surface modeling with oriented particle system szeliski and tonnesen siggraph 1992

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Surface Modeling with Oriented Particle System Szeliski and Tonnesen Siggraph 1992

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Page 1: Surface Modeling with Oriented Particle System Szeliski and Tonnesen Siggraph 1992

Surface Modeling with Oriented Particle System

Szeliski and Tonnesen

Siggraph 1992

Page 2: Surface Modeling with Oriented Particle System Szeliski and Tonnesen Siggraph 1992

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

Page 3: Surface Modeling with Oriented Particle System Szeliski and Tonnesen Siggraph 1992

Surface Modeling

Freeform Surface Modeling

Page 4: Surface Modeling with Oriented Particle System Szeliski and Tonnesen Siggraph 1992

Particle System

Oriented Particle System

Page 5: Surface Modeling with Oriented Particle System Szeliski and Tonnesen Siggraph 1992

Oriented Particles

Pi: particle (global) positionRi: 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.

Page 6: Surface Modeling with Oriented Particle System Szeliski and Tonnesen Siggraph 1992

Intermolecular Potential FunctionDynamics: long-range attraction force and short-range repulsion force

pi

pj

rij ,fij

Page 7: Surface Modeling with Oriented Particle System Szeliski and Tonnesen Siggraph 1992

Expect Particles to be Part of a Flat Surface …

Page 8: Surface Modeling with Oriented Particle System Szeliski and Tonnesen Siggraph 1992

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

Page 9: Surface Modeling with Oriented Particle System Szeliski and Tonnesen Siggraph 1992

Particle Dynamics

• Potential functions specify the “internal forces”

• Particle systems are under additional external forces and damping forces

i

ii

iii

vp

av

mfa

/

ii

ii

iii

q

I

1

Page 10: Surface Modeling with Oriented Particle System Szeliski and Tonnesen Siggraph 1992

Computation of Internal Forces

Page 11: Surface Modeling with Oriented Particle System Szeliski and Tonnesen Siggraph 1992

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)

Page 12: Surface Modeling with Oriented Particle System Szeliski and Tonnesen Siggraph 1992

Modeling Operations

Weld two surfaces together

Page 13: Surface Modeling with Oriented Particle System Szeliski and Tonnesen Siggraph 1992

Cutting a surfaces into two

Page 14: Surface Modeling with Oriented Particle System Szeliski and Tonnesen Siggraph 1992

Putting a crease into the surface

Page 15: Surface Modeling with Oriented Particle System Szeliski and Tonnesen Siggraph 1992

Particle Creation and 3D Interpolation

Page 16: Surface Modeling with Oriented Particle System Szeliski and Tonnesen Siggraph 1992

3D Interpolation

Page 17: Surface Modeling with Oriented Particle System Szeliski and Tonnesen Siggraph 1992
Page 18: Surface Modeling with Oriented Particle System Szeliski and Tonnesen Siggraph 1992
Page 19: Surface Modeling with Oriented Particle System Szeliski and Tonnesen Siggraph 1992

Homework

Oriented Particle: 2D version

Page 20: Surface Modeling with Oriented Particle System Szeliski and Tonnesen Siggraph 1992

Summary

• State of each particle:

• Design potential as in page 7

• Weighting function

iiiiii nwhereyx sin,cos,,

bab

y

a

xKyx

,

22exp,

2

2

2

2

Page 21: Surface Modeling with Oriented Particle System Szeliski and Tonnesen Siggraph 1992

Operation

• Anchored at two end points; fix one of the normal ()

• Insert middle points

• Deform the curve by moving one middle points

• Etc.