Ray Tracing, Part 1 of 2: Intersections, Ray Trees & Recursion

2 Lecture 31of 41 Lecture Outline

Ray Tracing, Part 1 of 2:  Reading for Last Class: §5.3, Eberly 2e; CGA Handout Intersections, Ray Trees & Recursion  Reading for Today: Chapter 14, Eberly 2e  Reading for Next Class: Ray Tracing Handout  Last Time: Animation Part 3 of 3 – Inverse Kinematics William H. Hsu  FK vs. IK Department of Computing and Information Sciences, KSU  IK  Autonomous agents vs. hand-animated movement KSOL course pages: http://bit.ly/hGvXlH / http://bit.ly/eVizrE  Public mirror web site: http://www.kddresearch.org/Courses/CIS636 Analytical vs. iterative solutions Instructor home page: http://www.cis.ksu.edu/~bhsu  Rag doll physics, rigid-body dynamics, physically-based models  End of Material on: Particle Systems, Collisions, CGA, PBM Readings:  Today: Ray Tracing, Part 1 of 2 Last class: §5.3, Eberly 2e – see http://bit.ly/ieUq45; CGA Handout  Vectors: Light/shadow (L), Reflected (R), Transmitted/refracted (T) Today: Chapter 14, Eberly 2e Next class: Ray Tracing Handout  Basic recursive ray tracing: ray trees Reference – Wikipedia, Ray Tracing: http://bit.ly/dV7lNm  Next Class: Ray Tracing Lab Reference – ACM Ray Tracing News: http://bit.ly/fqyZNQ

3 4 Acknowledgements: Where We Are Inverse Kinematics, Ray Tracing

David C. Brogan Visiting Assistant Professor, Computer Science Department, University of Virginia http://www.cs.virginia.edu/~dbrogan/ Susquehanna International Group (SIG) http://www.sig.com

Renata Melamud Ph.D. Candidate Mechanical Engineering Department Stanford University http://micromachine.stanford.edu/~rmelamud/

Dave Shreiner & Brad Grantham Adjunct Professor & Adjunct Lecturer, Santa Clara University ARM Holdings, plc http://www.plunk.org/~shreiner/ http://www.plunk.org/~grantham/

5 Review [1]: 6 Review [2]: Kinematics & Degrees of Freedom Joint Types

Adapted from slides  2000 – 2005 D. Brogan, University of Virginia Adapted from slides  2002 R. Melamud, Stanford University CS 551, Advanced CG & Animation – http://bit.ly/hUXrqd Mirrored at CMU 16-311 Introduction to Robotics, http://generalrobotics.org

 3 2 End Effector 1

Base    θx )f(  f Φe  Choi Rotenberg

Adapted from slides  2004 – 2005 S. Rotenberg, UCSD Adapted from slides  2002 K. J. Choi, Seoul National University CSE169: Computer Animation, Winter 2005 – http://bit.ly/f0ViAN Graphics and Media Lab ( http://graphics.snu.ac.kr ) – mirrored at: http://bit.ly/hnzSAN

9 Review [4]: 10 Inverse Kinematics: Inverse Kinematics Issues

For more on characters & IK, see: Advanced Topics in CG Lecture 05

?  3 2 ? End Effector 1

Base    1 xθ )(f  f 1eΦ  Choi Rotenberg

Adapted from slides  2002 K. J. Choi, Seoul National University Adapted from slides  2004 – 2005 S. Rotenberg, UCSD Graphics and Media Lab ( http://graphics.snu.ac.kr) – mirrored at: http://bit.ly/hnzSAN CSE169: Computer Animation, Winter 2005 – http://bit.ly/f0ViAN

11 Review [5]: 12 Review [6]: Inverse Kinematics Demos Ragdoll Physics  Type of Procedural Animation  Automatically generates CGA directives (rotations)  Based on simulation  Rigid-body dynamics  Articulated Figure  Gravity

© 2008 M. Kinzelman © 2007 A. Brown  No autonomous movement http://youtu.be/l52yZ491kPo http://youtu.be/6JdLOLazJJ0 Falling Bodies © 1997 – 2001 Animats  Used for inert body http://www.animats.com  Usually: character death (car impact, falling body, etc.)  Less often: unconscious, paralyzed character  Collisions with Multiple Bodies  Inter-character  Character-object

