Martin Desruisseaux created SIS155:

Summary: Area calculation on ellipsoid
Key: SIS155
URL: https://issues.apache.org/jira/browse/SIS155
Project: Spatial Information Systems
Issue Type: New Feature
Components: Referencing
Affects Versions: 0.3
Reporter: Martin Desruisseaux
We need a method for calculating the area inside a polygon on the ellipsoid. An algorithm
working in Cartesian coordinate system is available there:
* http://www.mathopenref.com/coordpolygonarea2.html
This algorithm can be adapted to spherical coordinate systems by replacing the area sum by
(note that this replacement uses vertical strips instead than horizontal ones):
{code:java}
s += (λ2  λ1) * (2 + sin(φ1) + sin(φ2));
{code}
and the final answer by:
{code:java}
area = abs(s * r² / 2);
{code}
The _r_ value could be approximated to the authalic radius (the radius of a hypothetical sphere
having the same surface than the ellipsoid). However an article on http://www.geodyssey.com/papers/ggelare.html
seems to use a more local approximation, where _a_ and _b_ are semimajor and semiminor axis
lengths:
{code:java}
s = sin(φ)
c = cos(φ)
r = (a²b) / (a²c² + b²s²)
{code}
This task just write down some ideas. We probably need to read the abovecited article and
other internet resources more carefully.

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