Light and Color in Nature Today: Water

1
Light and Color in Nature(Today Water)

• by Benjamin Peters
• and Martin Schäf
• WS0304

2
Intorduction

• Motivation
• Reflection and Refraction
• Illumination and Caustics
• Results
• Advanced Topics

3
Looking at a water surface

• Light is reflected and refracted at the same time
• There is a light pattern on the ground (Caustics)

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Reflection and Refraction

• What we need to know
• Reflection angle
• Refraction angle
• (Reflected light)/(Refracted light)
• What we know
• Incoming angle
• Vertex Normal

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Reflection and Refraction
Vertex Normal N
Reflection
a
a
Air
Water
ß
Refraction
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Snells Law

• a Incoming a Reflected
• sin(a)/sin(ß) Refractive Index R (material
  depending)
• e.g. RWater 1.33 RGlass 1.5
• Refractive Index can be found in any book about
  physics

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Fresnel Term

• Fresnel Term is often approximated to recieve
  better results
• Fresnel Term as found in books is
• F ½ (sin²(a-ß)/sin²(aß))
  tan²(a-ß)tan²(aß)
• Returns good results for strong reflecting water
  surfaces
• Not good to show the effect of caustics

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Example
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Approximated Fresnel Term

• F0 (R-1)2/(R1)2 is a minimum of incoming light
  parallel to the normal of the surface.
• Fa F0(1- cos(a))5 (1- F0) is a value
  between 0 and 1 depending on the angle between
  the incoming ray and the surface normal.
• e.g. F90 1, if the incoming ray is parallel to
  the surface, all light is reflected.

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Refraction and Reflection

• Result
• ß arcsin(1/Rwater sin(a)) arcsin(1/1.33sin(a
  ))
• color of intersection point
• (Facolorreflected) (1-Fa) colorrefracted

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Result
Scene without Fresnel Term and with one simple
direcional light source
Scene with Fresnel Term and with one simple
direcional light source
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Illumination and Caustics

• Light is refracted by the water surface
• Some spots are stronger illuminated then others

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A simple introduction in Photon Mapping

• A sum of photons is send from each light source
  to the scene
• Intersecting photons are stored in a kd-tree
• Illumination of each point can be computed by
  counting the number of photons in a certain
  distance

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A simple introduction in Photon Mapping
Light source
Camera
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Photon Mapping on a water surface
dark
bright
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Results

• Left image Fresnel Shading, no Photonmapping
• Right image Fresnel Shading, Photonmapping (only
  100 000 Photons)

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Results

• Left image Fresnel Shading, Photonmapping (1
  mil. Photons)
• Left image Fresnel Shading, Photonmapping (1
  mil. Photons) and Phongshading

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Advanced Topics

• Shafts of light and caustics
• http//nis-lab.is.s.u-tokyo.ac.jp/nis/cdrom/pg/pg
  2001_iwa.pdf

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Advanced Topics

• Modeling and animating realistic water surfaces
• http//graphics.stanford.edu/fedkiw/