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  2. Degree of curvature - Wikipedia

    en.wikipedia.org/wiki/Degree_of_curvature

    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.

  3. Arc length - Wikipedia

    en.wikipedia.org/wiki/Arc_length

    For a rectifiable curve these approximations don't get arbitrarily large (so the curve has a finite length). If a curve can be parameterized as an injective and continuously differentiable function (i.e., the derivative is a continuous function) f : [ a , b ] → R n {\displaystyle f\colon [a,b]\to \mathbb {R} ^{n}} , then the curve is ...

  4. Track geometry - Wikipedia

    en.wikipedia.org/wiki/Track_geometry

    The third type is reverse curve which comprises two or more simple curves that has the opposite direction of curvature (sometime known as "S" curve or serpentine curve). [ 3 ] [ 4 ] In Australia, there is a special definition for a bend (or a horizontal bend ) which is a connection between two tangent tracks at almost 180 degrees (with ...

  5. Radius of curvature - Wikipedia

    en.wikipedia.org/wiki/Radius_of_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 combinations thereof. [1] [2] [3]

  6. Curvature - Wikipedia

    en.wikipedia.org/wiki/Curvature

    The normal curvature, k n, is the curvature of the curve projected onto the plane containing the curve's tangent T and the surface normal u; the geodesic curvature, k g, is the curvature of the curve projected onto the surface's tangent plane; and the geodesic torsion (or relative torsion), τ r, measures the rate of change of the surface ...

  7. Slope - Wikipedia

    en.wikipedia.org/wiki/Slope

    Slope illustrated for y = (3/2)x − 1.Click on to enlarge Slope of a line in coordinates system, from f(x) = −12x + 2 to f(x) = 12x + 2. The slope of a line in the plane containing the x and y axes is generally represented by the letter m, [5] and is defined as the change in the y coordinate divided by the corresponding change in the x coordinate, between two distinct points on the line.

  8. Principal curvature - Wikipedia

    en.wikipedia.org/wiki/Principal_curvature

    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 ...

  9. Track transition curve - Wikipedia

    en.wikipedia.org/wiki/Track_transition_curve

    The design pattern for horizontal geometry is typically a sequence of straight line (i.e., a tangent) and curve (i.e. a circular arc) segments connected by transition curves. The degree of banking in railroad track is typically expressed as the difference in elevation of the two rails, commonly quantified and referred to as the superelevation .