Part I:Basics of Computer Graphics

Visible Surface Determination

Chapter 3

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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

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Back Face Culling

A polygon is front facing when (the angle between the viewing vector v and the normal n of the polygon) lies between -90o and 90o or cos

Use dot product to test visibility v . n = |v| |n| cos 0visible 0 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)

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n v

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

z

x

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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 bufferfor recording

pixel color

Depth bufferfor recordingpixel depth

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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

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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

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