FreeForm Deformations Dr Scott Schaefer 1 Deformation 228
- Slides: 75
Free-Form Deformations Dr. Scott Schaefer 1
Deformation 2/28
Deformation 3/28
Deformation Applications Toy Story © Disney / Pixar 4/28
Challenges in Deformation Large meshes – millions of polygons n Need efficient techniques for computing and specifying the deformation n Digital Michelangelo Project 5/28
Deformation Handles n Low-resolution auxiliary shape controls deformation of high-resolution model 6/28
Deformation Handles n Low-resolution auxiliary shape controls deformation of high-resolution model 7/28
Deformation Handles n Low-resolution auxiliary shape controls deformation of high-resolution model 8/28
Deformation Handles n Low-resolution auxiliary shape controls deformation of high-resolution model 9/28
FFD Contributions Smooth deformations of arbitrary shapes n Local control of deformation n Performing deformation is fast n n Widely used u Game/Movie industry u Part of nearly every 3 D modeler 10/28
Free-Form Deformations Embed object in uniform grid n Represent each point in space as a weighted combination of grid vertices n 11/28
Free-Form Deformations Embed object in uniform grid n Represent each point in space as a weighted combination of grid vertices n Assume xi are equally spaced and use Bernstein basis functions n 12/28
Free-Form Deformations Embed object in uniform grid n Represent each point in space as a weighted combination of grid vertices n Assume xi are equally spaced and use Bernstein basis functions n 13/28
Free-Form Deformations Embed object in uniform grid n Represent each point in space as a weighted combination of grid vertices n Assume xi are equally spaced and use Bernstein basis functions n 14/28
2 D Example 15/28
2 D Example 16/28
2 D Example 17/28
2 D Example 18/28
2 D Example 19/28
2 D Example 20/28
Applying the Deformation 21/28
Applying the Deformation 22/28
Applying the Deformation 23/28
Smoothness of Deformation n Constraining Bezier control points controls smoothness Image taken from “Free-form Deformations of Solid Geometric Models” 24/28
Volume Preservation n Must ensure that the jacobian of the deformation is 1 everywhere Images taken from “Free-form Deformations of Solid Geometric Models” 25/28
Advantages Smooth Deformation of arbitrary shapes n Local control of deformations n Computing the deformation is easy n Deformations are very fast n 26/28
Disadvantages Must use cubical cells for deformation n Restricted to uniform grid n Deformation warps space… not surface u Does not take into account geometry/topology of surface n May need many FFD’s to achieve a simple deformation n 27/28
Summary Widely used deformation technique n Fast, easy to compute n Some control over volume preservation/smoothness n n Uniform grids are restrictive 28/28
Barycentric Coordinates
Cage Based Deformation
Cage Based Deformation
Barycentric Coordinates
S-Patches
Indices
Indices
Indices
Indices
Indices
Degree Elevation
Degree Elevation
Degree Elevation
Cage Deformations
Cage Deformations
Selective Degree Elevation
Selective Degree Elevation
Selective Degree Elevation
Selective Degree Elevation 0
Selective Degree Elevation 0 0
Selective Degree Elevation 0
Selective Degree Elevation 0 Existing Control Points New Control Point
Concave Domain
Concave Domain
Domain with Holes
Domain with Holes
Elevation Effect
Elevation Effect
Elevation Effect
Elevation Effect
Elevation Effect
Elevation Effect
Elevation Effect
Elevation Effect
Elevation Effect
Elevation Effect
Cage Based Deformation
Cage Based Deformation
Cage Based Deformation
Cage Based Deformation
Cage Based Deformation
Cage Based Deformation
Cage Based Deformation
Cage Based Deformation
Cage Based Deformation
Cage Based Deformation
Cage Based Deformation