Transformation from spherical to cylindrical coordinates
0
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I have a coordinate on the surface of a sphere i.e latitude and longitude(two dimensions). I need to transform into a 2-D cylindrical coordinate frame i.e. r and the azimuth angle theta. Is there a transformation matrix between the two without converting to Cartesian in between ?
trigonometry coordinate-systems spherical-coordinates cylindrical-coordinates
asked Dec 24 '18 at 10:32
gansubgansub
158111
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add a comment |
0
$begingroup$
I have a coordinate on the surface of a sphere i.e latitude and longitude(two dimensions). I need to transform into a 2-D cylindrical coordinate frame i.e. r and the azimuth angle theta. Is there a transformation matrix between the two without converting to Cartesian in between ?
trigonometry coordinate-systems spherical-coordinates cylindrical-coordinates
asked Dec 24 '18 at 10:32
gansubgansub
158111
$endgroup$
add a comment |
0
0
0
$begingroup$
I have a coordinate on the surface of a sphere i.e latitude and longitude(two dimensions). I need to transform into a 2-D cylindrical coordinate frame i.e. r and the azimuth angle theta. Is there a transformation matrix between the two without converting to Cartesian in between ?
trigonometry coordinate-systems spherical-coordinates cylindrical-coordinates
asked Dec 24 '18 at 10:32
gansubgansub
158111
$endgroup$
I have a coordinate on the surface of a sphere i.e latitude and longitude(two dimensions). I need to transform into a 2-D cylindrical coordinate frame i.e. r and the azimuth angle theta. Is there a transformation matrix between the two without converting to Cartesian in between ?
trigonometry coordinate-systems spherical-coordinates cylindrical-coordinates
trigonometry coordinate-systems spherical-coordinates cylindrical-coordinates
asked Dec 24 '18 at 10:32
gansubgansub
158111
asked Dec 24 '18 at 10:32
gansubgansub
158111
asked Dec 24 '18 at 10:32
gansubgansub
158111
asked Dec 24 '18 at 10:32
gansubgansub
158111
asked Dec 24 '18 at 10:32
gansubgansub
158111
158111
add a comment |
add a comment |
1 Answer
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The point $(r, theta, phi)$ in spherical coordinates, can be represented as $(rho, varphi, z) = (rcostheta, phi, rsintheta)$ in cylindrical coordinates. In this convention $theta$ represents the latitude, and $phi$ the longitude
answered Dec 24 '18 at 10:43
caveraccaverac
14.6k31130
$endgroup$
$begingroup$
thanks for your answer. I am a bit confused. I do not have a "r" in my case as I only have 2D coordinates. Will this still work by taking r to be 1 ?
$endgroup$
– gansub
Dec 24 '18 at 10:45
$begingroup$
@gansub In the surface of a sphere $r$ is constant (the radius of the sphere)
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– caverac
Dec 24 '18 at 10:46
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so in my case "r" = 1 will be correct am I right ?
$endgroup$
– gansub
Dec 24 '18 at 10:47
$begingroup$
@gansub Kind of difficult to say without further context, but you can alway scale your problem. So yes, you can use $r=1$
$endgroup$
– caverac
Dec 24 '18 at 10:50
$begingroup$
final question before accepting your answer. So in my case latitude and longitude is nothing but phi and r cos theta in the cylindrical coordinate system right ? If you can edit your answer with a mapping that would be helpful.
$endgroup$
– gansub
Dec 24 '18 at 10:52
add a comment |
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1 Answer
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oldest
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1 Answer
1
active
oldest
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active
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votes
1
$begingroup$
The point $(r, theta, phi)$ in spherical coordinates, can be represented as $(rho, varphi, z) = (rcostheta, phi, rsintheta)$ in cylindrical coordinates. In this convention $theta$ represents the latitude, and $phi$ the longitude
answered Dec 24 '18 at 10:43
caveraccaverac
14.6k31130
$endgroup$
$begingroup$
thanks for your answer. I am a bit confused. I do not have a "r" in my case as I only have 2D coordinates. Will this still work by taking r to be 1 ?
$endgroup$
– gansub
Dec 24 '18 at 10:45
$begingroup$
@gansub In the surface of a sphere $r$ is constant (the radius of the sphere)
$endgroup$
– caverac
Dec 24 '18 at 10:46
$begingroup$
so in my case "r" = 1 will be correct am I right ?
$endgroup$
– gansub
Dec 24 '18 at 10:47
$begingroup$
@gansub Kind of difficult to say without further context, but you can alway scale your problem. So yes, you can use $r=1$
$endgroup$
– caverac
Dec 24 '18 at 10:50
$begingroup$
final question before accepting your answer. So in my case latitude and longitude is nothing but phi and r cos theta in the cylindrical coordinate system right ? If you can edit your answer with a mapping that would be helpful.
$endgroup$
– gansub
Dec 24 '18 at 10:52
add a comment |
1
$begingroup$
The point $(r, theta, phi)$ in spherical coordinates, can be represented as $(rho, varphi, z) = (rcostheta, phi, rsintheta)$ in cylindrical coordinates. In this convention $theta$ represents the latitude, and $phi$ the longitude
answered Dec 24 '18 at 10:43
caveraccaverac
14.6k31130
$endgroup$
$begingroup$
thanks for your answer. I am a bit confused. I do not have a "r" in my case as I only have 2D coordinates. Will this still work by taking r to be 1 ?
$endgroup$
– gansub
Dec 24 '18 at 10:45
$begingroup$
@gansub In the surface of a sphere $r$ is constant (the radius of the sphere)
$endgroup$
– caverac
Dec 24 '18 at 10:46
$begingroup$
so in my case "r" = 1 will be correct am I right ?
