Logistics. CS 586/480 Computer Graphics II. Questions from Last Week? Slide Credits

Transcription

1 CS 586/480 Computer Graphics II Dr. David Breen Matheson 408 Thursday 6PM Æ 8:50PM Presentation 4 10/28/04 Logistics Read research paper and prepare summary and question P. Hanrahan, "Ray Tracing Algebraic Surfaces," Proc. SIGGRAPH '83, July 1983, pp Shailaja Kaveti presents next week Questions from Last Week? Color models Light models Phong shading model Assignment 3 Slide Credits Leonard McMillan, Seth Teller, Fredo Durand, Barb Cutler - MIT David Luebke - University of Virginia Matt Pharr - Stanford University Jonathan Cohen - Johns Hopkins U. Kevin Suffern -University of Technology, Sydney, Australia 1

2 Extra rays needed for these effects Motivation Distribution Ray Tracing Soft shadows Anti-aliasing (getting rid of jaggies) Glossy reflection Motion blur Depth of field (focus) Shadows Soft Shadows one shadow ray per intersection per point light source no shadow rays multiple shadow rays to sample area light source one shadow ray one shadow ray lots of shadow rays 2

3 Antialiasing Supersampling multiple rays per pixel point light jaggies w/ antialiasing Reflection one reflection ray per intersection area light perfect mirror Glossy Reflection multiple reflection rays Motion Blur Sample objects temporally Justin Legakis polished surface Rob Cook 3

4 Depth of Field multiple rays per pixel film focal length Justin Legakis Algorithm Analysis Ray casting Lots of primitives Recursive Distributed Ray Tracing Effects Soft shadows Anti-aliasing Glossy reflection Motion blur Depth of field cost height * width * num primitives * intersection cost * num shadow rays * supersampling * num glossy rays * num temporal samples * max recursion depth *... can we reduce this? Bounding Regions 4

5 Acceleration of Ray Casting Goal: Reduce the number of ray/primitive intersection tests Conservative Bounding Region First check for an intersection with a conservative bounding region Early reject Conservative Bounding Regions tight Æ avoid false positives fast to intersect non-aligned bounding box bounding sphere axis-aligned bounding box Bounding Volumes What makes a good bounding volume? Tightness of fit (expressed how?) Simplicity of intersection Total cost = b*b + i*i b: # times volume tested for intersection B: cost of ray-volume intersection test i: # times item is tested for intersection I: cost of ray-item intersection test arbitrary convex region (bounding half-spaces) 5

6 Bounding Volumes Spheres Cheap intersection test Poor fit A pain to fit to data bounding sphere Bounding Volumes Axis-aligned bounding boxes (AABBs) Relatively cheap intersection test Usually better fit Trivial to fit to data axis-aligned bounding box 6

7 Bounding Volumes Oriented bounding boxes (OBBs) Medium-expensive intersection test Very good fit (asymptotically better) Medium-difficult to fit to data Bounding Volumes Slabs (parallel planes) Comparatively expensive Very good fit A pain to fit to data oriented bounding box arbitrary convex region (bounding half-spaces) Intersection with Axis-Aligned Box Bounding Box of a Triangle From Lecture 2 For all 3 axes, calculate the intersection t 1y t near t 1x t far x=x1 t 2y t 2x x=x2 y=y2 y=y1 distances t 1 and t 2 t near = max (t 1x, t 1y, t 1z ) t far = min (t 2x, t 2y, t 2z ) If t near > t far, box is missed If t far < 0, box is behind If box survived tests, report intersection at t near (x min, y min, z min ) = (min(x 0,x 1,x 2 ), min(y 0,y 1,y 2 ), min(z 0,z 1,z 2 )) (x 1, y 1, z 1 ) (x 0, y 0, z 0 ) (x 2, y 2, z 2 ) (x max, y max, z max ) = (max(x 0,x 1,x 2 ), max(y 0,y 1,y 2 ), max(z 0,z 1,z 2 )) 7

8 Bounding Box of a Sphere Bounding Box of a Group r (x max, y max, z max ) = (x+r, y+r, z+r) (x max_a, y max_a, z max_a ) (x max_b, y max_b, z max_b ) (x max, y max, z max ) = (max(x max_a,x max_b ), max(y max_a,y max_b ), max(z max_a,z max_b )) (x, y, z) (x min_b, y min_b, z min_b ) (x min_a, y min_a, z min_a ) (x min, y min, z min ) = (x-r, y-r, z-r) (x min, y min, z min ) = (min(x min_a,x min_b ), min(y min_a,y min_b ), min(z min_a,z min_b )) Acceleration Spatial Data Structures Spatial Data Structures Spatial partitioning techniques classify all space into non-overlapping portions Easier to generate automatically Can walk ray from partition to partition Hierarchical bounding volumes surround objects in the scene with (possibly overlapping) volumes Often tightest fit 8

