Generation and Fracturing of Thick Shells

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Generation and Fracturing of Thick Shells

Denis Steinemann Computer Graphics Laboratory ETH
Zürich Switzerland
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Motivation

• Objects usually represented by surface meshes.
  For stable simulation of physics, need 3-d
  volumetric representation.
• Many objects in reality are hollow ? inefficient
  to simulate over whole volume. 2.5-d Shell
  (thick surface) sufficient.
•  
• Using 2.5-d representation, new fracture methods
  become possible ? want to develop such methods
  that work on shells.

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Overview

• Previous Work
• Goals
• Implementation
• Shell Generation
• Fracturing and Deformation
• Rigid Bodies
• Results
• Software Demo

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Previous Work

• Shell Generation
• Enveloping surfaces for mesh simplification
• Use only inner surface for shell

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Previous Work

• Shell Animation
• FE-Methods
• FEM becomes slow for stiff materials, needs 3-D
  volumes
• Geometric approach
• stretching bending, but no thickness. Slow

OBrien
Müller
Grinspun
Wicke/Steinemann
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Goals

• Shell Generation
• given a non-intersecting, non-manifold polygonal
  surface mesh, construct thick surface
• Requirements
• no (self-)intersections
• evenly distributed thickness
• Fracture
• simulate fracture and deformation of a shell
• real-time
• Should look physically realistic

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Shell Generation

• Idea build a shell in small steps
• extrude vertices along opposite vertex normals
• if we detect a collision, move extruded vertices
  back
• I have developed two algorithms
• Single-Vertex Propagation
• Front Propagation

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Single-Vertex Propagation

• Single-Vertex Propagation
• extrude one vertex at a time
• if a collision is detected, move vertex back and
  try again, with half the step size. Try until no
  collision between triangles is detected or step
  size is too small
• go on to next vertex vertex
• each vertex tries to make k moves without
  collision

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Single-Vertex Propagation

• Single-Vertex Propagation
• detects almost all intersections/overlaps
• maximizes and evenly distributes thickness
• slow because a lot of collision detection

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Front Propagation

• Front Propagation
• extrude all vertices at once (the whole shell
  front)
• if a collision between triangles is detected,
  move back all vertices part of a such a triangle
• divide step size by 2 for those vertices
• move whole front again, k times

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Front Propagation

• Front Propagation
• may not detect overlap
• ? sometimes smaller step size helps avoid this
• thickness may not be maximized or evenly
  distributed, because no retries after vertex
  moved back
• faster than single-vertex propagation, because
  less collision detection (no retries)

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Stepsize Initialization

• How do we set the step sizes?
• Easy step size for vertex i
• Better precompute step size for each vertex
• Can avoid many collisions ? increase speed of
  algorithm
• Create line segment along opposite vertex normal,
  length
• Maximum vertex depth di distance to closest
  intersection point divided by 2.

vi
vj
Step size
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Fracturing

• Mass-Spring-Models
• compute dynamics and deformation
• Note fracturing is independent of force
  computation ? possible to replace mass-spring by
  FEM
• fracture criteria is spring length if a spring
  is too long, split one of its two vertices
• One Layer of springs on original surface
• Fast
• Thickness info used for rendering
• Unstable ? Not suited for deformation and ductile
  fracture

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Fracturing

• Two layers of springs
• more stable ? can simulate ductile and brittle
  fracture
• Use surface and volume preservation forces in
  addition to springs
• can model thickness a thin shell is more easily
  fractured than a thick one
• Spring constants k proportional to thickness

Large k
small k
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Fracturing

• 3 different types of fracture
• Fine-grained produces small pieces
• No constraints whenever a spring is too long,
  split one of its vertices
• Coarse-Grained produces larger pieces
• Constraint Keep some vertices from being split

Red vertices and springs cannot be split any more
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Fracturing

• Large-Fragment Fracture fracture shell into few
  but large pieces
• Constraint Limit total number of splits
• Artificially extend cracks
• Due to tessellation of shell, cracks often look
  jagged
• Local re-meshing
• Comparison

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Rigid Bodies

• Treat split-off shell fragments as rigid bodies
• Approximate fragment with object-oriented
  bounding box to speed up simulation
• Use Principal Component Analysis to compute OBB
• If a fragment is large, it must still be
  breakable ? must be turned back to
  mass-spring-model again

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Results

• Shell Generation
• Computation time a few seconds for models with up
  to 10000 vertices/triangles
• Shell can be loaded from file, so this is not a
  problem
• Fracturing/Rigid Bodies
• See Software Demo

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Future Work

• Shell Generation
• Manifold meshes
• Intersecting meshes
• Rigid Bodies
• No collision response between rigid body
  fragments and mass-spring-model fragments yet
• Do not approximate fragments by bounding boxes
  for even more realistic behavior

?
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Software Demo

• Have Fun!