Lecture 2 visible-surface determination Books Visible ... - Faculty

Lecture 2
visible-surface determination
Prof. Marcelo Kallmann
mkallmann@ucmerced.edu
Visible-surface Determination
M. Kallmann, Fall 2006, UCM
M. Kallmann, Fall 2006, UCM
Books
– 3-D Computer Graphics
Samuel R. Buss
– 3D Computer Graphics
Alan H. Watt
– Fundamentals of Computer Graphics
Peter Shirley et al
– Introduction to Computer Graphics
Foley, van Dam et al
– Computer Graphics: Principles
and Practice (1990)
Foley, van Dam et al
– OpenGL red book
http://www.rush3d.com/reference/opengl-redbook-1.1/
The Rendering Pipeline
Modeling
Transformations
Lighting
Viewing/Camera
Transformations
Projection
Transformation
Clipping
∀ Objects
Scan Conversion Image
M. Kallmann, Fall 2006, UCM
M. Kallmann, Fall 2006, UCM

Visible-surface Determination
• Which polygons go in front and which go
behind during rasterization?
– depth-sorting
– BSP trees
– z-buffer
– there are others
• scan line, area subdivision, etc
• Back-face culling
– only renders polygons facing camera
– easy to determine with polygon normal
Depth Sorting
M. Kallmann, Fall 2006, UCM
1. Sort polygons according to z coordinate
2. Resolve ambiguities when polygon’s z
extents overlap, split polygons if needed
3. Start “painting” the polygons farther away
from the camera
z
each polygon has to test
all others intersecting its
“z extent”
z
M. Kallmann, Fall 2006, UCM
Depth Sorting
• Also called the painters algorithm:
1. Sort polygons according to z coordinate
2. Start “painting” the polygons farther away
from the camera
Is that all?
BSP trees
z
M. Kallmann, Fall 2006, UCM
1. Build a tree “ordering” the polygons
according to “half spaces separability”
2. Traverse the tree according to view point
M. Kallmann, Fall 2006, UCM

BSP tree construction 1/3
5
1
4a
2
4
3
4b
BSP tree construction 3/3
5
1
4a
2
4
3
4b
4a
front
front
2 back
1 3
4a 4b
5
1
M. Kallmann, Fall 2006, UCM
2 back
3
5 4b
M. Kallmann, Fall 2006, UCM
BSP tree construction 2/3
5
1
4a
BSP tree traversal
2
4
3
4b
front
1
4a
5
if viewer in root polygon’s front half-space
else
1. display polygons in root’s rear half-space
2. display root
3. display polygons in root’s front half-space
1. display polygons in root’s front half-space
2. display root
3. display polygons in root’s rear half-space
recursively process root’s children
2 back
3
4b
M. Kallmann, Fall 2006, UCM
M. Kallmann, Fall 2006, UCM

BSP tree traversal
5
1
Z-Buffer
A
4a
A: 3, 4b, 2, 5, 1, 4a
B: 5, 1, 4a, 2, 4b, 3
2
4
3
4b
B
4a
front
1
2 back
3
5 4b
M. Kallmann, Fall 2006, UCM
• No sorting!
– Rasterize polygons in any order
• But maintain a buffer with same image size
– each pixel in the buffer stores the z-value of the
respective pixel in the image
– new pixels are only displayed if their z-value are
greater (closer to viewer) than previous value
z
z=4
M. Kallmann, Fall 2006, UCM
BSP tree traversal
• Tree is constructed at pre-processing
• Viewpoint can move but not polygons
– Tree has to be reconstructed/updated every
time a polygon moves
• Need to know “front” and “back” of polygons
– easy determination based on normals
Z-Buffer
4
4 4 4 4 4 4
4 4 4 4 4 4 4
4 4 4 4 4 4 4
4 4 4 4 4 4 4
4 4 4 4 4 4 4
4 4 4 4 4 4 4
4 4 4 4 4 4 4
M. Kallmann, Fall 2006, UCM
M. Kallmann, Fall 2006, UCM

Z-Buffer
Z-Buffer
• Very fast!
• Uses more memory
– for ex, 1600x1200x1 ≅ 2MB
– need to choose depth buffer resolution
– graphics cards have lots of memory
– memory is now cheap
4
4
4
4
4
4
4
4
4
4
4
4
4
4
• Most interactive graphics tools use z-buffer
– OpenGL uses z-buffer
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
M. Kallmann, Fall 2006, UCM
M. Kallmann, Fall 2006, UCM
Z-Buffer
Summary
7
7
8
8
6
6
7
7
8
8
9
9
6
6
6
6
7
7
7
8
8
9
9
9
5
5
5
6
6
7
7
7
8
8
9
• You need to know how the 3 algorithms
explained today work
– Depth-sorting, BSPs, depth buffer
4
5
5
5
6
6
7
7
7
8
4
4
5
5
5
6
6
6
7
• These same algorithms are also used for other
purposes
– Ex: desktop GUI management uses depth-sorting
4
4
4
5
5
5
6
6
3
4
4
4
4
5
5
5
3
4
4
4
4
4
5
4
3
4
4
4
4
4
4
4
3
3
3
3
3
2
2
2
2
1
1
1
1
0
0
M. Kallmann, Fall 2006, UCM
M. Kallmann, Fall 2006, UCM

Next Lecture
• Next Lecture
– Vector/Matrix algebra
– Transformation matrices
• Assignment 1
– First assignment will be posted after that
Notes: thanks to Fredo Durand for sharing some of his course notes
M. Kallmann, Fall 2006, UCM
Support Code
• Get started with OpenGL
– Support code is online
– Demonstration now!
• Which lab/platform is your preference?
• At least while ucmcrops is being updated,
CSE170 information will be posted at:
http://faculty.ucmerced.edu/mkallmann/cse170/
M. Kallmann, Fall 2006, UCM