9 Spatial Partitioning Some spatial partitioning schemes: Regular grid (2-D or 3-D) Octree k-d tree BSP-tree Acceleration Spatial Data Structures Regular Grid Regular Grid Create grid Find bounding box of scene Choose grid spacing grid x need not = grid y grid y Cell (i, j) grid x 9

10 Insert primitives into grid Primitives that overlap multiple cells? Insert into multiple cells (use pointers) For each cell along a ray Does the cell contain an intersection? Yes: return closest intersection No: continue Preventing repeated computation Perform the computation once, "mark" the object Don't re-intersect marked objects Don't return distant intersections If intersection t is not within the cell range, continue (there may be something closer) 10

11 Where do we start? Is there a pattern to cell crossings? Intersect ray with scene bounding box Ray origin may be inside the scene bounding box Cell (i, j) t next_v t next_h Yes, the horizontal and vertical crossings have regular spacing dt v = grid y / dir y t min t min t next_v t next_h (dir x, dir y ) dt h = grid x / dir x grid y grid x What's the next cell? if t next_v < t next_h i += sign x t min = t next_v t next_v += dt v else j += sign y t min = t next_h t next_h += dt h (dir x, dir y ) Cell (i+1, j) Cell (i, j) t min t next_v if (dir x > 0) sign x = 1 else sign x = -1 if (dir y > 0) sign y = 1 else sign y = -1 dt h t next_h dt v What's the next cell? 3DDDA Three Dimensional Digital Difference Analyzer 3D Bresenham Algorithm 11

12 Pseudo-code Regular Grid Discussion create grid insert primitives into grid for each ray r find initial cell c(i,j), t min, t next_v & t next_h compute dt v, dt h, sign x and sign y while c!= NULL for each primitive p in c intersect r with p if intersection in range found return c = find next cell Advantages? easy to construct easy to traverse Disadvantages? may be only sparsely filled geometry may still be clumped Acceleration Spatial Data Structures Adaptive Grids Subdivide until each cell contains no more than n elements, or maximum depth d is reached Adaptive Grids Nested Grids Octree/(Quadtree) 12

13 Primitives in an Adaptive Grid Can live at intermediate levels, or be pushed to lowest level of grid Adaptive Grid Discussion Advantages? grid complexity matches geometric density Disadvantages? more expensive to traverse (especially octree) Octree/(Quadtree) k-d Trees k-d tree pros: Moderately simple to generate More adaptive than octrees k-d tree cons: Less efficient to trace rays across Moderately complex data structure BSP Trees BSP tree pros: Extremely adaptive Simple & elegant data structure BSP tree cons: Very hard to create optimal BSP Splitting planes can explode storage Simple but slow to trace rays across 13

14 Acceleration Spatial Data Structures Bounding Volume Hierarchy Bounding Volume Hierarchy What makes a good bounding volume hierarchy? Grouped objects (or volumes) should be near each other Volume should be minimal Sum of all volumes should be minimal Top of the tree is most critical Constructing the hierarchy should pay for itself! Bounding Volume Hierarchy Find bounding box of objects Split objects into two groups Recurse Bounding Volume Hierarchy Find bounding box of objects Split objects into two groups Recurse 14

15 Bounding Volume Hierarchy Find bounding box of objects Split objects into two groups Recurse Bounding Volume Hierarchy Find bounding box of objects Split objects into two groups Recurse Bounding Volume Hierarchy Find bounding box of objects Split objects into two groups Recurse Where to split objects? At midpoint OR Sort, and put half of the objects on each side OR Use modeling hierarchy 15

16 Intersection with BVH Check subvolume with closer intersection first Intersection with BVH Don't return intersection immediately if the other subvolume may have a closer intersection Bounding Volume Hierarchy Discussion Advantages easy to construct easy to traverse binary Disadvantages may be difficult to choose a good split for a node poor split may result in minimal spatial pruning Transformation Hierarchy transform A transform B group transform C group transform transform D E Group & Transformation hierarchy may not be a good spatial hierarchy Flatten transform A B group transform C D transform C E 16

17 What s the best method? What kind of scene are you rendering? Teapot in a stadium vs. uniform distribution Impact on surface tessellation on distribution Parameter values are critical Shoot Fewer Rays Adaptive depth control Naïve ray tracer: spawn 2 rays per intersection until max recursion limit In practice, few surfaces are transparent or reflective Just shoot the rays you need Determine contribution of ray Don t shoot rays w/ contribution near 0% Shoot Fewer Rays Adaptive sampling Shoot rays coarsely, interpolating their values across pixels Where adjacent rays differ greatly in value, sample more finely Stop when some maximum resolution is reached Generalized Rays Beams, cones, pencils Area sampling, rather than point sampling Geometric computations are tricky (expensive?) Problems with reflection/refractions 17

18 Wrap Up Discuss next week s programming assignment Add an acceleration technique Uniform grid Adaptive grid Bounding volume hierarchy Supersample image Discuss status/problems/issues with this week s programming assignment 18