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Bidirectional texture function 13
Bidirectional texture function
Bidirectional texture function (BTF) [1] is a 7-dimensional function depending on planar texture coordinates (x,y)
as well as on view and illumination spherical angles. In practice this function is obtained as a set of several
thousands color images of material sample taken during different camera and light positions.
To cope with a massive BTF data with high redundancy, many compression method were proposed [1] [2] .
Its main application is a photorealistic material rendering of objects in virtual reality systems.
References
[1] Jiří Filip; Michal Haindl (2009). "Bidirectional Texture Function Modeling: A State of the Art Survey" (http:/ / www. computer. org/ portal/
web/ csdl/ doi/ 10. 1109/ TPAMI. 2008. 246). IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 31, no. 11. pp.
1921–1940. .
[2] Vlastimil Havran; Jiří Filip, Karol Myszkowski (2009). "Bidirectional Texture Function Compression based on Multi-Level Vector
Quantization" (http:/ / www3. interscience. wiley. com/ journal/ 123233573/ abstract). Computer Graphics Forum, vol. 29, no. 1. pp.
175–190. .
Bilinear filtering
Bilinear filtering is a texture filtering method used to smooth textures
when displayed larger or smaller than they actually are.
Most of the time, when drawing a textured shape on the screen, the
texture is not displayed exactly as it is stored, without any distortion.
Because of this, most pixels will end up needing to use a point on the
texture that's 'between' texels, assuming the texels are points (as
opposed to, say, squares) in the middle (or on the upper left corner, or
anywhere else; it doesn't matter, as long as it's consistent) of their
A zoomed small portion of a bitmap, using
nearest-neighbor filtering (left), bilinear filtering
(center), and bicubic filtering (right).
respective 'cells'. Bilinear filtering uses these points to perform bilinear interpolation between the four texels nearest
to the point that the pixel represents (in the middle or upper left of the pixel, usually).
The formula
In these equations, u k and v k are the texture coordinates and y k is the color value at point k. Values without a
subscript refer to the pixel point; values with subscripts 0, 1, 2, and 3 refer to the texel points, starting at the top left,
reading right then down, that immediately surround the pixel point. So y 0 is the color of the texel at texture
coordinate (u 0 , v 0 ). These are linear interpolation equations. We'd start with the bilinear equation, but since this is a
special case with some elegant results, it is easier to start from linear interpolation.
Assuming that the texture is a square bitmap,