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
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
Surface Modeling
Freeform Surface Modeling
Particle System
Oriented Particle System
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.
Intermolecular Potential FunctionDynamics: long-range attraction force and short-range repulsion force
pi
pj
rij ,fij
Expect Particles to be Part of a Flat Surface …
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
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
Computation of Internal Forces
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)
Modeling Operations
Weld two surfaces together
Cutting a surfaces into two
Putting a crease into the surface
Particle Creation and 3D Interpolation
3D Interpolation
Homework
Oriented Particle: 2D version
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
Operation
• Anchored at two end points; fix one of the normal ()
• Insert middle points
• Deform the curve by moving one middle points
• Etc.