1. Rick Parent - CIS681 Deforming Objects Free-Form Deformations (FFDs) Global Deformations Non-Uniform Scale Grid Deformations Skeletal Deformations

2. Rick Parent - CIS681 Non-uniform Scale Transformation matrix - diagonal elements 0 1 Sx Sy Sz 0 0 0 0 0 00 0 000

3. Rick Parent - CIS681 Non-uniform Scale

4. Rick Parent - CIS681 Global Deformations Transformation matrix elements - functions of coordinates f(x,y,z)g(x,y,z)

5. Rick Parent - CIS681 Global Deformations - taper

6. Rick Parent - CIS681 Global Deformations - taper

7. Rick Parent - CIS681 Global Deformations - twist x’ = x*cos(f(y)) – z*sin(f(y)) y’ = y z’ = x*sin(f(y)) + z*cos(f(y))

8. Rick Parent - CIS681 Global Deformations - twist

9. Rick Parent - CIS681 Global Deformations - rotate

10. Rick Parent - CIS681 Global Deformations - rotate

11. Rick Parent - CIS681 Global Deformations - compound

12. Rick Parent - CIS681 Skeletal Deformation

13. Rick Parent - CIS681 Skeletal Deformation Interior angle bisectors Perpendiculars at end points

14. Rick Parent - CIS681 Skeletal Deformation d L s Get object Draw polyline Map vertices to polyline Warp polyline Reposition vertices to polyline

15. Rick Parent - CIS681 Skeletal Deformation

16. Rick Parent - CIS681 Grid Deformation 2D technique used in the film HUNGER Overlay 2D grid on top of object Map object vertices to grid cells (create local coordinate system) User distorts 2D grid vertices Object vertices are remapped to local coordinate system of 2D grid by using bilinear interpolation

17. Rick Parent - CIS681 Grid Deformation

18. Rick Parent - CIS681 Grid Deformation 0.5 0.8 For each vertex Idenify cell Local u,v coorindate

19. Rick Parent - CIS681 Grid Deformation Bilinear interpolation Pu0 = (1-u)*P00 + u*P10 Pu1 = (1-u)*P01 + u*P11 Puv = (1-v)*P0u + v*P1u P00 P01 P11 Pu0 Pu1

20. Rick Parent - CIS681 Grid Deformation

21. Rick Parent - CIS681 Grid Deformation

22. Rick Parent - CIS681 Free-Form Deformations (not necessarily mutually perpendicular) S T U Define local coordinate system for deformation

23. Rick Parent - CIS681 FFD - register point in cell S T U

24. Rick Parent - CIS681 FFD - register point in cell s = (TxU). (P-P0) / ((TxU). S) TxU U S T P P0 ((TxU). S) (TxU). (P-P0) P = P0 + sS + tT + uU

25. Rick Parent - CIS681 FFD - create control grid (not necessarily mutually perpendicular)

26. Rick Parent - CIS681 FFD - move and reposition Move control grid points Usually tri-cubic interpolation is used with FFDs Originally Bezier interpolation was used. B-spline and Catmull-Romm interpolation have also been used (as well as tri-linear interpolation)

27. Rick Parent - CIS681 FFD - extensions Hierarchical FFDs Animated FFD Static FFD that object moves through Non-parallelpiped FFD

28. Rick Parent - CIS681 FFD - films and videos examples Boppin’ in Bean Town by John Chadwick Facit demo by Beth Hofer Balloon Guy by Chris Wedge