spheroid_boundingbox_area()

static double spheroid_boundingbox_area ( const GEOGRAPHIC_POINT *  southWestCorner, const GEOGRAPHIC_POINT *  northEastCorner, const SPHEROID *  spheroid  )

static

Computes the area on the spheroid of a box bounded by meridians and parallels.

The box is defined by two points, the South West corner and the North East corner. Formula based on Bagratuni 1967.

Parameters

southWestCorner	- lower left corner of bounding box.
northEastCorner	- upper right corner of bounding box.

Returns

area in square meters.

Definition at line 437 of file lwspheroid.c.

References SPHEROID::b, SPHEROID::e_sq, GEOGRAPHIC_POINT::lat, GEOGRAPHIC_POINT::lon, and POW2.

Referenced by spheroid_striparea().

{
        double z0 = (northEastCorner->lon - southWestCorner->lon) * POW2(spheroid->b) / 2.0;
        double e = sqrt(spheroid->e_sq);
        double sinPhi1 = sin(southWestCorner->lat);
        double sinPhi2 = sin(northEastCorner->lat);
        double t1p1 = sinPhi1 / (1.0 - spheroid->e_sq * sinPhi1 * sinPhi1);
        double t1p2 = sinPhi2 / (1.0 - spheroid->e_sq * sinPhi2 * sinPhi2);
        double oneOver2e = 1.0 / (2.0 * e);
        double t2p1 = oneOver2e * log((1.0 + e * sinPhi1) / (1.0 - e * sinPhi1));
        double t2p2 = oneOver2e * log((1.0 + e * sinPhi2) / (1.0 - e * sinPhi2));
        return z0 * (t1p2 + t2p2) - z0 * (t1p1 + t2p1);
}

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