Gnomonic projection: Difference between revisions
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==Equations== | ==Equations== | ||
===Gnomonic Projection=== | ===Gnomonic Projection=== | ||
Copied from Mathworld | Copied from [https://mathworld.wolfram.com/GnomonicProjection.html Mathworld] | ||
Inputs: | |||
<math>(\lambda, \phi)</math> Current spherical coordinate< | Inputs: | ||
<math>(\lambda_0, \phi_1)</math> Spherical coordinate of tangent plane. | * <math>(\lambda, \phi)</math> Current spherical coordinate with longitude <math>\lambda</math> and latitude <math>\phi</math> | ||
* <math>(\lambda_0, \phi_1)</math> Spherical coordinate of tangent plane. | |||
Outputs: <br> | Outputs: <br> | ||
* <math>(x,y) \in (-\infty, \infty) \times (-\infty, \infty)</math> Cartesian coordinates. | |||
<math>(x,y) \in (-\infty, \infty) \times (-\infty, \infty)</math> | |||
<math>x = \frac{\cos(\phi)\sin(\lambda - \lambda_0)}{\cos(c)}</math><br> | |||
<math>x = \frac{\cos(\ | |||
<math>y = \frac{\cos(\phi_1)\sin(\phi)-\sin(\phi_1)\cos(\phi)\cos(\lambda - \lambda_0)}{\cos(c)}</math><br> | <math>y = \frac{\cos(\phi_1)\sin(\phi)-\sin(\phi_1)\cos(\phi)\cos(\lambda - \lambda_0)}{\cos(c)}</math><br> | ||
where <math>c</math> is the angular distance of the point <math>(x,y)</math> from the center of the projection, given by<br> | where <math>c</math> is the angular distance of the point <math>(x,y)</math> from the center of the projection, given by<br> | ||