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

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

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  0 visible < 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) 3-3

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

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

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

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