Transcript 6.837 Lecture Notes - MIT Computer Science and Artificial

The Rendering Pipeline
Local Illumination Models
MIT EECS 6.837
Lecture 4, September 17th 2002
MIT EECS 6.837, Durand and Teller
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Administrative Notes
ROOM CHANGE:
th
19 ,
Starting this Thursday Sept.
6.837 will meet in room 2-190
(We will post signage to remind you.)
MIT EECS 6.837, Durand and Teller
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Administrative Notes
• Assignment 1: Due this Friday (9/20) at 5pm
– Questions about the assignment?
– Use turnin as directed on course page
• Final projects will be due December 4th
– Presentations scheduled for December 4th –10th
• Staff Office Hours
–
–
–
–
Durand: R 4-5 in 4-035 cluster; R 5-6 in NE43-254
Teller: W 3-4 in NE43-252; R 4-5 in 4-035 cluster
Ngan: R 2-6pm (location TBD)
Yu: TBD
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Inventor Resources for Assignment 1
• Example Files & Documentation
– Athena IRIX: /usr/share/data/models/
– Athena Linux: /mit/inventor/distrib/share/data/models
– athena% man SoCube, man SoTranslation, etc.
(must have /usr/share/catman or /mit/inventor/man in $MANPATH)
• On reserve at LCS reading room:
– Open Inventor C++ Reference Manual (The “green
book”)
– Inventor Mentor (The “orange book”)
• On Web:
– Various helpful links from course page
– Many illustrative Inventor files exist on-line
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Lecture Plan
• Last week:
– Object-space to world-space transformations
– Object modeling using Inventor language, tools
• Today:
– Overview of classical “rendering pipeline”
– Local illumination models (simplified)
• Thursday:
– Eye-space & perspective transformations
– Segment (2D) and polygon (frustum) clipping
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Rendering abstraction I
?
Input
Renderin
g
Pipeline
MIT EECS 6.837, Durand and Teller
Output
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Rendering inputs
•
•
•
•
Scene description
Lighting description & lighting model
Synthetic camera parameters
Raster viewport parameters
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Scene description
• Object geometry, placement, material
properties
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Lighting description & model
• Light source locations and characteristics
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Synthetic camera parameters
• Synthetic camera parameters
– Eye position and view frustum
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Raster viewport parameters
• Resolution (width x height) of pixel grid
onto which image plane is to be mapped
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Rendering output
• Framebuffer assignment
– Per-pixel intensity values suitable for display
• For example, an RGB value for each framebuffer
pixel
– Optionally, a depth (or z-value) at each pixel
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Rendering abstraction I
Scene description
Lighting description
Synthetic camera parameters
Raster viewport parameters
Input
Renderin
g
Pipeline
MIT EECS 6.837, Durand and Teller
Output
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Rendering Pipeline (Abstracted)
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Lighting
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Transforming normal vectors
• Suppose M takes object to world
coordinates:
p’ = M p
• How are normal vectors transformed?
n’ = ?
M
?
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Transforming normal vectors
• First attempt: just use transform M (e.g., shear):
 x'   1
  
 y '  0
 z '  = 0
  
 1  0
1
1
0
0
0 0  x 
 
0 0  y 
1 0  z 
 
0 1  1 
Normals (0,1) and (1,0)
transform to (1,1) and (1,0)!
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Transforming normal vectors
• We know that for p on H, n normal to H
nT p = 0
• And for any non-singular transform M that
nT (M-1 M) p = 0
• Which can be rewritten as
( nT M-1 ) ( M p ) = 0
• Thus the transpose of the transformed normal is
( nT M-1 )
• And the transformed normal itself is the transpose
( nT M-1 )T = M-T n
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Transforming normal vectors
• Thus under action of M, points transform as
p’ = M p
• And normal vectors transform as
n’ = M-T n
M
p’ = M p
n’ = M-T n
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Correct transformation
• Using same shear transform M as before:
Normals (0,1) and (1,0)
transform to (0,1) and (1,-1)
… are we done?
M-1
1

0
=
0

0
-1
1
0
0
0 0

0 0
1 0

0 1
M-T
1

-1
=
0

0
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0
1
0
0
0 0

0 0
1 0

0 1
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Lighting: Putting it all together
• Issue scene geometry to graphics pipeline,
transforming geometry, normals correctly
• Apply lighting equation at polygon vertices
by evaluating Phong illumination model there
• Interpolate vertex colors across polygon
interiors to produce color at each pixel
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Faceted and smooth shading
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Faceted and smooth shading
• Per-face normals:
# .../ivexamples/facetedpear.iv
Coordinate3 { ... }
NormalBinding { value PER_FACE }
IndexedFaceSet { coordIndex [ 0, 1, 2, -1,…
• Per-vertex normals
# .../ivexamples/smoothpear.iv
Coordinate3 { ... } # x y z per vertex
Normal { ... } # dx dy dz per vertex
NormalBinding { value PER_VERTEX }
IndexedFaceSet { coordIndex [ 0, 1, 2, -1,…
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When to Apply Lighting Equation?
• Apply in object space
– Adv: easy to compute normals
– Disadv: Must transform lights to object space
• So: apply in world coordinates
– Adv: lights usually specified in world space
• This is most common practice, but:
– 1) What if some vertices lie outside frustum?
– 2) Must transform normals to world space
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Next time, we’ll:
• Continue our trip down the graphics pipeline
• Study further relevant transformations
• See efficient segment and polygon clipping
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