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Deforming Objects

Deforming Objects. Non-Uniform Scale. Global Deformations. Skeletal Deformations. Grid Deformations. Free-Form Deformations (FFDs). Sx. 0. 0. 0. 0. Sy. 0. 0. 0. 0. Sz. 0. 0. 0. 0. 1. Non-uniform Scale. Transformation matrix - diagonal elements. Non-uniform Scale.

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Deforming Objects

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

  2. Sx 0 0 0 0 Sy 0 0 0 0 Sz 0 0 0 0 1 Non-uniform Scale Transformation matrix - diagonal elements

  3. Non-uniform Scale

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

  5. Global Deformations - taper

  6. Global Deformations - taper

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

  8. Global Deformations - twist

  9. Global Deformations - rotate

  10. Global Deformations - rotate

  11. Global Deformations - compound

  12. Skeletal Deformation

  13. Skeletal Deformation Interior angle bisectors Perpendiculars at end points

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

  15. Skeletal Deformation

  16. 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. Grid Deformation

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

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

  20. Grid Deformation

  21. Grid Deformation

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

  23. FFD - register point in cell T U S

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

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

  26. 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. FFD - extensions Hierarchical FFDs Animated FFD Static FFD that object moves through Non-parallelpiped FFD

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

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