Last Time

1
Last Time

• Shading Interpolation
• Texture Mapping introduction

2
Today

• Texture Mapping details
• Modeling Intro (maybe)
• Homework 5

3
Basic OpenGL Texturing

• Specify texture coordinates for the polygon
• Use glTexCoord2f(s,t) before each vertex
• Eg glTexCoord2f(0,0) glVertex3f(x,y,z)
• Create a texture object and fill it with texture
  data
• glGenTextures(num, indices) to get identifiers
  for the objects
• glBindTexture(GL_TEXTURE_2D, identifier) to bind
  the texture
• Following texture commands refer to the bound
  texture
• glTexParameteri(GL_TEXTURE_2D, , ) to specify
  parameters for use when applying the texture
• glTexImage2D(GL_TEXTURE_2D, .) to specify the
  texture data (the image itself)

MORE
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Basic OpenGL Texturing (cont)

• Enable texturing glEnable(GL_TEXTURE_2D)
• State how the texture will be used
• glTexEnvf()
• Texturing is done after lighting
• Youre ready to go

5
Nasty Details

• There are a large range of functions for
  controlling the layout of texture data
• You must state how the data in your image is
  arranged
• Eg glPixelStorei(GL_UNPACK_ALIGNMENT, 1) tells
  OpenGL not to skip bytes at the end of a row
• You must state how you want the texture to be put
  in memory how many bits per pixel, which
  channels,
• Textures must be square with width/height a power
  of 2
• Common sizes are 32x32, 64x64, 256x256
• Smaller uses less memory, and there is a finite
  amount of texture memory on graphics cards

6
Controlling Different Parameters

• The pixels in the texture map may be
  interpreted as many different things. For
  example
• As colors in RGB or RGBA format
• As grayscale intensity
• As alpha values only
• The data can be applied to the polygon in many
  different ways
• Replace Replace the polygon color with the
  texture color
• Modulate Multiply the polygon color with the
  texture color or intensity
• Similar to compositing Composite texture with
  base color using operator

7
Example Diffuse shading and texture

• Say you want to have an object textured and have
  the texture appear to be diffusely lit
• Problem Texture is applied after lighting, so
  how do you adjust the textures brightness?
• Solution
• Make the polygon white and light it normally
• Use glTexEnvi(GL_TEXTURE_2D, GL_TEXTURE_ENV_MODE,
  GL_MODULATE)
• Use GL_RGB for internal format
• Then, texture color is multiplied by surface
  (fragment) color, and alpha is taken from fragment

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Some Other Uses

• There is a decal mode for textures, which
  replaces the surface color with the texture
  color, as if you stick on a decal
• Texture happens after lighting, so the light info
  is lost
• BUT, you can use the texture to store lighting
  info, and generate better looking lighting
  (override OpenGLs lighting)
• You can put the color information in the polygon,
  and use the texture for the brightness
  information
• Called light maps
• Normally, use multiple texture layers, one for
  color, one for light

9
Textures and Aliasing

• Textures are subject to aliasing
• A polygon pixel maps into a texture image,
  essentially sampling the texture at a point
• The situation is very similar to resizing an
  image, but the resize ratios may change across
  the image
• Standard approaches
• Pre-filtering Filter the texture down before
  applying it
• Post-filtering Take multiple pixels from the
  texture and filter them before applying to the
  polygon fragment

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Point Sampled Texture Aliasing
Texture map
Polygon far from the viewer in perspective
projection
Rasterized and textured

• Note that the back row is a very poor
  representation of the true image

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Mipmapping (Pre-filtering)

• If a textured object is far away, one screen
  pixel (on an object) may map to many texture
  pixels
• The problem is how to combine them
• A mipmap is a low resolution version of a texture
• Texture is filtered down as a pre-processing
  step
• gluBuild2DMipmaps()
• When the textured object is far away, use the
  mipmap chosen so that one image pixel maps to at
  most four mipmap pixels
• Full set of mipmaps requires double the storage
  of the original texture

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Many Texels for Each Pixel
Texture map with pixels drawn on it. Some pixels
cover many texture elements (texels)
Polygon far from the viewer in perspective
projection
13
Mipmaps
For far objects
For middle objects
For near objects
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Mipmap Math

• Define a scale factor, ?texels/pixel
• A texel is a pixel from a texture
• ? is actually the maximum from x and y
• The scale factor may vary over a polygon
• It can be derived from the transformation
  matrices
• Define ?log2 ?
• ? tells you which mipmap level to use
• Level 0 is the original texture, level 1 is the
  next smallest texture, and so on
• If ?lt0, then multiple pixels map to one texel
  magnification

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Post-Filtering

• You tell OpenGL what sort of post-filtering to do
• Magnification When ?lt0 the image pixel is
  smaller than the texel
• glTexParameteri(GL_TEXTURE_2D, GL_TEXTURE_MAG_FILT
  ER, type)
• Type is GL_LINEAR or GL_NEAREST
• Minification When ?gt0 the image pixel is bigger
  than the texel
• GL_TEX_MIN_FILTER
• Can choose to
• Take nearest point in base texture, GL_NEAREST
• Linearly interpolate nearest 4 pixels in base
  texture, GL_LINEAR
• Take the nearest mipmap and then take nearest or
  interpolate in that mipmap, GL_NEAREST_MIPMAP_LINE
  AR
• Interpolate between the two nearest mipmaps using
  nearest or interpolated points from each,
  GL_LINEAR_MIPMAP_LINEAR

