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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; 3 rd 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 pipi pjpj r ij, f ij

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Expect Particles to be Part of a Flat Surface …

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Weighting Function (r) The weighting function (r)is a monotone decreasing function used to limit the range of inter-particle interactions. Convert to local coordinate

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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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Homework Oriented Particle: 2D version

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Summary State of each particle: Design potential as in page 7 Weighting function

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Operation Anchored at two end points; fix one of the normal ( ) Insert middle points Deform the curve by moving one middle points Etc.

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