Visible-Surface Detection

1. Visible-Surface Detection Jehee Lee Seoul National University

2. Visible-Surface Detection Methods • Determine what is visible within a scene from a chosen viewing position • Two approaches • Object-space methods: Decide which object, as a whole, is visible • Image-space methods: The visibility is decided point-by-point • Most visible-surface algorithms use image-space methods • Sometimes, these methods are referred to as hidden-surface elimination

3. Approaches • Back-Face Removal • Depth Buffer • A-Buffer • Scanline • Depth Sorting • BSP Tree • Area Subdivision • Octree • Raycasting

4. Back-Face Removal (Culling) • Used to remove unseen polygons from convex, closed polyhedron • Does not completely solve hidden surface problem since one polyhedron may obscure another

5. Back-Face Removal (Culling) • Compute the equation of the plane for each polygon • A point (x,y,z) is behind a polygon surface if • Determine back-face • In projection coordinates, we need to consider only the z component of the normal vector N

6. Depth-Buffer (Z-Buffer) • Z-Buffer has memory corresponding to each pixel location • Usually, 16 to 20 bits/location.

7. Depth-Buffer (Z-Buffer) • Initialize • Each z-buffer location  Max z value • Each frame buffer location  background color • For each polygon: • Compute z(x,y), polygon depth at the pixel (x,y) • If z(x,y) < z-buffer value at pixel (x,y), then • z buffer(x,y)  z(x,y) • pixel(x,y)  color of polygon at (x,y)

8. Depth Calculation • Calculate the z-value on the plane • Incremental calculation

9. Depth-Buffer (Z-Buffer) • Advantages/Disadvantages • Lots of memory (not anymore) • Linear performance • Polygons may be processed in any order • Modifications needed to implement antialiasing, transparency, translucency effects • Commonly implemented in hardware  very fast

10. Depth-Buffer (Z-Buffer) Backface culling Z-buffer algorithm

11. Accumulation Buffer (A-Buffer) • An extension of the depth-buffer for dealing with anti-aliasing, area-averaging, transparency, and translucency • The depth-buffer method identifies only one visible surface at each pixel position • Cannot accumulate color values for more than one transparent and translucent surfaces • Even more memory intensive • Widely used for high quality rendering

12. Accumulation Buffer (A-Buffer) • Each position in the A-buffer has two fields • Depth field: Stores a depth value • Surface data field • RGB intensity components • Opacity parameter (percent of transparency) • Depth • Percent of area coverage • Surface identifier

13. Scan Line Method • Intersect each polygon with a particular scanline and solve hidden surface problem for just that scan line • Requires a depth buffer equal to only one scan line • Requires the entire scene data at the time of scan conversion • Maintain an active polygon and active edge list • Can implement antialiasing as part of the algorithm

14. Depth Sorting • Painter’s algorithm • Draw polygons as an oil painters might do • Sort polygons by depth and draw them from back to front • Depth sorting is NOT simple

15. Depth Sorting • We need a partial ordering (not a total ordering) of polygons • The ordering indicates which polygon obscures which polygon • Some polygons may not obscure each other • Simple cases

16. Depth Sorting • We make the following tests for each polygon that has a depth overlap with S • If any one of these tests is true, no reordering is necessary for S and the polygon being tested • Polygon S is completely behind the overlapping surface relative to the viewing position • The overlapping polygon is completely in front of S relative to the viewing position • The boundary-edge projections of the two polygons onto the view plane do not overlap

17. Depth Sorting • Example

18. Depth Sorting • Cyclically overlapping surfaces that alternately obscure one another • We can divide the surfaces to eliminate the cyclic overlaps

19. BSP Trees • Binary space partitioning is an efficient method for determining object visibility • Paint surfaces into the frame buffer from back to front • Particularly useful when the view reference point changes, but the objects are at fixed positions

20. BSP Tree Construction • Choose a polygon T and compute the equation of the plane it defines • Test all the vertices of all the other polygons to determine if they are in front of, behind, or in the same plane as T. • If the plane intersects a polygon, divide the polygon at the plane • Polygons are placed into a binary search three with T as the root • Call the procedure recursively on the left and right subtree

21. Traversing BSP Trees EYE 1 A F2 B C +Z D E1 F1 D F1 C E2 F2 E2 A E1 B +X -X EYE 2

22. BSP Trees • BST tree construction requires a number of polygons to be fractured • It is possible for the number of triangles to increase exponentially but, in practice, it is found that the increase may be as small as two fold • A heuristic to help minimize the number of fractures is to enter the polygons into the tree in order from largest to smallest

23. Area Subdivision • Image-space method taking advantage of area coherence in a scene • Recursively subdivide a square area into equal-sized quadrants if the area is too complex to analyze easily

24. Area Subdivision • Four possible relationships between polygon surfaces and a rectangular section of the viewing plane • Terminating criteria • Case 1: An area has no inside, overlapping, or surrounding surfaces (all surfaces are ourside the area) • Case 2: An area has only one inside, overlapping or surrounding surfaces • Case 3: An area has one surrounding surface that obscures all other surfaces within the area boundaries

25. Octrees • Visible-surface identification is accomplished by searching octree nodes in a front-to-back order

26. Ray Casting • We consider the line of sight from the a pixel position through the scene • Useful for volume data • Ray casting is a special case of ray tracing that we will study later

27. Ray Casting Examples