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Filtering Example
Level 2
NEAREST_MIPMAP_NEAREST level 0, pixel (0,0)
LINEAR_MIPMAP_NEAREST level 0, pixel (0,0)
0.51 level 1, pixel (0,0) 0.49
Level 1
NEAREST_MIPMAP_LINEAR level 0, combination
of pixels (0,0), (1,0), (1,1), (0,1)
Level 0
s0.12,t0.1 ?1.4 ?0.49
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Boundaries

• You can control what happens if a point maps to a
  texture coordinate outside of the texture image
• All texture images are assumed to go from (0,0)
  to (1,1) in texture space
• The problem is how to extend the image to make an
  infinite space
• Repeat Assume the texture is tiled
• glTexParameteri(GL_TEXTURE_2D, GL_TEXTURE_WRAP_S,
  GL_REPEAT)
• Clamp to Edge the texture coordinates are
  truncated to valid values, and then used
• glTexParameteri(GL_TEXTURE_2D, GL_TEXTURE_WRAP_S,
  GL_CLAMP)
• Can specify a special border color
• glTexParameterfv(GL_TEXTURE_2D,
  GL_TEXTURE_BORDER_COLOR, R,G,B,A)

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Repeat Border
(1,1)
(0,0)
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Clamp Border
(1,1)
(0,0)
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Border Color
(1,1)
(0,0)
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Other Texture Stuff

• Texture must be in fast memory - it is accessed
  for every pixel drawn
• If you exceed it, performance will degrade
  horribly
• Skilled artists can pack textures for different
  objects into one image
• Texture memory is typically limited, so a range
  of functions are available to manage it
• Specifying texture coordinates can be annoying,
  so there are functions to automate it
• Sometimes you want to apply multiple textures to
  the same point Multitexturing is now in most new
  hardware

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Yet More Texture Stuff

• There is a texture matrix apply a matrix
  transformation to texture coordinates before
  indexing texture
• There are image processing operations that can
  be applied to the pixels coming out of the
  texture
• There are 1D and 3D textures
• Mapping works essentially the same
• 3D textures are very memory intensive, and how
  they are used is very application dependent
• 1D saves memory if the texture is inherently 1D,
  like stripes

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Procedural Texture Mapping

• Instead of looking up an image, pass the texture
  coordinates to a function that computes the
  texture value on the fly
• Renderman, the Pixar rendering language, does
  this
• Available in a limited form with vertex shaders
  on current generation hardware
• Advantages
• Near-infinite resolution with small storage cost
• Idea works for many other things
• Has the disadvantage of being slow in many cases

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Other Types of Mapping

• Environment mapping looks up incoming
  illumination in a map
• Simulates reflections from shiny surfaces
• Bump-mapping computes an offset to the normal
  vector at each rendered pixel
• No need to put bumps in geometry, but silhouette
  looks wrong
• Displacement mapping adds an offset to the
  surface at each point
• Like putting bumps on geometry, but simpler to
  model
• All are available in software renderers like
  RenderMan compliant renderers
• All these are becoming available in hardware

25
The Story So Far

• Weve looked at images and image manipulation
• Weve looked at rendering from polygons
• Next major section
• Modeling

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Modeling Overview

• Modeling is the process of describing an object
• Sometimes the description is an end in itself
• eg Computer aided design (CAD), Computer Aided
  Manufacturing (CAM)
• The model is an exact description
• More typically in graphics, the model is then
  used for rendering (we will work on this
  assumption)
• The model only exists to produce a picture
• It can be an approximation, as long as the visual
  result is good
• The computer graphics motto If it looks right
  it is right
• Doesnt work for CAD

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Issues in Modeling

• There are many ways to represent the shape of an
  object
• What are some things to think about when choosing
  a representation?

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Categorizing Modeling Techniques

• Surface vs. Volume
• Sometimes we only care about the surface
• Rendering and geometric computations
• Sometimes we want to know about the volume
• Medical data with information attached to the
  space
• Some representations are best thought of defining
  the space filled, rather than the surface around
  the space
• Parametric vs. Implicit
• Parametric generates all the points on a surface
  (volume) by plugging in a parameter eg (sin?
  cos?, sin? sin?, cos?)
• Implicit models tell you if a point in on (in)
  the surface (volume) eg x2 y2 z2- 1 0

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Techniques We Will Examine

• Polygon meshes
• Surface representation, Parametric representation
• Prototype instancing and hierarchical modeling
• Surface or Volume, Parametric
• Volume enumeration schemes
• Volume, Parametric or Implicit
• Parametric curves and surfaces
• Surface, Parametric
• Subdivision curves and surfaces
• Procedural models