Search results
Results from the WOW.Com Content Network
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 ...
The following can be used to find the versine of a given constant radius curve: [2] The Hallade method is to use the chord to continuously measure the versine in an overlapping pattern along the curve. The versine values for the perfect circular curve would have the same number. [3]
Intuitively, the curvature describes for any part of a curve how much the curve direction changes over a small distance travelled (e.g. angle in rad/m), so it is a measure of the instantaneous rate of change of direction of a point that moves on the curve: the larger the curvature, the larger this rate of change.
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.
A space curve; the vectors T, N, B; and the osculating plane spanned by T and N. In differential geometry, the Frenet–Serret formulas describe the kinematic properties of a particle moving along a differentiable curve in three-dimensional Euclidean space, or the geometric properties of the curve itself irrespective of any motion.
A plane curve with non-vanishing curvature has zero torsion at all points. Conversely, if the torsion of a regular curve with non-vanishing curvature is identically zero, then this curve belongs to a fixed plane. The curvature and the torsion of a helix are constant. Conversely, any space curve whose curvature and torsion are both constant and ...
The osculating circle provides a way to understand the local behavior of a curve and is commonly used in differential geometry and calculus. More formally, in differential geometry of curves , the osculating circle of a sufficiently smooth plane curve at a given point p on the curve has been traditionally defined as the circle passing through p ...
A double-end Euler spiral. The curve continues to converge to the points marked, as t tends to positive or negative infinity. An Euler spiral is a curve whose curvature changes linearly with its curve length (the curvature of a circular curve is equal to the reciprocal of the radius). This curve is also referred to as a clothoid or Cornu spiral.