Visualization Tools for Adaptive Mesh Refinement Data

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Visualization Tools for Adaptive Mesh Refinement Data. Gunther H. Weber 1 , Vincent E. Beckner 1 , Hank Childs 2 , Terry J. Ligocki 1 , Mark C. Miller 2 , Brian Van Straalen 1 and E. Wes Bethel 1 1 Lawrence Berkeley National Laboratory 2 Lawrence Livermore National Laboratory. Outline. - PowerPoint PPT Presentation

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<ul><li><p>Visualization Tools for Adaptive Mesh Refinement DataGunther H. Weber1, Vincent E. Beckner1, Hank Childs2, Terry J. Ligocki1, Mark C. Miller2, Brian Van Straalen1 and E. Wes Bethel11Lawrence Berkeley National Laboratory 2Lawrence Livermore National Laboratory</p><p>Current State of the Art in Adaptive Mesh Refinement Visualization</p></li><li><p>OutlineIntroduction to Berger-Colella AMR</p><p>Visualization of Scalar AMR Data</p><p>Specialized AMR Visualization Tools</p><p>Visualization Tools with AMR Support</p><p>Short overview of VisIt</p><p>Current State of the Art in Adaptive Mesh Refinement Visualization</p></li><li><p>Adaptive Mesh RefinementComputational fluid dynamics techniqueTopological simplicity of regular gridsAdaptivity of unstructured meshesNested rectilinear patches, increasing resolutionReduce simulation timeReduce storage spaceBerger-Colella AMR: axis-aligned patchesVery often: Cell centered data</p><p>Current State of the Art in Adaptive Mesh Refinement Visualization</p></li><li><p>Berger-Colella AMR Format</p><p>Current State of the Art in Adaptive Mesh Refinement Visualization</p></li><li><p>Effective Visualization of Scalar AMR Data</p><p>Hierarchical AMR simulationIsosurfacesDirect Volume RenderingAim: Use inherently hierarchical structure for efficient visualizationVisualizationVisualizationExtraction of continuous crack-free isosurfaces </p><p>Effective utilization of the hierarchy for efficient renderingGood interpolation functions</p><p>Current State of the Art in Adaptive Mesh Refinement Visualization</p></li><li><p>AMR Visualization In the Beginning</p><p>Translation of AMR to unstructured meshes [Norman et al. 1999]Visualization with standard tool (VTK, IDL, AVS)Ineffective utilization of computational resourcesDirect Volume RenderingMention AMR data without further details [Max 1993]PARAMESH [Ma 1999]ResamplingBlock-based</p><p>Current State of the Art in Adaptive Mesh Refinement Visualization</p></li><li><p>Isosurfaces</p><p>Current State of the Art in Adaptive Mesh Refinement Visualization</p></li><li><p>Marching Cubes and Dangling NodesMarching cubes needs vertex centered dataResample data set to vertex centered caseDangling nodes := only present in fine level (yellow + red)Choice of consistent values to avoid problems?</p><p>Compare [Westermann, Kobbelt, Ertl 1999]Linear interpolationavoids problemsSame in coarseand fine gridNo unique valueavoids problems</p><p>Current State of the Art in Adaptive Mesh Refinement Visualization</p></li><li><p>Previous Crack-fixing SolutionsMostly in context of Octree-based hierarchies[Shu et al., 1995]: Create polygon to fit crack[Shekhar et al., 1996]: Collapse polyline to line[Westermann et al., 1999]: Create triangle fan</p><p>[Shekar et al., 1996][Westermann et al., 1999]</p><p>Current State of the Art in Adaptive Mesh Refinement Visualization</p></li><li><p>First Approach: Use of Dual GridsAvoid interpolation whenever possible!</p><p>Avoid interpolation apart from linear interpolation along edges, which is part of marching cubes</p><p>Use dual grid := grid formed by connecting cell centers</p><p>Current State of the Art in Adaptive Mesh Refinement Visualization</p></li><li><p>Dual Grid Original Grid</p><p>Current State of the Art in Adaptive Mesh Refinement Visualization</p></li><li><p>Dual Grids Both Grids</p><p>Current State of the Art in Adaptive Mesh Refinement Visualization</p></li><li><p>Dual Grids</p><p>Current State of the Art in Adaptive Mesh Refinement Visualization</p></li><li><p>Advantages of Dual Grid Approach</p><p>Use of values original data for marching cubes</p><p>No dangling nodes</p><p>Instead: Gaps between hierarchy levels!