![Page 1: 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](https://reader035.vdocuments.us/reader035/viewer/2022062407/56649e4b5503460f94b3feef/html5/thumbnails/1.jpg)
A Survey on FFD
Reporter: Gang XuMar 15, 2006
![Page 2: 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](https://reader035.vdocuments.us/reader035/viewer/2022062407/56649e4b5503460f94b3feef/html5/thumbnails/2.jpg)
Overview Volumn-based FFD Surface-based FFD Curve-based FFD Point-based FFD Accurate FFD Future Work
Outline
![Page 3: 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](https://reader035.vdocuments.us/reader035/viewer/2022062407/56649e4b5503460f94b3feef/html5/thumbnails/3.jpg)
Overview
FFD (Free Form Deformation) : Sederberg and Parry, 1986
Application : Animate, Modeling , Image processing.
Software: Maya, 3D max, Softimage
![Page 4: 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](https://reader035.vdocuments.us/reader035/viewer/2022062407/56649e4b5503460f94b3feef/html5/thumbnails/4.jpg)
Classification Non-Accurate FFD
Sample points
Accurate FFD (Jieqing Feng, 1998)
No sample points
![Page 5: 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](https://reader035.vdocuments.us/reader035/viewer/2022062407/56649e4b5503460f94b3feef/html5/thumbnails/5.jpg)
Non-Accurate FFD
No deformation tools
Having deformation tools
![Page 6: 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](https://reader035.vdocuments.us/reader035/viewer/2022062407/56649e4b5503460f94b3feef/html5/thumbnails/6.jpg)
No deformation tools
Barr, 1984. Deformation by matrices whose com
ponents are functions of one space coordinate.
Tapering, twisting , bending
![Page 7: 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](https://reader035.vdocuments.us/reader035/viewer/2022062407/56649e4b5503460f94b3feef/html5/thumbnails/7.jpg)
Having deformation tools
Volume-based FFD Surface-based FFD
Curve-based FFD
Point-based FFD
![Page 8: 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](https://reader035.vdocuments.us/reader035/viewer/2022062407/56649e4b5503460f94b3feef/html5/thumbnails/8.jpg)
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.
![Page 9: 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](https://reader035.vdocuments.us/reader035/viewer/2022062407/56649e4b5503460f94b3feef/html5/thumbnails/9.jpg)
Bezier volume-based FFD
![Page 10: 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](https://reader035.vdocuments.us/reader035/viewer/2022062407/56649e4b5503460f94b3feef/html5/thumbnails/10.jpg)
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.
![Page 11: 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](https://reader035.vdocuments.us/reader035/viewer/2022062407/56649e4b5503460f94b3feef/html5/thumbnails/11.jpg)
Subdivision volume based FFD
MacCracken and Joy , 1996 arbitrary topology lattices
![Page 12: 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](https://reader035.vdocuments.us/reader035/viewer/2022062407/56649e4b5503460f94b3feef/html5/thumbnails/12.jpg)
Weighted T-spline based FFD Song Wenhao, 2005Weighted T-spline volume,Octree subidivision.
![Page 13: 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](https://reader035.vdocuments.us/reader035/viewer/2022062407/56649e4b5503460f94b3feef/html5/thumbnails/13.jpg)
Scalar field based FFD
Hua and Qing, 2003
![Page 14: 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](https://reader035.vdocuments.us/reader035/viewer/2022062407/56649e4b5503460f94b3feef/html5/thumbnails/14.jpg)
Summary and discussion
The basic idea is same, only the tool is
different. Is there other good tool?
![Page 15: 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](https://reader035.vdocuments.us/reader035/viewer/2022062407/56649e4b5503460f94b3feef/html5/thumbnails/15.jpg)
Surface based FFD(1)
Feng Jieqing, Ma Lizhuang, 1996
The parametric surface is considered as the deformation tool
![Page 16: 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](https://reader035.vdocuments.us/reader035/viewer/2022062407/56649e4b5503460f94b3feef/html5/thumbnails/16.jpg)
Step 1
The deformation tool is defined: a B-spline surface forming a rectangular Planar grid on XOY plane.
