Ray Tracing I

1
Ray Tracing I
2
Reflection and Transmission
Light Source
S5
R1
R3
S6
Eye
S3
Eye Ray
S1
R2
T1
S2
S4
Light Source
3
Recursive Ray Tracing

• If an eye ray intersects an object
• Cast shadow rays to each light source.
• diffuse illumination
• shadows
• Cast reflection ray, search for object
  intersection.
• ambient illumination
• Cast transmission ray, search for object
  intersection.
• Transparency
• For each new reflection and transmission ray,
  repeat.
• Until no intersection
• Until N intersections (recursion depth) (3 ? N ?
  7)

4
Reflection Vector
-I
?N
I, Incident Ray
R, Reflected Ray
N
?
?

• Assume that I N R 1, I, R, and
  N are coplanar
• We know (-I)N RN (unit vectors with same
  angle)
• (-I)R ?N, where ? is the length of (-I)R

5
Reflection Vector Calculation

• (-I)R ?N
• (-IR)N ?NN ?
• (-IN)(NR) ?
• (-IN)(-IN) ?
• 2(-IN) ?
• -I R ?N 2(-IN)N
• R 2(-IN)N I

-I
?N
I
R
N
?
?
6
Transmission

• Let ?i be the index of refraction of medium i
  with respect to a vacuum.
• Let ?t be the index of refraction of medium t
  with respect to a vacuum.
• Snells law states
• We also know that
• T ?I ?N
• (All vectors are of unit length!)

Medium i
N
I
Ai
At
I
-N
T
Medium t
7
Transmission Vector
8
Transmission Vector (cont.)
1

• We now have two equations and two unknowns!
• Some algebra and a look at the geometry gives us

9
Index of Refraction

• Medium Index of Refraction
• Water 1.33
• Ethyl Alcohol 1.36
• Carbon Bisulfide 1.63
• Air 1.0003
• Methylene Iodide 1.74
• Fused Quartz 1.46
• Glass, Crown 1.52
• Glass, Dense Flint 1.66
• Sodium Chloride 1.53
• Note These are approximations. The index of
  refraction actually differs with each wavelength
  of light.

10
Total Internal Reflection

• Total Internal Reflection occurs when the angle
  of the incident ray with the surface is too
  shallow.
• Traveling from dense to less-dense medium
• Becomes a reflection ray
• Critical angle occurs when At 90, after which
  the radical in ? calculation is negative

11
Antialiased Ray Tracing

• Adaptive Supersampling (Weighted sub-pixel
  averaging)

• Cast rays through pixel corners (not centers)
• Take average of corner values
• If one corner differs significantly from average,

• Subdivide, adding 5 corners
• Repeat for each sub-area, averaging to obtain
  area value

Value for pixel BCEF
12
Ray Tracing Example

• Created by Anto Matkovic

13
Problems With Ray Tracing

• Ray/object intersection calculations become
  expensive with complex objects and more objects.
• Light from other objects (other than pure
  reflection) is not modeled.
• Still use the constant ambient light component.
• Shadows often appear too sharp
• Surfaces appear too glossy or smooth
• Images take a long time to render, must
  recalculate for each new view
• Have to tweak illumination model constants to get
  desired effect