Martin Desruisseaux created SIS451:

Summary: Verify map projection derivative by comparaison with Snyder terms
Key: SIS451
URL: https://issues.apache.org/jira/browse/SIS451
Project: Spatial Information Systems
Issue Type: Test
Components: Referencing
Reporter: Martin Desruisseaux
Map projections in Apache SIS can provide derivatives as Jacobian matrices. However those
formulas do not appear in the John Parr Snyder's book _Map Projections: A Working Manual_
(1987); we had to derive them ourselves, with the risk of errors. However Snyder provides
the following terms in addition of _x_ and _y_ projection results:
* _h_: scale factor along meridian.
* _k_: scale factor along parallel.
* _ω_: maximal angular deformation.
Those terms are related to Jacobian matrix terms on sphere as below (Snyder 410 and 11):
* _h_ = hypot(∂x/∂φ, ∂y/∂φ)
* _k_ = hypot(∂x/∂λ, ∂y/∂λ)
Ellipsoidal case (Snyder 427 and 28):
* _h_ = hypot(∂x/∂φ, ∂y/∂φ) ⋅ (1  ℯ²⋅sin²φ)^1.5 / (a⋅(1  ℯ²))
* _k_ = hypot(∂x/∂λ, ∂y/∂λ) ⋅ (1  ℯ²⋅sin²φ)^0.5 / (a⋅cos φ)
Formulas for _h_ and _k_ are provided for most map projections. We should implement them,
which would allow us to compare with Jacobian matrix terms at least on a rowbyrow basis.

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