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atan2(y, x) returns the angle θ between the positive x-axis and the ray from the origin to the point (x, y), confined to (−π, π].Graph of (,) over /. In computing and mathematics, the function atan2 is the 2-argument arctangent.
Note that the arctan functions implemented in computer languages only produce results between −π/2 and π/2, which is why atan2 is used to generate all the correct orientations. Moreover, typical implementations of arctan also might have some numerical disadvantages near zero and one.
Note that atan2(a, b) is equivalent to arctan a / b where it also takes into account the quadrant that the point (b, a) is in; see atan2. When implementing the conversion, one has to take into account several situations: [5] There are generally two solutions in the interval [−π, π] 3.
3D visualization of a sphere and a rotation about an Euler axis (^) by an angle of In 3-dimensional space, according to Euler's rotation theorem, any rotation or sequence of rotations of a rigid body or coordinate system about a fixed point is equivalent to a single rotation by a given angle about a fixed axis (called the Euler axis) that runs through the fixed point. [6]
calculate = (¯ , ¯ ), where atan2 is a computer function, also called the arctangent of two arguments, that returns the arctangent of the ratio of the two values given. Note that in Microsoft Excel the two arguments are reversed, so the proper syntax would be = atan2(AC*\sin(beta), BC*\sin(alpha)) .
The axes of the original frame are denoted as x, y, z and the axes of the rotated frame as X, Y, Z.The geometrical definition (sometimes referred to as static) begins by defining the line of nodes (N) as the intersection of the planes xy and XY (it can also be defined as the common perpendicular to the axes z and Z and then written as the vector product N = z × Z).
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It can be computed using Arg(x + iy) = atan2(y, x). Log( z ) is the principal value of the complex logarithm function and has imaginary part in the range (− π , π ] .