CS4620/5620: Lecture 36

Ray Tracing (Shading and Sampling)

Announcements

• PA3A due Tuesday night

• PPA3 out

• Compute light reﬂected toward camera • Inputs: – eye direction – light direction (for each of many lights) l n – surface normal v – surface parameters (color, shininess, …)

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

(glazed material on ﬂoor)

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

Computing the Transmission Vector, t

• 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

Whitted Ray Tracing

• 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

Specular reﬂection from metal

• Reﬂectance does depend on angle Aluminum – but not much – safely ignored in basic rendering

• 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

Brewster’s Angle

• Black glazed sphere – reﬂection from glass surface – transmitted ray is discarded

Constant reﬂectance Fresnel reﬂectance

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

• For graphics, a quick hack to get close with less computation:

• R0 is easy to compute:

Fresnel reﬂection [Mike & Gaain Hill Kwan | Stanford cs348 competition 2001] Cornell CS4620/5620 Fall 2012 • Lecture 36 © 2012 Kavita Bala • 18 (with previous instructors James/Marschner) Hmm, ... how do we render beer?

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

)

Shader for Transparent Objects (pp. 306-7)

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

• 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

Antialiasing in ray tracing

aliased image

one sample per pixel

Antialiasing in ray tracing

antialiased image

four samples per pixel

one sample/pixel 9 samples/pixel

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)); }

Cause of soft shadows

point lights cast hard shadows

area lights cast soft shadows

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