The 3D Pipeline

1
The 3D Pipeline

• Jim Van Verth (jim_at_essentialmath.com)
• Lars M. Bishop (lars_at_essentialmath.com)

2
The 3D Pipeline

• Three problems
• want to construct hierarchy of objects
• transformation of object combined with its
  children
• want to manipulate camera
• viewing transformation
• want to render objects to screen
• projection/screen transformation

3
The 3D Pipeline

• Where geometric objects are transformed through a
  series of spaces
• They are fed in as 3D objects in their own space
  (model space)
• They come out as pixels on the screen (screen
  space)

Model
World
View
Screen
NDC
4
Model Space
z
x
y

• AKA local space, object space
• Where object vertices are defined
• Origin at center of object (or at pivot)
• Right-handed is common
• Z up arbitrary, also see Y-axis up

5
World Space
z
x
y

• Where objects are placed
• Origin at center of world or scene
• Right-handed is good (consistency)
• View position, orientation usually expressed here

6
Hierarchical Spaces

• Suppose have arm connected to body in world
• First transform arm to body space
• Then transform arm to world space
• Standard order scale, rotate, translate
• Often, objects are modeled around a pivot point
  (e.g. shoulder for arm)

7
Hierarchical Transforms

• First transform arm to body space

MAB TARAsA
Arm in Arms Model Space
Arm in Bodys Model Space
DEMO
8
Hierarchical Transforms

• Then body, arm to world space

MBW TBRBsB
MAW MBWMAB
DEMO
9
Hierarchical Transforms

• In practice, body and arm have separate
  transforms
• Arm transform is relative to body
• Draw body with its transform (MBW)
• Draw arm with concatenation of body and arm
  transforms (MBW MAB)
• Objects can move independently

10
Scene Graph

• Common structure for hierarchical scenes
• Jointed (or skinned) characters are the most
  frequent applications
• Using like a tree doesnt have to be
• Instancing makes it a DAG

11
Example Scene Graph
Node
Node
Body
Scene Graph need not be a binary tree! Nodes can
have as many children as needed
Node
Turret
Barrel
12
Scene Graph(One Implementation)

• Spatial
• Base class, handles transforms, bounds
• Node
• Maintains hierarchy (array of children)
• Geometry
• Leaf nodes, contain renderable geometry

13
Using Scene Graph

• Update transforms
• Pass down from top to geometry nodes
• Concatenate and store world transforms at each
  level
• Used for collision, culling
• Render
• Recursively call Render() on all children
• Bounding volumes allow for fast culling

DEMO
14
References

• Foley, James D., Andries van Dam, et. al.,
  Computer Graphics Principles and Practice,
  Addison-Wesley, Reading, MA, 1990.
• Blinn, Jim, Jim Blinns Corner A Trip Down the
  Graphics Pipeline, Morgan Kaufman, San Francisco,
  1996.
• Eberly, David H., 3D Game Engine Design, Morgan
  Kaufmann, San Francisco, 2001.