Texturing

1
Texturing

• Surfaces texture its look feel
• Graphics a process that takes a surface and
  modifies its appearance using
• An image
• A function
• Other dataset
• Gained importance in 80s enhance Phong shaded
  scenes
• Environment mapping Reflect the surrounding
  environments into shiny animated objects

2
Mapping Techniques Texture and Environment
Mapping

• Texture A 2D image or pattern
• Goal Map the texture or detail onto a 3D object
• Mapping Finding two u,v values from three values
  from one of the 3-D coordinate spaces
• R3 -gt R2

3
Main Issues in Texture Mapping

• Anti-aliasing
• What attribute or parameter of the model is to be
  modulated?
• How is texture mapping carried out? Define a
  mapping between the 2D domain of texture maps and
  3D object domain

4
Modulating Different Parameters

• Surface color Modulating the diffuse
  coefficient. Most common Catmull1974
• Specular Diffuse Reflection (Environment
  mapping) Blinn 1976
• Normal Vector Perturbation Perturbs the surface
  normal Blinn 1978. Extended to frame mapping
  (tangent, normal, binormal) Kajiya1985

5
Modulating Different Parameters

• Heckbert1986 Review Paper, IEEE CG A
• Specularity Surface roughness function in the
  Cook-Torrance reflection model (variable
  shininess) Blinn1978
• Transparency Doesnt apply texture to an object,
  but generates a complete object a cloud using a
  mathematical texture function to modulate the
  transparency of an ellipsoid

6
Main Approaches and Categories

• General texture mapping a 2D texture domain is
  pasted onto the object
• View-dependent mapping techniques e.g. chrome,
  environment, reflection and refraction
• Bump mapping techniques Alters the geometry of
  the surface

7
Texture Mapping and Object Representation

• Polygonal models The mapping or the projection
  function needs to be computed
• Pasting Cannot paste a 2D pattern onto a
  polygonal object of arbitrary topology without
  cutting the pattern
• Parametric analytic models computing the mapping
  function is relatively simple (e.g. rational
  parametric surfaces)

8
Texture Mapping Pipeline

• Compute object space location (x,y,z)
• Use mapping function to find (u,v)
• Use corresponder function(s) to compute texel
• Apply value transform function
• Modify illumination equation value

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Practical Approach for Polygonal Models

• Associate a texture map coordinate (u,v) with
  each vertex of the polygonal mesh
• Derive a mapping or projection function F() such
  that
• (u,v) F(x,y,z)
• Develop algorithms for associating texture values
  internal to the polygon, as it gets clipped and
  rendered.

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Standard mapping or projection functions

• Cylindrical mapping function
• Spherical mapping function
• Box mapping function
• Planar projections

11
Mapping during Modeling

• Object is approximately cylindrical or spherical
  (e.g. bananas)
• Bend the objects without changing the mapping
  function to the vertices

12
Texture Mapping Pipeline

• Compute object space location (x,y,z)
• Use mapping function to find (u,v)
• Use corresponder function(s) to compute texel
• Apply value transform function
• Modify illumination equation value

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Corresponder Functions

• Transform the parameter space values (u,v) into
  a texture space value (texels)
• Examples
• array indices into an image texture (sampling,
  anti-aliasing, mipmapping)
• Optional matrix transformation (OpenGL) rotate,
  scale
• Image application warp, repeat, mirror
• Can apply multiple corresponder functions

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Texture Application

• RGB or RGB\alpha, where \alpha is the opacity
  value
• Change surface attribute using texture blending
  functions
• Replace Replace the original color with texture
  color
• Modulate Multiply the surface color by texture
  color

15
Other Mappings or Visual Representations

• Volume textures Evaluated on any point in space
• Hypertexture volumetric modeling technique
• Texel-mapping Maps an entire surface description
  onto the surface of an object
• Displacement Maps Moves the surface by a given
  amount in a given direction

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Reverse Mapping Techniques

• Active area of research
• Optimization methods
• Harmonic maps
• Divide-and-conquer approaches
• Multi-resolution approaches
• A huge literature on surface parameterization
  over last 10 years

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Mapping Polygon Interior Points

• Associate (u,v) values with the interior of the
  polygon
• Simple solution Include the (u,v) coordinates
  with the screen coordinates and normals. Use
  Phong interpolation approach.

