CS4620/5620: Lecture 36
Ray Tracing (Shading and Sampling)
Cornell CS4620/5620 Fall 2012 • Lecture 36
© 2012 Kavita Bala •
1
© 2012 Kavita Bala •
2
(with previous instructors James/Marschner)
Announcements
• PA3A due Tuesday night
• PPA3 out
Cornell CS4620/5620 Fall 2012 • Lecture 36
(with previous instructors James/Marschner)
Shading
• Compute light reflected toward camera
• Inputs:
– eye direction
– light direction
(for each of many lights)
– surface normal
– surface parameters
(color, shininess, …)
l
Cornell CS4620/5620 Fall 2012 • Lecture 36
n
v
© 2012 Kavita Bala •
(with previous instructors James/Marschner)
3
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 •
(with previous instructors James/Marschner)
4
Diffuse + mirror reflection (glazed)
(glazed material on floor)
Cornell CS4620/5620 Fall 2012 • Lecture 36
© 2012 Kavita Bala •
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© 2012 Kavita Bala •
6
(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 normaldirection component
– total internal reflection
Cornell CS4620/5620 Fall 2012 • Lecture 36
(with previous instructors James/Marschner)
Computing the Transmission Vector, t
Cornell CS4620/5620 Fall 2012 • Lecture 36
© 2012 Kavita Bala •
(with previous instructors James/Marschner)
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Computing the Transmission Vector, t
Cornell CS4620/5620 Fall 2012 • Lecture 36
© 2012 Kavita Bala •
(with previous instructors James/Marschner)
8
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 •
(with previous instructors James/Marschner)
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Whitted Ray Tracing
Cornell CS4620/5620 Fall 2012 • Lecture 36
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(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
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(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
proper appearance
Cornell CS4620/5620 Fall 2012 • Lecture 36
Perfect transmission at Brewster’s angle
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(with previous instructors James/Marschner)
Brewster’s Angle
Cornell CS4620/5620 Fall 2012 • Lecture 36
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(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
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(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
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(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
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(with previous instructors James/Marschner)
[Mike Hill & Gaain Kwan | Stanford cs348 competition 2001]
Fresnel reflection
Cornell CS4620/5620 Fall 2012 • Lecture 36
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Hmm, ... how do we render beer?
Cornell CS4620/5620 Fall 2012 • Lecture 36
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(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
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(with previous instructors James/Marschner)
[Josh Wills | 2003 UCSD Rendering Competition]
Not just for beer...
Cornell CS4620/5620 Fall 2012 • Lecture 36
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(with previous instructors James/Marschner)
Shader for
Transparent
Objects
(pp. 306-7)
Cornell CS4620/5620 Fall 2012 • Lecture 36
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(with previous instructors James/Marschner)
[Glassner 89]
Basic ray traced image
Cornell CS4620/5620 Fall 2012 • Lecture 36
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(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
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(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
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(with previous instructors James/Marschner)
Antialiasing in ray tracing
aliased image
Cornell CS4620/5620 Fall 2012 • Lecture 36
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(with previous instructors James/Marschner)
Antialiasing in ray tracing
aliased image
one sample per pixel
Cornell CS4620/5620 Fall 2012 • Lecture 36
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(with previous instructors James/Marschner)
Antialiasing in ray tracing
antialiased image
four samples per pixel
Cornell CS4620/5620 Fall 2012 • Lecture 36
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(with previous instructors James/Marschner)
Antialiasing in ray tracing
one sample/pixel
9 samples/pixel
Cornell CS4620/5620 Fall 2012 • Lecture 36
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Details of supersampling
• For image coordinates with integer pixel centers:
// one sample per pixel
for iy = 0 to (ny-1) by 1
for ix = 0 to (nx-1) by 1 {
ray = camera.getRay(ix, iy);
image.set(ix, iy, trace(ray));
}
Cornell CS4620/5620 Fall 2012 • Lecture 36
// ns^2 samples per pixel
for iy = 0 to (ny-1) by 1
for ix = 0 to (nx-1) by 1 {
Color sum = 0;
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));
}
© 2012 Kavita Bala • 30
(with previous instructors James/Marschner)
Soft shadows
Cornell CS4620/5620 Fall 2012 • Lecture 36
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(with previous instructors James/Marschner)
Cause of soft shadows
point lights cast hard shadows
Cornell CS4620/5620 Fall 2012 • Lecture 36
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Cause of soft shadows
area lights cast soft shadows
Cornell CS4620/5620 Fall 2012 • Lecture 36
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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
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(with previous instructors James/Marschner)