Texture = Arbitrary Illumination

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Texture Arbitrary Illumination

• Vary a surface property non-linearly
• Rasterization does bi-linear interpolation
• Examples of usage
• Paste a picture
• picture of environment
• picture of scene
• Modify surface normals
• Create bumps and detail

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Texture Mapping

• Texture aka function of a surface
• f (x,y,z) some attribute value
• Would like f to be arbitrary
• No continuity constraints
• Look-up table is a possible implementation
• But not all x,y,z has the surface through it
• Surface is only a 2-manifold
• 2D look-up table
• But want to map every point on a surface to a 2D
  space ltu,vgt
• parameterization

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Texture Mapping
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Texture Coordinates
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Pixel Texture Coordinates
Triangle
Pixel
Screen
Texture
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Pixel Texture Lookup
Texel
Pixel
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Texture-Minification
Texels
Pixels
These texels should also contribute to the pixel
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Mip-Mapping

• Filter 2x2 texel blocks into one texel
• Weighted average
• Log(n) levels of an n xn texture map
• Choose level closest to 1 texel/pixel
• Pixel derivative

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Derivative
Texels
Tex coord t0
t1
Pixels
WxH texture gt texel size 1/W x 1/H
x x
t1 t0 (?t u, ?t v )
t2 t0 (?tyu , ?tyv)
?t max (?txu , ?tyu), max(?txu , ?tyv)
Use divided difference t1 t-1
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Anisotropic Filter
Texels
Pixels
Use Smallest minification May read several texels
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Texture Border

• Extra texel needed for linear interpolation

u 0
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Other Texture Usage

• Alpha Map
• Transparent texture
• Light Map
• Diffused lighting independent of viewer
• How do you generate it?
• Texel to Object space reverse-mapping
• Specular Map
• Displacement Map
• Bump Map
• Environment Map
• Point Sprites

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Point Sprites

• Draw points
• E.g., as a k x k pixel square
• Map a (small) texture on the point
• Typically used with transparency
• For example a cursor

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Bump Mapping
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Bump Mapping

• Physically displace
• Generate many triangles
• Simulate
• Change the normal
• Normal affects lighting

N
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Bump Mapping

• Assume
• Bump to the surface is small
• In the direction of the normal
• aka Height-map
• Simulation

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Bump Mapping

• Tangent to the surface P(u,v) at a point (u,v)
  Pu, Pv
• The normal is then
• N(u,v) Pu ? Pv
• P'(u,v) P(u,v) B(u,v) N
• P'u Pu Bu N B Nu ? P'u Pu Bu N
• P'v Pv Bv N B Nv ? P'v Pv Bv N
• (if B is small)
• P'u x P'v
• Pu ? Pv Bu(N ? Pv) - Bv(N ?
  Pu) Bu Bv(N ? N)

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Bump Mapping

• N'(u,v)
• Pu ? Pv Bu(N ? Pv) - Bv(N ? Pu) Bu Bv(N
  ? N)
• N Bu(N ? Pv) - Bv(N ? Pu)
• ? N - BuPu BvPv
• if tangents are almost perpendicular
• Note
• Store Bu and Bv as
• 2-component texture
• Normalize N

D
N
N
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Normal Mapping

• Directly store the new normal per texel
• From bump map
• Nx (0, 1, Bu)
• Ny (1, 0, Bv)
• N Nx X Ny
• Remember to normalize
• (and range compress)

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Displacement Mapping

• Modifies the surface position
• Along surface normal, typically
• Use if Bumps are large
• Get silhouettes, shadows right
• Much more expensive
• Tessellate geometry
• Some support in modern GPUs

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Environment Mapping

• Global Illumination
• For each point on the surface
• Render the entire scene
• Pick pixels in useful directions
• Environment Map
• Assume high gloss
• Find ideal reflected direction
• Look-up the value in that direction
• Use one rendering
• Eye at the center of the object
• Where is the image plane?
• Introduces distortions in the reflection
• Good for small objects in a large room

Reflected direction
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Example
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Cube Mapping

• Map onto surfaces of a cube (around the object)
• Axis-aligned often
• Find desired direction from a surface point
• Cube map accessed by the direction
• One of the six faces of the cube intersects
• The corresponding texture is looked up
• For environment mapping
• Render scene from object-center onto cube face
• Use, e.g, the six axis-aligned directions
• Rendering may be pre-computed at high quality
• E.g., 6 photos of a real environment

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Cube Map Example