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  • 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!