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  1. Spatial Information Systems
  2. SIS-451

Verify map projection derivative by comparaison with Snyder terms

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    • Type: Test
    • Status: Open
    • Priority: Major
    • Resolution: Unresolved
    • Affects Version/s: None
    • Fix Version/s: None
    • Component/s: Referencing
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      Description

      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 4-10 and -11):

      • h = hypot(∂x/∂φ, ∂y/∂φ)
      • k = hypot(∂x/∂λ, ∂y/∂λ)

      Ellipsoidal case (Snyder 4-27 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 row-by-row basis.

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            • Assignee:
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              Reporter:
              desruisseaux Martin Desruisseaux
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