1 Free-Form Deformations Dr. Scott Schaefer

2/28 Deformation

3/28 Deformation

4/28 Deformation Applications Toy Story © Disney / Pixar

5/28 Challenges in Deformation Large meshes – millions of polygons Need efficient techniques for computing and specifying the deformation Digital Michelangelo Project

6/28 Deformation Handles Low-resolution auxiliary shape controls deformation of high-resolution model

7/28 Deformation Handles Low-resolution auxiliary shape controls deformation of high-resolution model

8/28 Deformation Handles Low-resolution auxiliary shape controls deformation of high-resolution model

9/28 Deformation Handles Low-resolution auxiliary shape controls deformation of high-resolution model

10/28 FFD Contributions Smooth deformations of arbitrary shapes Local control of deformation Performing deformation is fast Widely used  Game/Movie industry  Part of nearly every 3D modeler

11/28 Free-Form Deformations Embed object in uniform grid Represent each point in space as a weighted combination of grid vertices

12/28 Free-Form Deformations Embed object in uniform grid Represent each point in space as a weighted combination of grid vertices Assume x i are equally spaced and use Bernstein basis functions

13/28 Free-Form Deformations Embed object in uniform grid Represent each point in space as a weighted combination of grid vertices Assume x i are equally spaced and use Bernstein basis functions

14/28 Free-Form Deformations Embed object in uniform grid Represent each point in space as a weighted combination of grid vertices Assume x i are equally spaced and use Bernstein basis functions

15/28 2D Example

16/28 2D Example

17/28 2D Example

18/28 2D Example

19/28 2D Example

20/28 2D Example

21/28 Applying the Deformation

22/28 Applying the Deformation

23/28 Applying the Deformation

24/28 Smoothness of Deformation Constraining Bezier control points controls smoothness Image taken from “Free-form Deformations of Solid Geometric Models”

25/28 Volume Preservation Must ensure that the jacobian of the deformation is 1 everywhere Images taken from “Free-form Deformations of Solid Geometric Models”

26/28 Advantages Smooth Deformation of arbitrary shapes Local control of deformations Computing the deformation is easy Deformations are very fast

27/28 Disadvantages Must use cubical cells for deformation Restricted to uniform grid Deformation warps space… not surface  Does not take into account geometry/topology of surface May need many FFD’s to achieve a simple deformation

28/28 Summary Widely used deformation technique Fast, easy to compute Some control over volume preservation/smoothness Uniform grids are restrictive