Deformation http://www.cse.iitd.ac.in/ Deformation IIT Delhi - - PowerPoint PPT Presentation

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Deformation http://www.cse.iitd.ac.in/ Deformation IIT Delhi - - PowerPoint PPT Presentation

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IIT Delhi Deformation http://www.cse.iitd.ac.in/ Deformation IIT Delhi http://www.cse.iitd.ac.in/ Deformation IIT Delhi Deformation causes change in the shape keeping typically the same topology Geometric deformation (does not account for

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Deformation

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Deformation

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Deformation

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

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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Deformation

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Deformation

  • 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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Deformation

  • sformation
  • (x,y,z)

(x,y,z)

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Deformation

  • If vertex i is displaced by (x, y, z) units

Displace each neighbor, j, of i by

(x, y, z) * f (i, j)

f (i,j) is typically a function of distance

Euclidean distance Number of edges from i to j Distance along surface (i.e., geodesics)

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Deformation

  • f all vertices
  • control a few

vertices wh

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Deformation

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Deformation

  • ;

1 . 1 ) ( ; 1 . 1 ) (

1 1

  • k

n i i f k n i i f

k k

STNY BRK

STATE UNIVERSITY OF NEW YORK

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Deformation

  • Assumption
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Deformation

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Deformation

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Deformation

  • CSE528
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Deformation

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Deformation

STNY BRK

STATE UNIVERSITY OF NEW YORK

CSE528

!"#$%$&'"&%())

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Deformation

  • compute
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Deformation

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Local Deformation

Hierarchical B-Spline Surfaces

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Local Deformation

Hierarchical B-Spline Surfaces

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Local Deformation

Hierarchical B-Spline Surfaces

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Local Deformation

Hierarchical B-Spline Surfaces

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Local Deformation

Hierarchical B-Spline Surfaces

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Local Deformation

Hierarchical B-Spline Surfaces

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Local Deformation

Hierarchical B-Spline Surfaces

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Global Deformation

A Barr SIGGRAPH 1984

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Global Deformation

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Global Deformation

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Global Deformation

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Global Deformation

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Global Deformation

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Global Deformation

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Global Deformation

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Free Form Deformation

  • 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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Free Form Deformation

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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Free Form Deformation

  • x

1

x

2

x

3

x v

  • i

i ix

w v

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Free Form Deformation

  • x

1

x

2

x

3

x v

  • i

i ix

w v

  • is functions

x x x x

  • i

i i i d i i i

x t t i d x w v ) 1 (

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Free Form Deformation

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Free Form Deformation

  • 3

2 5 4 , 3 2 5 4

  • v

u

2 2

) 1 ( ) 1 ( v u

  • 2

) 1 ( ) 1 ( 2 v u u

  • 2

2

) 1 ( v u

  • 2

2v

u

2 2

) 1 ( v u

  • 2

) 1 ( 2 uv 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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Free Form Deformation

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Free Form Deformation

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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Free Form Deformation

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Free Form Deformation

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Free Form Deformation

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Free Form Deformation

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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Free Form Deformation

Can enforce Ckcontinuity

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Free Form Deformation

Can enforce Ckcontinuity

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Free Form Deformation

Volume Preservation

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Extended Free Form Deformation

Non Parallelopiped Lattice

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Extended Free Form Deformation

Non Parallelopiped Lattice

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Extended Free Form Deformation

Non Parallelopiped Lattice

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Extended Free Form Deformation

Some Results

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Animation Free Form Deformation

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Animation Free Form Deformation

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Animation Free Form Deformation

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Free Form Deformation

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Animation Free Form Deformation

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Direct Free Form Deformation

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Direct Free Form Deformation

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Direct Free Form Deformation

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References

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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References

http://www.pmp-book.org/download/slides/Deformation.pdf http://www.cs.sunysb.edu/~qin/courses/graphics/graphics-deformation.pdf http://caig.cs.nctu.edu.tw/course/CA/Lecture/deformation.pdf