1 / 15

CS 551/651: Advanced Computer Graphics

CS 551/651: Advanced Computer Graphics. Accelerating Ray Tracing. Ray-Sphere Intersection. Ray R = O + tD x = O x + t * D x y = O y + t * D y z = O z + t * D z Sphere at ( l, m, n ) of radius r is: ( x - l ) 2 + ( y - m ) 2 + ( z - n ) 2 = r 2

simone-gaines
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 Accelerating Ray Tracing David Luebke 111/17/2014

  2. Ray-Sphere Intersection • Ray R = O + tD x = Ox + t * Dx y = Oy + t * Dy z = Oz + t * Dz • Sphere at (l, m, n) of radius r is: (x - l)2 + (y - m)2 + (z - n)2 = r 2 • Substitute for x,y,z and solve for t… David Luebke 211/17/2014

  3. Ray-Sphere Intersection • Works out as a quadratic equation: at2 + bt + c = 0 where a = Dx2 + Dy2 + Dz2 b =2Dx(Ox - l) + 2Dy(Oy - m) + 2Dz(Oz - n) c = l2 + m2 + n2 + Ox2 + Oy2 + Oz2 - 2(l Ox + m Oy + n Oz + r2) David Luebke 311/17/2014

  4. Ray-Sphere Intersection • If solving for t gives no real roots: ray does not intersect sphere • If solving gives 1 real root r, ray grazes sphere where t = r • If solving gives 2 real roots (r1, r2), ray intersects sphere at t = r1& t = r2 • Ignore negative values • Smallest value is first intersection David Luebke 411/17/2014

  5. Ray-Sphere Intersection • Find intersection point Pi = (xi, yi, zi) by plugging t back into ray equation • Find normal at intersection point by subtracting sphere center from Pi and normalizing: (When might we need the normal? When not?) David Luebke 511/17/2014

  6. Ray-Polygon Intersection • Polygons are the most common model representation (Why?) • Basic approach: • Find plane equation of polygon • Find intersection of ray and plane • Does polygon contain intersection point? David Luebke 611/17/2014

  7. y N P2 P1 d x Ray-Polygon Intersection • Find plane equation of polygon:ax + by + cz + d = 0 • How? N = [a, b, c] d = N  P1 (How to find N ?) David Luebke 711/17/2014

  8. Ray-Polygon Intersection • Find intersection of ray and plane: t = -(aOx + bOy + cOz + d) / (aDx + bDy + cDz) • Does poly contain intersection point Pi ? • Book’s algorithm: • Draw line from Pi to each polygon vertex • Measure angles between lines (how?) • If sum of angles between lines is 360°, polygon contains Pi David Luebke 811/17/2014

  9. Ray-Box Intersection • Often want to find whether a ray hits an axis-aligned box (Why?) • One way: • Intersect the ray with the pairs of parallel planes that form the box • If the intervals of intersection overlap, the ray intersects the box. David Luebke 911/17/2014

  10. Shadow Ray Problems:Too Much Computation • Light buffer (Haines/Greenberg, 86) • Precompute lists of polygons surrounding light source in all directions • Sort each list by distance to light source • Now shadow ray need only be intersected with appropriate list! ShadowRay Light Buffer Occluding Polys Current Intersection Point David Luebke 1011/17/2014

  11. Shadow Ray Problems:Sharp Shadows • Why are the shadows sharp? • A: Infinitely small point light sources • What can we do about it? • A: Implement area light sources • How? David Luebke 1111/17/2014

  12. Shadow Ray Problems: Area Light Sources • Could trace a conical beam from point of intersection to light source: • Track portion of beam blocked by occluding polygons: 30% blockage David Luebke 1211/17/2014

  13. Shadow Ray Problems:Area Light Sources • Too hard! Approximate instead: • Sample the light source over its area and take weighted average: 50% blockage David Luebke 1311/17/2014

  14. Shadow Ray Problems:Area Light Sources • Disadvantages: • Less accurate (50% vs. 30% blockage) • Oops! Just quadrupled (at least) number of shadow rays • Moral of the story: • Soft shadows are very expensive in ray tracing David Luebke 1411/17/2014

  15. The End David Luebke 1511/17/2014

More Related