a survey on ffd reporter: gang xu mar 15, 2006. overview volumn-based ffd surface-based ffd...

A Survey on FFD

Reporter: Gang XuMar 15, 2006

Outline OverviewVolumn-based FFDSurface-based FFD Curve-based FFDPoint-based FFDAccurate FFD Future Work

OverviewFFD (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 components are functions of one space coordinate. Tapering, twisting , bending

Having deformation toolsVolume-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 FFDSong Wenhao, 2005Weighted T-spline volume,Octree subidivision.

Scalar field based FFDHua 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 1The deformation tool is defined: a B-spline surface forming a rectangular Planar grid on XOY plane.

Step 2The object is associated to the deformation tool

Step 3 and Step 4 The deformation tool is modified.

The object is deformationed.

Results

Subdivision surface based FFDFeng Jieqing, 2005Arbitrary topology. Multiresolution FFD.

Process

Process

Generation of control meshPrimitive mesh and Boolean operations Reed graph method

Generation of deformation space

Subdivision Method

ParameterizationAttaching object on the subdivision surface The nearest point rule

Modify the control mesh

Multiresolution space deformation

Implementation results

SummaryArbitrary topology MultiresolutionNo parametric formCosts

Other surface based FFDMean value coordinate (Ju Tao, 2005)

Other surface based FFDTriangular mesh based FFD (Kobayashi ,2003)

Curve based FFD The deformation tool is curve

Build coordinate systems

Generalized de Casteljau FFD de Casteljau algorithm (Chang, 1994) line---curve

Generalized de Casteljau FFD

Results

Results

Generalization Rectangular domain (Bechmann, 2001) Rectangular-----SurfaceTriangular 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.

ProcessDefine 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 DeformationPeng, 1999

Wire-based FFD (singh, 1998)

FFD with curve pairsXu Jianquan, 2001.

Point-based FFDDirect manipulate of FFD, Hsu,1992 Through a given point Least square method

Dirichlet FFD(Moccozet, 1997)

Computational GeometryConvex hull ,Delaunay triangulationVoronoi graph, FFD

Constraint optimal based DFFDHu 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 constraintsTheorem. A direct manipulation of FFD with h point constraints can be decomposed into h manipulationswith single point constraints.

Modeling example

Modeling example

Accurate FFDFeng Jieqing, 1998No 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 volumeThe object is then subdivided and re-triangulated. Each triangle of the object mesh is within a Bezier volume

Process (2)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 FFDBernstein interpolation: efficient

Trimmed Bezier surface (Feng, 2002): Consistent with the industrial standard

Result

Results

Dynamic deformationLinear interpolation (Feng ,1997)

SummaryTool 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 workFFD 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)

Curve based dynamic FFD

Surface based dynamic FFD

Volume based dynamic FFD

Morphing based dynamic FFDCurve morphing and curve based FFDSurface morphing and surface based FFD

Thanks!