1. Extended Free-Form Deformation Xiao, Yongqin CMPS260 Winter 2003 Instructor: Alex Pang

2. What is “free-form”? Parametric surfaces are free-form surfaces.  The flexibility in this technique of deformation allows us deform the model in a free-form manner. Any surface patches global or local deformation continuity in local deformation volume preservation

3. FFD key idea --- proposed by Sederberg and Parry Impose a local coordinate system on a parallelepiped region.  Compute the (s,t,u) coordinates of the model points in the region.  Impose a (l, m, n) grid of control points on the parallelepiped.

4. FFD key idea (cont.)  Move the control points around.  Evaluate new position of model point based on trivariate Bersntein polynomials or other type of volumes.

5. Some formulas used in FFD A point in the STU coordinate system: A deformed point:

6. Evaluate FFD Advantages:  Independent of surface geometry  Intuitive, interactive  Efficient, flexible Disadvantages: The parallelpipedical shape of FFD lattice prohibits arbitrarily shaped deformation. E.g. can hardly design a circular bump on the surface

7. EFFD ----- extended FFD Edit the FFD lattice before associating the model with it. Moving Merging Deleting The control points Arbitrary lattices:  Prismatic lattices  Tetrahedral  …

8. Compute (s, t, u) coordinates Decide if a surface point inside the lattice using Convex Hull property. Previous position of control points matters in this case.  Surface normal needed for the convex hull. Finding the (s, t, u) coordinates Subdivision Newton iteration Projection (very limited, but fast)

9. Steps for deforming a object model Load in a object model Subdivide the object surface Loop 1: load in a lattice model move the lattice to a appropriate position set (l, m, n) dimension for the lattice “freeze” the lattice Loop 2 : deform the lattice update the object model end 2 “unfreeze” the lattice end 1

10. Example of deforming an object

11. Smooth the deformed surface Can be done by properly set the lattice position and (l, m, n ) dimension

12. Design a lattice holding many lattice blocks  Design an array of (3l+1)(3m+1)(3n+1) lattice blocks.  Only interact with the corner points, other control points will be automatically set.  Apply EFFD one by one with each block.

13. reference Free-Form Deformation of Solid Geometric Models by T.W. Sederberg & S.R. Parry Extended Free-Form Deformation: A sculpturing Tool for 3D Geometri Modeling by S. Coquillart Free-Form Deformations With Lattices of Arbitrary Topology by R. MacCracken & K.I. Joy All the images are from the first and third paper.

14. thanks