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Convert global to local coordinates


lclCoord = global2localcoord(gCoord, OPTION)
gCoord = global2localcoord(___,localOrigin)
gCoord = global2localcoord(___,localAxes)


lclCoord = global2localcoord(gCoord, OPTION) returns the local coordinate lclCoord corresponding to the global coordinate gCoord. OPTION determines the type of global-to-local coordinate transformation.

gCoord = global2localcoord(___,localOrigin) specifies the origin of the local coordinate system.

gCoord = global2localcoord(___,localAxes) specifies the axes of the local coordinate system.

Input Arguments


Global coordinates in rectangular or spherical coordinate form. gCoord is a 3-by-1 vector or 3-by-N matrix. Each column represents a global coordinate.

If the coordinates are in rectangular form, the column represents (X,Y,Z) in meters.

If the coordinates are in spherical form, the column represents (az,el,r). az is the azimuth angle in degrees, el is the elevation angle in degrees, and r is the radius in meters.

The origin of the global coordinate system is at [0; 0; 0]. That system’s axes are the standard unit basis vectors in three-dimensional space, [1; 0; 0], [0; 1; 0], and [0; 0; 1].


Type of coordinate transformation. Valid types are

'rr'Global rectangular to local rectangular
'rs'Global rectangular to local spherical
'sr'Global spherical to local rectangular
'ss'Global spherical to local spherical


Origin of local coordinate system. localOrigin is a 3-by-1 column vector containing the rectangular coordinate of the local coordinate system origin with respect to the global coordinate system.

Default: [0; 0; 0]


Axes of local coordinate system. localAxes is a 3-by-3 matrix with the columns specifying the local X, Y, and Z axes in rectangular form with respect to the global coordinate system.

Default: [1 0 0;0 1 0;0 0 1]

Output Arguments


Local coordinates in rectangular or spherical coordinate form.


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Convert global rectangular coordinates, (0,1,0), to local rectangular coordinates. The local coordinate origin is (1,1,1).

lclCoord = global2localcoord([0;1;0],'rr',[1;1;1])
lclCoord = 3×1


Convert global spherical coordinates to local rectangular coordinates.

lclCoord = global2localcoord([45;45;50],'sr',[50;50;50])
lclCoord = 3×1


More About

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Azimuth Angle, Elevation Angle

The azimuth angle of a vector is the angle between the x-axis and the orthogonal projection of the vector onto the xy plane. The angle is positive in going from the x axis toward the y axis. Azimuth angles lie between –180 and 180 degrees. The elevation angle is the angle between the vector and its orthogonal projection onto the xy-plane. The angle is positive when going toward the positive z-axis from the xy plane. These definitions assume the boresight direction is the positive x-axis.


The elevation angle is sometimes defined in the literature as the angle a vector makes with the positive z-axis. The MATLAB® and Phased Array System Toolbox™ products do not use this definition.

This figure illustrates the azimuth angle and elevation angle for a vector that appears as a green solid line. The coordinate system is relative to the center of a uniform linear array, whose elements appear as blue circles.


[1] Foley, J. D., A. van Dam, S. K. Feiner, and J. F. Hughes. Computer Graphics: Principles and Practice in C, 2nd Ed. Reading, MA: Addison-Wesley, 1995.

Extended Capabilities

Introduced in R2011a