CS4620/5620: Lecture 36 Ray Tracing (Shading and Sampling) Cornell CS4620/5620 Fall 2012 • Lecture 36 © 2012 Kavita Bala • 1 (with previous instructors James/Marschner) Announcements • PA3A due Tuesday night • PPA3 out Cornell CS4620/5620 Fall 2012 • Lecture 36 © 2012 Kavita Bala • 2 (with previous instructors James/Marschner) Shading • Compute light reflected toward camera • Inputs: – eye direction – light direction (for each of many lights) l n – surface normal v – surface parameters (color, shininess, …) Cornell CS4620/5620 Fall 2012 • Lecture 36 © 2012 Kavita Bala • 3 (with previous instructors James/Marschner) Mirror reflection • Consider perfectly shiny surface – there isn’t only a highlight – instead there’s a reflection of other objects • Can render this using recursive ray tracing – to find out mirror reflection color, ask what color is seen from surface point in reflection direction – already computing reflection direction for Phong… • “Glazed” material has mirror reflection and direct – where Lm is evaluated by tracing a new ray Cornell CS4620/5620 Fall 2012 • Lecture 36 © 2012 Kavita Bala • 4 (with previous instructors James/Marschner) Diffuse + mirror reflection (glazed) (glazed material on floor) Cornell CS4620/5620 Fall 2012 • Lecture 36 © 2012 Kavita Bala • 5 (with previous instructors James/Marschner) Snell’s Law • Tells us where the refracted ray goes – a.k.a. transmission vector • Computation – ratio of sines is ratio of in-plane components – project to surface; scale by eta ratio; recompute normal- direction component – total internal reflection Cornell CS4620/5620 Fall 2012 • Lecture 36 © 2012 Kavita Bala • 6 (with previous instructors James/Marschner) Computing the Transmission Vector, t Cornell CS4620/5620 Fall 2012 • Lecture 36 © 2012 Kavita Bala • 7 (with previous instructors James/Marschner) Computing the Transmission Vector, t Cornell CS4620/5620 Fall 2012 • Lecture 36 © 2012 Kavita Bala • 8 (with previous instructors James/Marschner) Ray tracing dielectrics • Like a simple mirror surface, use recursive ray tracing • But we need two rays – One reflects off the surface (same as mirror ray) – The other crosses the surface (computed using Snell’s law) • Doesn’t always exist (total internal reflection) • Splitting into two rays, recursively, creates a ray tree – Very many rays are traced per viewing ray – Ways to prune the tree • Limit on ray depth • Limit on ray attenuation Cornell CS4620/5620 Fall 2012 • Lecture 36 © 2012 Kavita Bala • 9 (with previous instructors James/Marschner) Whitted Ray Tracing Cornell CS4620/5620 Fall 2012 • Lecture 36 © 2012 Kavita Bala • 10 (with previous instructors James/Marschner) Specular reflection • Smooth surfaces of pure materials have ideal specular reflection (said this before) – Metals (conductors) and dielectrics (insulators) behave differently • Reflectance (fraction of light reflected) depends on angle metal dielectric Cornell CS4620/5620 Fall 2012 • Lecture 36 © 2012 Kavita Bala • 11 (with previous instructors James/Marschner) Specular reflection from metal • Reflectance does depend on angle Aluminum – but not much – safely ignored in basic rendering Cornell CS4620/5620 Fall 2012 • Lecture 36 © 2012 Kavita Bala • 12 (with previous instructors James/Marschner) Specular reflection from glass/water • Dependence on angle is dramatic! Glass – about 4% at normal incidence – 100% at grazing – remaining light is transmitted • Important for Perfect transmission at Brewster’s angle proper appearance Cornell CS4620/5620 Fall 2012 • Lecture 36 © 2012 Kavita Bala • 13 (with previous instructors James/Marschner) Brewster’s Angle Cornell CS4620/5620 Fall 2012 • Lecture 36 © 2012 Kavita Bala • 14 (with previous instructors James/Marschner) Fresnel reflection • Black glazed sphere – reflection from glass surface – transmitted ray is discarded Constant reflectance Fresnel reflectance Cornell CS4620/5620 Fall 2012 • Lecture 36 © 2012 Kavita Bala • 15 (with previous instructors James/Marschner) Fresnel’s formulas • They predict how much light reflects from a smooth interface between two materials – usually one material is empty space – R is the fraction that is reflected – (1 – R) is the fraction that is transmitted Cornell CS4620/5620 Fall 2012 • Lecture 36 © 2012 Kavita Bala • 16 (with previous instructors James/Marschner) Schlick’s approximation • For graphics, a quick hack to get close with less computation: • R0 is easy to compute: Cornell