CS 551 / 645: Introductory Computer Graphics

1. CS 551 / 645: Introductory Computer Graphics David Luebke cs551@cs.virginia.edu http://www.cs.virginia.edu/~cs551 David Luebke 6/5/2014

2. Administrivia • Note changes on homework web page • We were always drawing the icosahedron inside out…oops David Luebke 6/5/2014

3. Recap: Visible Surface Determination • Reasons for invisible polygons: • Polygon outside the field of view • Polygon is backfacing • Polygon is occludedby object(s) nearer the viewpoint • Algorithms for determining which potions of which polygons are visible (unoccluded) are known as visible surface algorithms David Luebke 6/5/2014

4. Recap: Occlusion • For most interesting scenes, some polygons will overlap: • To render the correct image, we need to determine which polygons occlude which David Luebke 6/5/2014

5. Recap: Painter’s Algorithm • Simple approach: render the polygons from back to front, “painting over” previous polygons: • Doesn’t work in general case • Intersecting polygons • Visibility cycles: David Luebke 6/5/2014

6. Recap: Binary Space Partition(BSP) Trees • Fuchs et al, 1980 • Assumptions: • Static scene • Moving camera • Commonly used in 3-D video games (e.g., Quake), but going out of style • Still a very powerful, general idea, used in many graphics algorithms David Luebke 6/5/2014

7. Recap: BSP Trees • Preprocess: overlay a binary (BSP) tree on objects in the scene • Runtime: correctly traversing this tree enumerates objects from back to front • Idea: divide space recursively into half-spaces by choosing splitting planes • Splitting planes can be arbitrarily oriented • Notice: nodes are always convex David Luebke 6/5/2014

8. Recap: BSP Trees David Luebke 6/5/2014

9. Recap: BSP Trees David Luebke 6/5/2014

10. Recap: BSP Trees David Luebke 6/5/2014

11. Recap: BSP Trees David Luebke 6/5/2014

12. Recap: BSP Trees David Luebke 6/5/2014

13. Recap: Rendering BSP Trees renderBSP(BSPtree *T) BSPtree *near, far; if (T is a leaf node) renderObject(T) if (eye on left side of T->plane) near = T->left; far = T->right; else near = T->right; far = T->left; renderBSP(far); renderBSP(near); David Luebke 6/5/2014

14. Recap: Rendering BSP Trees David Luebke 6/5/2014

15. Recap: Rendering BSP Trees David Luebke 6/5/2014

16. Ouch Recap: BSP Tree Cons • No bunnies were harmed in my example • But what if a splitting plane passes through an object? • Split the object; give half to each node: • Worst case: can create up to O(n3) objects! David Luebke 6/5/2014

17. BSP Demo • Really cool demo: http://symbolcraft.com/pjl/graphics/bsp David Luebke 6/5/2014

18. Warnock’s Algorithm (1969) • Elegant scheme based on a powerful general approach common in graphics: if the situation is too complex, subdivide • Start with a root viewport and a list of all primitives • Then recursively: • Clip objects to viewport • If number of objects incident to viewport is zero or one, visibility is trivial • Otherwise, subdivide into smaller viewports, distribute primitives among them, and recurse David Luebke 6/5/2014

19. Warnock’s Algorithm • What is the terminating condition? • How to determine the correct visible surface in this case? David Luebke 6/5/2014

20. Warnock’s Algorithm • Pros: • Very elegant scheme • Extends to any primitive type • Cons: • Hard to embed hierarchical schemes in hardware • Complex scenes usually have small polygons and high depth complexity • Thus most screen regions come down to the single-pixel case David Luebke 6/5/2014

21. The Z-Buffer Algorithm • Both BSP trees and Warnock’s algorithm were proposed when memory was expensive • Example: first 512x512 framebuffer > $50,000! • Ed Catmull (mid-70s) proposed a radical new approach called z-buffering. • The big idea: resolve visibility independently at each pixel David Luebke 6/5/2014

22. The Z-Buffer Algorithm • We know how to rasterize polygons into an image discretized into pixels: David Luebke 6/5/2014

23. The Z-Buffer Algorithm • What happens if multiple primitives occupy the same pixel on the screen? Which is allowed to paint the pixel? David Luebke 6/5/2014

24. The Z-Buffer Algorithm • Idea: retain depth (Z in eye coordinates) through projection transform • Recall canonical viewing volumes (see slide) • Can transform canonical perspective volume into canonical parallel volume with: David Luebke 6/5/2014

25. The Z-Buffer Algorithm • Augment framebuffer with Z-buffer or depth buffer which stores Z value at each pixel • At frame beginning initialize all pixel depths to  • When rasterizing, interpolate depth (Z) across polygon and store in pixel of Z-buffer • Suppress writing to a pixel if its Z value is more distant than the Z value already stored there • “More distant”: greater than or less than, depending David Luebke 6/5/2014

26. Interpolating Z • Edge equations: Z is just another planar parameter: z = Ax + By + C • Look familiar? • Total cost: • 1 more parameter to increment in inner loop • 3x3 matrix multiply for setup • See interpolating color discussion from lecture 10 • Edge walking: just interpolate Z along edges and across spans David Luebke 6/5/2014

27. The Z-Buffer Algorithm • How much memory does the Z-buffer use? • Does the image rendered depend on the drawing order? • Does the time to render the image depend on the drawing order? • How much of the pipeline do occluded polgyons traverse? • What does this imply for the front of the pipeline? • How does Z-buffer load scale with visible polygons? With framebuffer resolution? David Luebke 6/5/2014

28. Z-Buffer Pros • Simple!!! • Easy to implement in hardware • Polygons can be processed in arbitrary order • Easily handles polygon interpenetration • Enables deferred shading • Rasterize shading parameters (e.g., surface normal) and only shade final visible fragments • When does this help? David Luebke 6/5/2014

29. Z-Buffer Cons • Lots of memory (e.g. 1280x1024x32 bits) • Read-Modify-Write in inner loop requires fast memory • Hard to do analytic antialiasing • Hard to simulate translucent polygons • Precision issues (scintillating, worse with perspective projection) David Luebke 6/5/2014