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# Bitangent Vector

Let and be differentiable scalar functions defined at all points on a surface . In computer graphics, the functions and often represent texture coordinates for a 3-dimensional polygonal model. A rendering technique known as bump mapping orients the basis vectors of the tangent plane at any point so that they are aligned with the direction in which the derivative of or is zero. In this context, the tangent vector is specifically defined to be the unit vector lying in the tangent plane for which and is positive. The bitangent vector is defined to be the unit vector lying in the tangent plane for which and is positive. The vectors and are not necessarily orthogonal and may not exist for poorly conditioned functions and .

The vector given by

is a unit normal to the surface at the point . For a closed surface , this normal vector can be characterized as outward-facing or inward-facing. The basis vectors of the local tangent space at the point are defined to be , , and , with negated in the case that it is inward-facing.

## See also

Bitangent, Tangent Vector

This entry contributed by Eric Lengyel

## References

Lengyel, E. "Bump Mapping." §6.8 in Mathematics for 3D Game Programming and Computer Graphics, 2nd ed. Hingham, MA: Charles River Media, pp. 182-189, 2004.

Bitangent Vector

## Cite this as:

Lengyel, Eric. "Bitangent Vector." From MathWorld--A Wolfram Web Resource, created by Eric W. Weisstein. https://mathworld.wolfram.com/BitangentVector.html