Computer Graphics For Games Part 2

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Computer Graphics For Games Part 2
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The Pink Bunny

• Triangle Rasterization
• Hidden Surface Elimination
• Lighting
• Other stuff

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Triangles

• Why do we use triangles in graphics?
• Normals are unique Important for lighting
• Space filling triangles tile so they can be used
  to represent surfaces.
• Atomic All polygons decompose into triangles

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Scan Conversion

• Ray tracing determines a pixels color by tracing
  the path of light through the scene to arbitrary
  precision.
• The result is an extremely realistic image.
• In scanline rendering surfaces are projected on
  the screen and space filling rasterizing
  algorithms are used to fill in the color.
• Color values from light are approximated.

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Quick Math!!
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Barycentric Coordinates

• The axis of a coordinate system dont have to be
  perpendicular.
• If you use two sides of a triangle as axis, you
  can create a coordinate system called barycentric
  coordinates.
• Basically, in the barycentric coordinate system
  you have three coordinates ?,?,? which represents
  the signed distance from each of the triangle
  edges.

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Why are Barycentric coordinates useful?

• For any point x, if the barycentric
  representation of that point x?,x?, x?
• Also ?,?,? can be used as a mass function across
  the surface of a triangle to be used for
  interpolation.
• This is used to interpolate normals across the
  surface of a triangle to make polygon surfaces
  look rounder.

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Definitions

• In this example the origin is at point a.
• The ? and ? axis are the normalized vectors

A barycentric coordinate can Be represented by
the equation
Where
And
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Calculating ?,? and ? for anarbitrary point,
(x,y)

• These are derived from the implicit line equation.

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Math Done!!
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Rasterize This!(Rasterization intuition)

• When we render a triangle we want to determine if
  a pixel is within a triangle. (barycentric
  coords)
• Calculate the color of the pixel.
• Draw the pixel.
• Repeat until the triangle is appropriately filled.

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Rasterization Pseudo Code
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A simple optimization
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Hidden Surface Removal

• Currently our projection and rasterization
  process doesnt preserve any 3d depth
  information.
• This will cause some problems when triangles
  overlap eachother.

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BSP Trees

• A BSP tree is an example of a painters
  algorithm.
• The polygons are painted in back to front order
  from the perspective of the viewer, this handles
  the hidden surface problem.
• BSP trees are typically pre-computed in games for
  performance.

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The Z-Buffer
Note You must use the z value of the 3d
coordinate after perspective projection but
BEFORE the homogenizing step!!
Typically this algorithm is implemented in
hardware
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Surface Shading

• For now we will assume that when light interacts
  with objects of various compositions it is either
  diffuse or reflected.
• Diffuse light represent light that is partially
  absorbed by the surface. Diffuse lighting is also
  called matte shading.
• Reflected light, is light that bounces directly
  off of the object (like a mirror) and primarily
  maintains the original color of the light source.

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Lamberts Law

• We assume Lamberts Law to approximate light.
• Basically we assume that the effect of a light
  source on the color of a surface is proportional
  to the cosine of the angle between the surface
  normal and the direction to the light.
• We know when the surface points away from the
  light if the cosine is negative.

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What is a Normal!?

• A normal is a vector that is perpendicular to two
  other vectors.
• It is calculated as the cross product of the two
  vectors.
• Triangles are nice b.c. theres a unique normal
  (2 actually) for every triangle.
• Remember the right-hand/left-hand rule applies
  here!

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How do we compute the Cosine betweenTwo vectors
quickly?!

• The dot product of two vectors is equal to the
  cosine of the angle between the two vectors!
• Note The vectors have to be unit vectors for
  this to be true, otherwise youve got to
  normalize them.

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Diffuse Shading
To Deal with negative light
Add in the ambient light
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Reflective Shading(phong shading)

• Phong shading is a simplified reflection model.
• Basically it puts a bright spot which is colored
  with the light color on surfaces that are nearest
  to the light origin.
• Generally we want the bright spot to be brightest
  when the reflected component r is going right
  into the viewers eye and fall off from there.

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Phong Math
p is the phong exponent, which determines the
falloff rate
We can approximate r with h to eliminate negative
values
This gives us our final phong equation
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What happens when you vary p ?
p 1
p 2
p 8
p 4
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Final Lighting
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Our Pipeline is Complete!
The Bunny Model
Triangle and line drawing
Z buffering
Projection matrices
Diffuse/phong shading
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Other topics

• Alpha blending
• Texture mapping
• Bump mapping
• Shadows
• Surface effects
• Tessellation (curved surfaces)
• Level Of detail

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Alpha Blending
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Texture Mapping
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Bump Mapping
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Normal Interpolation
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Hair
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Surface Shaders
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Tessellation
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Shadows
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Level of Detail