CS4620/5620 Fall 2012 • Lecture 36 © 2012 Kavita Bala • 17 (with previous instructors James/Marschner) Fresnel reflection [Mike Hill & Gaain Kwan | Stanford cs348 competition 2001] | Stanford Hill & GaainKwan [Mike Cornell CS4620/5620 Fall 2012 • Lecture 36 © 2012 Kavita Bala • 18 (with previous instructors James/Marschner) Hmm, ... how do we render beer? Cornell CS4620/5620 Fall 2012 • Lecture 36 © 2012 Kavita Bala • 19 (with previous instructors James/Marschner) Beer's Law! Light-carrying ray intensity I is attenuated with distance traveled x according to Therefore, the attenuated per-channel intensity is Evaluated on a per-channel basis, e.g., the color of white light after traveling unit distance is ) Cornell CS4620/5620 Fall 2012 • Lecture 36 © 2012 Kavita Bala • 20 (with previous instructors James/Marschner) Not just for beer... [Josh Wills | 2003 UCSD Rendering Competition] Wills| 2003 UCSD Rendering [Josh Cornell CS4620/5620 Fall 2012 • Lecture 36 © 2012 Kavita Bala • 21 (with previous instructors James/Marschner) Shader for Transparent Objects (pp. 306-7) Cornell CS4620/5620 Fall 2012 • Lecture 36 © 2012 Kavita Bala • 22 (with previous instructors James/Marschner) Basic ray traced image [Glassner 89] [Glassner Cornell CS4620/5620 Fall 2012 • Lecture 36 © 2012 Kavita Bala • 23 (with previous instructors James/Marschner) Basic ray tracing • Basic ray tracer: one sample for everything – one ray per pixel – one shadow ray for every point light – one reflection ray per intersection • one refraction ray (if necessary) per intersection • Many advanced methods build on the basic ray tracing paradigm Cornell CS4620/5620 Fall 2012 • Lecture 36 © 2012 Kavita Bala • 24 (with previous instructors James/Marschner) Discontinuities in basic RT • Perfectly sharp object silhouettes in image – leads to aliasing problems (stair steps) • Perfectly sharp shadow edges – everything looks like it’s in direct sun • Perfectly clear mirror reflections – reflective surfaces are all highly polished • Perfect focus at all distances – camera always has an infinitely tiny aperture • Perfectly frozen instant in time (in animation) – motion is frozen as if by strobe light Cornell CS4620/5620 Fall 2012 • Lecture 36 © 2012 Kavita Bala • 25 (with previous instructors James/Marschner) Antialiasing in ray tracing aliased image Cornell CS4620/5620 Fall 2012 • Lecture 36 © 2012 Kavita Bala • 26 (with previous instructors James/Marschner) Antialiasing in ray tracing aliased image one sample per pixel Cornell CS4620/5620 Fall 2012 • Lecture 36 © 2012 Kavita Bala • 27 (with previous instructors James/Marschner) Antialiasing in ray tracing antialiased image four samples per pixel Cornell CS4620/5620 Fall 2012 • Lecture 36 © 2012 Kavita Bala • 28 (with previous instructors James/Marschner) Antialiasing in ray tracing one sample/pixel 9 samples/pixel Cornell CS4620/5620 Fall 2012 • Lecture 36 © 2012 Kavita Bala • 29 (with previous instructors James/Marschner) Details of supersampling • For image coordinates with integer pixel centers: // one sample per pixel // ns^2 samples per pixel for iy = 0 to (ny-1) by 1 for iy = 0 to (ny-1) by 1 for ix = 0 to (nx-1) by 1 { for ix = 0 to (nx-1) by 1 { ray = camera.getRay(ix, iy); Color sum = 0; image.set(ix, iy, trace(ray)); for dx = -(ns-1)/2 to (ns-1)/2 by 1 } for dy = -(ns-1)/2 to (ns-1)/2 by 1 { x = ix + dx / ns; y = iy + dy / ns; ray = camera.getRay(x, y); sum += trace(ray); } image.set(ix, iy, sum / (ns*ns)); } Cornell CS4620/5620 Fall 2012 • Lecture 36 © 2012 Kavita Bala • 30 (with previous instructors James/Marschner) Soft shadows Cornell CS4620/5620 Fall 2012 • Lecture 36 © 2012 Kavita Bala • 31 (with previous instructors James/Marschner) Cause of soft shadows point lights cast hard shadows Cornell CS4620/5620 Fall 2012 • Lecture 36 © 2012 Kavita Bala • 32 (with previous instructors James/Marschner) Cause of soft shadows area lights cast soft shadows Cornell CS4620/5620 Fall 2012 • Lecture 36 © 2012 Kavita Bala • 33 (with previous instructors James/Marschner) Creating soft shadows • For area lights: use many shadow rays – and each shadow ray gets a different point on the light • Choosing samples – general principle: start with uniform in square Cornell CS4620/5620 Fall 2012 • Lecture 36 © 2012 Kavita Bala • 34 (with previous instructors James/Marschner) Creating soft shadows Cornell CS4620/5620 Fall 2012 • Lecture 36 © 2012 Kavita Bala • 35 (with previous instructors James/Marschner) .