TNB frame

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"Binormal" redirects here. For the category-theoretic meaning of this word, see Normal morphism.

Given a point on a curve in space, the tangent vector (T), normal vector (N) and binormal vector (B) are three orthogonal vectors of unit length which together form a natural coordinate system at that point, the TNB frame.

Given a parametrization x(t) of the curve and the arc-length function s(t) of the curve, these vectors can be defined as follows:

• T(t) is the unit tangent vector to the curve at the point x(t):

.

• N(t) is the unit normal vector at x(t). It is perpendicular to T and points towards the center of curvature of the curve at the point x(t):

.

• B(t) is the binormal vector at x(t). It is the cross product of T(t) and N(t).

This frame is useful in differential geometry and kinematics. It is the three-dimensional case of the more general Frenet frame.

[edit] See also

• Differential geometry of curves
• Frenet-Serret formulas