CSL%20859:%20Advanced%20Computer%20Graphics

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CSL 859 Advanced Computer Graphics

• Dept of Computer Sc. Engg.
• IIT Delhi

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Ray Tracing
Courtesy POV-Ray gallery
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Ray Tracing Forward Rendering
Color
Light Direction
normal
Point Directional Or Both
View Direction
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Basic Ray-casting

• For each pixel
• Form the Ray
• For each Object
• Find point of intersection
• If closest, save object
• Shade Ray
• If no intersection, return background color
• Otherwise, shade(saved object)
• For each light
• Form light ray
• Shade surface and accumulate color

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Ray-traced picture
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Shadow Rays

• Shade Ray
• If no intersection, return Background
• Otherwise, For each light
• Compute Shadow Ray
• If(shadow Ray doesnt intersect light first)
• ignore and continue
• Otherwise
• shade surface and accumulate color

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Shadow Rays
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Recursive Ray Tracing
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Recursive Ray Tracing
L
n
v
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Recursive Ray Tracing

• Color RayTrace(Ray ray, int depth)
• Point IntersectionPoint
• if (depth gt MAX) return Background
• if(! intersect(IntersectionPoint, ray))
• return Background
• Ilocal kaIa Ip.v.(kd(n.l) ks.(h.n)m)
• return Ilocal krRayTrace(ReflectRay,
  depth1)
• ktRayTrace(RefractRay
  , depth1)

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Computing the reflection direction

• Ideal reflection
• ? ?
• -v r -2(v.n) n
• r v - 2(v.n)n

n
?
?
r
v
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Refraction
n
n
v
?
index of refraction
?1
m
?2
t
ß
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Refracted Ray Computation

• Notes
• Negative root gt Total internal reflection
• Transparent gt Invert light behind object

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Specular Transmission

• A transparent surface can be illuminated from
  behind and this should be calculated in Ilocal

l
n
v
?
?1
?2
l
ß
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Make Ray
tan(fovy/2)

• Origin
• Direction
• o t d

tan(fovx/2)
ref
y
x
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Algebraic Intersection

• Point satisfies
• o t d
• f (x, y, z) 0
• f (ox t dx , oy t dy, oz t dz) 0
• Example
• (0, 0, 5) t (0, 0, 1)
• X2y2z2 1
• 0 0 (5t)2 1, i.e., t -1 5, -4/-6
• (0, 0, 5) 4(0, 0, 1) (0, 0, 1)

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Geometric Intersection
d2 r2 (c-e).(c-e) - (c-e).d
c
(c-e).d
(c-e).(c-e)
d
e
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Triangle Intersection?

• Intersect with plane
• Ax By Cz 1
• Check if point inside triangle
• Barycentric coordinates must be ve
• Point must be in the positive half-planes

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Half-plane Method
Ax By Cz 1
p
n op X oq n.(p-o) gt 0
v1
v2
Orient edges in CW order
o
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Distributed Ray Tracing
Multiple randomly jittered rays
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Depth of Field

• Use multiple origins
• Distributed on a disk

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Motion Blur

• Jitter rays in time

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Soft Shadows

• Light has area
• Shoot multiple rays to light
• Take average contribution

Courtesy H.P. Seidel
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Monte-Carlo Integration

• At intersection
• Generate multiple rays
• Typically based on material properties
• Weighted average of resulting ray colors
• Path tracing
• Global illumination
• More later

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Tracing Efficiency

• Embarassingly parallel
• Bounding volume hierarchy

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Bounding Box Test
ty1
tx1
ty0
tx0
ox t dx a t (a ox )/dx
o t d
x a