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  2. Frenet–Serret formulas - Wikipedia

    en.wikipedia.org/wiki/Frenet–Serret_formulas

    The tangent, normal, and binormal unit vectors, often called T, N, and B, or collectively the Frenet–Serret frame (TNB frame or TNB basis), together form an orthonormal basis that spans, and are defined as follows: T is the unit vector tangent to the curve, pointing in the direction of motion.

  3. Fundamental theorem of curves - Wikipedia

    en.wikipedia.org/wiki/Fundamental_theorem_of_curves

    From just the curvature and torsion, the vector fields for the tangent, normal, and binormal vectors can be derived using the Frenet–Serret formulas. Then, integration of the tangent field (done numerically, if not analytically) yields the curve.

  4. Differentiable curve - Wikipedia

    en.wikipedia.org/wiki/Differentiable_curve

    T is the unit tangent, P the unit normal, and B the unit binormal. A Frenet frame is a moving reference frame of n orthonormal vectors e i (t) which are used to describe a curve locally at each point γ(t). It is the main tool in the differential geometric treatment of curves because it is far easier and more natural to describe local ...

  5. Tangential and normal components - Wikipedia

    en.wikipedia.org/wiki/Tangential_and_normal...

    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.

  6. Tangent vector - Wikipedia

    en.wikipedia.org/wiki/Tangent_vector

    In mathematics, a tangent vector is a vector that is tangent to a curve or surface at a given point. Tangent vectors are described in the differential geometry of curves in the context of curves in R n. More generally, tangent vectors are elements of a tangent space of a differentiable manifold. Tangent vectors can also be described in terms of ...

  7. Torsion of a curve - Wikipedia

    en.wikipedia.org/wiki/Torsion_of_a_curve

    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

  8. Osculating plane - Wikipedia

    en.wikipedia.org/wiki/Osculating_plane

    A space curve, Frenet–Serret frame, and the osculating plane (spanned by T and N). In mathematics, particularly in differential geometry, an osculating plane is a plane in a Euclidean space or affine space which meets a submanifold at a point in such a way as to have a second order of contact at the point.

  9. Normal plane (geometry) - Wikipedia

    en.wikipedia.org/wiki/Normal_plane_(geometry)

    The normal section of a surface at a particular point is the curve produced by the intersection of that surface with a normal plane. [1] [2] [3] The curvature of the normal section is called the normal curvature. If the surface is bow or cylinder shaped, the maximum and the minimum of these curvatures are the principal curvatures.