GeographicLib: GeographicLib::experimental::JacobiConformal Class Reference (original) (raw)

Jacobi's conformal projection of a triaxial ellipsoid.

NOTE: This is just sample code. It is not part of GeographicLib itself.

This is a conformal projection of the ellipsoid to a plane in which the grid lines are straight; see Jacobi, Vorlesungen über Dynamik, §28. The constructor takes the semi-axes of the ellipsoid (which must be in order). Member functions map the ellipsoidal coordinates ω and β separately to x and y. Jacobi's coordinates have been multiplied by (a_2−_c_2)1/2 / (2_b) so that the customary results are returned in the cases of a sphere or an ellipsoid of revolution.

The ellipsoid is oriented so that the large principal ellipse, \(Z=0\), is the equator, \(\beta=0\), while the small principal ellipse, \(Y=0\), is the prime meridian, \(\omega=0\). The four umbilic points, \(\left|\omega\right| = \left|\beta\right| = \frac12\pi\), lie on middle principal ellipse in the plane \(X=0\).

For more information on this projection, see Jacobi's conformal projection.

Definition at line 45 of file JacobiConformal.hpp.