</p><p>Fill those gaps with stitch cells</p><p>Current State of the Art in Adaptive Mesh Refinement Visualization</p></li><li><p>Stitching the GapsTessellation scheme for filling the gap between two hierarchy levelsConstraintsOnly gap region is tessellatedThe complete gap region is tessellatedOnly vertices, edges and complete faces are shared</p><p>In 3D space: Cannot use tetrahedra because cells must share quadrilaterals as faces</p><p>Current State of the Art in Adaptive Mesh Refinement Visualization</p></li><li><p>Stitching Process</p><p>Current State of the Art in Adaptive Mesh Refinement Visualization</p></li><li><p>Stitch Cells 3D CaseCell FacesCell EdgesCell Vertices</p><p>Current State of the Art in Adaptive Mesh Refinement Visualization</p></li><li><p>First ResultsCoarse PatchStitch CellsFine PatchAMR simulation of star cluster formation Root level 32x32x32</p><p>[Data set: Greg Bryan, Theoretical Astronomy Group, MIT]</p><p>Current State of the Art in Adaptive Mesh Refinement Visualization</p></li><li><p>Multiple PatchesMultiple patches can be connected using the same scheme</p><p>However: Special care must be taken with adjacent fine patches.</p><p>Must merge adjacent grids (i. e., upgrade edges to quadrilaterals and vertices to edges)</p><p>Current State of the Art in Adaptive Mesh Refinement Visualization</p></li><li><p>Multiple Patches Example</p><p>Current State of the Art in Adaptive Mesh Refinement Visualization</p></li><li><p>Multiple Patches Example</p><p>Current State of the Art in Adaptive Mesh Refinement Visualization</p></li><li><p>Multiple Patches Example</p><p>Current State of the Art in Adaptive Mesh Refinement Visualization</p></li><li><p>Multiple Patches Cell FacesPyramid (2 basis configurations):Unrefined coarse grid point No changeRefined coarse grid point Becomes cuboid</p><p>Triangle prism (3 basis configurations):All coarse grid points unrefined No changeOne refined coarse grid pointBoth coarse grid points refined Becomes cuboid</p><p>Current State of the Art in Adaptive Mesh Refinement Visualization</p></li><li><p>Multiple Patches Fine Edge to Coarse EdgesAll coarse grid points unrefinedTwo neighboring coarse grid points refinedTwo diagonally opposed coarse grid points refinedAll coarse grid points refined</p><p>Current State of the Art in Adaptive Mesh Refinement Visualization</p></li><li><p>Multiple Patches (3D) Remaining CasesAll remaining cases consider 8 verticesQuadrilateral Cell</p><p>Actual vertex positions irrelevant!</p><p>Information per vertex: refined or unrefined?</p><p>Current State of the Art in Adaptive Mesh Refinement Visualization</p></li><li><p>Multiple Patches (3D) Generating TessellationsDraw cell to tessellate as a cubeMark each vertex as refined or unrefinedUse canonical subdivisions for boundary faces</p><p>Use implied tessellation for cellIf more than one tessellation is possible, use arbitrary oneCoarse patchFine patch</p><p>Current State of the Art in Adaptive Mesh Refinement Visualization</p></li><li><p>Multiple Patches Example Tessellation</p><p>Current State of the Art in Adaptive Mesh Refinement Visualization</p></li><li><p>Multiple Patches Example Tessellation</p><p>Current State of the Art in Adaptive Mesh Refinement Visualization</p></li><li><p>Reducing Amount of CasesQuadrilateral to quadrilateral (16 cases)No reduction necessaryEdge to quadrilaterals (64 cases)Upgrade to quadrilateral case (-24 cases)In certain cases: Can consider two independent triangular prisms (- 14 cases)26 cases (- further symmetry considerations)Vertex to QuadrilateralsEither upgrade to edge case or consider three pyramids independently</p><p>Current State of the Art in Adaptive Mesh Refinement Visualization</p></li><li><p>Problem Case</p><p>Current State of the Art in Adaptive Mesh Refinement Visualization</p></li><li><p>Problem Case</p><p>Current State of the Art in Adaptive Mesh Refinement Visualization</p></li><li><p>Isosurface - One LevelAMR simulation of star cluster formation Root level 32x32x32</p><p>[Data set: Greg Bryan, Theoretical Astronomy Group, MIT]</p><p>Current State of the Art in Adaptive Mesh Refinement Visualization</p></li><li><p>Isosurface - Two LevelsAMR simulation of star cluster formation First levelStitch cells (1/2)Second level</p><p>Current State of the Art in Adaptive Mesh Refinement Visualization</p></li><li><p>Isosurface - Three LevelsAMR simulation of star cluster