1. CECS461 Computer Graphics II University of Missouri at Columbia Hidden Surface Removal

2. CECS461 Computer Graphics II University of Missouri at Columbia Hidden Surface Removal Object-Space and Image-Space Approaches Back-Face Culling Z-Buffer Algorithm Depth Sort and Painter’s Algorithm Object-Space and Image-Space Approaches Back-Face Culling Z-Buffer Algorithm Depth Sort and Painter’s Algorithm

3. CECS461 Computer Graphics II University of Missouri at Columbia Algorithm Classifications Object-Space Methods: –Visibility is decided by comparing objects in object- space. –e.g. painter’s algorithm. Image-Space Methods: –Visibility is decided at each pixel position in the projection plane. –e.g. Z-Buffer algorithm Object-Space Methods: –Visibility is decided by comparing objects in object- space. –e.g. painter’s algorithm. Image-Space Methods: –Visibility is decided at each pixel position in the projection plane. –e.g. Z-Buffer algorithm

4. CECS461 Computer Graphics II University of Missouri at Columbia Back Face Culling x z

5. CECS461 Computer Graphics II University of Missouri at Columbia Back Face Culling x z A polygon is a back face if V N > 0. For OpenGL, V=(0,0,-1) A polygon is a back face if V N > 0. For OpenGL, V=(0,0,-1)

6. CECS461 Computer Graphics II University of Missouri at Columbia Z-Buffer Algorithm x (x, y) z y Most widely used Image-space algorithm. Easy to implement, both in software and hardware. Incremental computation. Most widely used Image-space algorithm. Easy to implement, both in software and hardware. Incremental computation.

7. CECS461 Computer Graphics II University of Missouri at Columbia Z-Buffer Algorithm x (x, y) z y

8. CECS461 Computer Graphics II University of Missouri at Columbia Z-Buffer Algorithm Can be conducted with scan-conversion. Assume the plane equation of the triangle is ax + by + cz + d = 0 let (x 1, y 1, z 1 ) and (x 2, y 2, z 2 ) be two points on the triangle.  x = x 2 - x 1,  y = y 2 - y 1,  z = z 2 - z 1 then a  x + b  y + c  z = 0 since  x = 1,  y = 0, then  z = - a/c. Can be conducted with scan-conversion. Assume the plane equation of the triangle is ax + by + cz + d = 0 let (x 1, y 1, z 1 ) and (x 2, y 2, z 2 ) be two points on the triangle.  x = x 2 - x 1,  y = y 2 - y 1,  z = z 2 - z 1 then a  x + b  y + c  z = 0 since  x = 1,  y = 0, then  z = - a/c.

9. CECS461 Computer Graphics II University of Missouri at Columbia Painter’s Algorithm Back-to-front rendering: polygons are sorted by z-coordinates in object space, and are rendered in back-to-front order. x z y A C B

10. CECS461 Computer Graphics II University of Missouri at Columbia Painter’s Algorithm Need to check for overlapping using BSP tree or Octree. Overlapped triangles need to be spitted. Need to check for overlapping using BSP tree or Octree. Overlapped triangles need to be spitted.