Texture Mapping: We first parameterize the surface into UV. In texture mapping, we no longer care about the actual geometry. So that we only associate UV to each pixel in texture.
There are a few ways to create UV:
planar projection
cubical projection
spherical projection
cylindrical projection
combined projection
mesh projection
Deals with Interpolation: magnification
nearest
bilinear
bicubic
Deals with texture too small:
clamp
repeat
seamlessly tileable texture
Deals with texture too big: minification
mipmap (for square texture)
ripmap (downscale independently in x and y)
summed area tables (look up table)
We can use map to look up for:
color, diffuse, specular
roughness, bump map
surface normal, displacement map
environment map
reflection map
shadow map
and more...
People also use all different technologies to capture environment maps:
We can store environment maps as:
latitude / longitude map
cube map
or other parameterization
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