a survey on ffd reporter: gang xu mar 15, 2006. overview volumn-based ffd surface-based ffd...
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A Survey on FFD
Reporter: Gang XuMar 15, 2006
Overview Volumn-based FFD Surface-based FFD Curve-based FFD Point-based FFD Accurate FFD Future Work
Outline
Overview
FFD (Free Form Deformation) : Sederberg and Parry, 1986
Application : Animate, Modeling , Image processing.
Software: Maya, 3D max, Softimage
Classification Non-Accurate FFD
Sample points
Accurate FFD (Jieqing Feng, 1998)
No sample points
Non-Accurate FFD
No deformation tools
Having deformation tools
No deformation tools
Barr, 1984. Deformation by matrices whose com
ponents are functions of one space coordinate.
Tapering, twisting , bending
Having deformation tools
Volume-based FFD Surface-based FFD
Curve-based FFD
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.
Bezier volume-based FFD
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.
Subdivision volume based FFD
MacCracken and Joy , 1996 arbitrary topology lattices
Weighted T-spline based FFD Song Wenhao, 2005Weighted T-spline volume,Octree subidivision.
Scalar field based FFD
Hua and Qing, 2003
Summary and discussion
The basic idea is same, only the tool is
different. Is there other good tool?
Surface based FFD(1)
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.
The object is associated to the deformation tool
Step 2
The deformation tool is modified.
The object is deformationed.
Step 3 and Step 4
Results
Subdivision surface based FFD
Feng Jieqing, 2005 Arbitrary topology. Multiresolution FFD.
Process
Process
Generation of control mesh
Primitive mesh and Boolean operations
Reed graph method
Generation of deformation space
Subdivision Method
Parameterization
Attaching object on the subdivision surface The nearest point rule
Modify the control mesh
Multiresolution space deformation
Implementation results
Summary
Arbitrary topology Multiresolution No parametric form Costs
Other surface based FFD
Mean value coordinate (Ju Tao, 2005)
Triangular mesh based FFD (Kobayashi ,2003)
Other surface based FFD
Curve based FFD
The deformation tool is curve
Build coordinate systems
de Casteljau algorithm (Chang, 1994) line---curve
Generalized de Casteljau FFD
Generalized de Casteljau FFD
Results
Results
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
Axial deformation (Lararus, 94) Initial curve can be arbitrary.
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.
Result
Arc-length based AxDf and Length preserving Deformation
Peng, 1999
Wire-based FFD (singh, 1998)
FFD with curve pairs
Xu Jianquan, 2001.
Direct manipulate of FFD, Hsu,1992
Through a given point Least square method
Point-based FFD
Dirichlet FFD(Moccozet, 1997)
Computational Geometry Convex hull ,Delaunay triangulation Voronoi graph, FFD
Constraint optimal based DFFD
Hu Shimin, 2001
efficient explicit solutions
decomposable multiple point constraints
Constraint optimal method
FFD using NURBS volume
Explicit solution for directmanipulation of FFD
Explicit solution for directmanipulation of FFD
Decomposability of multiplepoint constraints
Theorem. A direct manipulation of FFD with h point constraints can be decomposed into h manipulationswith single point constraints.
Modeling example
Modeling example
Accurate FFD Feng Jieqing, 1998 No sample points, every point
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
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
Results
Results
Improved accurate FFD
Bernstein interpolation: efficient
Trimmed Bezier surface (Feng, 2002): Consistent with the industrial standard
Result
Results
Dynamic deformation Linear interpolation (Feng ,1997)
0 1(1 )S t S tS
Summary
Tool is different but idea is same
Four steps
Other method? Other idea?
Future work
FFD with DMS spline volume
Difficult
The choice of domain and control mesh
Future work
FFD with DMS spline surface
Difficult The choice of domain and control
mesh Generate the control mesh by
mesh simplification
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
Curve based dynamic FFD
Surface based dynamic FFD
2 2 2
2 2 2( ) ( , , ) 0X u v tu v t
Volume based dynamic FFD
2 2 2 2
2 2 2 2( ) ( , , , ) 0X u v w tu v w t
Morphing based dynamic FFD Curve morphing and curve based
FFD Surface morphing and surface
based FFD
Thanks!
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