![Page 17: 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](https://reader035.vdocuments.us/reader035/viewer/2022062407/56649e4b5503460f94b3feef/html5/thumbnails/17.jpg)
The object is associated to the deformation tool
Step 2
![Page 18: 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](https://reader035.vdocuments.us/reader035/viewer/2022062407/56649e4b5503460f94b3feef/html5/thumbnails/18.jpg)
The deformation tool is modified.
The object is deformationed.
Step 3 and Step 4
![Page 19: 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](https://reader035.vdocuments.us/reader035/viewer/2022062407/56649e4b5503460f94b3feef/html5/thumbnails/19.jpg)
Results
![Page 20: 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](https://reader035.vdocuments.us/reader035/viewer/2022062407/56649e4b5503460f94b3feef/html5/thumbnails/20.jpg)
Subdivision surface based FFD
Feng Jieqing, 2005 Arbitrary topology. Multiresolution FFD.
![Page 21: 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](https://reader035.vdocuments.us/reader035/viewer/2022062407/56649e4b5503460f94b3feef/html5/thumbnails/21.jpg)
Process
![Page 22: 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](https://reader035.vdocuments.us/reader035/viewer/2022062407/56649e4b5503460f94b3feef/html5/thumbnails/22.jpg)
Process
![Page 23: 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](https://reader035.vdocuments.us/reader035/viewer/2022062407/56649e4b5503460f94b3feef/html5/thumbnails/23.jpg)
Generation of control mesh
Primitive mesh and Boolean operations
Reed graph method
![Page 24: 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](https://reader035.vdocuments.us/reader035/viewer/2022062407/56649e4b5503460f94b3feef/html5/thumbnails/24.jpg)
Generation of deformation space
![Page 25: 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](https://reader035.vdocuments.us/reader035/viewer/2022062407/56649e4b5503460f94b3feef/html5/thumbnails/25.jpg)
Subdivision Method
![Page 26: 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](https://reader035.vdocuments.us/reader035/viewer/2022062407/56649e4b5503460f94b3feef/html5/thumbnails/26.jpg)
Parameterization
Attaching object on the subdivision surface The nearest point rule
![Page 27: 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](https://reader035.vdocuments.us/reader035/viewer/2022062407/56649e4b5503460f94b3feef/html5/thumbnails/27.jpg)
Modify the control mesh
![Page 28: 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](https://reader035.vdocuments.us/reader035/viewer/2022062407/56649e4b5503460f94b3feef/html5/thumbnails/28.jpg)
Multiresolution space deformation
![Page 29: 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](https://reader035.vdocuments.us/reader035/viewer/2022062407/56649e4b5503460f94b3feef/html5/thumbnails/29.jpg)
Implementation results
![Page 30: 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](https://reader035.vdocuments.us/reader035/viewer/2022062407/56649e4b5503460f94b3feef/html5/thumbnails/30.jpg)
Summary
Arbitrary topology Multiresolution No parametric form Costs
![Page 31: 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](https://reader035.vdocuments.us/reader035/viewer/2022062407/56649e4b5503460f94b3feef/html5/thumbnails/31.jpg)
Other surface based FFD
Mean value coordinate (Ju Tao, 2005)
![Page 32: 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](https://reader035.vdocuments.us/reader035/viewer/2022062407/56649e4b5503460f94b3feef/html5/thumbnails/32.jpg)
Triangular mesh based FFD (Kobayashi ,2003)
Other surface based FFD
![Page 33: 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](https://reader035.vdocuments.us/reader035/viewer/2022062407/56649e4b5503460f94b3feef/html5/thumbnails/33.jpg)
Curve based FFD
The deformation tool is curve
Build coordinate systems
![Page 34: 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](https://reader035.vdocuments.us/reader035/viewer/2022062407/56649e4b5503460f94b3feef/html5/thumbnails/34.jpg)
de Casteljau algorithm (Chang, 1994) line---curve
Generalized de Casteljau FFD
![Page 35: 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](https://reader035.vdocuments.us/reader035/viewer/2022062407/56649e4b5503460f94b3feef/html5/thumbnails/35.jpg)
Generalized de Casteljau FFD
![Page 36: 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](https://reader035.vdocuments.us/reader035/viewer/2022062407/56649e4b5503460f94b3feef/html5/thumbnails/36.jpg)
Results
![Page 37: 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](https://reader035.vdocuments.us/reader035/viewer/2022062407/56649e4b5503460f94b3feef/html5/thumbnails/37.jpg)
Results
![Page 38: 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](https://reader035.vdocuments.us/reader035/viewer/2022062407/56649e4b5503460f94b3feef/html5/thumbnails/38.jpg)
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
![Page 39: 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](https://reader035.vdocuments.us/reader035/viewer/2022062407/56649e4b5503460f94b3feef/html5/thumbnails/39.jpg)
Axial deformation (Lararus, 94) Initial curve can be arbitrary.
