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Radius of curvature and center of curvature. 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 approximates the curve at that point. For surfaces, the radius of curvature is the radius of a circle that best fits a normal section or ...
This is the osculating circle to the curve. The radius of the circle R(s) is called the radius of curvature, and the curvature is the reciprocal of the radius of curvature: = (). The tangent, curvature, and normal vector together describe the second-order behavior of a curve near a point.
Curvature is usually measured in radius of curvature.A small circle can be easily laid out by just using radius of curvature, but degree of curvature is more convenient for calculating and laying out the curve if the radius is as large as a kilometer or mile, as is needed for large scale works like roads and railroads.
The minimum railway curve radius is the shortest allowable design radius for the centerline of railway tracks under a particular set of conditions. It has an important bearing on construction costs and operating costs and, in combination with superelevation (difference in elevation of the two rails) in the case of train tracks , determines the ...
Radius of curvature, the reciprocal of the curvature in differential geometry Minimum railway curve radius , the shortest allowable design radius for the centerline of railway tracks Topics referred to by the same term
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 maximum and minimum values of this curvature. Here the curvature of a curve is by definition the reciprocal of the radius of the osculating circle. The curvature is taken to be positive if the curve ...
Base curve radius (BCR) or simply base curve (BC) is the measure of an important parameter of a lens in optometry. On a spectacle lens, it is the flatter curvature of the front surface. On a contact lens it is the curvature of the back surface and is sometimes referred to as the back central optic radius (BCOR). Typical values for a contact ...
Even though the given curve is not smooth at the sharp corner, its parallel curve may be smooth with a continuous normal, or it may have cusps when the distance from the curve matches the radius of curvature at the sharp corner.