CIS 536/636 Computing & Information Sciences CIS 536/636 Computing & Information Sciences Lecture 31 of 41 Lecture 31 of 41 Introduction to Computer Graphics Kansas State University Introduction to Computer Graphics Kansas State University 13 Review [7]: 14 Review [8}: Ragdoll Physics Demos Physically-Based Modeling (PBM)  Particle Dynamics  Emitters  0-D (points), 1-D (lines), 2-D (planes, discs, cross-sections)  e.g., fireworks (0-D); fountains (0/1/2-D); smokestacks, jets (2-D)  Simulation: birth-death process, functions of particle age/trajectory  Rigid-Body Dynamics © 2006 P. Pelt © 2007 N. Picouet  http://youtu.be/6JdLOLazJJ0 Constrained systems of connected parts http://youtu.be/ohNqCb--aSs See also: http://youtu.be/5_QIsI0fyaU  Examples: falling rocks, colliding vehicles, rag dolls  Articulated Figures: Primarily IK  Rocks fall  More References  Everyone dies  ACM, Intro to Physically-Based Modeling : http://bit.ly/hhQvXd  Wikipedia, Physics Engine: http://bit.ly/h4PIRt  Wikipedia, N-Body Problem: http://bit.ly/1ayWwe  PBM System: nVidia (Ageia) PhysX: http://bit.ly/cp7bnA

15 Ray Tracing [1]: 16 Ray Tracing [2]: Overview Why Use It?

 What is it?  Simulate rays of light  Why use it?  Produces natural lighting effects  Basics  Advanced topics  Reflection  Depth of Field  References  Refraction  Motion Blur

© 2006 – 2007 H. Kuijpers,  Soft Shadows  Caustics Capgemini Netherlands http://bit.ly/erkKrC  Hard to simulate effects with rasterization techniques (OpenGL)  Rasterizers require many passes  Ray-tracing easier to implement

Adapted from slides  2001 D. Shreiner & B. Grantham, SCU Adapted from slides  2001 D. Shreiner & B. Grantham, SCU COEN 290: Computer Graphics I, Winter 2001 – http://bit.ly/hz1kfU COEN 290: Computer Graphics I, Winter 2001 – http://bit.ly/hz1kfU

17 Ray Tracing [3]: 18 Ray Tracing [4]: Who Uses It? Brief History

 Entertainment (Movies, Commercials)  Decartes, 1637 A.D. - analysis of rainbow  Games pre-production  Arthur Appel, 1968 - used for lighting 3D models  Simulation  Turner Whitted, 1980 - “An Improved Illumination Model for Shaded Display” really kicked everyone off.  1980-now - Lots of research

 Simulate light rays from light source to eye  Generating Rays  Intersecting Rays with Scene  Lighting Eye Light  Shadowing  Reflections

ay Inc ed r iden lect t ray Ref Surface

21 22 “Forward” Ray Tracing “Backward” Ray Tracing

 Trace rays from light  Trace rays from eye instead  Lots of work for little return  Do work where it matters

Light Light Image Image Light Rays Plane Plane

Eye Eye Object Object

This is what most people mean by “ray tracing”.

23 24 Ray: Parametric Form Generating Rays [1]

 Ray expressed as function of a single parameter ( “t”)  Trace one ray for each pixel (u, v) in image plane

tan(fovx) * 2 = + t *

= ro + trd Image t = 2.5 Plane

rd = t = 2.0 fovx

ro = t = 1.0 Eye Eye

t = 0.0 (Looking down from the top)

 Trace one ray for each pixel (u, v) in image plane  Trace one ray for each pixel (u, v) in image plane

renderImage(){ (Looking from the side) for each pixel i, j in the image m ray.setStart(0, 0, 0); // ro ray.setDir ((.5 + i) * tan(fov )* 2 / m, (tan(fov )* 2) / m x x (.5 + j) * tan(fov )* 2 / n, Eye y 1.0); // rd (tan(fovy)* 2) / n n ray.normalize(); image[i][j] = rayTrace(ray); }

Adapted from slidesImage  2001 D. Shreiner & B. Grantham, SCU Adapted from slides  2001 D. Shreiner & B. Grantham, SCU COEN 290: ComputerPlane Graphics I, Winter 2001 – http://bit.ly/hz1kfU COEN 290: Computer Graphics I, Winter 2001 – http://bit.ly/hz1kfU CIS 536/636 Computing & Information Sciences CIS 536/636 Computing & Information Sciences Lecture 31 of 41 Lecture 31 of 41 Introduction to Computer Graphics Kansas State University Introduction to Computer Graphics Kansas State University

