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On the example of a torus knot, the tangent vector T, the normal vector N, and the binormal vector B, along with the curvature κ(s), and the torsion τ(s) are displayed. At the peaks of the torsion function the rotation of the Frenet–Serret frame ( T , N , B ) around the tangent vector is clearly visible.
Illustration of tangential and normal components of a vector to a surface. In mathematics, given a vector at a point on a curve, that vector can be decomposed uniquely as a sum of two vectors, one tangent to the curve, called the tangential component of the vector, and another one perpendicular to the curve, called the normal component of the vector.
A normal vector of length one is called a unit normal vector. A curvature vector is a normal vector whose length is the curvature of the object. Multiplying a normal vector by −1 results in the opposite vector, which may be used for indicating sides (e.g., interior or exterior).
In mathematics, a norm is a function from a real or complex vector space to the non-negative real numbers that behaves in certain ways like the distance from the origin: it commutes with scaling, obeys a form of the triangle inequality, and is zero only at the origin.
A unit vector is often denoted by a lowercase letter with a circumflex, or "hat", as in ^ (pronounced "v-hat"). The term normalized vector is sometimes used as a synonym for unit vector. The normalized vector û of a non-zero vector u is the unit vector in the direction of u, i.e.,
Distance from the origin O to the line E calculated with the Hesse normal form. Normal vector in red, line in green, point O shown in blue. In analytic geometry, the Hesse normal form (named after Otto Hesse) is an equation used to describe a line in the Euclidean plane, a plane in Euclidean space, or a hyperplane in higher dimensions.
Animation of the torsion and the corresponding rotation of the binormal vector. Let r be a space curve parametrized by arc length s and with the unit tangent vector T.If the curvature κ of r at a certain point is not zero then the principal normal vector and the binormal vector at that point are the unit vectors
A real random vector = (, …,) is called a centered normal random vector if there exists a matrix such that has the same distribution as where is a standard normal random vector with components. [ 1 ] : p. 454