![Page 40: 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](https://reader035.vdocuments.us/reader035/viewer/2022062407/56649e4b5503460f94b3feef/html5/thumbnails/40.jpg)
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.
![Page 41: 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](https://reader035.vdocuments.us/reader035/viewer/2022062407/56649e4b5503460f94b3feef/html5/thumbnails/41.jpg)
Result
![Page 42: 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](https://reader035.vdocuments.us/reader035/viewer/2022062407/56649e4b5503460f94b3feef/html5/thumbnails/42.jpg)
Arc-length based AxDf and Length preserving Deformation
Peng, 1999
![Page 43: 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](https://reader035.vdocuments.us/reader035/viewer/2022062407/56649e4b5503460f94b3feef/html5/thumbnails/43.jpg)
Wire-based FFD (singh, 1998)
![Page 44: 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](https://reader035.vdocuments.us/reader035/viewer/2022062407/56649e4b5503460f94b3feef/html5/thumbnails/44.jpg)
FFD with curve pairs
Xu Jianquan, 2001.
![Page 45: 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](https://reader035.vdocuments.us/reader035/viewer/2022062407/56649e4b5503460f94b3feef/html5/thumbnails/45.jpg)
Direct manipulate of FFD, Hsu,1992
Through a given point Least square method
Point-based FFD
![Page 46: 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](https://reader035.vdocuments.us/reader035/viewer/2022062407/56649e4b5503460f94b3feef/html5/thumbnails/46.jpg)
Dirichlet FFD(Moccozet, 1997)
Computational Geometry Convex hull ,Delaunay triangulation Voronoi graph, FFD
![Page 47: 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](https://reader035.vdocuments.us/reader035/viewer/2022062407/56649e4b5503460f94b3feef/html5/thumbnails/47.jpg)
Constraint optimal based DFFD
Hu Shimin, 2001
efficient explicit solutions
decomposable multiple point constraints
Constraint optimal method
![Page 48: 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](https://reader035.vdocuments.us/reader035/viewer/2022062407/56649e4b5503460f94b3feef/html5/thumbnails/48.jpg)
FFD using NURBS volume
![Page 49: 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](https://reader035.vdocuments.us/reader035/viewer/2022062407/56649e4b5503460f94b3feef/html5/thumbnails/49.jpg)
Explicit solution for directmanipulation of FFD
![Page 50: 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](https://reader035.vdocuments.us/reader035/viewer/2022062407/56649e4b5503460f94b3feef/html5/thumbnails/50.jpg)
Explicit solution for directmanipulation of FFD
![Page 51: 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](https://reader035.vdocuments.us/reader035/viewer/2022062407/56649e4b5503460f94b3feef/html5/thumbnails/51.jpg)
Decomposability of multiplepoint constraints
Theorem. A direct manipulation of FFD with h point constraints can be decomposed into h manipulationswith single point constraints.
