IMS-NUS: CdB 17ims.nus.edu.sg/events/2017/wspline/files/jorg.pdf · (12 slides) fix the shape (and...
Transcript of IMS-NUS: CdB 17ims.nus.edu.sg/events/2017/wspline/files/jorg.pdf · (12 slides) fix the shape (and...
Design & Analysis on Manifolds with Irregular Layout
Jorg Peters
IMS-NUS: CdB 17
Support: NSF CCF-0728797 DARPA TRADES ← PhD (postdoc) opening
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---What I would be happy to discuss, but will not present---
SIAC = Smoothness increasing accuracy conservingDG = Discontinuous Galerkin filter → convolution 2
Position-dependent SIAC spline filters for DG
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---What I would be happy to discuss, but will not present---
Design & Analysis on Manifolds with Irregular Layout
Jorg Peters
IMS-NUS 17
Support: NSF CCF-0728797 DARPA TRADES
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---What I am happy to discuss, and will present---
Design (appearance)
5Straker, styling
Design and Analysis (properties)
6Thin shell elastics of deformation, simulation
Irregular patch layout -- Surface quality
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Farin
Zebra C1 Uniform, parallel → good
A Brief History and Overview of Surface Constructions with Irregular Layout (5 slides)
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Design
Evolution of rendering quality
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Pixel spline
Evolution of surface constructions
10Malcolm Sabin 68 no figures
Evolution of surface quality
Gregory/Zhou Loop et al 11
Irregular patch layoutOverview
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transfinite
Shape, CAD compatibility. degree,...?
Irregular patch layoutTrimmed NURBS
13Automobile styling Autogenerated trim
Analysis & Surface constructionsat irregularities (45 slides)
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Analysis & Surface constructions with Irregular layout
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https://www.cise.ufl.edu/research/SurfLab/pubs.shtml
General Theorem for IGA for Gk
Poisson’s Equation on the disk and other planar domains
New: G1 construction
Analysis & Surface constructions with Irregular layout [NKP13]
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https://www.cise.ufl.edu/research/SurfLab/pubs.shtml
Thin plate
Analysis & Surface constructions with Irregular layout
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Computing with Irregular layout
DDG, triangular macro elements (Powell-Sabin) 18
Computing with Irregular layout
Cirak et al 02, Stam 03, Grinspun&Schroeder 0x, Barendrecht 15, de Goes et al,...Loop subdiv: 19
Catmull-Clark subdivision [CC 78]
20Convex -- saddle `no good’
Analysis & Surface constructions➢ Guided Subdivision (12 slides)
fix the shape (and smoothness) problem
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Guided subdivision [KP07]
Separate shape-finding from mathematical constraints of final output surface
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Guided subdivision [KP07]
Separate shape-finding from mathematical constraints of final output surface
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Tensor border
n=5
Guided subdivision [KP07]
Separate shape-finding from mathematical constraints of final output surface
Guide surface → shape ➢ not exactly fit surrounding surface➢ not nec. smooth everywhere
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Tensor border
n=5
Guided subdivision [KP07]
Separate shape-finding from mathematical constraints of final output surface
Guide surface → shape not exactly fit surrounding surface not nec. smooth
Subdivision rings → flexibility smoothly connect to surface, absorb extra degrees of freedom by closely approximating the guide shape
25Not: gambling with functionals! (similar to surface reconstruction)
Guided subdivision [KP17]
Separate shape finding from mathematical constraints of final output surface
Guide surface Subdivision rings
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Guided subdivision -- what is under the hood
Separate shape finding from mathematical constraints of final output surface
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Corner jet constructor
Guided subdivision -- what is under the hood
Separate shape finding from mathematical constraints of final output surface
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Guided subdivision -- what is under the hood
Separate shape finding from mathematical constraints of final output surface
29Scalable ring
domain subdiv rings
Guided subdivision -- what is under the hood
Separate shape finding from mathematical constraints of final output surface
30scalable
smart sampling !
Range subdiv ring
Smartsampling
Guided subdivision -- Smoothness
Separate shape finding from mathematical constraints of final output surface
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C2 subdivision for irregular layout !!!
