Texture Mapping

1
Texture Mapping

• Aaron Bloomfield
• CS 445 Introduction to Graphics
• Fall 2006
• (Slide set originally by David Luebke)

2
Overview

• Motivation and Examples
• Fundamentals
• Algorithms
• Perspective-Correct Texturing
• Transparency and Anti-Aliasing
• MIP-Maps
• Bump and Displacement Maps
• Illumination Maps

3
Texture Mapping Motivation

• Scenes created with diffuse lighting look
  convincingly three-dimensional, but are flat,
  chalky, and cartoonish
• Phong lighting lets us simulate materials like
  plastic and (to a lesser extent) metal, but
  scenes still seem very cartoonish and unreal
• Big problem polygons are too coarse-grained to
  usefully model fine surface detail
• Solution texture mapping

4
Texture Mapping Motivation

• Adding surface detail helps keep CG images from
  looking simple and sterile
• Explicitly modeling this detail in geometry can
  be very expensive
• Zebra stripes, wood grain, writing on a
  whiteboard
• Texture mapping pastes images onto the surfaces
  in the scene, adding realistic fine detail
  without exploding the geometry

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Texture Mapping Examples
7
Texture Mapping Examples
Doom III (ID Software)
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Texture Mapping

• In short it is impractical to explicitly model
  fine surface detail with geometry
• Solution use images to capture the texture of
  surfaces
• Texture maps can modulate many factors that
  affect the rendering of a surface
• Color or reflectance (diffuse, ambient, specular)
• Transparency (smoke effects)
• What else?

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Overview

• Motivation and Examples
• Fundamentals
• Algorithms
• Perspective-Correct Texturing
• Transparency and Anti-Aliasing
• MIP-Maps
• Bump and Displacement Maps
• Illumination Maps

10
Texture Mapping Fundamentals

• A texture is typically a 2-D image
• Can also be
• A 2-D procedural texture
• A 3-D procedural texture
• See video
• A 3-D volumetric texture (rarely used)

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Texture Mapping Fundamentals

• A texture is typically a 2-D image
• Image elements are called texels
• Value stored at a texel affects surface
  appearance in some way
• Example diffuse reflectance, shininess,
  transparency
• The mapping of the texture to the surface
  determines the correspondence, i.e., how the
  texture lies on the surface
• Mapping a texture to a triangle is easy (why?)
• Mapping a texture to an arbitrary 3-D shape is
  more complicated (why?)

12
Texturing Fundamentals

• A texture is typically a 2-D array of texels
• Mapping the texture to an arbitrary 3-D shape is
  complex

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Texturing Fundamentals

• A texture is typically a 2-D array of texels
• Mapping the texture to an arbitrary 3-D shape is
  complex

14
Texturing Fundamentals

• A texture is typically a 2-D array of texels
• Mapping the texture to an arbitrary 3-D shape is
  complex

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Texturing Fundamentals

• A texture is typically a 2-D array of texels
• Mapping the texture to an arbitrary 3-D shape is
  complex!
• http//www.cs.virginia.edu/gfx/Courses/2003/Intro
  .spring.03/animations/unfold.mov

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How to map a texture

• There are a number of possibilities
• Flat
• Cube
• Tube (i.e. cylinder)
• Sphere
• The slides on the next slide are from
  http//mediawiki.blender.org/index.php/Manual/Map_
  Input2D_to_3D_Mapping

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Overview

• Motivation and Examples
• Fundamentals
• Algorithms
• Perspective-Correct Texturing
• Transparency and Anti-Aliasing
• MIP-Maps
• Bump and Displacement Maps
• Illumination Maps

19
Texture Mapping Rendering

• Rendering uses the mapping
• Find the visible surface at a pixel
• Find the point on that surface corresponding to
  that pixel
• Find the point in the texture corresponding to
  that point on the surface
• Use the parameters associated with that point on
  the texture to shade the pixel
• Using triangulated meshes reduces the problem to
  mapping a portion of the image to each triangle

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Texture Mapping Rendering
21
Texture MappingUser-Generated Mappings

• For complex 3-D objects, mapping textures is
  still something of an artso we often let the
  user do it

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Texture Mapping Rendering

• We typically parameterize the texture as a
  function in (u, v)
• For simplicity, normalize u v to 0, 1
• Associate each triangle with a texture
• Give each vertex of the triangle a texture
  coordinate (u, v)
• For other points on the triangle, interpolate
  texture coordinate from the vertices
• Much like interpolating color or depth
• But theres a catch...

23
Naïve Texture Mapping

• A first cut at a texture-mapping rasterizer
• For each pixel
• Interpolate u v down edges and across spans
• Look up nearest texel in texture map
• Color pixel according to texel color (possibly
  modulated by lighting calculations)
• McMillans demo of this is at http//graphics.lcs.
  mit.edu/classes/6.837/F98/Lecture21/Slide05.html
• What artifacts do you see in this demo?

