This performance transforms three-dimensional coordinates from a Cartesian system (x, y, z) to a cylindrical system (, , z). The Cartesian system makes use of three perpendicular axes to outline a degree in area, whereas the cylindrical system makes use of a radial distance, an azimuthal angle, and a vertical peak. As an illustration, a degree (3, 4, 5) in rectangular coordinates is perhaps represented as (5, 0.93, 5) in cylindrical coordinates, the place 5 is the radial distance from the origin within the xy-plane, 0.93 radians is the angle from the constructive x-axis, and 5 stays the vertical peak. Instruments offering this conversion usually settle for rectangular coordinates as enter and output the equal cylindrical coordinates.
This transformation is crucial in numerous fields, together with physics, engineering, and pc graphics. It simplifies mathematical descriptions and computations for programs with cylindrical symmetry, corresponding to pipes, electromagnetic fields round wires, and rotational movement. Traditionally, cylindrical coordinates emerged as a pure extension of polar coordinates in two dimensions to embody three-dimensional area, facilitating the evaluation of issues exhibiting cylindrical symmetry.
