differential geometry, the two principal curvatures at a given point of a surface are the maximum and minimum values of the curvature as expressed by the eigenvalues...

In mathematics, curvature is any of several strongly related concepts in geometry that intuitively measure the amount by which a curve deviates from being...

Gaussian curvature or Gauss curvature Κ of a smooth surface in three-dimensional space at a point is the product of the principal curvatures, κ1 and κ2...

In differential geometry, the radius of curvature, R, is the reciprocal of the curvature. For a curve, it equals the radius of the circular arc which best...

differential geometry, the curvature form describes curvature of a connection on a principal bundle. The Riemann curvature tensor in Riemannian geometry...

such as the first and second fundamental forms, Gaussian, mean, and principal curvatures can all be computed from a given parametrization. The simplest type...

called the principal curvatures. Their average is called the mean curvature of the surface, and their product is called the Gaussian curvature. There are...

maximal curvature κ 1 {\displaystyle \kappa _{1}} and minimal curvature κ 2 {\displaystyle \kappa _{2}} are known as the principal curvatures of S {\displaystyle...

with equal and opposite principal curvatures. Additionally, this makes minimal surfaces into the static solutions of mean curvature flow. By the Young–Laplace...

Look up affine in Wiktionary, the free dictionary. The principal curvature-based region detector, also called PCBR is a feature detector used in the fields...

also coincide with minimum and maximum radius of curvature. There are two principal radii of curvature: along the meridional and prime-vertical normal...

of the principal curvatures is the Gaussian curvature of the surface (negative for saddle shaped surfaces). The mean of the principal curvatures is the...

total mean curvature among all convex solids with a given surface area. The mean curvature is the average of the two principal curvatures, which is constant...

horizontally along a radius, non-zero principal curvatures are created along the bend, dictating that the other principal curvature at these points must be zero...

In differential geometry, the Ricci curvature tensor, named after Gregorio Ricci-Curbastro, is a geometric object which is determined by a choice of Riemannian...

section’s profile and the helix angle. In particular, the first principal curvature is calculated as κ 1 s = cos ⁡ ( φ ) r m − r b cos ⁡ ( φ ) {\displaystyle...

The principal curvatures are the eigenvalues of the shape operator, the principal curvature directions are its eigenvectors, the Gaussian curvature is...

function, the principal curvature across the edge would be much larger than the principal curvature along it. Finding these principal curvatures amounts to...

mathematical field of Riemannian geometry, the scalar curvature (or the Ricci scalar) is a measure of the curvature of a Riemannian manifold. To each point on a...

length of the lens, d is its thickness, and r1 and r2 are the radii of curvature of its surfaces. Positive signs indicate distances to the right of the...

centers of the curvature spheres, which are the tangential spheres whose radii are the reciprocals of one of the principal curvatures at the point of...

result on the curvature of curves on a surface. The theorem establishes the existence of principal curvatures and associated principal directions which...

downward or upward, at the junction of the head and shaft of the penis. The curvature is usually most obvious during erection, but resistance to straightening...

three, typically, principal components of the system are of interest (representing "shift", "twist", and "curvature"). These principal components are derived...

and the eigenvectors are the principal directions of curvature. (See Gaussian curvature § Relation to principal curvatures.) Hessian matrices are used...

introduced an abstract and rigorous way to define curvature for these manifolds, now known as the Riemann curvature tensor. Similar notions have found applications...

and then specializes when the curves move in the direction of the principal curvatures. At each point p of an oriented surface, one may attach a unit normal...

of a curve, its points of extreme curvature: in some sense the vertices of a polygon are points of infinite curvature, and if a polygon is approximated...

points the normal curvatures in all directions are equal, hence, both principal curvatures are equal, and every tangent vector is a principal direction. The...

dimensions has a ridge point when a line of curvature has a local maximum or minimum of principal curvature. The set of ridge points form curves on the...