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cart2sph

Transform Cartesian coordinates to spherical

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Syntax

[azimuth,elevation,r] = cart2sph(x,y,z)

Description

example

[方位,elevation,r] = cart2sph(x,y,z)transforms corresponding elements of the Cartesian coordinate arraysx,y, andzto spherical coordinates方位,elevation, andr.

Examples

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Convert the Cartesian coordinates defined by corresponding entries in the matricesx,y, andzto spherical coordinatesaz,el, andr. These points correspond to the eight vertices of a cube.

x = [1 1 1 1; -1 -1 -1 -1]
x =1 1 1 1 -1 -1 -1 -1
y = [1 1 -1 -1; 1 1 -1 -1]
y =1 1 -1 -1 1 1 -1 -1
z = [1 -1 1 -1; 1 -1 1 -1]
z =1 -1 1 -1 1 -1 1 -1
[az,el,r] = cart2sph(x,y,z)
az =0.7854 0.7854 -0.7854 -0.7854 2.3562 2.3562 -2.3562 -2.3562
el =0.6155 -0.6155 0.6155 -0.6155 0.6155 -0.6155 0.6155 -0.6155
r =1.7321 1.7321 1.7321 1.7321 1.7321 1.7321 1.7321 1.7321

Input Arguments

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Cartesian coordinates, specified as scalars, vectors, matrices, or multidimensional arrays.x,y, andzmust be the same size, or any of them can be scalar.

Data Types:single|double

Output Arguments

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Azimuth angle, returned as an array.方位is the counterclockwise angle in thex-yplane measured in radians from the positivex-axis.

Elevation angle, returned as an array.elevationis the elevation angle in radians from thex-yplane.

Radius, returned as an array.ris the distance from the origin to a point. The length units ofrare arbitrary, matching the units of the input arraysx,y, andz.

Algorithms

The mapping from three-dimensional Cartesian coordinates to spherical coordinates is

方位= atan2(y,x) elevation = atan2(z,sqrt(x.^2 + y.^2)) r = sqrt(x.^2 + y.^2 + z.^2)

The notation for spherical coordinates is not standard. For thecart2sphfunction,elevationis measured from thex-yplane. Notice that ifelevation = 0, the point is in thex-yplane. Ifelevation = pi/2, then the point is on the positivez-axis.

Extended Capabilities

C/C++ Code Generation
Generate C and C++ code using MATLAB® Coder™.

See Also

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Introduced before R2006a

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