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!