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Naïve Texturing Artifacts

• Another serious artifact is warping at the edges
  of triangles making up the mesh
• A more obvious example http//graphics.lcs.mit.e
  du/classes/6.837/F98/Lecture21/Slide06.html
• To address this, need to consider the geometry of
  interpolating parameters more carefully

25
Interpolating Parameters

• The problem turns out to be fundamental to
  interpolating parameters in screen-space
• Uniform steps in screen space ? uniform steps in
  world coords

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Interpolating Parameters

• Perspective foreshortening is not getting applied
  to our interpolated parameters
• Parameters should be compressed with distance
• Linearly interpolating them in screen-space
  doesnt do this
• Is this a problem with Gouraud shading?
• Is everything I taught wrong?
• A It can be, but we usually dont notice (why?)

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Overview

• Motivation and Examples
• Fundamentals
• Algorithms
• Perspective-Correct Texturing
• Transparency and Anti-Aliasing
• MIP-Maps
• Bump and Displacement Maps
• Illumination Maps

28
Perspective-Correct Interpolation

• Skipping a bit of math to make a long story
  short
• Rather than interpolating u and v directly,
  interpolate u/z and v/z
• These do interpolate correctly in screen space
• Also need to interpolate z and multiply per-pixel
• Problem we dont know z anymore
• Solution we do know w ? 1/z
• Sointerpolate uw and vw and w, and compute u
  uw/w and v vw/w for each pixel
• This unfortunately involves a divide per pixel
  (Just 1?)

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Perspective-Correct Texturing

• Known as perspective-correct texture mapping
• Early PC cards and game consoles didnt support
  it
• So how did they avoid the warping problem?
• http//graphics.lcs.mit.edu/classes/6.837/F98/Lect
  ure21/Slide15.html
• As mentioned, other interpolation schemes really
  ought to use perspective correction
• E.g., Gouraud shading
• Generally get away without it because it is more
  important to be smooth than correct
• Java code fragment from McMillans edge-equation
  triangle rasterizer

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Perspective-Correct Texturing Code

• ...
• PlaneEqn(uPlane, (u0w0), (u1w1), (u2w2))
• PlaneEqn(vPlane, (v0w0), (v1w1), (v2w2))
• PlaneEqn(wPlane, w0, w1, w2)
• ...
• for (y yMin y lt yMax y raster.width)
  
• e0 t0 e1 t1 e2 t2
• u tu v tv w tw
  z tz
• boolean beenInside false
• for (x xMin x lt xMax x)
• if ((e0 gt 0) (e1 gt 0) (e2 gt
  0)))
• int iz (int) z
• if (iz lt raster.zbuffyx)
• float denom 1.0f / w
• int uval (int) (u denom
  0.5f)
• uval tile(uval,
  texture.width)
• int vval (int) (v denom
  0.5f)
• vval tile(vval,
  texture.height)
• int pix texture.getPixel(uv
  al, vval)

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Texture Tiling

• It is often handy to tile a repeating texture
  pattern onto a surface
• The previous code does this via tile()
• int uval (int) (u denom 0.5f)
• uval tile(uval, texture.width)
• int vval (int) (v denom 0.5f)
• vval tile(vval, texture.height)
• int pix texture.getPixel(uval, vval)
• int tile(int val, int size) while
  (val gt size) val - size
  while (val lt 0) val size
• See http//graphics.lcs.mit.edu/classes/6.837/F98/
  Lecture21/Slide18.html

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Overview

• Motivation and Examples
• Fundamentals
• Algorithms
• Perspective-Correct Texturing
• Transparency and Anti-Aliasing
• MIP-Maps
• Bump and Displacement Maps
• Illumination Maps

33
Texture Transparency

• McMillans code also includes a quick fix for
  handling transparent texture
• if ((pix 0xff000000) ! 0)
• raster.pixelyx pix
• raster.zbuffyx iz
• Note that this doesnt handle partial
  transparency (How might such partial transparency
  arise?)
• Demo at http//graphics.lcs.mit.edu/classes/6.83
  7/F98/Lecture21/Slide19.html

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Texture Map Aliasing

• Naive texture mapping looks blocky, pixelated
• Problem using a single texel to color each
  pixel
• int uval (int) (u denom 0.5f)
• int vval (int) (v denom 0.5f)
• int pix texture.getPixel(uval, vval)
• Actually, each pixel maps to a region in texture
• If the pixel is larger than a texel, we should
  average the contribution from multiple texels
  somehow
• If the pixel is smaller than a texel, we should
  interpolate between texel values somehow
• Even if pixel size ? texel size, a pixel will in
  general fall between four texels
• An example of a general problem called aliasing

36
Texture Map Antialiasing

• Use bilinear interpolation to average nearby
  texel values into a single pixel value (Draw it)
• Find 4 nearest texture samples
• Round u v up and down
• Interpolate texel values in u
• Interpolate resulting values in v
• Also addresses the problem of many pixels
  projecting to a single texel (Why?)

