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Eurographics 2012, Cagliari, Italy GPU based ARAP Deformation using Volumetric Lattices M. Zollhöfer, E. Sert, G. Greiner and J. Süßmuth Computer Graphics Group, University Erlangen-Nuremberg, Germany

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Eurographics 2012, Cagliari, ItalyMotivation/Requirements Intuitive modeling –Handle-based –Direct manipulation 2

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Eurographics 2012, Cagliari, ItalyMotivation/Requirements Intuitive modeling –Handle-based –Direct manipulation Interactivity –Even for high quality models 3

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Eurographics 2012, Cagliari, ItalyMotivation/Requirements Intuitive modeling –Handle-based –Direct manipulation Interactivity –Even for high quality models Physical plausibility –Globally smooth deformations –Detail preservation 4

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Eurographics 2012, Cagliari, Italy Recent Work ARAP Surface Modeling 5 [SA07]

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Eurographics 2012, Cagliari, Italy Recent Work ARAP Surface Modeling Deformation Graphs 6 [SA07] [SSP07]

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Eurographics 2012, Cagliari, Italy Recent Work ARAP Surface Modeling Deformation Graphs Coupled Prisms/Rigid Cells 7 [SA07] [SSP07] [BPGK06, BPWG07]

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Eurographics 2012, Cagliari, Italy Recent Work ARAP Surface Modeling Deformation Graphs Coupled Prisms/Rigid Cells Hybrid Mesh Editing 8 [SA07] [SSP07] [BPGK06, BPWG07] [BHZN10 ]

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Eurographics 2012, Cagliari, ItalyFacts/Contribution Method –Based on the non-linear ARAP energy [SA07] –Volumetric proxy geometry –Multi-res GPU deformation pipeline 9

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Eurographics 2012, Cagliari, ItalyFacts/Contribution Method –Based on the non-linear ARAP energy [SA07] –Volumetric proxy geometry –Multi-res GPU deformation pipeline Benefits –The optimization is decoupled from the model’s geometric complexity –Volume-awareness –Fast even for high quality models –Easy to integrate into existing systems 10

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Eurographics 2012, Cagliari, ItalyOverview Preprocessing –Construct volumetric lattice Decouples the optimization from the model’s geometric complexity Transparent for the user 11

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Eurographics 2012, Cagliari, ItalyOverview Preprocessing –Construct volumetric lattice Decouples the optimization from the model’s geometric complexity Transparent for the user Runtime loop –Modify handle positions –Deform lattice using our multi-res GPU ARAP solver –Use lattice to deform the input model 12

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Eurographics 2012, Cagliari, Italy Proxy Geometry Starting point –Uniform voxel grid –Delete cubes which are entirely outside Volumetric Lattice 13

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Eurographics 2012, Cagliari, Italy Proxy Geometry Starting point –Uniform voxel grid –Delete cubes which are entirely outside Volumetric Lattice Express vertices in local coordinates –Interactive modeling Tri-linear interpolation –Offline high quality poses B-Splines 14

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Eurographics 2012, Cagliari, Italy Optimization Problem Paradigm –ARAP [SA07] on a volumetric lattice 15

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Eurographics 2012, Cagliari, Italy Optimization Problem Paradigm –ARAP [SA07] on a volumetric lattice Objective function –Plausibility of deformation Rigidity of local transformations 16

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Eurographics 2012, Cagliari, Italy Optimization Problem Paradigm –ARAP [SA07] on a volumetric lattice Objective function –Plausibility of deformation Rigidity of local transformations –Fulfillment of user constraints Distance of vertices to handles 17

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Eurographics 2012, Cagliari, Italy Optimization Problem Paradigm –ARAP [SA07] on a volumetric lattice Objective function –Plausibility of deformation Rigidity of local transformations –Fulfillment of user constraints Distance of vertices to handles Non-linear optimization 18

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Eurographics 2012, Cagliari, Italy Minimizing the Objective Function Why do we use the ARAP paradigm? –Non-linear rotation-aware objective function –Minimization does not require a general-purpose non-linear solver 19

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Eurographics 2012, Cagliari, Italy Minimizing the Objective Function Why do we use the ARAP paradigm? –Non-linear rotation-aware objective function –Minimization does not require a general-purpose non-linear solver Iterative flip-flop solver [SA07] –Compute optimal local rotations SVDs are independent –Compute new control points Iterative linear solver 20

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Eurographics 2012, Cagliari, Italy Minimizing the Objective Function Why do we use the ARAP paradigm? –Non-linear rotation-aware objective function –Minimization does not require a general-purpose non-linear solver Iterative flip-flop solver [SA07] –Compute optimal local rotations SVDs are independent –Compute new control points Iterative linear solver Massively parallel GPU implementation 21

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Eurographics 2012, Cagliari, Italy GPU Deformation Pipeline CUDA Implementation –SVD Kernel (per control point) 22

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Eurographics 2012, Cagliari, Italy GPU Deformation Pipeline CUDA Implementation –SVD Kernel (per control point) –Solve Kernel (per control point) Parallel Gauss-Seidel solver or gradient descent Use new positions ASAP 23

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Eurographics 2012, Cagliari, Italy GPU Deformation Pipeline CUDA Implementation –SVD Kernel (per control point) –Solve Kernel (per control point) Parallel Gauss-Seidel solver or gradient descent Use new positions ASAP Transfer Kernel (per vertex) 24

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Eurographics 2012, Cagliari, Italy GPU Deformation Pipeline CUDA Implementation –SVD Kernel (per control point) –Solve Kernel (per control point) Parallel Gauss-Seidel solver or gradient descent Use new positions ASAP Transfer Kernel (per vertex) Synchronize between kernel calls 25

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Eurographics 2012, Cagliari, Italy Multi-res GPU Deformation Pipeline New Proxy Geometry –Hierarchy of lattices Join 8 adjacent cubes Encode lattices w.r.t. the next coarser one 26 Level 0 Level 1 …

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Eurographics 2012, Cagliari, Italy Multi-res GPU Deformation Pipeline 27 Level 0 Level 1 …

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Eurographics 2012, Cagliari, ItalyResults/Properties Volume-awareness 28 ARAP Ours

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Eurographics 2012, Cagliari, ItalyResults/Properties Volume-awareness Smoothness 29 ARAP Ours Tri-linear B-Spline

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Eurographics 2012, Cagliari, ItalyFacts Evaluation –Core i7 860 CPU with an NVidia GeForce 580 GPU –71ms (14fps) to deform a 2M polygon model (40k lattice) 30 Triangle Mesh Polygon SoupMultiple Components Triangle Mesh Polygon Soup

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Eurographics 2012, Cagliari, ItalyFacts Evaluation –Core i7 860 CPU with an NVidia GeForce 580 GPU –71ms (14fps) to deform a 2M polygon model (40k lattice) –Multi-res solver gives a 3x speedup compared to the single level version Less iterations per hierarchy level required to converge 31 Triangle Mesh Polygon SoupMultiple Components Triangle Mesh Polygon Soup

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Eurographics 2012, Cagliari, ItalyConclusion Summary –Intuitive mesh editing paradigm using a simple volumetric lattice –Data-parallel multi-res GPU deformation pipeline 32

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Eurographics 2012, Cagliari, ItalyConclusion Summary –Intuitive mesh editing paradigm using a simple volumetric lattice –Data-parallel multi-res GPU deformation pipeline Future Work –Construct lattice hierarchy in a topology preserving way –Monitor deformation error to solve the optimization problem locally up to a given threshold 33

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Eurographics 2012, Cagliari, ItalyQuestions? 34 Thanks for your attention!

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