- #1
jk22
- 729
- 24
I read the Wikipedia article : https://en.m.wikipedia.org/wiki/Mercator_projection
Section : Mathematics of the Mercator projection.
For a map to be conformal should not it be $$k(\phi)=C,h(\phi)=C$$, or the shrinking coefficient shall be not only equal but homogeneous, in order to be conformal ? We then get two partial differential equations and their solution is Simply obtained by integrating a constant towards the variable of integration :
$$x(\lambda,\phi)=Ccos(\phi)\lambda$$
$$y(\lambda,\phi)=C\phi$$
Does this anyhow makes sense ?
Section : Mathematics of the Mercator projection.
For a map to be conformal should not it be $$k(\phi)=C,h(\phi)=C$$, or the shrinking coefficient shall be not only equal but homogeneous, in order to be conformal ? We then get two partial differential equations and their solution is Simply obtained by integrating a constant towards the variable of integration :
$$x(\lambda,\phi)=Ccos(\phi)\lambda$$
$$y(\lambda,\phi)=C\phi$$
Does this anyhow makes sense ?
![{\displaystyle x=R(\lambda -\lambda _{0}),\qquad y=R\ln \left[\tan \left({\frac {\pi }{4}}+{\frac {\varphi }{2}}\right)\right].}](https://wikimedia.org/api/rest_v1/media/math/render/svg/62ea14e55f1e378a2a82a2ff70bee9d2f8cabf8d "{\displaystyle x=R(\lambda -\lambda _{0}),\qquad y=R\ln \left[\tan \left({\frac {\pi }{4}}+{\frac {\varphi }{2}}\right)\right].}")