formation</p><p>First levelStitch cells (1/2)Second levelStitch cells (2/3)Third level</p><p>Current State of the Art in Adaptive Mesh Refinement Visualization</p></li><li><p>Second Approach: Keep GridVertex/node centered dataRetain identity of cells (debugging)Subdivide boundary cells into pyramidsEliminates non-linear hanging nodesStandard isosurface techniques for pyramids</p><p>Current State of the Art in Adaptive Mesh Refinement Visualization</p></li><li><p>2D CaseForms basis of 3D caseSplit cell faces to eliminate hanging nodes along edgesObtain values at newly created hanging by linear interpolation</p><p>Current State of the Art in Adaptive Mesh Refinement Visualization</p></li><li><p>2D ResultsExtracted contourCells due to added samples</p><p>Current State of the Art in Adaptive Mesh Refinement Visualization</p></li><li><p>3D Cell Face SubdivisionSubdivide lower-resolution cell face to match higher resolution faceSubdivide cell face to eliminate hanging nodes</p><p>Current State of the Art in Adaptive Mesh Refinement Visualization</p></li><li><p>3D Cell SubdivisionSubdivide cell into pyramids with common apex point</p><p>Current State of the Art in Adaptive Mesh Refinement Visualization</p></li><li><p>Second Approach Results</p><p>Cells: 44,332Triangles: 10,456Cells: 74,358Triangles: 14,332 Time: 2.30 sec</p><p>Current State of the Art in Adaptive Mesh Refinement Visualization</p></li><li><p>Second Approach Results</p><p>Cells: 303,759Triangles: 77,029Cells: 680,045Triangles: 78,127 Time: 7.73 sec</p><p>Current State of the Art in Adaptive Mesh Refinement Visualization</p></li><li><p>Volume Rendering</p><p>Current State of the Art in Adaptive Mesh Refinement Visualization</p></li><li><p>Hardware-accelerated Preview of AMR DataInteractive DVR for choosing view point and transfer function</p><p>Subdivide data set in regions of constant resolution</p><p>AMR Partition Tree (generalized kD-tree)</p><p>Traverse AMR Partition tree and render regions using hardware-accelerated DVR</p><p>Current State of the Art in Adaptive Mesh Refinement Visualization</p></li><li><p>Homogenization</p><p>Current State of the Art in Adaptive Mesh Refinement Visualization</p></li><li><p>Homogenization</p><p>Current State of the Art in Adaptive Mesh Refinement Visualization</p></li><li><p>Homogenization</p><p>Current State of the Art in Adaptive Mesh Refinement Visualization</p></li><li><p>Homogenization</p><p>Current State of the Art in Adaptive Mesh Refinement Visualization</p></li><li><p>AMR Partition TreeGeneralized kD-treePartitions data-set into regions of constant resolutionNode types:Unrefined grid part (CU): Region is only available at resolution of current levelCompletely refined grid part (CR): Region is completely available at next higher resolutionPartition node (PN): Partitions bounding box along one of the axes</p><p>Current State of the Art in Adaptive Mesh Refinement Visualization</p></li><li><p>Partition Tree ExamplePNCUPNCUCUCRCUCUCRCRCUPNCUPNPN = Partition node along one axisCU = Completely unrefined regionCR = Completely refined region = Transition to next level</p><p>Current State of the Art in Adaptive Mesh Refinement Visualization</p></li><li><p>Adaptive Tree TraversalView-dependent criteria:Avoid unnecessary computation timeNo quality loss</p><p>Time-dependent criteria:Sacrifice render quality to obtain specified frame rate</p><p>Current State of the Art in Adaptive Mesh Refinement Visualization</p></li><li><p>Hardware-accelerated Rendering InteractiveAMR simulation of star cluster formation Root level 32x32x32</p><p>[Data set: Greg Bryan, Theoretical Astronomy Group, MIT]</p><p>Current State of the Art in Adaptive Mesh Refinement Visualization</p></li><li><p>Hardware-accelerated Rendering Maximum QualityAMR simulation of star cluster formation Root level 32x32x32</p><p>[Data set: Greg Bryan, Theoretical Astronomy Group, MIT]</p><p>Current State of the Art in Adaptive Mesh Refinement Visualization</p></li><li><p>High-quality DVR of AMR DataUse cell projection [Ma &amp; Crockett 1997] to display individual patchesTraverse patches and construct ray segments [object space based]Ma &amp; Crockett: Sort ray segments</p><p>Current State of the Art in Adaptive Mesh Refinement Visualization</p></li><li><p>Progressive DVR of