![Page 52: 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](https://reader035.vdocuments.us/reader035/viewer/2022062407/56649e4b5503460f94b3feef/html5/thumbnails/52.jpg)
Modeling example
![Page 53: 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](https://reader035.vdocuments.us/reader035/viewer/2022062407/56649e4b5503460f94b3feef/html5/thumbnails/53.jpg)
Modeling example
![Page 54: 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](https://reader035.vdocuments.us/reader035/viewer/2022062407/56649e4b5503460f94b3feef/html5/thumbnails/54.jpg)
Accurate FFD Feng Jieqing, 1998 No sample points, every point
![Page 55: 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](https://reader035.vdocuments.us/reader035/viewer/2022062407/56649e4b5503460f94b3feef/html5/thumbnails/55.jpg)
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
![Page 56: 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](https://reader035.vdocuments.us/reader035/viewer/2022062407/56649e4b5503460f94b3feef/html5/thumbnails/56.jpg)
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
![Page 57: 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](https://reader035.vdocuments.us/reader035/viewer/2022062407/56649e4b5503460f94b3feef/html5/thumbnails/57.jpg)
Results
![Page 58: 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](https://reader035.vdocuments.us/reader035/viewer/2022062407/56649e4b5503460f94b3feef/html5/thumbnails/58.jpg)
Results
![Page 59: 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](https://reader035.vdocuments.us/reader035/viewer/2022062407/56649e4b5503460f94b3feef/html5/thumbnails/59.jpg)
Improved accurate FFD
Bernstein interpolation: efficient
Trimmed Bezier surface (Feng, 2002): Consistent with the industrial standard
![Page 60: 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](https://reader035.vdocuments.us/reader035/viewer/2022062407/56649e4b5503460f94b3feef/html5/thumbnails/60.jpg)
Result
![Page 61: 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](https://reader035.vdocuments.us/reader035/viewer/2022062407/56649e4b5503460f94b3feef/html5/thumbnails/61.jpg)
Results
![Page 62: 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](https://reader035.vdocuments.us/reader035/viewer/2022062407/56649e4b5503460f94b3feef/html5/thumbnails/62.jpg)
Dynamic deformation Linear interpolation (Feng ,1997)
0 1(1 )S t S tS
![Page 63: 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](https://reader035.vdocuments.us/reader035/viewer/2022062407/56649e4b5503460f94b3feef/html5/thumbnails/63.jpg)
Summary
Tool is different but idea is same
Four steps
Other method? Other idea?
![Page 64: 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](https://reader035.vdocuments.us/reader035/viewer/2022062407/56649e4b5503460f94b3feef/html5/thumbnails/64.jpg)
Future work
FFD with DMS spline volume
![Page 65: 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](https://reader035.vdocuments.us/reader035/viewer/2022062407/56649e4b5503460f94b3feef/html5/thumbnails/65.jpg)
Difficult
The choice of domain and control mesh
![Page 66: 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](https://reader035.vdocuments.us/reader035/viewer/2022062407/56649e4b5503460f94b3feef/html5/thumbnails/66.jpg)
Future work
FFD with DMS spline surface
![Page 67: 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](https://reader035.vdocuments.us/reader035/viewer/2022062407/56649e4b5503460f94b3feef/html5/thumbnails/67.jpg)
Difficult The choice of domain and control
mesh Generate the control mesh by
mesh simplification
![Page 68: 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](https://reader035.vdocuments.us/reader035/viewer/2022062407/56649e4b5503460f94b3feef/html5/thumbnails/68.jpg)
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
![Page 69: 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](https://reader035.vdocuments.us/reader035/viewer/2022062407/56649e4b5503460f94b3feef/html5/thumbnails/69.jpg)
Curve based dynamic FFD
![Page 70: 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](https://reader035.vdocuments.us/reader035/viewer/2022062407/56649e4b5503460f94b3feef/html5/thumbnails/70.jpg)
Surface based dynamic FFD
2 2 2
2 2 2( ) ( , , ) 0X u v tu v t
![Page 71: 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](https://reader035.vdocuments.us/reader035/viewer/2022062407/56649e4b5503460f94b3feef/html5/thumbnails/71.jpg)
Volume based dynamic FFD
2 2 2 2
2 2 2 2( ) ( , , , ) 0X u v w tu v w t
![Page 72: 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](https://reader035.vdocuments.us/reader035/viewer/2022062407/56649e4b5503460f94b3feef/html5/thumbnails/72.jpg)
Morphing based dynamic FFD Curve morphing and curve based
FFD Surface morphing and surface
based FFD
![Page 73: 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](https://reader035.vdocuments.us/reader035/viewer/2022062407/56649e4b5503460f94b3feef/html5/thumbnails/73.jpg)
Thanks!