[SIS-478] Improve inverse projection using Jacobian matrix for high eccentricities

• Type: Improvement
• Status: Open
• Priority: Major
• Resolution: Unresolved
• Component/s: Referencing
• Assignee: Unassigned
• Reporter: Martin Desruisseaux
• Created: 23/Oct/19 17:48
• Updated: 23/Oct/19 19:13

Description

When a map projection has exact formulas for the forward projection but approximate formulas (e.g. using series expansion) for inverse projection, the accuracy of inverse projection with celestial bodies having high eccentricities may be improved as below:

Take a first estimation of (λ,φ), compute the forward projection (E′,N′) for that estimation, compute the errors compared to specified (E,N) values, convert that (ΔE,ΔN) error into a (Δλ,Δφ) error using the inverse of Jacobian matrix, correct (λ,φ) and continue iteratively until the error is small enough. This algorithm described in EPSG guidance note for the Orthographic projection could be applied to any map projection, not only Orthographic.

See org.apache.sis.referencing.operation.projection.Orthographic.inverseTransform for implementation.

Issue Links

• is a child of: SIS-465 Referencing on celestial bodies with high flattening factor
• relates to: SIS-223 Orthographic (EPSG:9840)