1. CS 450: COMPUTER GRAPHICS VISIBLE SURFACE DETECTION SPRING 2015 DR. MICHAEL J. REALE

2. INTRODUCTION We’ve talked about drawing surfaces, but what happens when a surface is hidden? E.g., at the back of an object, obscured by another surface, etc. We need to determine which surfaces (or parts of surfaces) are visible Two general categories (which sometimes overlap): Object-space approaches  deal with objects/primitives themselves Image-space approaches  deal with projected primitives at pixel level

3. OVERVIEW In this slide deck, we will cover the following approaches: Back-face detection Depth-buffer/Z-buffer A-buffer BSP trees Octrees Ray-casting

4. BACK-FACE DETECTION

5. BACK-FACE CULLING If the normal is facing away from the camera, then the surface is probably behind an object In other words, given a normal N and a view direction V, if: …the surface is pointing away from the camera and can be removed If we’ve already performed the view transform, we only need look at the z coordinate of the normal: Back-face culling = removing polygons that are facing away from the camera

6. BACK-FACE CULLING All non-overlapping, convex shapes  done! Concave shapes  may obscure themselves  more work to do Overlapping shapes (convex or concave)  still more work to do However, it is always a good preprocessing step to other approaches  generally cuts the total number of polygons to render in half

7. OPENGL FACE CULLING To enable or disable face culling in OpenGL: glEnable(GL_CULL_FACE); glDisable(GL_CULL_FACE); Notice I said FACE culling (not back-face culling). In OpenGL, you can specify what you want culled with glCullFace: glCullFace(GL_BACK)  cull back faces (default) glCullFace(GL_FRONT)  cull front faces glCullFace(GL_FRONT_AND_BACK)  cull front AND back faces  no faces drawn (but lines/points still drawn) NOTE: Remember that vertices should be in COUNTERclockwise order!

8. DEPTH-BUFFER/Z-BUFFER

9. Depth-buffer/Z-buffer approach Pretty much the standard for depth sorting in almost all applications Implemented in graphics hardware Have depth buffer = separate buffer that holds depth values Initialize to 1.0 (remember: normalized device coordinates) If projected pixel z < depth[x,y]: Depth[x,y] = z Color[x,y] = pixel’s color Otherwise, ignore pixel

10. DEPTH-BUFFER/Z-BUFFER

11. Advantages: Very easy to implement For opaque surfaces, does not matter what order they are rendered in! Disadvantages: Does not work properly with transparent or semi-transparent surfaces (if drawn out of order) Can be a little inefficient  might already have nearest pixel, but still have to check every other overlapping polygon on that pixel

12. DEPTH-BUFFER/Z-BUFFER IN OPENGL To enable/disable depth-buffer/z-buffer testing in OpenGL: glEnable(GL_DEPTH_TEST); glDisable(GL_DEPTH_TEST); You can also set how the z-buffer works with glDepthFunc() When clearing your color buffer, you should also clear out your depth buffer: glClear(GL_COLOR_BUFFER_BIT | GL_DEPTH_BUFFER_BIT); In GLUT, you also have to make sure you have a depth-buffer, so you have to pass in GLUT_DEPTH to glutInitDisplayMode(): glutInitDisplayMode(GLUT_DOUBLE | GLUT_RGB | GLUT_DEPTH);

13. A-BUFFER

14. A-buffer Extension of the z-buffer Unlike the z-buffer, can store multiple fragments per pixel Each position in A-buffer has two fields: Depth field = stores real-number value (positive, negative, or zero) Surface data field = stores surface data OR a pointer If (depth field >= 0): Depth field = depth of surface Surface data field = color (and other info) of fragment Otherwise: Surface data field = linked list of surface data (RGB, depth, opacity, percent of area coverage, surface identifier, etc.) Final rendering  merge lists appropriately to get final color

15. ACCUMULATION BUFFER The buffer used for the A-buffer approach is called an accumulation buffer That said, accumulation buffers in OpenGL are implemented as a buffer with a single color value per pixel Do not draw directly into; copy/add whole color buffer into it Use glAccum(GLenum op, GLfloat value); values of op: GL_ACCUM = read from color buffer, multiply by value, and add to accumulation buffer GL_LOAD = same as GL_ACCUM, except it REPLACES the values in the accumulation buffer GL_RETURN = takes values from the accumulation buffer, multiplies them by value, and places the result in the color buffer(s) enabled for writing. GL_ADD /GL_MULT = simply add or multiply the value of each pixel in the accumulation buffer by value and then return it to the accumulation buffer. For GL_MULT, value is clamped to be in the range [-1.0,1.0]. For GL_ADD, no clamping occurs. Used for anti-aliasing and motion blur