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Mapping Polygon Interior Points Known Projection
Function

• Compute the function as the polygon is clipped
  and rendered
• Transform the vertices of the clipped polygon to
  the object space
• Apply the projection function to the transformed
  vertices to compute the texture coordinates

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Environment Mapping

• Approximation to ray tracing
• Object is surrounded by a closed 3D surface onto
  which the environment is projected
• Used for seeing recognizable detail in the
  reflected information

20
Location in the Environment

• Mapping the environment to inside of a large
  sphere
• Trace a ray from the eye-point to the surface of
  the rendered object
• Reflect the ray about the normal and trace the
  ray to the sphere
• Greater distortion The farther an object is from
  the eye-point or larger the object

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Mapping to a Large Cube Greene86

• Explicit representation by 6 raster images
• Take six separate, appropriately oriented
  photographs of the scene, using a 900 flat field
  lens
• Project the photographs onto the six inside faces
  of the cube
• Can combine Lambertian diffuse and specular
  reflection in the environment map
• Mapping function is not spherical and has less
  distortion

22
Rough Appearance

• Texture Mapping Adding texture patterns to
  smooth surfaces.
• Rough Appearance Adding rough-texture pattern to
  a smooth surface?

23
Bump Mapping

• Perturb the surface normal Blinn76
• Given Q(u,v), let the surface normal be n,
• where n Qu X Qv, and let n be the normalized
  unit vector
• For any point on Q(u,v), the position vector is
• Q(u,v) Q(u,v) P(u,v) n,
• where P(u,v) is a perturbation function.
• The normal of the perturbed surface is
• n Pu (n X Qv) Pv (Qu X n)

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Choice of Perturbation Function

• Any first order continuous function
• Examples grid pattern, character bit maps,
  Z-buffer patterns, random hand-drawn patterns
• Nonmathematical patterns The perturbation
  function is a 2D lookup table. Derivatives are
  computed by table lookup.

25
Procedural Textures (Solid Textures)

• Define a texture function throughout a 3D volume
• Object is embedded in the 3D texture volume
• Textured surface intersection of the object and
  3D texture volume
• Coherent appearance with no texture
  discontinuities
• Independent of surface geometry or coordinate
  system

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Procedural Textures (Wood Grain Examples)

• Coaxial alternating light and dark cylinders
• Lack of distortion or aliasing

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Other Issues in Texture Mapping

• Magnification (use of bilinear interpolation)
• Minification
• Sampling and filtering (aliasing problems)
• Use of mipmapping for anti-aliasing
• Texture caching and compression (limited texture
  memory)
• Multitexturing (and multi-pass rendering) two or
  more textures are accessed during the same pass

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Texture Antialiasing

• Aliasing is a constant aspect of texture mapping
• Frequency domain analysis silhouette edges and
  perspective can cause high frequency patterns in
  image space
• Point sampling (mapping the center of image pixel
  to texture space and use the nearest texture
  pixel) a texture pattern can generate lots of
  aliasing problems
• Wide literature on different filters to
  circumvent the problem

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Mip-mapping

• Generates many images of decreasing resolution by
  averaging multiple pixels
• Original image and the averaged lower resolution
  images are stored in multiple tables
• Equivalent to convolution with a square box
  filter
• Stacking the mipmaps in 3 space forms a pyramid
• Memory 4/3 times the original texture image
• Widely used texture filtering method fast and
  little memory

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Summed Area Tables

• Extension of mipmaps to rectangular texture
  regions
• Reduce the table to one using summed area table
• Each entry represents the sum of the intensities
  of all texture pixels in a rectangle defined by
  lower left corner and the pixel of interest
• Average intensity Divide this by number of
  pixels
• Used summed areas to technique to compute the
  intensity of each pixel
• Prefilter the texture image, using a box filter
  function prior to summing