A Survey on FFD Reporter: Gang Xu Mar 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, Deformation by matrices whose components 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, 2005 Weighted 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

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

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 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 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 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

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 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

Improved accurate FFD Bernstein interpolation: efficient Trimmed Bezier surface (Feng, 2002): Consistent with the industrial standard

Result

Results

Dynamic deformation Linear interpolation (Feng,1997)

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)

Curve based dynamic FFD

Surface based dynamic FFD

Volume based dynamic FFD

Morphing based dynamic FFD Curve morphing and curve based FFD Surface morphing and surface based FFD

Thanks!