Surface Modeling with Oriented Particle System

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Surface Modeling with Oriented Particle System

• Szeliski and Tonnesen
• Siggraph 1992

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Overview

• Use particle systems to simulate deformable
  surface models
• Set up potential functions for internal forces
• The dynamics controlled by external forces,
  internal forces, gravity, and damping

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Surface Modeling
Freeform Surface Modeling
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Particle System
Oriented Particle System
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Oriented Particles
Pi particle (global) position Ri particles
orientation 3rd column of Ri is the local normal
vector
Behavior of (oriented) particles is governed by
external forces and desired potential functions.
Equilibrium states rest at lowest energy state.
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Intermolecular Potential Function
Dynamics long-range attraction force and
short-range repulsion force
pj
rij ,fij
pi
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Expect Particles to be Part of a Flat Surface
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Particle Dynamics

• Potential functions specify the internal forces
• Particle systems are under additional external
  forces and damping forces

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Computation of Internal Forces
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Misc.

• Numerical time integration
• Euler method, Runge-Kutta, semi-implicit methods,
  
• Controlling Complexity
• Kd tree to subdivide the tree to efficiently find
  the neighbors within some radius

• Rendering
• Axes, discs, triangulation (wireframe or shaded)

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Modeling Operations
Weld two surfaces together
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Cutting a surfaces into two
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Putting a crease into the surface
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Particle Creation and 3D Interpolation
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3D Interpolation
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