1 Meshing: A (Biased) Crash Course Meshing: A (Biased) Crash Course Mathieu Desbrun Discrete Differential Geometry: An Applied Introduction ACM SIGGRAPH 2005 Course Discrete Differential Geometry: An Applied Introduction ACM SIGGRAPH 2005 Course 2 The Big Picture Meshing, an essential preprocessing step For surface representation complex geometry with a few basic geometric primitives For simulation of physical phenomena realistic/accurate animation of fluid, deformable solids, electromagnetism − often modeled as PDE domain discretization − Then FEM/FVM to integrate PDE in space (& time) Discrete Differential Geometry: An Applied Introduction ACM SIGGRAPH 2005 Course 3 The Big Picture Meshing, an essential preprocessing step For surface representation complex geometry with a few basic geometric primitives For simulation of physical phenomena realistic/accurate animation of fluid, deformable solids, electromagnetism − often modeled as PDE domain discretization − Then FEM/FVM to integrate PDE in space (& time) Discrete Differential Geometry: An Applied Introduction ACM SIGGRAPH 2005 Course 4 The Big Picture Meshing, an essential preprocessing step For surface representation complex geometry with a few basic geometric primitives For simulation of physical phenomena realistic/accurate animation of fluid, deformable solids, electromagnetism − often modeled as PDE domain discretization − Then FEM/FVM to integrate PDE in space (& time) Discrete Differential Geometry: An Applied Introduction ACM SIGGRAPH 2005 Course 5 The Big Picture Meshing, an essential preprocessing step For surface representation complex geometry with a few basic geometric primitives For simulation of physical phenomena realistic/accurate animation of fluid, deformable solids, electromagnetism − often modeled as PDE domain discretization − Then FEM/FVM to integrate PDE in space (& time) Discrete Differential Geometry: An Applied Introduction ACM SIGGRAPH 2005 Course 6 What is Meshing? General Idea: breaking up a physical domain 2D domain in 2D, or in 3D, or 3D domain,… into simpler subdomains—the elements simplices (triangles, tetrahedra) or not (quads, polygons, hexahedra, polyhedra) “flat” 2D “flat” 3D
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1
Meshing: A (Biased) Crash Course
Meshing: A (Biased) Crash Course
Mathieu Desbrun
Discrete Differential Geometry: An Applied IntroductionACM SIGGRAPH 2005 Course
Discrete Differential Geometry: An Applied IntroductionACM SIGGRAPH 2005 Course
2
The Big PictureMeshing, an essential preprocessing step
For surface representationcomplex geometrywith a few basic geometric primitives
For simulation of physical phenomenarealistic/accurate animation of fluid, deformable solids, electromagnetism− often modeled as PDE
domain discretization− Then FEM/FVM to integrate PDE in space (& time)
Discrete Differential Geometry: An Applied IntroductionACM SIGGRAPH 2005 Course
3
The Big PictureMeshing, an essential preprocessing step
For surface representationcomplex geometrywith a few basic geometric primitives
For simulation of physical phenomenarealistic/accurate animation of fluid, deformable solids, electromagnetism− often modeled as PDE
domain discretization− Then FEM/FVM to integrate PDE in space (& time)
Discrete Differential Geometry: An Applied IntroductionACM SIGGRAPH 2005 Course
4
The Big PictureMeshing, an essential preprocessing step
For surface representationcomplex geometrywith a few basic geometric primitives
For simulation of physical phenomenarealistic/accurate animation of fluid, deformable solids, electromagnetism− often modeled as PDE
domain discretization− Then FEM/FVM to integrate PDE in space (& time)
Discrete Differential Geometry: An Applied IntroductionACM SIGGRAPH 2005 Course
5
The Big PictureMeshing, an essential preprocessing step
For surface representationcomplex geometrywith a few basic geometric primitives
For simulation of physical phenomenarealistic/accurate animation of fluid, deformable solids, electromagnetism− often modeled as PDE
domain discretization− Then FEM/FVM to integrate PDE in space (& time)
Discrete Differential Geometry: An Applied IntroductionACM SIGGRAPH 2005 Course
6
What is Meshing?General Idea:
breaking up a physical domain2D domain in 2D, or in 3D, or 3D domain,…
into simpler subdomains—the elementssimplices (triangles, tetrahedra)or not (quads, polygons, hexahedra, polyhedra)
“flat” 2D “flat” 3D
2
Discrete Differential Geometry: An Applied IntroductionACM SIGGRAPH 2005 Course