1 / 44

CS 551/651: Advanced Computer Graphics

CS 551/651: Advanced Computer Graphics. Advanced Ray Tracing Radiosity. Administrivia. Quiz 1: Tuesday, Feb 20 Yes, I’ll have your homework graded by then (somehow) Normal written exam (oral later). Recap: Distributed Ray Tracing.

clinton-sullivan
Download Presentation

CS 551/651: Advanced Computer Graphics

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. CS 551/651: Advanced Computer Graphics Advanced Ray Tracing Radiosity David Luebke 111/17/2014

  2. Administrivia • Quiz 1: Tuesday, Feb 20 • Yes, I’ll have your homework graded by then (somehow) • Normal written exam (oral later) David Luebke 211/17/2014

  3. Recap: Distributed Ray Tracing • Distributed ray tracing: an elegant stochastic approach that distributes rays across: • Pixel for antialiasing • Light sourcefor soft shadows • Reflection function for soft (glossy) reflections • Time for motion blur • Lens elements for depth of field • Cook: 16 rays suffice for all of these David Luebke 311/17/2014

  4. Recap: Backwards Ray Tracing • Two-pass algorithm: • Rays are cast from light into scene • Rays are cast from the eye into scene, picking up illumination showered on the scene in the first pass • Backwards ray tracing can capture: • Indirect illumination • Color bleeding • Caustics David Luebke 411/17/2014

  5. Recap: Backwards Ray Tracing • Arvo: illumination mapstile surfaces with regular grids, like texture maps • Shoot rays outward from lights • Every ray hit deposits some of its energy into surface’s illumination map • Ignore first generation hits that directly illuminate surface (Why?) • Eye rays look up indirect illumination using bilinear interpolation David Luebke 511/17/2014

  6. Recap: Radiosity • Ray tracing: • Models specular reflection easily • Diffuse lighting is more difficult • View-dependent, generates a picture • Radiosity methods explicitly model light as an energy-transfer problem • Models diffuse interreflection easily • But only diffuse; no shiny (specular) surfaces • View-independent, generates a 3-D model David Luebke 611/17/2014

  7. Recap: Radiosity • Basic idea: represent surfaces in environment as many discrete patches • A patch, or element, is a polygon over which light intensity is constant • Model light transfer between patches as a system of linear equations • Solve this system for the intensity at each patch • Solve for R,G,B intensities; get color at each patch • Render patches as colored polygons in OpenGL David Luebke 711/17/2014

  8. Recap: Fundamentals • Definition: • The radiosity of a surface is the rate at which energy leaves the surface • Radiosity = rate at which the surface emits energy + rate at which the surface reflects energy • Simplifying assumptions • Environment is closed • All surfaces have Lambertian reflectance • Surface patches emit and reflect light uniformly over their entire surface David Luebke 811/17/2014

  9. Radiosity • For each surface i: Bi = Ei + i Bj Fji(Aj / Ai) where Bi, Bj= radiosity of patch i, j Ai, Aj= area of patch i, j Ei= energy/area/time emitted by i i = reflectivity of patch i Fji = Form factor from j to i David Luebke 911/17/2014

  10. Form Factors • Form factor: fraction of energy leaving the entirety of patch i that arrives at patch j, accounting for: • The shape of both patches • The relative orientation of both patches • Occlusion by other patches • We’ll return later to the calculation of form factors David Luebke 1011/17/2014

  11. Form Factors • Some examples… Form factor: nearly 100% David Luebke 1111/17/2014

  12. Form Factors • Some examples… Form factor: roughly 50% David Luebke 1211/17/2014

  13. Form Factors • Some examples… Form factor: roughly 10% David Luebke 1311/17/2014

  14. Form Factors • Some examples… Form factor: roughly 5% David Luebke 1411/17/2014

  15. Form Factors • Some examples… Form factor: roughly 30% David Luebke 1511/17/2014

  16. Form Factors • Some examples… Form factor: roughly 2% David Luebke 1611/17/2014

  17. Form Factors • In diffuse environments, form factors obey a simple reciprocity relationship: Ai Fij = Ai Fji • Which simplifies our equation:Bi = Ei + i Bj Fij • Rearranging to:Bi - i Bj Fij = Ei David Luebke 1711/17/2014

  18. Form Factors • So…light exchange between all patches becomes a matrix: • What do the various terms mean? David Luebke 1811/17/2014

  19. Form Factors 1 - 1F11 - 1F12 … - 1F1n B1E1 - 2F21 1 - 2F22 … - 2F2n B2E2 . . … . . . . . … . . . . . … . . . - pnFn1- nFn2 … 1 - nFnn Bn En • Note: Ei values zero except at emitters • Note: Fii is zero for convex or planar patches • Note: sum of form factors in any row = 1 (Why?) • Note: n equations, n unknowns! David Luebke 1911/17/2014

  20. Radiosity • Now “just” need to solve the matrix! • W&W: matrix is “diagonally dominant” • Thus Guass-Siedel must converge (what’s that?) • End result: radiosities for all patches • Solve RGB radiosities separately, color each patch, and render! • Caveat: for rendering, we actually color vertices, not patches (see F&vD p 795) David Luebke 2011/17/2014

  21. Radiosity • Q: How many form factors must be computed? • A: O(n2) • Q: What primarily limits the accuracy of the solution? • A: The number of patches David Luebke 2111/17/2014

  22. Roadmap • So, we know the basic radiosity algorithm • Represent light transfer as a matrix • Solve the matrix to get radiosity (=color) per patch • Next topics: • Evaluating form factors • Progressive radiosity: viewing an approximate solution early • Hierarchical radiosity: increasing patch resolution on an as-needed basis David Luebke 2211/17/2014

