Spherical image
In differential geometry, the spherical image of a unit-speed curve is given by taking the curve's tangent vectors as points, all of which must lie on the unit sphere. The movement of the spherical image describes the changes in the original curve's direction   If  is a unit-speed curve, that is , and  is the unit tangent vector field along , then the curve  is the spherical image of . All points of  must lie on the unit sphere because .

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Differential geometry