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Material Type: Notes; Class: Computer Graphics; Subject: Engineering Computer Science; University: University of California - Davis; Term: Unknown 1989;
Typology: Study notes
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Visible−Surface Detection
Identifying those parts of a scene that are visible from a chosen viewing position, and only process (scan−convert) those parts
Two approaches:
Two main strategies:
Visible −Surface Detection Algorithms:
Back−face detection
Z−buffer (cont’d)
z values can be calculated incrementally
x x+
y y−
Ax + By + Cz + D = 0
z’ = −A(x+1) − By −D C
= z −
top
y scan line
bottom
x’ = x −
m
z’ =
A/m + B
C
−A(x−(1/m)) − B(y−1) −D C
= z +
− Large amount of memory space is needed. What to do if short of memory space?
Z−buffer (cont’d)
− Aliasing problem!
− Handle only opaque surfaces
− Other use of z−buffer
Scan−Line Algorithm:
− combine polygon scan conversion with hidden surface removal
− scanline by scanline rather than polygon by polygon
a (^) b
c
d
i
j
− perform depth calculation only when more than one polygon intersects with the current scanline
− require sophisticated data structures to quickly locate the polygon/edges intersecting with current scanline
Painter’s algorithm:
− depth sort the polygons
− an object space algorithm
− analogous to the way an oil painter might render a scene
− scan−convert polygons in back−to−front order
How to depth sort?
p
p
zmin zmax
p
p xmax xmin
BSP−tree Method
− binary space partitioning tree
− storing relative positioning information
A
B
C
D
− applicable to data of arbitrary dimensions
− at each stage, the space is partitioned into two parts of arbitrary size
− each subdivision plane (or line) can have an arbitrary orientation
− view−dependent operations can be applied apropriately to the resulting two half−spaces
Area Subdivision (Warnock’s algorithm)
− try to make an easy decision about which polygon is visible in a section of the image. If a decision cannot be made, subdivide the area recursively until one can be made.
− work at image precision for subdivision, and at object precision for depth comparison
3 4
Octree Methods
− an octree is constructed by recursively partitioning the space into eight subspaces each of which is called an octant.
− regular partitioning
− spatial presorted and octants can be visited with a tree traversal
− back−to−front or front−to−back
− hierarchical Z−buffering for occlusion culling
Wireframe Methods
− may still want to draw the hidden lines!
− for drawing polygon mesh, computational mesh, outline of an object, illustration, ...
− visibility testing can be achieved with variations of clipping methods and other visible−surface methods
Coherence
− Object coherence 2 entirely separated objects can be compared at the object level
− Face coherence surface properties typically vary smoothly across a face
− Edge coherence an edge may change visibility only where it crosses behind a visible edge or penetrates a face
− Scan−line coherence the set of visible object spans determined for consecutive scanlines are often the same
− Area coherence a group of adjacent pixels is often covered by the same visible face
− Depth coherence adjacent parts of the same surface are typically close in depth
− Frame coherence two consecutive frames are likely to be similar
the degree to which parts of an environment or its projection exhibit local similarities
