Texture Mapping

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Texture Mapping
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Motivation

• Modeling the fine detail in real objects with
  triangles is just too hard sometimes.
• Phong lighting looks like plastic or rubber,
  maybe sometimes sort-of-like metal.

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Motivation

• Added surface detail can help computer graphics
  images look more real.
• We cant explicitly model all of the detail, its
  just too expensive.
• Texture mapping lets us use real images in our
  CG scenes to add realistic fine detail without
  the high geometric costs.

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Texture mapping uses

• Replacing fine detail geometry with images
• What might we use the texture to modulate?
• Color ambient, diffuse, specular
• Alpha transparency
• Normals lighting effects
• More?
• Well come back to this next time
• How do we do it?

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Fundamentals

• Textures are most often 2D images
• A single element of texture is called a texel
• The value of the texel is used to modify surface
  appearance in some way
• The mapping between texture and surface
  determines how pixels and texels correspond

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Spherical mapping
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Cylindrical mapping

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How do we find the right texel?

• Find the visible pixel (z-buffer, or whatever)
• Find the point on the surface the corresponds to
  the visible pixel
• Find the point in the texture (texel) that maps
  to the point on the surface
• Use the texel values as appropriate to shade the
  pixel

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Picking texture coordinates

• Texture mapping is not automatic its often an
  art.
• For objects where we have a parametric form of
  the surface, it can be easy to find the 2D
  texture mapping.
• x fx(u, v) y fy(u, v) z fz(u, v)
• Otherwise, the coordinates have to be specified
  manually.

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Texture coordinates
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Texture rendering

• Parameterize the texture function of u and v
• Normalized coordinates 0, 1
• Associate each triangle with a texture
• Give each triangle vertex a (u, v) texture
  coordinate
• Interpolate texture coordinates across the
  triangle during rasterization
• Like interpolating color, except

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Texture Mapping Applications
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What can we use texture for?

• From an architecture independent (theoretical)
  standpoint
• Color
• Transparency
• Lighting
• Geometry
• Volumetric effects
• Special effects (lens flare, explosions, etc)
• OpenGL treats texturing separate from lighting
  part of the shading phase only.
• Modern (vendor) extensions to OpenGL are allowing
  textures to be part of the lighting process.

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Using alpha to trim geometry

• You can use an alpha channel in a texture to
  control what parts of the geometry are rendered
  into the scene.
• Alpha blending alpha used to combine existing
  pixels in frame buffer with texel (as specified
  by some operator)
• Alpha testing only those texels with specified
  alpha values are drawn into the frame buffer
  (like depth testing)

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Lightmaps

• Lightmaps or illumination maps are only valid for
  the specific geometry for which they were created
  by an artist or an algorithm.
• Texture only
• Texture
• Lightmap

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Environment mapping
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Environment mapping

• Our light model contains a simple hack for
  indirect reflection ambient reflection which
  is constant everywhere.
• Using textures, we can approximate first bounce
  indirect lighting on shiny objects.
• Pretend the object is inside a sphere, and we
  have a mapping from the sphere to an image of the
  objects surroundings.
• Then we need only determinewhere in the
  environment the reflection
• vector points.

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Spherical mapping

• We can map the entire environment into a sphere
  theres only one singular point in the map (0, 0,
  -1).
• How do we map R into 2D coordinates?
• But that singularity can be a problem.
• Okay if you never see the back side.

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Cube mapping

• Layout in a cube (typically actually 6 separate
  textures).
• The largest component of R tells us which of the
  6 textures to use (the one associated with the
  face of the cube R point to)
• We can scale the remaining components to get
  texture coordinates within the appropriate face
  texture.

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Environment maps for transparent objects
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Cel-shading
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Anisotropic lighting
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Bump mapping

• The theory of bump mapping is that we use a
  texture to determine how to displace the surface
  normal.
• Displacements are calculated from the directional
  derivatives of the texture.
• We make some assumptions
• Displacements are small (dont have to
  renormalize)
• Displacements are in the tangent plane to the
  surface
• Texture coordinates span the tangent plane

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Bump mapping

• In a standard graphics pipeline say, OpenGL
  can we implement bump mapping as described? Why
  not?
• We can, however, approximate it by multiple
  passes the most common technique is emboss bump
  mapping.
• Pass 1 Render with diffuse lighting
• Pass 2 Subtract a shifted version of the bump
  map
• Pass 3 Add the bump map
• How is it shifted?
• In the direction of the projection of the light
  vector on the tangent plane.
• Works okay for planar objects and small
  perturbations.

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Bump mapping
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Bump mapping

• How do you recognize bump-mapped objects?

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Displacement mapping

• Displacement mapping actually changes the
  geometry according to the texture.
• Not done in typical graphics hardware.

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Projective textures

• Slide projectors, additional spotlights, masked
  lights, and shadows can all be added by
  projective textures.
• What if we started with an image, and wanted to
  project the image onto the geometry in the scene.
  But then we want to view that geometry, and the
  results of the projection, from elsewhere.

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Shadow textures

• Projective textures will end up projecting to all
  surface elements which can map back to valid
  texture coordinates.
• This includes back facing (from the point of view
  of the projection source) and otherwise occluded
  surfaces.
• But, if we really did render from that point of
  view, we could collect a depth map to correspond
  to the projective texture.

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Shadow textures

• We can transform depth similarly to geometry, and
  look up in the depth texture whether a piece of
  surface was visible to the other point of view.
• If not visible, we dont apply the
• projective texture.
• We could also override previous
• lighting calculations and leave
• the surface in shadow.

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3D textures

• Useful for a better approximation of objects
  carved/sculpted from a solid piece of some
  material more realistic looking than warping an
  image around the surface.
• Effectively computes
• the intersection of
• the object with the
• texture.
• Wood, granite, and
• marble objects are
• often textured this
• way.