27 Ray/Triangle Intersection [1]: 28 Ray/Triangle Intersection [2]: Intersection Test Revisited Ray/Plane Intersection Point p

 Want to know: at what point p does ray intersect triangle?  Step 1 : Intersect with plane  Compute lighting, reflected rays, shadowing from that point ( Ax + By + Cz + D = 0 )

Plane normal n = p p = tmin rd rd ro ro (t = ???) tmin = p = -(n  ro + D) / (n  rd )

29 Ray/Triangle Intersection [3]: 30 Triangle Normals Triangle Containment for Shading  Step 2 : Check against triangle edges  Could use plane normals (flat shading) n V 1  Better to interpolate from vertices

V0V1 E = V V x n (plane A, B, C) nV1 E p i i i+1 V1 Find areas 0 d = -A.N (plane D) V i 0 n n V0 c p a V 2 b V0 nV2 Plug p into (p  Ei + di ) for each edge if signs are all positive or negative, point is inside triangle! V2 Adapted from slides  2001 D. Shreiner & B. Grantham, SCU Adapted from slides  2001 D.n Shreiner = an & B. Grantham, + bn SCU + cn COEN 290: Computer Graphics I, Winter 2001 – http://bit.ly/hz1kfU COEN 290: Computer Graphics I, Winter 2001V0 – http://bit.ly/hz1kfUV1 V2

 Check all triangles, keep closest intersection tmin  We’ll use triangles for lights  Can build complex shapes from triangles hitObject(ray) {  Some lighting terms for each triangle in scene does ray intersect triangle? if(intersected and was closer) Light Eye save that intersection N if(intersected) return intersection point and normal } I R

33 Lighting [2]: 34 Ambient Light Modified Phong Illumination

 Iambient – simulates indirect lighting in a scene  Use modified Phong lighting  similar to OpenGL  simulates rough and shiny surfaces Eye for each light

In = IambientKambient + . IdiffuseKdiffuse (L N) + . n IspecularKspecular (R V) Light

 May not need for RT!

35 36 Diffuse Light Specular Light

 Idiffuse – simulates direct lighting on rough surface  Ispecular simulates direct lighting on a smooth surface  Viewer-independent  Viewer dependent  Paper, rough wood, brick, etc...  Plastic, metal, polished wood, etc...

Eye Eye

Light Light

 Check against other objects to see if point is shadowed  Angle of incidence = angle of reflection (I = R )  I, R, N lie in the same plane

Eye N

R = I - 2 (N  I) N I I R R

Shadowing object Light

39 Putting It All Together [1]: 40 Putting It All Together [2]: Recursive Calculation & Ray Tree Applying Lighting

 Recursive ray evaluation  Calculating surface color

lighting(point) { rayTrace(ray) { color = ambient color; hitObject(ray, p, n, triangle); for each light color = object color; if(hitObject(shadow ray)) if(object is light) color += lightcolor * return(color); dot(shadow ray, n); else color += rayTrace(reflection) * return(lighting(p, n, color)); Ray tree pow(dot(reflection, ray), shininess); © 2000 N. Patrikalakis, MIT } http://bit.ly/fjcGGk return(color); I = Incident ray } S = light Source vector ( aka L) R = reflected ray  Generates ray tree shown at right T = transmitted ray

41 Putting It All Together [3]: 42 Good Start: Main Program What next?

 Lighting, Shadows, Reflection are enough to make some compelling images main() {  Want better lighting and objects triangles = readTriangles();  Need more speed image = renderImage(triangles); writeImage(image); }

 Better Lighting + Forward Tracing  Keep track of medium (air, glass, etc)  Texture Mapping  Need index of refraction ()  Modeling Techniques  Need solid objects  Distributed Ray Tracing: Techniques N  Motion Blur   Depth of Field I I Medium 1  Blurry Reflection/Refraction sin( )  (e.g., air) I = 1  Wikipedia, Distributed Ray Tracing: http://bit.ly/ihyVUs    Improving Image Quality sin( T) 2 Medium 2  Acceleration Techniques T (e.g., water) T

45 Refraction [2]: 46 Improved Light Model: Example Cook-Torrance

 Cook-Torrance model  Based on a microfacet model  Wikipedia: http://bit.ly/hX3U30  Metals have different color at angle  Oblique reflections leak around corners

