/*
**--------------------------------------------------------------
** Function name: Etrs2Rdnap
** Description: convert ETRS89 coordinates to RD and NAP coordinates
**
** Parameter Type In/Out Req/Opt Default
** phi double in req none
** lambda double in req none
** h double in req none
** xRd double out - none
** yRd double out - none
** nap double out - none
**
** Additional explanation of the meaning of parameters
** phi, lambda, h input ETRS89 coordinates
** xRd, yRd, nap output RD and NAP coordinates
**
** Return value: (besides the standard return values)
** none
**--------------------------------------------------------------
*/
/// <summary>
/// Converts ETRS89 (EPSG:4258) coordinates to RD_New (EPSG:28992) coordinates (including a vertical NAP coordinate).
/// </summary>
/// <param name="etrs">a <seealso cref="Geographic" /> object containing ETRS89 coordinates.</param>
/// <returns>a <seealso cref="Cartesian" /> object containing RD coordinates.</returns>
public static Cartesian Etrs2Rdnap(Geographic etrs)
{
var rd = Etrs2Rd(etrs);
var betterH = Etrs2Nap(etrs);
if (betterH.HasValue)
{
return(rd.WithZ(betterH.Value));
}
return(rd);
}
/*
**--------------------------------------------------------------
** Function name: Etrs2Nap
** Description: convert ellipsoidal ETRS89 height to NAP height
**
** Parameter Type In/Out Req/Opt Default
** phi double in req none
** lambda double in req none
** h double in req none
** nap double out - none
**
** Additional explanation of the meaning of parameters
** phi, lambda, h input ETRS89 coordinates
** nap output NAP height
**
** Return value: (besides the standard return values) none
** on error (outside geoid grid) nap is not computed here
** instead in Etrs2RdNap nap=hBessel
**--------------------------------------------------------------
*/
/// <summary>
/// Converts AN ellipsoidal ETRS89 (EPSG:28992) height to an NAP (EPSG:4258) height.
/// </summary>
/// <param name="etrs">a <seealso cref="Geographic" /> object containing ETRS89 coordinates.</param>
/// <returns>a nullable double containing the NAP height (if all went well).</returns>
public static double?Etrs2Nap(Geographic etrs)
{
/*
**--------------------------------------------------------------
** Explanation of the meaning of variables:
** n geoid height
** on error (outside geoid grid) nap is not computed
** instead in etrs2rdnap nap=hBessel
**--------------------------------------------------------------
*/
var n = GrdFile.GridFileGeoid.InterpolateGrid(etrs.Lambda, etrs.Phi);
if (n.HasValue)
{
return(etrs.H - n.Value + 0.0088);
}
return(null);
}
/*
**--------------------------------------------------------------
** Function name: RdProjection
** Description: stereographic double projection
**
** Parameter Type In/Out Req/Opt Default
** phi double cartesian req none
** lambda double cartesian req none
** xRd double out - none
** yRd double out - none
**
** Additional explanation of the meaning of parameters
** phi input Bessel latitude cartesian degrees
** lambda input Bessel longitude cartesian degrees
** xRd, yRd output RD coordinates
**
** Return value: (besides the standard return values)
** none
**--------------------------------------------------------------
*/
/// <summary>
/// Projects Geographic coordinates (EPSG:4258) to RD_New coordinates(EPSG:28992).
/// </summary>
/// <param name="geographic">The geographic coordinates container.</param>
/// <returns>Cartesian object containing the converted coordinates.</returns>
internal static Cartesian RdProjection(Geographic geographic)
{
/*
**--------------------------------------------------------------
** Source: G. Bakker, J.C. de Munck and G.L. Strang van Hees, "Radio Positioning at Sea". Delft University of Technology, 1995.
