filling arbitrary holes in finite element models 17 th international meshing roundtable 2008...
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![Page 1: Filling Arbitrary Holes in Finite Element Models 17 th International Meshing Roundtable 2008 Schilling, Bidmon, Sommer, and Ertl](https://reader035.vdocuments.us/reader035/viewer/2022062714/56649d485503460f94a246f2/html5/thumbnails/1.jpg)
Filling Arbitrary Holes in Finite Element Models
17th International Meshing Roundtable
2008Schilling, Bidmon, Sommer, and
Ertl
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Motivation
Source: Schilling et al.
• Computer-Aided Engineering (CAE)– Preprocessing for Finite Element
analysis• e.g. computational fluid dynamics
simulation for acoustics• thousands of holes
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Related Work• Volumetric Approaches
– Split region around a hole into inner and outer parts• Boundary layer defines missing surface
– [Davis et al.]: Signed distance function is “extended through the volume” until it spans all holes
• Resulting quality not sufficient for CAE– [Podolak et al.] Spatial decomposition for complex holes
• Hard to treat many independent meshes• Geometry-Based Techniques (more promising)
– [Wang et al.]: Moving least squares (MLS) to reconstruct locally smooth surface
• MLS: Evaluate vertices’ neighborhood using weighted least squares • Unsuitable for CAE general hole shapes
– [Tekumalla et al.]*: Advancing front method to close holes incrementally
– [Liepa et al.]*: Dynamic programming to create minimal surfaces– Holes need not be planar
– * basis of this new work
Source: Schilling et al.
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Types of Holes
Source: Schilling et al.
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Hole Patching Requirements
• Preserve existing geometric features.
• Provide acceptable results even when neighborhood information is absent.
• Interactive influence on shape of patching mesh.
Source: Schilling et al.
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Setting up Semantic Holes across Multiple Meshes
• Balance user effort and computation speed for complex semantic holes.
• vs, vt are selected by user (could be from different meshes)
• Use a bounding volume hierarchy to calculate distances and find connecting node pairs.
• Connection criteria (see Figure 3):1) Minimize . 2) Minimize ||dj|| 3) Minimize
Source: Schilling et al.vj1
j
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Setting up Semantic Holes across Multiple Meshes (continued)
Source: Schilling et al.
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Patching Holes: Advancing Front
• Adapted from [Tekumalla et al.]*• Edge (by default) is part of advancing front.
Source: Schilling et al.
makeConvex addVertices
bisector of edge
uses MLS
*DP approach from [Liepa et al.] is adapted to fill small, simple holes with minimal surfaces.
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Patching Holes: Potential Advancing Front
Problems• Enclosed feature lines can be removed by
makeConvex.• MLS in addVertices can extend patching mesh
too far (see Figure 6.)
Source: Schilling et al.
[11]= Tekumalla et al. [12] = Wang et al.
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Patching Holes: Fixing Advancing Front
Problems• In makeConvex, test & avoid cutting feature lines
(Fig. 7a).
• Instead of MLS, place new node in plane of adjacent element. User-defined bending angle is enforced
later.
Source: Schilling et al.
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Patching Holes: User-Defined Bending
Source: Schilling et al.
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Patching Holes: Collinearity Issue
• Collinear neighboring nodes can prevent a node from moving, hindering optimization.
– Moving might increase distance to neighbors.
Source: Schilling et al.
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Patching Holes: Fronts Missing Each Other
• Fronts not oriented towards each other can miss each other as they grow.
Source: Schilling et al.
consider as a neighbor
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Patching Holes: Bending Enforced by User
• Sometimes only C0 continuity is desired.
• Initial maximum bend is allowed.
Source: Schilling et al.
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Patching Holes:Edge Lengths of New
Triangles• Two user-controllled edge length
options:
Source: Schilling et al.
leaves gap between meshes
(a) (b)
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Results• Hole detection, hole meshing and volume mesh generation
can be done now in hours rather than days.• Hole classification filters help reduce number of holes.
– Car model: 463 parts and 3359 initial holes, reduced to 248 holes. 201 holes closed automatically.
Source: Schilling et al.
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Results
Source: Schilling et al.
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Results
Source: Schilling et al.