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The tangent line is said to be "going in the same direction" as the curve, and is thus the best straight-line approximation to the curve at that point. The tangent line to a point on a differentiable curve can also be thought of as a tangent line approximation, the graph of the affine function that best approximates the original function at the ...
A horizontal curve with a significantly smaller radius than those before it may need enhanced curve signs. [13] This is an improvement on the concept of design speed, which only sets a lower limit for geometric design. In the example given above, a long tangent followed by a sharp curve would be acceptable if a 30 mph design speed was chosen.
Alternatively, the tangent lines and tangent points can be constructed more directly, as detailed below. Note that in degenerate cases these constructions break down; to simplify exposition this is not discussed in this section, but a form of the construction can work in limit cases (e.g., two circles tangent at one point).
Local tangent plane coordinates (LTP) are part of a spatial reference system based on the tangent plane defined by the local vertical direction and the Earth's axis of rotation. They are also known as local ellipsoidal system, [1] [2] local geodetic coordinate system, [3] local vertical, local horizontal coordinates (LVLH), or topocentric ...
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 deviation not more than 1 degree 50 minutes) without an intermediate curve. There is a set of speed limits for the bends separately from normal tangent track. [5]
At each point in the fiber , the vertical fiber is unique. It is the tangent space to the fiber. The horizontal fiber is non-unique. It merely has to be transverse to the vertical fiber. In mathematics, the vertical bundle and the horizontal bundle are vector bundles associated to a smooth fiber bundle.
The horizontal position has two degrees of freedom, and thus two parameters are sufficient to uniquely describe such a position. However, similarly to the use of Euler angles as a formalism for representing rotations , using only the minimum number of parameters gives singularities , and thus three parameters are required for the horizontal ...
The word horizontal is derived from the Latin horizon, which derives from the Greek ὁρῐ́ζων, meaning 'separating' or 'marking a boundary'. [2] The word vertical is derived from the late Latin verticalis, which is from the same root as vertex, meaning 'highest point' or more literally the 'turning point' such as in a whirlpool.