** G. Strang van Hees, "Globale en lokale geodetische systemen". Delft: Nederlandse Commissie voor Geodesie (NCG), 1997.
**--------------------------------------------------------------
*/
/*
**--------------------------------------------------------------
** Explanation of the meaning of constants:
** f flattening of the ellipsoid
** ee first eccentricity squared (e squared cartesian some notations)
** e first eccentricity
** eea second eccentricity squared (e' squared cartesian some notations)
**
** phiAmersfoortSphere latitude of projection base point Amersfoort on sphere cartesian degrees
** lambdaAmersfoortSphere longitude of projection base point Amersfoort on sphere cartesian degrees
**
** r1 first (North South) principal radius of curvature cartesian Amersfoort (M cartesian some notations)
** r2 second (East West) principal radius of curvature cartesian Amersfoort (N cartesian some notations)
** rSphere radius of sphere
**
** n constant of Gaussian projection n = 1.000475...
** qAmersfoort isometric latitude of Amersfoort on ellipsiod
** wAmersfoort isometric latitude of Amersfoort on sphere
** m constant of Gaussian projection m = 0.003773... (also named cartesian cartesian some notations)
**--------------------------------------------------------------
*/
var f = 1 / InvFBessel;
var ee = f * (2 - f);
var e = Math.Sqrt(ee);
var eea = ee / (1.0 - ee);
var phiAmersfoortSphere = DegAtan(DegTan(PhiAmersfoortBessel) / Math.Sqrt(1 + eea * Math.Pow(DegCos(PhiAmersfoortBessel), 2)));
var lambdaAmersfoortSphere = LambdaAmersfoortBessel;
var r1 = ABessel * (1 - ee) / Math.Pow(Math.Sqrt(1 - ee * Math.Pow(DegSin(PhiAmersfoortBessel), 2)), 3);
var r2 = ABessel / Math.Sqrt(1.0 - ee * Math.Pow(DegSin(PhiAmersfoortBessel), 2));
var rSphere = Math.Sqrt(r1 * r2);
var n = Math.Sqrt(1 + eea * Math.Pow(DegCos(PhiAmersfoortBessel), 4));
var qAmersfoort = Atanh(DegSin(PhiAmersfoortBessel)) - e * Atanh(e * DegSin(PhiAmersfoortBessel));
var wAmersfoort = Math.Log(DegTan(45 + 0.5 * phiAmersfoortSphere));
var m = wAmersfoort - n * qAmersfoort;
/*
**--------------------------------------------------------------
** Explanation of the meaning of variables:
** q isometric latitude on ellipsoid
** w isometric latitude on sphere
** phiSphere latitude on sphere cartesian degrees
** deltaLambdaSphere difference cartesian longitude on sphere with Amersfoort cartesian degrees
** psi distance angle from Amersfoort on sphere
** alpha azimuth from Amersfoort
** r distance from Amersfoort cartesian projection plane
**--------------------------------------------------------------
*/
var q = Atanh(DegSin(geographic.Phi)) - e * Atanh(e * DegSin(geographic.Phi));
var w = n * q + m;
var phiSphere = 2 * DegAtan(Math.Exp(w)) - 90;
var deltaLambdaSphere = n * (geographic.Lambda - lambdaAmersfoortSphere);
var sinHalfPsiSquared = Math.Pow(DegSin(0.5 * (phiSphere - phiAmersfoortSphere)), 2) + Math.Pow(DegSin(0.5 * deltaLambdaSphere), 2) * DegCos(phiSphere) * DegCos(phiAmersfoortSphere);
var sinHalfPsi = Math.Sqrt(sinHalfPsiSquared);
var cosHalfPsi = Math.Sqrt(1 - sinHalfPsiSquared);
var tanHalfPsi = sinHalfPsi / cosHalfPsi;
var sinPsi = 2 * sinHalfPsi * cosHalfPsi;
var cosPsi = 1 - 2 * sinHalfPsiSquared;
var sinAlpha = DegSin(deltaLambdaSphere) * (DegCos(phiSphere) / sinPsi);
var cosAlpha = (DegSin(phiSphere) - DegSin(phiAmersfoortSphere) * cosPsi) / (DegCos(phiAmersfoortSphere) * sinPsi);
var r = 2 * ScaleRd * rSphere * tanHalfPsi;
var xRd = r * sinAlpha + XAmersfoortRd;
var yRd = r * cosAlpha + YAmersfoortRd;
return(new Cartesian(xRd, yRd));
}
