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Hypocycloid ( parametric equation Y- coordinate)

A hypocycloid is a special plane curve generated by the trace of a fixed point on a small circle that rolls within a larger circle. It is comparable to the ... more

Limaçon of Pascal

A limaçon is a bicircular rational plane algebraic curve of degree 4. Limaçon of Pascal, is defined as a roulette formed when a circle rolls around the ... more

Crest curve length when S>L (Vertical curves for highway design)

Crest vertical curves are curves which, when viewed from the side, are convex upwards. This includes vertical curves at hill crests, but it also includes ... more

Crest curve length when S<L (Vertical curves for highway design)

Crest vertical curves are curves which, when viewed from the side, are convex upwards. This includes vertical curves at hill crests, but it also includes ... more

Standard logistic sigmoid function (k=1, x0=0, L=1)

A logistic function or logistic curve is a common “S” shape (sigmoid curve). Data that follows an increasing logistic curve usually describes ... more

Accident modification factor

The safety of a horizontal curve is affected by the length of the curve, the curve radius, whether spiral transition curves are used, and the ... more

Eccentricity of an ellipse

Ellipse is a curve on a plane surrounding two focal points such that a straight line drawn from one of the focal points to any point on the curve and then ... more

General Logistic Sigmoid Function

A logistic function or logistic curve is a common “S” shape (sigmoid curve). Data that follows an increasing logistic curve usually describes ... more

Vertical Curve - Offset

Offsets are vertical distances from the initial tangent to the curve, play a significant role in vertical curve design.

Vertical Curves are the ... more

Hyperboloid of one sheet equation

In mathematics, a hyperboloid is a quadric – a type of surface in three dimensions – . A hyperboloid of revolution of one sheet can be obtained by ... more

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