gauss

Attraction Cycles

Loop 20 Non-Planar : 1%

Structural Membranes 2015 19.10.2015 Barcelona / Spain Dipl. Ing. Florian Gauss

Attraction Cycles

Loop 25 Non-Planar : 1%

Structural Membranes 2015 19.10.2015 Barcelona / Spain Dipl. Ing. Florian Gauss

Attraction Cycles

Loop 30 Non-Planar : 1%

Structural Membranes 2015 19.10.2015 Barcelona / Spain Dipl. Ing. Florian Gauss

Mesh Distortions

Structural Membranes 2015 19.10.2015 Barcelona / Spain Dipl. Ing. Florian Gauss

Thank you very much for your attention!