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Clipping and Hidden Surface Removal in Game Technology - Lecture #2.2

This lecture covers crucial techniques in computer graphics, focusing on clipping and hidden surface removal. It explains how to define view volumes, the challenges of clipping arbitrary polygons, and various methods like Z-buffers and BSP trees to manage visibility in 3D graphics. The Sutherland-Hodgman algorithm and the Liang-Barsky method are introduced for efficient polygon clipping. Additionally, the lecture discusses memory issues, depth testing techniques, and the importance of depth values in rendering. Suggested readings are provided for further exploration of these concepts.

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Clipping and Hidden Surface Removal in Game Technology - Lecture #2.2

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  1. CS-378: Game Technology • Lecture #2.2: Clipping and • Hidden Surfaces • Prof. Okan Arikan • University of Texas, Austin • Thanks to James O’Brien, Steve Chenney, Zoran Popovic, Jessica Hodgins • V2005-06-1.1

  2. Today • Clipping • Clipping to view volume • Clipping arbitrary polygons • Hidden Surface Removal • Z-Buffer • BSP Trees • Others

  3. Clipping • Stuff outside view volume should not be drawn • Too close: obscures view

  4. Clipping • Stuff outside view volume should not be drawn • Too close: obscures view • Too far: • Complexity • Z-buffer problems • Too high/low/right/left: • Memory errors • Broken algorithms • Complexity

  5. Clipping Line to Line/Plane Line segment to be clipped Line/plane that clips it

  6. Clipping Line to Line/Plane Line segment to be clipped Line/plane that clips it

  7. Clipping Line to Line/Plane • Segment may be on one side • Lines may be parallel

  8. Polygon Clip to Convex Domain • Convex domain defined by collection of planes (or lines or hyper-planes) • Planes have outward pointing normals • Clip against each plane in turn • Check for early/trivial rejection

  9. Polygon Clip to Convex Domain

  10. Polygon Clip to Convex Domain

  11. Polygon Clip to Convex Domain • Sutherland-Hodgman algorithm • Basically edge walking • Clipping done often... should be efficient • Liang-Barsky parametric space algorithm • See text for clipping in 4D homogenized coordiantes

  12. General Polygon Clipping

  13. General Polygon Clipping • Weiler Algorithm • Double edges

  14. Hidden Surface Removal • True 3D to 2D projection would put every thing overlapping into the view plane. • We need to determine what’s in front and display only that.

  15. Z-Buffers • Add extra depth channel to image • Write Z values when writing pixels • Test Z values before writing

  16. Z-Buffers • Benefits • Easy to implement • Works for most any geometric primitive • Parallel operation in hardware • Limitations • Quantization and aliasing artifacts • Overfill • Transparency does not work well

  17. Z-Buffers • Transparency requires partial sorting:

  18. Z-Buffers Recall depth-value distortions. It’s a feature... More resolution near viewer Best use of limited precision

  19. A-Buffers • Store sorted list of “fragments” at each pixel • Draw all opaque stuff first then transparent • Stuff behind full opacity gets ignored • Nice for antialiasing...

  20. Scan-line Algorithm • Assume polygons don’t intersect • Each time an edge is crossed determine who’s on top

  21. Painter’s Algorithm • Sort Polygons Front-to-Back • Draw in order • Back-to-Front works also, but wasteful • How to sort quickly? • Intersecting polygons? • Cycles?

  22. BSP-Trees • Binary Space Partition Trees • Split space along planes • Allows fast queries of some spatial relations • Simple construction algorithm • Select a plane as sub-tree root • Everything on one side to one child • Everything on the other side to other child • Use random polygon for splitting plane

  23. BSP-Trees

  24. BSP-Trees

  25. BSP-Trees

  26. BSP-Trees

  27. BSP-Trees

  28. + - + + + - + - + + + + BSP-Trees

  29. Visibility Traversal • Variation of in-order-traversal • Child one • Sub-tree root • Child two • Select “child one” based on location of viewpoint • Child one on same side of sub-tree root as viewpoint

  30. BSP-Trees

  31. BSP-Trees

  32. Suggested Reading • Fundamentals of Computer Graphics by Pete Shirley • Chapter 7 • Clipping in chapter 11.1 and 11.2

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