47 Using “Forward” Ray Tracing [1]: 48 Using “Forward” Ray Tracing [2]: Lensed Caustics for Indirect Lighting Example

 Backward tracing doesn’t handle indirect lighting too well  To get caustics, trace forward, store results in texture map

CIS 536/636 Computing & Information Sciences CIS 536/636 Computing & Information Sciences Lecture 31 of 41 Lecture 31 of 41 Introduction to Computer Graphics Kansas State University Introduction to Computer Graphics Kansas State University 49 Texture Mapping & Ray Tracing [1]: 50 Texture Mapping & Ray Tracing [2]: Applying Surface Detail Example

 Using texture maps  Add surface detail  Think of it like texturing in OpenGL  Diffuse, specular colors  Shininess value  Bump map  Transparency value

51 52 Parametric Surfaces Constructive Solid Geometry

 More expressive than triangle  Union, Subtraction, Intersection of solid objects  Intersection is probably slower  u and v on surface can be used as texture s, t  Have to keep track of intersections

53 54 Distributed Ray Tracing [1]: Hierarchical Transformation Basic Idea

 Scene made of parts  Average multiple rays instead of just one ray  Each part made of smaller parts  Use for both shadows, reflections, transmission (refraction)  Each smaller part has transformation linking it to larger part  Use for motion blur  Transformation can change over time: animation (CGA)  Use for depth of field

CIS 536/636 Computing & Information Sciences CIS 536/636 Computing & Information Sciences Lecture 31 of 41 Lecture 31 of 41 Introduction to Computer Graphics Kansas State University Introduction to Computer Graphics Kansas State University 55 Distributed Ray Tracing [2]: 56 Distributed Ray Tracing [3]: Example Supersampling

 One ray is not enough (jaggies)  Can use multiple rays per pixel - supersampling  Can use a few samples, continue if they’re very different - adaptive supersampling  Texture interpolation & filtering

57 58 Acceleration! Bounding Volumes

 1280x1024 image with 10 rays/pixel  1000 objects (triangle, CSG, NURBS)  Use simple shape for quick test, keep BV hierarchy  3 levels recursion

39321600000 intersection tests 100000 tests/second -> 109 days! Must use an acceleration method!

59 Spatial Partitioning: 60 Parallelism Subdivision

 Break your space into pieces  Can always throw more processors at it  Search the structure linearly  Parallel computing model  Multiple processes or threads  Data parallel: separate pixel for each

 Error analysis  Introduction to Ray-Tracing, Glassner et al., 1989, 0-12-286160-4  Hybrid radiosity/ray-tracing  Advanced Animation and Rendering Techniques , Watt & Watt,  Metropolis Light Transport 1992, 0-201-54412-1  Memory-Coherent Ray-tracing  Computer Graphics: Image Synthesis, Joy et al., 1988, 0-8186- 8854-4  SIGGRAPH Proceedings (All)

63 64 Summary Terminology

 Reading for Last Class: §5.3, Eberly 2e; CGA Handout  Joints: Parts of Robot / Articulated Figure That Turn, Slide  Reading for Today: Chapter 14, Eberly 2e  Effectors: Parts of Robot / Articulated Figure That Act ( e.g., Hand, Foot)  Reading for Next Class: Ray Tracing Handout  Bones: Effectors, Other Parts That Rotate about, Slide through Joints  Last Class: Particle Systems, Collisions, IK/CGA Concluded  Procedural Animation: Automatic Generation of Motion via Simulation  Dynamics vs. kinematics, forward vs. inverse revisited  Ray Tracing aka Ray Casting  IK: autonomous vs. hand-animated; solution approaches  Given: screen with pixels ( u, v)  Rag doll physics, rigid-body dynamics, physically-based models  Find intersection tmin(u, v) of rays through each (u, v) with scene  Today: Ray Tracing, Part 1 of 2  Calculate vectors emanating from world-space coordinate of tmin  Vectors  Light (L): to point light sources (or shadows)  Light (L): to point light sources (or shadows)  Reflected (R): from object surface  Reflected (R): from object surface  Transmitted or Transparency (T): through transparent object  Transmitted or Transparency (T): through transparent object  Recursive RT: call raytracer for each intersection found

 tmin: distance to intersection between ray and bounding volume  Builds ray tree rooted at intersection point

 Ways to find tmin  Base cases: unobstructed vector to light; depth limit  Basic recursive ray tracing: ray trees  Parallel RT: use multiple threads/processes for each ( u, v) or t