16. BSP TREES

17. BSP Trees = Binary Space Partitioning Trees Used for depth sorting objects Also used for collision detection and intersection calculations (e.g., for ray tracing) Two varieties: axis-aligned and polygon-aligned Basic idea: Use plane to divide space in two Sort geometry into these two spaces Repeat process recursively Traverse trees in a certain way  contents sorted from front-to-back from any point of view Sorting approximate for axis-aligned and exact for polygon-aligned BSPs

18. AXIS-ALIGNED BSP TREES Enclose whole scene in axis-aligned bounding box (AABB) Recursively subdivide that box into smaller boxes Splitting plane may split box exactly in half OR may shift a little in position Each child box contains some number of objects  repeat splitting until some criteria met What plane should we use? Can cycle through each axis for each plane (first x, then y, then z, then x again, and so on)  k-d trees Can pick largest side of box and split along this direction Want to avoid splitting objects if possible; if object is split, you can either: Store at current level of tree  only one copy of object in tree, but not as efficient if small objects get stuck up in upper levels Store in both child nodes  tighter bounds for larger objects, but objects in multiple locations

19. AXIS-ALIGNED BSP TREES To traverse tree: Start at root node Recursively pick branch on same side as viewer When you reach the bottom, go back and do other side of tree Effectively a depth-first traversal Not EXACTLY sorted front-to-back, since: Contents of leaf nodes may not be sorted themselves Objects may be in multiple nodes of the tree, depending on how splitting is done

20. POLYGON-ALIGNED BSP TREES Particularly useful for rendering static/rigid geometry in an exact sorted order Popular for games like Doom, back when there was no hardware Z-buffer Still used for collision detection Polygons = dividing planes Start with one polygon as root Divide all other polygons into inside and outside plane of polygon If other polygon intersects plane  split polygon Choose another polygon in each half-space as divider Repeat process recursively until all polygons in BSP tree Time-consuming process  usually create tree once and store for further use http://vignette2.wikia.nocookie.net/doom/imag es/b/b3/Imp.png/revision/latest/scale-to- width/256?cb=20050113171050

21. POLYGON-ALIGNED BSP TREES Challenge: ideally want balanced BSP tree  i.e., depth of all branches is the same Useful property: for a given view, tree can be traversed in strictly back to front (or front to back) order Determine on which side the root plane the camera is located Go down branch on other side of camera Repeat process recursively Go back up to other branches when hit bottom

22. POLYGON-ALIGNED BSP TREES Example above (back to front): Start at A  C on other side At C  G on other side Output G  go back up tree Output C  go down other branch F Output F  go back up tree Go back up to A Output A  go down other branch B At B  E on other side Output E  go back up tree Output B  go down other branch D Output D Final drawing order: G, C, F, A, E, B, D

23. OCTREES

24. Octrees Similar to axis-aligned BSP tree Enclosed entire area in minimal axis-aligned box Split simultaneously in all 3 axes  split point at center of box  makes eight new boxes Keep splitting recursively until max depth is reached or have certain number of objects in box 3D version of a quadtree: Example: split until box is 1) empty or 2) contains only one object

25. OCTREES What if object straddles two leaf nodes? Just store in both leaf nodes Use smallest box that contains entire object  inefficient for a small object in the center of a large node E.g., star object in example above Split objects  introduces more primitives Have pointer to object  less efficient and makes editing octree more difficult

26. OCTREES VS. BSP TREES BSP tree can partition things the same way as an octree Octree doesn’t need to store additional plane information like BSP trees BSP trees can be more efficient because of better splitting

27. RAY-CASTING

28. Ray-casting = shooting a ray from the camera through each position in the projection plane and checking what object(s) we intersect with  nearest one is used as color for a pixel Alternative (non-real-time) rendering approach Works with polygonal objects as well as implicit objects (e.g., F(x,y,z) = 0) Must intersect ray with ALL objects in scene and pick nearest point  inefficient Partial solution: use BSP trees or similar approaches to reduce intersection computations

29. RAY-CASTING VS. RAY-TRACING Ray-casting = shooting ray to nearest object; special case of ray-tracing Ray-tracing = traces multiple ray paths to get global reflection, refraction, etc.