a survey on ffd
DESCRIPTION
A Survey on FFD. Reporter: Gang Xu Mar 15, 2006. Outline. 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 Application : Animate, Modeling , Image processing. - PowerPoint PPT PresentationTRANSCRIPT
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A Survey on FFD
Reporter: Gang XuMar 15, 2006
![Page 2: A Survey on FFD](https://reader035.vdocuments.us/reader035/viewer/2022081515/56815a33550346895dc772c1/html5/thumbnails/2.jpg)
Overview Volumn-based FFD Surface-based FFD Curve-based FFD Point-based FFD Accurate FFD Future Work
Outline
![Page 3: A Survey on FFD](https://reader035.vdocuments.us/reader035/viewer/2022081515/56815a33550346895dc772c1/html5/thumbnails/3.jpg)
Overview
FFD (Free Form Deformation) : Sederberg and Parry, 1986
Application : Animate, Modeling , Image processing.
Software: Maya, 3D max, Softimage
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Classification Non-Accurate FFD
Sample points
Accurate FFD (Jieqing Feng, 1998)
No sample points
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Non-Accurate FFD
No deformation tools
Having deformation tools
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No deformation tools
Barr, 1984. Deformation by matrices whose com
ponents are functions of one space coordinate.
Tapering, twisting , bending
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Having deformation tools
Volume-based FFD Surface-based FFD
Curve-based FFD
Point-based FFD
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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
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Extensions of Bezier FFD 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.
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Subdivision volume based FFD
MacCracken and Joy , 1996 arbitrary topology lattices
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Weighted T-spline based FFD Song Wenhao, 2005Weighted T-spline volume,Octree subidivision.
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Scalar field based FFD
Hua and Qing, 2003
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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)
Feng Jieqing, Ma Lizhuang, 1996
The parametric surface is considered as the deformation tool
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Step 1
The deformation tool is defined: a B-spline surface forming a rectangular Planar grid on XOY plane.
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The object is associated to the deformation tool
Step 2
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The deformation tool is modified.
The object is deformationed.
Step 3 and Step 4
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Results
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Subdivision surface based FFD
Feng Jieqing, 2005 Arbitrary topology. Multiresolution FFD.
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Process
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Process
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Generation of control mesh
Primitive mesh and Boolean operations
Reed graph method
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Generation of deformation space
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Subdivision Method
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Parameterization
Attaching object on the subdivision surface The nearest point rule
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Modify the control mesh
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Multiresolution space deformation
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Implementation results
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Summary
Arbitrary topology Multiresolution No parametric form Costs
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Other surface based FFD
Mean value coordinate (Ju Tao, 2005)
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Triangular mesh based FFD (Kobayashi ,2003)
Other surface based FFD
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Curve based FFD
The deformation tool is curve
Build coordinate systems
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de Casteljau algorithm (Chang, 1994) line---curve
Generalized de Casteljau FFD
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Generalized de Casteljau FFD
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Results
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Results
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Generalization
Rectangular domain (Bechmann, 2001) Rectangular-----Surface Triangular domain (Mikita, 1996) Triangular---------Surface
Generalize to trivariate case, just the FFD proposed by Sedeberg and Parry
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Axial deformation (Lararus, 94) Initial curve can be arbitrary.
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Process Define initial curve and the zone of influence para
meters. The source curve is recursively subdivided into a li
ne 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.
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Result
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Arc-length based AxDf and Length preserving Deformation
Peng, 1999
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Wire-based FFD (singh, 1998)
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FFD with curve pairs
Xu Jianquan, 2001.
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Direct manipulate of FFD, Hsu,1992
Through a given point Least square method
Point-based FFD
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Dirichlet FFD(Moccozet, 1997)
Computational Geometry Convex hull ,Delaunay triangulation Voronoi graph, FFD
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Constraint optimal based DFFD
Hu Shimin, 2001
efficient explicit solutions
decomposable multiple point constraints
Constraint optimal method
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FFD using NURBS volume
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Explicit solution for directmanipulation of FFD
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Explicit solution for directmanipulation of FFD
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Decomposability of multiplepoint constraints
Theorem. A direct manipulation of FFD with h point constraints can be decomposed into h manipulationswith single point constraints.
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Modeling example
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Modeling example
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Accurate FFD Feng Jieqing, 1998 No sample points, every point
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Process (1)
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 re-triangulated. Each triangle of the object mesh is within a Bezier volume
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Process (2) We conduct the functional compositio
n via shifting operators for each Bezier volume
The result of the deformation is a set of triangular Bezier patches, whos
e degree is the sum of three directional degrees of the B-spline volume
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Results
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Results
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Improved accurate FFD
Bernstein interpolation: efficient
Trimmed Bezier surface (Feng, 2002): Consistent with the industrial standard
![Page 60: A Survey on FFD](https://reader035.vdocuments.us/reader035/viewer/2022081515/56815a33550346895dc772c1/html5/thumbnails/60.jpg)
Result
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Results
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Dynamic deformation Linear interpolation (Feng ,1997)
0 1(1 )S t S tS
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Summary
Tool is different but idea is same
Four steps
Other method? Other idea?
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Future work
FFD with DMS spline volume
![Page 65: A Survey on FFD](https://reader035.vdocuments.us/reader035/viewer/2022081515/56815a33550346895dc772c1/html5/thumbnails/65.jpg)
Difficult
The choice of domain and control mesh
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Future work
FFD with DMS spline surface
![Page 67: A Survey on FFD](https://reader035.vdocuments.us/reader035/viewer/2022081515/56815a33550346895dc772c1/html5/thumbnails/67.jpg)
Difficult The choice of domain and control
mesh Generate the control mesh by
mesh simplification
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Future work Harmonic-type equation based
dynamic deformation (curve based deformation)
2 2
2 2( ) ( , ) 0X u vu v
2 2
2 2( ) ( , ) 0X u tu t
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Curve based dynamic FFD
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Surface based dynamic FFD
2 2 2
2 2 2( ) ( , , ) 0X u v tu v t
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Volume based dynamic FFD
2 2 2 2
2 2 2 2( ) ( , , , ) 0X u v w tu v w t
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Morphing based dynamic FFD Curve morphing and curve based
FFD Surface morphing and surface
based FFD
![Page 73: A Survey on FFD](https://reader035.vdocuments.us/reader035/viewer/2022081515/56815a33550346895dc772c1/html5/thumbnails/73.jpg)
Thanks!