Transcript Slide 1

A Survey on FFD
Reporter: Gang Xu
Mar 15, 2006
Outline
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Overview
Volumn-based FFD
Surface-based FFD
Curve-based FFD
Point-based FFD
Accurate FFD
Future Work
Overview
FFD (Free Form Deformation) :
Sederberg and Parry, 1986
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Application : Animate, Modeling , Image
processing.
Software: Maya, 3D max, Softimage
Classification
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Non-Accurate FFD
Sample points
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Accurate FFD (Jieqing Feng, 1998)
No sample points
Non-Accurate FFD
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No deformation tools
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Having deformation tools
No deformation tools
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Barr, 1984.
Deformation by matrices whose
components are functions of one space
coordinate.
Tapering, twisting , bending
Having deformation tools
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Volume-based FFD
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Surface-based FFD
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Curve-based FFD
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Point-based FFD
Volume-based FFD
Bezier volume-based FFD(Sederbeg, 1986)
 Four steps
Create deformation tools.
Associate the object to the deformation space
Modify the deformation tools.
The object is deformed.
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Bezier volume-based FFD
Extensions of Bezier FFD
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B-spline volume (GP 89, Com89)
NURBS volume (LW94)
They are both simple Extensions of
Bezier FFD, but have good property:
local deformation and weight.
Subdivision volume based FFD
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MacCracken and Joy , 1996
arbitrary topology lattices
Weighted T-spline based FFD
Song Wenhao, 2005
Weighted T-spline volume,
Octree subidivision.
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Scalar field based FFD
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Hua and Qing, 2003
Summary and discussion
The basic idea is same, only the tool is
different.
 Is there other good tool?
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Surface based FFD(1)
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Feng Jieqing, Ma Lizhuang, 1996
The parametric surface is considered as
the deformation tool
Step 1
The deformation tool is defined: a B-spline surface forming a
rectangular Planar grid on XOY plane.
Step 2
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The object is associated to the
deformation tool
Step 3 and Step 4
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The deformation tool is modified.
The object is deformationed.
Results
Subdivision surface based FFD
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Feng Jieqing, 2005
Arbitrary topology.
Multiresolution FFD.
Process
Process
Generation of control mesh
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Primitive mesh and Boolean operations
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Reed graph method
Generation of deformation space
Subdivision Method
Parameterization
Attaching object on the subdivision surface
 The nearest point rule
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Modify the control mesh
Multiresolution space deformation
Implementation results
Summary
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Arbitrary topology
Multiresolution
No parametric form
Costs
Other surface based FFD
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Mean value coordinate
(Ju Tao, 2005)
Other surface based FFD
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Triangular mesh based FFD
(Kobayashi ,2003)
Curve based FFD
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The deformation tool is curve
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Build coordinate systems
Generalized de Casteljau FFD
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de Casteljau algorithm (Chang, 1994)
line---curve
Generalized de Casteljau FFD
Results
Results
Generalization
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Rectangular domain (Bechmann, 2001)
Rectangular-----Surface
Triangular domain (Mikita, 1996)
Triangular---------Surface
Generalize to trivariate case, just the
FFD proposed by Sedeberg and Parry
Axial deformation (Lararus, 94)
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Initial curve can be arbitrary.
Process
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Define initial curve and the zone of influence
parameters.
The source curve is recursively subdivided into a line
segment approximation. The Rotation minimizing
orthogonal frame are then constructed for each line
segment. All sample points are parametrised with
respect to the approximated curve by establishing the
closest point on the curve S(ti).
The curve is reshaped by the user.
The deformation of the curve is transmitted to the
object.
Result
Arc-length based AxDf and
Length preserving Deformation
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Peng, 1999
Wire-based FFD (singh, 1998)
FFD with curve pairs
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Xu Jianquan, 2001.
Point-based FFD
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Direct manipulate of FFD, Hsu,1992
Through a given point
Least square method
Dirichlet FFD(Moccozet, 1997)
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Computational Geometry
Convex hull ,Delaunay triangulation
Voronoi graph, FFD
Constraint optimal based DFFD
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Hu Shimin, 2001
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efficient explicit solutions
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decomposable multiple point constraints
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Constraint optimal method
FFD using NURBS volume
Explicit solution for direct
manipulation of FFD
Explicit solution for direct
manipulation of FFD
Decomposability of multiple
point constraints
Theorem. A direct manipulation of
FFD with h point constraints can be
decomposed into h manipulations
with single point constraints.
Modeling example
Modeling example
Accurate FFD
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Feng Jieqing, 1998
No sample points, every point
Process (1)
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B-spline volume is first converted (using
cutting planes determined by its knot
vectors) to a piecewise continuous
Bezier volume
The object is then subdivided and retriangulated. Each triangle of the object
mesh is within a Bezier volume
Process (2)
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We conduct the functional composition
via shifting operators for each Bezier
volume
The result of the deformation is a
set of triangular Bezier patches, whose
degree is the sum of three directional
degrees of the B-spline volume
Results
Results
Improved accurate FFD
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Bernstein interpolation: efficient
Trimmed Bezier surface (Feng, 2002):
Consistent with the industrial standard
Result
Results
Dynamic deformation
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Linear interpolation (Feng ,1997)
S  (1  t )S0  tS1
Summary
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Tool is different but idea is same
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Four steps
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Other method? Other idea?
Future work
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FFD with DMS spline volume
Difficult
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The choice of domain and control mesh
Future work
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FFD with DMS spline surface
Difficult
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The choice of domain and control mesh
Generate the control mesh by mesh
simplification
Future work
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Harmonic-type equation based dynamic
deformation (curve based deformation)
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( 2  2 ) X (u, v)  0
u
v
2
2
2
2
( 2   2 ) X (u, t )  0
u
t
Curve based dynamic FFD
Surface based dynamic FFD
2
2
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( 2  2   2 ) X (u, v, t )  0
u v
t
Volume based dynamic FFD
2
2
2
2
( 2 
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  2 ) X (u, v, w, t )  0
2
2
u
v
w
t
Morphing based dynamic FFD
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Curve morphing and curve based FFD
Surface morphing and surface based
FFD
Thanks!