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Texture Map Antialiasing

• What if a single pixel covers many texels?
• Problem sampling those texels at a single point
  (the center of the pixel)
• Produces Moire patterns in coherent texture
  (checkers)
• Leads to flicker or texture crawling as the
  texture moves

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Moire Patterns
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Texture Map Antialiasing

• What if a single pixel covers many texels?
• Approach blur the image under the pixel,
  averaging the contributions of the covered texels
  
• But calculating which texels every pixel covers
  is way too expensive, especially as the texture
  is compressed
• Solution pre-calculate lower-resolution versions
  of the texture that incorporate this averaging

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Overview

• Motivation and Examples
• Fundamentals
• Algorithms
• Perspective-Correct Texturing
• Transparency and Anti-Aliasing
• MIP-Maps
• Bump and Displacement Maps
• Illumination Maps

41
MIP-maps

• For a texture of 2n x 2n pixels, compute n-1
  textures, each at ½ the resolution of previous
• This multiresolution texture is called a MIP-map

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Generating MIP-maps

• Generating a MIP-map from a texture is easy
• For each texel in level i, average the values of
  the four corresponding texels in level i-1
• If a texture requires n bytes of storage, how
  much storage will a MIP-map require?
• Answer 4n/3

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Representing MIP-maps

• Trivia MIP Multum In Parvo (many things in a
  small place)

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Using MIP-maps

• Each level of the MIP-map represents a
  pre-blurred version of multiple texels
• A texel at level n represents 2n original texels
• When rendering
• Figure out the texture coverage of the pixel
  (i.e., the size of the pixel in texels of the
  original map)
• Find the level of the MIP map in which texels
  average approximately that many original texels
• Interpolate the value of the four nearest texels

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Using MIP-maps

• Even better
• Likely, the coverage of the pixel will fall
  somewhere between the coverage of texels in two
  adjacent levels of the MIP map
• Find the pixels value in each of the two
  textures using two bilinear interpolations
• Using a third interpolation, find a value in
  between these two values, based on the coverage
  of the pixel versus each of the MIP-map levels
• This is (misleadingly?) called trilinear
  interpolation

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MIP-map Example

• No filtering
• MIP-map texturing

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Can We Do Better?

• What assumption does MIP-mapping implicitly make?
• A The pixel covers a square region of the
  texture
• More exactly, the compression or oversampling
  rate is the same in u and v
• Is this a valid assumption? Why or why not?

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MIP-maps and Signal Processing

• An aside aliasing and antialiasing are properly
  topics in sampling theory
• Nyquist theorem, convolution and reconstruction,
  filters and filter widths
• Textures are particularly difficult because a
  tiled texture can easily generate infinite
  frequencies
• E.g., a checkered plane receding to an infinite
  horizon
• Using a MIP-map amounts to prefiltering the
  texture image to reduce artifacts caused by
  sampling at too low a rate

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Summed-Area Tables

• A technique called summed-area tables lets us
  integrate texels covered by the pixel more
  exactly (but still quickly)
• Details in the book
• Example

MIP-map texturing
Summed-area table texturing
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Overview

• Motivation and Examples
• Fundamentals
• Algorithms
• Perspective-Correct Texturing
• Transparency and Anti-Aliasing
• MIP-Maps
• Bump and Displacement Maps
• Illumination Maps

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Texture Mapping Variations

• In addition to the texture, we add the lighting
  model also

Texture asR,G,B
Texture withlighting
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Bump Mapping

• The texture map can modulate the surface normal
  used for shading

Sphere w/ diffuse textureand swirly bump map
Sphere w/ diffuse texture
Swirly bump map
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More Bump Mapping

• How can you tell a bumped-mapped object from an
  object in which the geometry is explicitly
  modeled?

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Another Bump Mapping Example

• From Wikipedia

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Displacement Map

• A displacement map actually displaces the
  geometry
• Treats the texture as a height field to be
  applied to the surface
• Starting to appear in the interactive graphics
  pipeline
• First supported in Matrox Parhelia card
• Can sort of implement with beta drivers in ATI
  NVIDIA cards
• Will soon appear in all cards
• Implemented by recursive subdivision of
  triangles/quads

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Displacement Map Example

• What is the biggest visual difference between
  displacement mapping and bump mapping?

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Overview

• Motivation and Examples
• Fundamentals
• Algorithms
• Perspective-Correct Texturing
• Transparency and Anti-Aliasing
• MIP-Maps
• Bump and Displacement Maps
• Illumination Maps

58
Illumination Maps

• Quake introduced illumination maps or light maps
  to capture lighting effects in video games

Texture map
Light map
Texture map light map
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Illumination Maps

• Illumination maps differ from texture maps in
  that they
• Usually apply to only a single surface
• Are usually fairly low resolution
• Usually capture just intensity (1 value) rather
  than color (3 values)
• Illumination maps can be
• Painted by hand Disneys Aladdin ride
• Calculated by a global illumination process
  Nintendo64 demo, modern level builders

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Other Texture Applications

• Lots of other interesting applications of the
  texture-map concept (well return to some)
• Shadow maps
• 3-D textures (marble, wood, clouds)
• Procedural textures
• Environment maps cube maps
• For a neat explanation of the first three (with
  cool applets, as usual) check out
• http//graphics.lcs.mit.edu/classes/6.837/F98/Lect
  ure22/Slide21.html