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Deformation causes change in the shape keeping typically the same - - PowerPoint PPT Presentation
Deformation causes change in the shape keeping typically the same - - PowerPoint PPT Presentation
Deformation causes change in the shape keeping typically the same topology Geometric deformation (does not account for any law of physics) Local or global deformation Deformation: A transformation/mapping of the positions of every particle in
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Deformation causes change in the shape keeping typically the same topology Geometric deformation (does not account for any law of physics) Local or global deformation
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Deformation: A transformation/mapping of the positions
- f every particle in the original object to those in the
deformed body Each particle represented by a point p is moved by φ(•): p → φ (t, p) where p represents the original position and φ(t, p) represents the position at time t.
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- Changing an object’s shape
–Usually refers to non-simulated algorithms –Usually relies on user guidance
- Easiest when the number of faces and vertices of a
shape is preserved, and the shape topology is not changed either –Define the movements of vertices
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Hierarchical B-Spline Surfaces
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Hierarchical B-Spline Surfaces
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Hierarchical B-Spline Surfaces
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Hierarchical B-Spline Surfaces
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Hierarchical B-Spline Surfaces
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Hierarchical B-Spline Surfaces
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Hierarchical B-Spline Surfaces
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A Barr SIGGRAPH 1984
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- Physical Analogy: A clear, flexible plastic
parallelepiped with one or more objects embedded in it.
- The embedded objects are also flexible so that they
deform with the object.
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Parametric surfaces are free-form surfaces. The flexibility in this technique of deformation allows us deform the model in a free-form manner. Any surface patches Global or local deformation Continuity in local deformation Volume preservation
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- Department of Computer Science
Center for Visual Computing
CSE528
- 3
2 5 4 , 3 2 5
- v
2 2
) 1 ( ) 1 ( v u
- 2
) 1 ( ) 1 ( 2 v u u
- 2
2
) 1 ( v u
- v
v u ) 1 ( ) 1 ( 2
2
- v
v u ) 1 ( 2
2
- v
v u u ) 1 ( ) 1 ( 4
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Basic idea: deform space by deforming a lattice around an
- bject
- The deformation is defined by
moving the control points of the lattice
- Imagine it as if the object were
enclosed by rubber
- The key is how to define
–Local coordinate system –The mapping
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Can enforce Ckcontinuity
- Surface (s, t, u) = (s(v, w), t(v, w), u(v, w))
- Two adjacent FFDs X1(s1, t1, u1) & X2(s2, t2, u2)
with common boundary s1= s2= 0
- Conditions for first derivative continuity
–∂X1(0, t, u) / ∂s = ∂X2(0, t, u) / ∂s –∂X1(0, t, u) / ∂t = ∂X2(0, t, u) / ∂t –∂X1(0, t, u) / ∂u = ∂X2(0, t, u) / ∂u
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Can enforce Ckcontinuity
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Can enforce Ckcontinuity
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Volume Preservation
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Non Parallelopiped Lattice
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Non Parallelopiped Lattice
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Non Parallelopiped Lattice
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Some Results
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1. Hirearchical B-spline refinement, DR Forsey and RH Bartels, SIGGRAPH 88, Computer Graphics, Vol 22, No 4, August 1988
- 2. Fee form deformation of solid geometric models, TW Sederberg, SR Parry,
SIGGRAPH 86, Computer Graphics, Vol 20, No 4, August 1986
- 3. Extended free form deformation: A sculpting tool for 3D geometric modeling,
S Coquillart, SIGGRAPH 90, Computer Graphics, Vol 24, No 4, Aug 1990
- 4. Direct manipulation of free form deformations, WM Hsu, JF Hughes, H Kaufman,
SIGGRAPH 92, Computer Graphics, Vol 26, No 2, July 1992
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