Rick Parent - CIS681

Deforming Objects

Free-Form Deformations (FFDs)

Global Deformations

Non-Uniform Scale

Grid Deformations

Skeletal Deformations

Rick Parent - CIS681

Non-uniform Scale

Transformation matrix - diagonal elements

0

1

Sx

Sy

Sz

0

0

0

0

0

0 0

0

00 0

Rick Parent - CIS681

Non-uniform Scale

Rick Parent - CIS681

Global Deformations

Transformation matrix elements - functions of coordinates

f(x,y,z) g(x,y,z)

Rick Parent - CIS681

Global Deformations - taper

Rick Parent - CIS681

Global Deformations - taper

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))

Rick Parent - CIS681

Global Deformations - twist

Rick Parent - CIS681

Global Deformations - rotate

Rick Parent - CIS681

Global Deformations - rotate

Rick Parent - CIS681

Global Deformations - compound

Rick Parent - CIS681

Skeletal Deformation

Rick Parent - CIS681

Skeletal Deformation

Interior angle bisectors

Perpendiculars at end points

Rick Parent - CIS681

Skeletal Deformation

d

L

s

Get object

Draw polyline

Map vertices to polyline

Warp polyline

Reposition vertices to polyline

Rick Parent - CIS681

Skeletal Deformation

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

Rick Parent - CIS681

Grid Deformation

Rick Parent - CIS681

Grid Deformation

0.5

0.8

For each vertexIdenify cellLocal u,v coorindate

Rick Parent - CIS681

Grid Deformation

Bilinear interpolationPu0 = (1-u)*P00 + u*P10Pu1 = (1-u)*P01 + u*P11Puv = (1-v)*P0u + v*P1u

P00

P01

P01

P11

Pu0

Pu1

Rick Parent - CIS681

Grid Deformation

Rick Parent - CIS681

Grid Deformation

Rick Parent - CIS681

Free-Form Deformations

(not necessarily mutually perpendicular)

S

T

U

Define local coordinate system for deformation

Rick Parent - CIS681

FFD - register point in cell

S

T

U

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

Rick Parent - CIS681

FFD - create control grid

(not necessarily mutually perpendicular)

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)

Rick Parent - CIS681

FFD - extensions

Hierarchical FFDs

Animated FFD

Static FFD that object moves through

Non-parallelpiped FFD

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