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global2localcoord

Convert global to local coordinates

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Syntax

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

Description

lclCoord= global2localcoord(gCoord)converts the global rectangular coordinatesgCoordto the local rectangular coordinateslclCoord. In this syntax, the global coordinate origin is located at (0, 0, 0) and the coordinate axes are the unit vectors in thex,y, andzdirections.

lclCoord= global2localcoord(gCoord,option)converts global coordinates to local coordinates using the coordinate transformation typeoption.

example

lclCoord= global2localcoord(___,localOrigin)specifies the origin of the local coordinate systemlocalOrigin. Use this syntax with any of the input arguments in previous syntaxes.

example

lclCoord= global2localcoord(___,localAxes)specifies the axes of the local coordinate systemlocalAxes. Use this syntax with any of the input arguments in previous syntaxes.

Examples

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Open Live Script

Convert the 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 =3×1-1 0 -1

Convert global spherical coordinates to local rectangular coordinates.

lclCoord = global2localcoord([45;45;50],"sr",[50;50;50])
lclCoord =3×1-25.0000 -25.0000 -14.6447
Open Live Script

Convert two vectors from global to local coordinates using theglobal2localcoord函数。然后将它们转换为back from local to global coordinates using thelocal2globalcoord函数。

Start with two vectors in global coordinates, (0, 1, 0) and (1, 1, 1). The local coordinate origins are (1, 5, 2) and (-4, 5, 7), respectively.

gCoord = [0 1;1 1;0 1]
gCoord =3×20 1 1 1 0 1
lclOrig = [1 -4;5 5;2 7];

Construct two rotation matrices using the rotation functions.

lclAxes(:,:,1) = rotz(45)*roty(-15); lclAxes(:,:,2) = roty(45)*rotx(35);

Convert the vectors from global coordinates to local coordinates.

lclCoord = global2localcoord(gCoord,"rr",lclOrig,lclAxes)
lclCoord =3×2-3.9327 7.7782 -2.1213 -3.6822 -1.0168 1.7151

Convert the vectors from local coordinates back to global coordinates.

gCoord1 = local2globalcoord(lclCoord,"rr",lclOrig,lclAxes)
gCoord1 =3×2-0.0000 1.0000 1.0000 1.0000 0 1.0000

Input Arguments

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Global coordinates in rectangular or spherical coordinate form, specified as a 3-by-Nmatrix. Each column represents one set of global coordinates.

If the coordinates are in rectangular form, each column contains the (x,y,z) components. Units are in meters.

If the coordinates are in spherical form, each column contains (az,el,r) components.azis theazimuth anglein degrees,elis theelevation anglein degrees, andris the radius in meters.

The origin of the global coordinate system is assumed to be (0, 0, 0). The global system axes are the standard unit basis vectors in three-dimensional space, (1, 0, 0), (0, 1, 0), and (0, 0, 1).

Data Types:double

Type of coordinate transformation, specified as a string scalar or character vector. Specify one of the following values.

Value Transformation
"rr"or'rr' Global rectangular to local rectangular
"rs"or'rs' Global rectangular to local spherical
"sr"or'sr' Global spherical to local rectangular
"ss"or'ss' Global spherical to local spherical

Data Types:string|char

Origin of the local coordinate system, specified as a 3-by-Nmatrix containing the rectangular coordinates of the local coordinate system origin with respect to the global coordinate system.Nmust match the number of columns ofgCoord. Each column represents a separate origin. Alternatively, you can specifylocalOriginas a 3-by-1 vector. If you do so,localOriginexpands to a 3-by-Nmatrix with identical columns.

Data Types:double

Axes of the local coordinate system, specified as a 3-by-3-by-Narray. Each page contains a 3-by-3 matrix representing axes for a different local coordinate system. The columns of the 3-by-3 matrices specify the localx,y, andzaxes in rectangular form with respect to the global coordinate system. Alternatively, you can specifylocalAxesas a single 3-by-3 matrix. If you do so,localAxesexpands to a 3-by-3-by-Narray with identical 3-by-3 matrices. The default value is the identity matrix.

Data Types:double

Output Arguments

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Local coordinates in rectangular or spherical coordinate form, returned as a 3-by-Nmatrix. The dimensions oflclCoordmatch the dimensions ofgCoord.

Data Types:double

More About

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Azimuth and Elevation Angles

Theazimuth angleof a vector is the angle between thex-axis and the orthogonal projection of the vector onto thexy-plane. The angle is positive from thex-axis toward they-axis. Azimuth angles lie between –180 and 180 degrees. Theelevation angleis the angle between the vector and its orthogonal projection onto thexy-plane. The angle is positive toward the positivez-axis from thexy-plane. By default, the boresight direction of an element or array is aligned with the positivex-axis. The boresight direction is the direction of the main lobe of an element or array.

Note

The elevation angle is sometimes defined as the angle a vector makes with the positivez-axis. The MATLAB®andCommunications Toolbox™products do not use this definition.

This figure illustrates the azimuth and elevation angles of a direction vector.

References

[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

Version History

Introduced in R2020a

See Also

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