SI31 Advanced Computer Graphics AGR

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SI31Advanced Computer GraphicsAGR

• Lecture 13
• An Introduction to Ray Tracing

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Ray Tracing

• Ray tracing is an alternative rendering approach
  to the polygon projection, shading and z-buffer
  way of working
• It is capable of high quality images through
  taking account of global illumination

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Ray Tracing Example
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Firing Rays
light
The view plane is marked with a grid
corresponding to pixel positions on screen. A
ray is traced from the camera through each pixel
in turn.
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Finding Intersections
light
We calculate the intersection of the ray with
all objects in the scene. The nearest
inter- section will be the visible surface
for that ray
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Intensity Calculation
The intensity at this nearest intersection is
found from the usual Phong reflection
model. Stopping at this point gives us a
very simple rendering method. Often called ray
casting
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Phong Reflection Model
light source
N
R
L
eye
?
V
?
surface
dist distance attenuation factor
Here V is direction of incoming ray, N is normal,
L is direction to light source, and R is
direction of perfect spec. reflection.
Note R.V calculation replaced by H.N for speed -
H (LV)/2
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Intensity Calculation
Thus Phong reflection model gives us intensity
at point based on a local model I I
local where I local I ambient I diffuse I
specular
Intensity calculated separately for red, green,
blue
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Shadows
To determine if the point is in shadow, we can
fire a ray at the light source(s) - in direction
L. If the ray intersects another object, then
point is in shadow from that light. In this
case, we just use ambient component I local I
ambient Otherwise the point is fully lit.
shadow ray
Note this has to be done for every light source
in scene.
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Reflected Ray
Ray tracing models reflections by looking for
light coming in along a secondary ray, making a
perfect specular reflection.
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Reflected Ray- Intersection and Recursion
light
We calculate the intersection of this reflected
ray, with all objects in the scene. The
intensity at the nearest intersection point is
calculated, and added as a contribution attenuate
d by distance. This is done recursively.
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Reflected Ray - Intensity Calculation
light
The intensity calculation is now I I local k
r I reflected
Here I reflected is calculated recursively k r
is a reflection coefficient (similar to k s )
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Ray Termination
Rays terminate - on hitting diffuse surface - on
going to infinity - after several reflections -
why?
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Transmitted Ray
If the object is semi- transparent, we also need
to take into account refraction
light
Thus we follow also transmitted rays, eg T1.
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Refraction
?r
?i
Change in direction is determined by
the refractive indices of the materials, ??i and
??r
T
?r
N
?i
Snells Law sin ? r (? i / ? r ) sin ? i
V
T (? i / ? r ) V - ( cos ? r - (? i / ? r ) cos
? i ) N
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Refraction Contribution

• The contribution due to transmitted light is
  taken as
• kt It( ? )
• where
• kt is the transmission coefficient
• It( ? ) is the intensity of transmitted light,
  again calculated separately for red, green, blue

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Intensity Calculation
The intensity calculation is now I I local k
r I reflected k t I transmitted
I reflected and I transmitted are calculated
recursively
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Binary Ray Tracing Tree
S4
light
S1
T1
R1
S2
S3
S2
S3
R1
T1
S1
S4
The intensity is calculated by traversing the
tree and accumulating intensities
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Calculating Ray Intersections

• A major part of ray tracing calculation is the
  intersection of ray with objects
• Two important cases are
• sphere
• polygon

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Ray - Sphere Intersection
Let camera position be (x1, y1, z1) Let pixel
position be (x2, y2, z2) Any point on ray
is x(t) x1 t (x2 - x1) x1 t i y(t)
y1 t (y2 - y1) y1 t j z(t) z1 t
(z2 - z1) z1 t k As t increases from zero,
x(t), y(t), z(t) traces out the line from (x1,
y1, z1) through (x2, y2, z2). Equation of
sphere, centre (l, m, n) and radius r (x - l)2
(y - m)2 (z - n)2 r2
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Ray - Sphere Intersection
Putting the parametric equations for x(t), y(t),
z(t) in the sphere equation gives a quadratic in
t at2 bt c 0 Exercise write down a, b,
c in terms of i, j, k, l, m, n, x1, y1,
z1 Solving for t gives the intersection
points b2 - 4ac lt 0 no intersections b2 - 4ac
0 ray is tangent b2 - 4ac gt 0 two
intersections, we want smallest positive
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Ray - Polygon Intersection
Equation of ray x(t) x1 t i y(t) y1 t
j z(t) z1 t k Equation of plane ax
by cz d 0 Intersection t - (ax1 by1
cz1 d) / (ai bj ck) Need to check
intersection within the extent of the polygon.
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Ray Tracing - Limitations

• This basic form of ray tracing is often referred
  to as Whitted ray tracing after Turner Whitted
  who did much of the early work...
• Ray tracing in its basic form is computationally
  intensive
• Much research has gone into increasing the
  efficiency and this will be discussed in next
  lecture.

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Ray Tracing Example
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Depth 0
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Depth 1
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Depth 2
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Depth 3
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Depth 4
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Depth 7
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Acknowledgements

• As ever, thanks to Alan Watt for the excellent
  images