1. Part I: Basics of Computer Graphics
Chapter 3
Visible Surface Determination
3-1

2. Visible Surface Determination
When 3D objects are projected onto the 2D screen, occlusion happens
From a given viewpoint, what is in front?
Viewpoint dependent problem
Object-based algorithms
Image-based algorithms
Major algorithms:
Back face culling
Depth-sort (painter’s) algorithm
Z-buffer algorithm
Scanline algorithm
Area coherence algorithm
Ray-casting and ray-tracing algorithm
3-2

3. Back Face Culling q v n
A polygon is front facing when q (the angle between the viewing vector v and the normal n of the polygon) lies between -90o and 90o or cos q  0
Use dot product to test visibility v . n = |v| |n| cos q  visible < invisible
All polygon vertices must be ordered in anti-clockwise fashion to yield a correctly directed normal vector
Might not remove all invisible objects (those due to occlusion)
Might remove objects we want. Sometimes we want back facing polygon (when inside an object)
3-3

4. x z Sort all polygons according to the furthest z coordinates
Depth-sort algorithm
Sort all polygons according to the furthest z coordinates
Resolve problems of overlapping (in z) polygons (e.g. subdivision)
Scan convert (project 3D polygon to 2D and draw it) each polygon in ascending order of z coordinate (back to front)
The mechanism is similar to how a painter draws layers of objects from back to front
Also known as painter’s algorithm x z
3-4

5. Maintain a Z-buffer with same resolution as frame buffer
Z-Buffer Algorithm
Maintain a Z-buffer with same resolution as frame buffer
During scan conversion compare
Z value of pixel about to be stored and
Z value of current pixel in Z-buffer
If new pixel’s Z value is closer, store new pixel value (color) in frame buffer and new Z value in Z-buffer
Running time is linear to the number of objects
Suffers from aliasing if precision is low
Frequent hardware implementations because of its simplicity and speed
Frame buffer
for recording
pixel color
Depth buffer
for recording
pixel depth
3-5

6. Use of data structures reduce computation Exploits edge coherence
Scanline algorithm
Use of data structures reduce computation
Exploits edge coherence
While advancing along scan-line
determine surface that projects to pixel
choose closest surface from the sorted list
Due to the complexity of manipulating the data structure, it is less popular
3-6

7. Actually backward ray tracing
Ray tracing algorithm
Actually backward ray tracing
Send ray from the eye, through the pixel into the modeled virtual world
Determine which surface is intersected first
Can be combined with lighting algorithms
Extremely slow: O(resolution*number of objects)
Comprehensive solution to shadow generation, reflection, and refraction
Partially solves the global illumination problem
3-7