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kronchev
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Does anyone have a quick method to do this?
I believe [tex]z = \rho \cos{\phi}[/tex] and [tex]x = \rho \cos{\theta} \sin{\phi}[/tex]cookiemonster said:It's just a straight application of the spherical coordinate transformation.
[tex]x = \rho \sin{\theta} \cos{\phi}[/tex]
[tex]y = \rho \sin{\theta} \sin{\phi}[/tex]
[tex]z = \rho \cos{\theta}[/tex]
Where [itex]\phi[/itex] is the longitude, [itex]\theta[/itex] is the latitude, and [itex]\rho[/itex] is the radius of the Earth.
cookiemonster
deltabourne said:I believe [tex]z = \rho \cos{\phi}[/tex] and [tex]x = \rho \cos{\theta} \sin{\phi}[/tex]
HallsofIvy said:Maybe this is an "America against the rest of the world" thing but every text I've ever seen defines φ to be the angle the straight line from (0,0,0) to the point makes with the positive z axis while θ is the angle the projection of that line onto the xy-plane makes with the positive x-axis.
MathWorld said:A system of curvilinear coordinates which is natural for describing positions on a sphere or spheroid. Define [tex]\theta[/tex] to be the azimuthal angle in the xy-plane from the x-axis and [tex]\phi[/tex] to be the polar angle from the z-axis with ...
Unfortunately, the convention in which the symbols and are reversed is frequently used, especially in physics, leading to unnecessary confusion. The symbol [tex]\rho[/tex] is sometimes also used in place of r. Arfken (1985) uses [tex](r, \phi, \theta)[/tex], whereas Beyer (1987) uses [tex](\rho, \theta, \phi)[/tex]. Be very careful when consulting the literature.
kronchev said:Does anyone have a quick method to do this?
kronchev said:Does anyone have a quick method to do this?
The purpose of converting latitude/longitude to Cartesian coordinates is to express geographic locations in a format that is easier to work with mathematically. This conversion allows for distance and direction calculations, as well as plotting points on a two-dimensional plane.
To convert latitude/longitude to Cartesian coordinates, you can use the following formula:x = R * cos(lat) * cos(lon)y = R * cos(lat) * sin(lon)z = R * sin(lat)Where R is the radius of the Earth, lat is the latitude in radians, and lon is the longitude in radians.
Latitude/longitude coordinates are used to identify a location on a spherical surface, such as the Earth. Cartesian coordinates, on the other hand, represent a location on a two-dimensional plane. While latitude/longitude use angles and distance from a reference point, Cartesian coordinates use x and y coordinates from a fixed origin point.
Yes, there are limitations to converting latitude/longitude to Cartesian coordinates. This conversion assumes a spherical Earth, which is not entirely accurate. Additionally, the formula does not account for changes in elevation, which can affect the accuracy of the coordinates. It is also important to note that this conversion only works for locations on the Earth's surface, not for points in the Earth's interior.
Converting latitude/longitude to Cartesian coordinates is commonly used in the fields of geography, geology, cartography, and navigation. It is also used in industries such as transportation, surveying, and GIS (Geographic Information Systems). Additionally, it is used in various mapping and GPS applications.