AMR DataBottom-upRender fine grids, fill gaps with coarse grid dataTop-downRender coarse grids (preview), replace data with finer representation</p><p>Current State of the Art in Adaptive Mesh Refinement Visualization</p></li><li><p>InterpolationNearest neighbor (constant) interpolation debuggingPiecewise Linear Method (PLM) DiscontinuitiesDual grids (trilinear) and stitch cellsBilinearLinear</p><p>Current State of the Art in Adaptive Mesh Refinement Visualization</p></li><li><p>Cell-projection Scan Convert Front Facing BoundariesRay segment queues</p><p>Current State of the Art in Adaptive Mesh Refinement Visualization</p></li><li><p>Piecewise Linear Method One Hierarchy LevelAMR simulation of star cluster formation Root level 32x32x32</p><p>[Data set: Greg Bryan, Theoretical Astronomy Group, MIT]</p><p>Current State of the Art in Adaptive Mesh Refinement Visualization</p></li><li><p>Piecewise Linear Method Two Hierarchy LevelsAMR simulation of star cluster formation Root level 32x32x32</p><p>[Data set: Greg Bryan, Theoretical Astronomy Group, MIT]</p><p>Current State of the Art in Adaptive Mesh Refinement Visualization</p></li><li><p>Piecewise Linear Method Three Hierarchy LevelsAMR simulation of star cluster formation Root level 32x32x32</p><p>[Data set: Greg Bryan, Theoretical Astronomy Group, MIT]</p><p>Current State of the Art in Adaptive Mesh Refinement Visualization</p></li><li><p>Mapping to Standard Elements (1/3)Save standard element coordinates in cell verticesWorld coordinatesStandard element coordinates</p><p>Current State of the Art in Adaptive Mesh Refinement Visualization</p></li><li><p>Mapping to Standard Elements (2/3)Interpolate standard element coordinates during rasterizationWorld coordinatesStandard element coordinates</p><p>Current State of the Art in Adaptive Mesh Refinement Visualization</p></li><li><p>Mapping to Standard Elements(3/3)Use standard element coordinates for interpolation along ray segmentWorld coordinatesStandard element coordinates</p><p>Current State of the Art in Adaptive Mesh Refinement Visualization</p></li><li><p>Interpolation with Stitch Cells One Hierarchy LevelSimulation of an Argon bubble in a surrounding gas hit by a shockwave</p><p>[Data set: Center for Computational Sciences and Engineering (CCSE), Lawrence Berkeley National Laboratory]</p><p>Current State of the Art in Adaptive Mesh Refinement Visualization</p></li><li><p>Interpolation with Stitch Cells Two Hierarchy LevelsSimulation of an Argon bubble in a surrounding gas hit by a shockwave</p><p>[Data set: Center for Computational Sciences and Engineering (CCSE), Lawrence Berkeley National Laboratory]</p><p>Current State of the Art in Adaptive Mesh Refinement Visualization</p></li><li><p>Interpolation with Stitch Cells Three Hierarchy LevelsSimulation of an Argon bubble in a surrounding gas hit by a shockwave</p><p>[Data set: Center for Computational Sciences and Engineering (CCSE), Lawrence Berkeley National Laboratory]</p><p>Current State of the Art in Adaptive Mesh Refinement Visualization</p></li><li><p>Level-dependent Transfer FunctionsProblem case: A fine level is completely enclosed within a coarse levelThe coarse level can hide interesting regions of the fine levelCoarse level necessary to provide context (orientation aid) for fine levelCannot completely discard coarse levelScale opacity and/or color saturation of coarse level</p><p>Current State of the Art in Adaptive Mesh Refinement Visualization</p></li><li><p>No Transfer Function ScalingAMR simulation of star cluster formation Root level 32x32x32</p><p>[Data set: Greg Bryan, Theoretical Astronomy Group, MIT]</p><p>Current State of the Art in Adaptive Mesh Refinement Visualization</p></li><li><p>Opacity ScalingAMR simulation of star cluster formation Root level 32x32x32</p><p>[Data set: Greg Bryan, Theoretical Astronomy Group, MIT]</p><p>Current State of the Art in Adaptive Mesh Refinement Visualization</p></li><li><p>Opacity and Saturation ScalingAMR simulation of star cluster formation Root level 32x32x32</p><p>[Data set: Greg Bryan, Theoretical Astronomy Group, MIT]</p><p>Current State of the Art in Adaptive Mesh Refinement Visualization</p></li><li><p>Texture-based AMR Volume Rende...</p></li></ul>

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