Texture Mapping

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Texture Mapping
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Definitions

• Texel
• Occlusion
• Multi-texturing
• Images
• Light Maps
• Height Maps

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• Texture mapping maps the texels of a texture in
  UV space to the coordinates of a polygon and the
  pixels of the screen in the same way that a
  function, say f, maps one value to another
• ie. f(x) y

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Mapping of Images

• Two distinct categories of image mapping
• (non-exclusive)
• -Linear (Affine) Mapping
• -Perspective Correct Mapping

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Linear (Affine) Mapping

• Pros
• Fast
• Easy to implement

• Cons
• Distorted textures

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Linear (Affine) Mapping

• Essentially, the equation for linear mapping is
• ua (1 a)u0 au1, where 0 a 1
• To interpolate a texture coordinate ua between
  two endpoints u0 and u1.Source Wikipedia.org

• Simple equation
• No divisons
• Fast

Approach used in original Doom game ?
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• Linear mapping does not take depth information
  into account.
• Distortion worsens as angle increases
• Effect can be minimized

Area Subdivision
Scanline Subdivision (Quake)
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Perspective Correct Mapping

• Pros
• Correct rendering of textures

• Cons
• More complex implementation (barely)
• Slower

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Perspective Correct Mapping
(1 a)(u0/z0) a(u1/z1)
3x the operations with 5 divisions.
ua
(1 a)(1/ z0) a(1/z1)
Perspective Correct Mapping takes depth
information into account (note the z variables),
but at a greater cost of execution.
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Multi-Texturing

• Light Mapping
• Bump Mapping
• Normal Mapping
• Parallax Mapping
• Displacement Mapping

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Bump Mapping

• Creates a textured look without altering the
  geometry of the object.

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Bump Mapping

• Uses a height map to recalculate the normal for a
  surface at a pixel

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Bump Mapping

• Examples

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Bump Mapping
Without Bump Mapping
With Bump Mapping
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Normal Mapping

• Similar to bump mapping
• Perturbs surface normal
• Uses Normal Map instead of Height Map
• Creates the illusion of a detailed texture
• Does not change any object geometry

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Normal Mapping

• The Normal Map encodes information about the
  surface normal as a color instead of determining
  the slope at a pixel

Height Map
Normal Map
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Normal Mapping

• Example

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Normal Mapping
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• Can be used to significantly reduce the number of
  polygons needed for a model

80001 polygonal compression!
Image Source www.Wikipedia.org
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Parallax Mapping

• Aka. Offset Mapping or Virtual Displacement
  Mapping
• Uses a height map
• Capable of generating more exaggerated textures
• Does not change object geometry

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Parallax Mapping

• Builds on the idea of bump mapping. Displaces
  pixels based on height, creating a smear
  effect.
• The texture is able to make it look like there is
  more geometry than actually present

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Problems with Bump, Normal, and Parallax Mapping

• Pros
• Geometry is not altered
• Less costly

• Cons
• Geometry is not altered!
• Rendering Issues

Low cost techniques that add detail to a scene,
but do not take into account occlusion and
silhouetting . Various methods exist to properly
render occlusion and silhouetting, but at high
cost
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Enter Displacement Mapping
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Displacement Mapping

• Pros
• Alters geometry of an object granting proper
  occlusion and silhouetting
• Adds high levels of detail to an object
• Can use height maps the same as bump mapping

• Cons
• One of the highest overheads of all texturing
  techniques
• Polygon count can quickly grow to unmanageable
  numbers

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Displacement Mapping

• Example

Bump Mapping
Displacement Mapping
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Displacement Mapping

• Example

Height (Displacement) Map
Displacement Mapping
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Displacement Mapping

• Example

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Fin