Guided subdivision -- implementation via generating functions
Separate shape finding from mathematical constraints of final output surface
n Patches 6 neighbors
Coefficients = control points =nodes of input net
tabulate
tabulate
tabulate
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Stencils
Guided subdivision -- finite caps
Separate shape finding from mathematical constraints of final output surface
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Guided subdivision -- Shape ← obstacle course
Separate shape finding from mathematical constraints of final output surface
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Separate shape finding from mathematical constraints of final output surface
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Guided subdivision -- Shape ← obstacle course
Guided subdivision -- Eigenfunctions (contraction by ½)
Separate shape finding from mathematical constraints of final output surface
36Boundary set to zero
Guided subdivision -- d.o.f. for analysis
Separate shape finding from mathematical constraints of final output surface
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Analysis & Surface constructions➢ Guided Subdivision ➢ Polar constructions (3 slides)
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Computing with Irregular layout
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Polar surface constructions
Surfaces with Polar Structure Karciauskas Peters Dagstuhl 2005
A C² Polar Jet Subdivision Karciauskas, Peters, Eurographics/SGP 2006
Bicubic Polar Subdivision Karciauskas,Peters ACM Transactions on Graphics 2007
Extending Catmull-Clark Subdivision and PCCM with Polar Structures Myles Karciauskas Peters
Pacific Graphics 2007 40
Polar surface constructions
Pairs of Bi-Cubic Surface Constructions Supporting Polar Connectivity Feb. 2008
An introduction to guided and polar surfacing June 2008
Bi-3 C2 Polar Subdivision SIGGRAPH 2009
Finite curvature continuous polar patchworks Karciauskas Peters IMA Surfaces, 2009
C2 Splines Covering Polar Configurations Myles Peters Computer Aided Design , 2011
Multi-degree smooth polar splines: A framework for geometric modeling and isogeometric analysis Toshniwal Speleers Hughes CMAME 2017 41
Analysis & Surface constructions➢ Guided Subdivision ➢ Polar constructions➢ G-splines (4 slides)
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Computing with Irregular layout
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← as many as spline families
G-splines
General Theorem for geometrically continuous constructions
➢ in any number of variables, ➢ for any smoothness, ➢ any manifold (including, of course, planar ones),...
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https://www.cise.ufl.edu/research/SurfLab/pubs.shtml
gIGA for irregularities on manifolds
Finite Element Obstacle course: meshing-less analysis
use spline for geometry & displacement function → g(eneralized) IGA
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gIGA: Layered trivariate manifolds
https://www.cise.ufl.edu/research/SurfLab/pubs.shtml
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https://www.cise.ufl.edu/research/SurfLab/pubs.shtml
https://www.cise.ufl.edu/research/SurfLab/pubs.shtml
gIGA: basis functions
https://www.cise.ufl.edu/research/SurfLab/pubs.shtml
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https://www.cise.ufl.edu/research/SurfLab/pubs.shtml
Analysis & Surface constructions➢ Guided Subdivision ➢ Polar constructions➢ G-splines➢ Corner Collapsed Control Nets (10 slides)
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https://www.cise.ufl.edu/research/SurfLab/pubs.shtml
C1 singular
Computing with Irregular layout: singular parameterization
Refinable $C^1$ spline elements for irregular quad layout Thien Nguyen and Jörg Peters CAGD, 2016
C1 singular
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Refinable C1 spline elements for irregular quad layout Thien Nguyen and Jörg Peters CAGD, 2016
Linearly independent
2⨉2=4 degrees of freedom
per quadrilateral
Computing with Irregular layoutComputing with Irregular layout: singular parameterization
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T-junctions (trivial) B-spline-level mesh
Refinable C1 spline elements for irregular quad layout Thien Nguyen and Jörg Peters CAGD, 2016
➢ Linearly independent➢ 2x2 dof/quad ➢ C^1 proof: Reif 95 ! ➢ poor shape➢ robust
Computing with Irregular layout: singular parameterization
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B-spline-like
Bezier, collapsed
Distribution Statement 53
heat dissipation on thin shell 14K bi-3 pieces, 27.5K spline-dof, 100 time steps =3.6 secs on NVidia 1080 GPU
Spline manifold
Quad mesh
Design and Analysis
Refinable C1 spline elements for irregular quad layout Thien Nguyen and Jörg Peters CAGD, 2016
Computing with Irregular layout: singular parameterization
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➢ Linearly independent➢ 2x2 dof/quad ➢ C1
➢ poor shape ➢ robust➢ refinable ➢ Naturally integrates
with THP splines B-spline-like
Bezier
B-spline-like
Improved shape: SPM 2017
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Refinable C1 spline elements for irregular quad layout Thien Nguyen and Jörg Peters CAGD, 2016
Computing with Irregular layoutComputing with Irregular layout: singular parameterization
Parametrizing singularly to enclose vertices by a smooth parametric surface 91
Degenerate polynomial patches of degree 4 and 5 Neamtu,Pfluger 93
A note on degenerate triangular Bézier patches, Reif 95
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Refinable C1 spline elements for irregular quad layout Thien Nguyen and Jörg Peters CAGD, 2016
➢ Generalizes to m dimensions (m variables)➢ Challenge (recently solved): multi-dimensional irregularities ➢ Projection & proof of C1
Computing with Irregular layoutComputing with Irregular layout: singular parameterization
57Irregular edges, vertices,...
Analysis & Surface constructions on manifolds with irregularities
➢ Guided Subdivision ➢ Polar constructions➢ G-splines➢ Collapsed Control Nets
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C1 singular
THANK YOU
Support: NSF CCF-0728797 DARPA TRADES
Design & Analysis on Manifolds with Irregular Layout
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