Static Models
Our models are static sets of polygons
We can only move them via transformations
• translate, scale, rotate, or any other 4x4 matrix
This does not allow us to simulate very realistic motion
So how do we fix this?
A Multitude of Spaces
Recall that transformations move us
between different coordinate spaces
Vertices move through many spaces
We change spaces for convenience
• as with the view transform
e1
e2e′1
e′2
Object Space
World Space
Eye Space
Clip Space
Normalized Device Coordinates
Window Coordinates
Model Transform
View Transform
Projection
Perspective Division
Viewport Transform
First Step: Break the thing Apart
Model object as hierarchy of components
• each object node has a local coordinate
system
• each component defined relative to
parent
• each one can move
• and they move relative to parent
How do they move?
• with transformations
Body
Upper Head Lower
L Arm Torso R Arm
Introduce Transformation Nodes
Traverse hierarchy during draw
• object nodes: draw them
• transform nodes
– multiply into current matrix on way down
– remove from current matrix on way up
Constantly changing local coordinate system
Allows changes at different scales
• apply rotation above “Body”
• vs. rotation above “L Arm”
Body
Upper
L Arm
body
M
upper
M
larm
M
Current Matrix
body
MM⋅
body upper
MM M⋅⋅
body upper larm
MM M M⋅⋅ ⋅