  23. Form Factors • Calculating form factors is hard • Analytic form factor between two polygons in general case: open problem till last few years • Q: So how might we go about it? • Hint: Clearly form factors are related to visibility: how much of patch j can patch i “see”? David Luebke 2311/17/2014

  24. Form Factors: Hemicube • Hemicube algorithm: Think Z-buffer • Render the model onto a hemicubeas seen from the center of patch i • Store item IDs instead of color • Use Z-buffer to resolve visibility • See W&W p 278 • Q: Why hemicube, not hemisphere? David Luebke 2411/17/2014

  25. Form Factors: Hemicubes • Advantages of hemicubes • Solves shape, size, orientation, and occlusion problems in one framework • Can use hardware Z-buffers to speed up form factor determination (How?) David Luebke 2511/17/2014

  26. Form Factors: Hemicubes • Q: What are some disadvantages of hemicubes? • Aliasing! Low resolution buffer can’t capture actual polygon contributions very exactly • Causes “banding” near lights (plate 41) • Actual form factor is over area of patch; hemicube samples visibility at only center point on patch (So?) David Luebke 2611/17/2014

  27. Form Factors: Ray Casting • Idea: shoot rays from center of patch in hemispherical pattern David Luebke 2711/17/2014

  28. Form Factors: Ray Casting • Advantages: • Hemisphere better approximation than hemicube • More even sampling reduces aliasing • Don’t need to keep item buffer • Slightly simpler to calculate coverage David Luebke 2811/17/2014

  29. Form Factors: Ray Casting • Disadvantages: • Regular sampling still invites aliasing • Visibility at patch center still isn’t quite the same as form factor • Ray tracing is generally slower than Z-buffer-like hemicube algorithms • Depends on scene, though • Q: What kind of scene might ray tracing actually be faster on? David Luebke 2911/17/2014

  30. Form Factors • Source-to-vertex form factors • Calculating form factors at the patch vertices helps address some problems: for every patch vertex for every source patch sample source evenly with rays visibility = % rays that hit • Q: What are the problems with this approach? David Luebke 3011/17/2014

  31. Form Factors • Summary of form factor computation • Analytical: • Expensive or impossible (in general case) • Hemicube • Fast, especially using graphics hardware • Not very accurate; aliasing problems • Ray casting • Conceptually cleaner than hemicube • Usually slower; aliasing still possible David Luebke 3111/17/2014

  32. Substructuring • More patches  better results • Problem: # form factors grows quadratically with # patches • Substructuring: adaptively subdivide patches into elements where high radiosity gradient is found David Luebke 3211/17/2014

  33. Substructuring • Elements are second-class patches: • When a patch is subdivided, form factors are computed from the elements to other patches • But form factors from the other patches to the elements are not computed • However, the form factors from other patches to the subdivided patch are updated using more accurate area-weighted average of elements David Luebke 3311/17/2014

  34. Substructuring • Elements vs. patches, cont. • Elements “gather” radiosity from other patches • But those other patches only gather radiosity from the “parent” patch, not the individual elements • So an element’s contribution to other patches is approximated coarsely by it’s patch’s radiosity David Luebke 3411/17/2014

  35. Substructuring • Bottom line: • Substructuring allows subpatch radiosities to be computed without changing the size of the form-factor matrix • Show examples: • W&W plate 38, F&vD plate III.21 • Note: texts aren’t clear about adaptive subdivision vs substructuring David Luebke 3511/17/2014

  36. Progressive Radiosity • Good news: iterative solver of radiosity matrix will converge • Bad news: can take a longtime • Progressive radiosity: reorder computation to allow viewing of partial results David Luebke 3611/17/2014

  37. Progressive Radiosity • Radiosity as described uses Gauss-Seidel iterative solver • Must do an entire iteration to get an estimate of patch radiosities • Must precompute and store all O(n2) form factors David Luebke 3711/17/2014

  38. Progressive Radiosity 1 - 1F11 - 1F12 … - 1F1n B1E1 - 2F21 1 - 2F22 … - 2F2n B2E2 . . … . . . . . … . . . . . … . . . - pnFn1- nFn2 … 1 - nFnn Bn En • Evaluating row i estimates radiosity of patch i based on all other patches • We say the patch gathers light from the environment David Luebke 3811/17/2014

  39. Progressive Radiosity • Progressive radiosity shoots light from a patch into the environment: Bjdue to Bi = j Bj Fjij rather thanBidue to Bj = i Bj Fijj • Given an estimate of Bi, evaluating this equation estimates patch i’s contribution to the rest of the scene David Luebke 3911/17/2014

  40. Progressive Radiosity • A problem: evaluating the equationBjdue to Bi = j Bj Fjij requires knowing Fji for each patch j • Determining these values requires a hemicube computation per patch • Use reciprocity relationship to getBjdue to Bi = j Bj Fij(Ai/Aj)j David Luebke 4011/17/2014

  41. Progressive Radiosity • Now evaluation requires only a single hemicube about patch i • Compute, use, and discard form factors • Drastically reduces total storage! • Reorder radiosity computation: • Pick patch w/ highest estimated radiosity • Shoot to all other patches • Update their estimates • Pick new “brightest” patch and repeat David Luebke 4111/17/2014

  42. Progressive Radiosity • We can look at the scene after every iteration through this loop • Q: How will it look after 1 loop? • Q: 2 loops? • Q: If m = # of light sources, how will it look after m loops? After 2m loops? David Luebke 4211/17/2014

  43. Progressive Radiosity • Subtleties: • Pick patch with most energy to shoot • Energy = radiosity * area = Bj Ai • A patch may be selected to shoot again after new light has been shot to it • So don’t shoot Bj , shoot Bj, the amount of radiosity patch i has received since it was last shot David Luebke 4311/17/2014

  44. The End David Luebke 4411/17/2014

More Related