$endgroup$
– gansub
Dec 24 '18 at 10:47
$begingroup$
@gansub Kind of difficult to say without further context, but you can alway scale your problem. So yes, you can use $r=1$
$endgroup$
– caverac
Dec 24 '18 at 10:50
$begingroup$
final question before accepting your answer. So in my case latitude and longitude is nothing but phi and r cos theta in the cylindrical coordinate system right ? If you can edit your answer with a mapping that would be helpful.
$endgroup$
– gansub
Dec 24 '18 at 10:52
add a comment |
1
1
1
$begingroup$
The point $(r, theta, phi)$ in spherical coordinates, can be represented as $(rho, varphi, z) = (rcostheta, phi, rsintheta)$ in cylindrical coordinates. In this convention $theta$ represents the latitude, and $phi$ the longitude
answered Dec 24 '18 at 10:43
caveraccaverac
14.6k31130
$endgroup$
The point $(r, theta, phi)$ in spherical coordinates, can be represented as $(rho, varphi, z) = (rcostheta, phi, rsintheta)$ in cylindrical coordinates. In this convention $theta$ represents the latitude, and $phi$ the longitude
answered Dec 24 '18 at 10:43
caveraccaverac
14.6k31130
edited Dec 24 '18 at 10:54
answered Dec 24 '18 at 10:43
caveraccaverac
14.6k31130
answered Dec 24 '18 at 10:43
caveraccaverac
14.6k31130
answered Dec 24 '18 at 10:43
caveraccaverac
14.6k31130
14.6k31130
$begingroup$
thanks for your answer. I am a bit confused. I do not have a "r" in my case as I only have 2D coordinates. Will this still work by taking r to be 1 ?
$endgroup$
– gansub
Dec 24 '18 at 10:45
$begingroup$
@gansub In the surface of a sphere $r$ is constant (the radius of the sphere)
$endgroup$
– caverac
Dec 24 '18 at 10:46
$begingroup$
so in my case "r" = 1 will be correct am I right ?
$endgroup$
– gansub
Dec 24 '18 at 10:47
$begingroup$
@gansub Kind of difficult to say without further context, but you can alway scale your problem. So yes, you can use $r=1$
$endgroup$
– caverac
Dec 24 '18 at 10:50
$begingroup$
final question before accepting your answer. So in my case latitude and longitude is nothing but phi and r cos theta in the cylindrical coordinate system right ? If you can edit your answer with a mapping that would be helpful.
$endgroup$
– gansub
Dec 24 '18 at 10:52
add a comment |
$begingroup$
thanks for your answer. I am a bit confused. I do not have a "r" in my case as I only have 2D coordinates. Will this still work by taking r to be 1 ?
$endgroup$
– gansub
Dec 24 '18 at 10:45
$begingroup$
@gansub In the surface of a sphere $r$ is constant (the radius of the sphere)
$endgroup$
– caverac
Dec 24 '18 at 10:46
$begingroup$
so in my case "r" = 1 will be correct am I right ?
$endgroup$
– gansub
Dec 24 '18 at 10:47
$begingroup$
@gansub Kind of difficult to say without further context, but you can alway scale your problem. So yes, you can use $r=1$
$endgroup$
– caverac
Dec 24 '18 at 10:50
$begingroup$
final question before accepting your answer. So in my case latitude and longitude is nothing but phi and r cos theta in the cylindrical coordinate system right ? If you can edit your answer with a mapping that would be helpful.
$endgroup$
– gansub
Dec 24 '18 at 10:52
$begingroup$
thanks for your answer. I am a bit confused. I do not have a "r" in my case as I only have 2D coordinates. Will this still work by taking r to be 1 ?
$endgroup$
– gansub
Dec 24 '18 at 10:45
$begingroup$
thanks for your answer. I am a bit confused. I do not have a "r" in my case as I only have 2D coordinates. Will this still work by taking r to be 1 ?
$endgroup$
– gansub
Dec 24 '18 at 10:45
$begingroup$
@gansub In the surface of a sphere $r$ is constant (the radius of the sphere)
$endgroup$
– caverac
Dec 24 '18 at 10:46
$begingroup$
@gansub In the surface of a sphere $r$ is constant (the radius of the sphere)
$endgroup$
– caverac
Dec 24 '18 at 10:46
$begingroup$
so in my case "r" = 1 will be correct am I right ?
$endgroup$
– gansub
Dec 24 '18 at 10:47
$begingroup$
so in my case "r" = 1 will be correct am I right ?
$endgroup$
– gansub
Dec 24 '18 at 10:47
$begingroup$
@gansub Kind of difficult to say without further context, but you can alway scale your problem. So yes, you can use $r=1$
$endgroup$
– caverac
Dec 24 '18 at 10:50
$begingroup$
@gansub Kind of difficult to say without further context, but you can alway scale your problem. So yes, you can use $r=1$
$endgroup$
– caverac
Dec 24 '18 at 10:50
$begingroup$
final question before accepting your answer. So in my case latitude and longitude is nothing but phi and r cos theta in the cylindrical coordinate system right ? If you can edit your answer with a mapping that would be helpful.
$endgroup$
– gansub
Dec 24 '18 at 10:52
$begingroup$
final question before accepting your answer. So in my case latitude and longitude is nothing but phi and r cos theta in the cylindrical coordinate system right ? If you can edit your answer with a mapping that would be helpful.
$endgroup$
– gansub
Dec 24 '18 at 10:52
add a comment |
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