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TNB frame

The moving frame of three mutually perpendicular unit vectors \mathbf{T}, \mathbf{N}, \mathbf{B} that rides along a curve.

The TNB frame is a moving 3D coordinate frame built from the unit tangent \mathbf{T}, the principal unit normal \mathbf{N}, and the binormal \mathbf{B}=\mathbf{T}\times\mathbf{N} — three mutually perpendicular unit vectors that travel with the curve instead of sitting fixed like \mathbf{i},\mathbf{j},\mathbf{k}.

Examples

  • The TNB frame and the pair {curvature, torsion} together determine a curve, up to position and orientation, completely.

See also

Unit tangent vector Principal unit normal vector Binormal vector
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