Search results
Results From The WOW.Com Content Network
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.
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.
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).
Let n(u, v) be the unit normal vector and let (E, F, G) and (L, M, N) be the coefficients of the first and second fundamental forms of this surface, respectively. The Weingarten equation gives the first derivative of the unit normal vector n at point P in terms of the tangent vectors r u and r v:
Through each tangent vector to M at p, there passes a normal plane P X which cuts out a curve in M. That curve has a certain curvature κ X when regarded as a curve inside P X. Provided not all κ X are equal, there is some unit vector X 1 for which k 1 = κ X 1 is as large as possible, and another unit vector X 2 for which k 2 = κ X 2 is as ...
A normal plane at p is one that contains the normal vector, and will therefore also contain a unique direction tangent to the surface and cut the surface in a plane curve, called normal section. This curve will in general have different curvatures for different normal planes at p. The principal curvatures at p, denoted k 1 and k 2, are the ...
Visulization of flux through differential area and solid angle. As always ^ is the unit normal to the incident surface A, = ^, and ^ is a unit vector in the direction of incident flux on the area element, θ is the angle between them.
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.