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181 lines
6.4 KiB
181 lines
6.4 KiB
/** |
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* Contains methods for transforming point on sphere to |
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* Cartesian coordinates using various projections. |
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* @class |
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*/ |
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jvm.Proj = { |
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degRad: 180 / Math.PI, |
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radDeg: Math.PI / 180, |
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radius: 6381372, |
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sgn: function(n){ |
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if (n > 0) { |
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return 1; |
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} else if (n < 0) { |
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return -1; |
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} else { |
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return n; |
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} |
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}, |
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/** |
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* Converts point on sphere to the Cartesian coordinates using Miller projection |
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* @param {Number} lat Latitude in degrees |
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* @param {Number} lng Longitude in degrees |
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* @param {Number} c Central meridian in degrees |
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*/ |
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mill: function(lat, lng, c){ |
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return { |
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x: this.radius * (lng - c) * this.radDeg, |
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y: - this.radius * Math.log(Math.tan((45 + 0.4 * lat) * this.radDeg)) / 0.8 |
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}; |
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}, |
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/** |
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* Inverse function of mill() |
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* Converts Cartesian coordinates to point on sphere using Miller projection |
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* @param {Number} x X of point in Cartesian system as integer |
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* @param {Number} y Y of point in Cartesian system as integer |
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* @param {Number} c Central meridian in degrees |
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*/ |
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mill_inv: function(x, y, c){ |
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return { |
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lat: (2.5 * Math.atan(Math.exp(0.8 * y / this.radius)) - 5 * Math.PI / 8) * this.degRad, |
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lng: (c * this.radDeg + x / this.radius) * this.degRad |
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}; |
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}, |
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/** |
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* Converts point on sphere to the Cartesian coordinates using Mercator projection |
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* @param {Number} lat Latitude in degrees |
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* @param {Number} lng Longitude in degrees |
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* @param {Number} c Central meridian in degrees |
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*/ |
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merc: function(lat, lng, c){ |
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return { |
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x: this.radius * (lng - c) * this.radDeg, |
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y: - this.radius * Math.log(Math.tan(Math.PI / 4 + lat * Math.PI / 360)) |
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}; |
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}, |
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/** |
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* Inverse function of merc() |
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* Converts Cartesian coordinates to point on sphere using Mercator projection |
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* @param {Number} x X of point in Cartesian system as integer |
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* @param {Number} y Y of point in Cartesian system as integer |
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* @param {Number} c Central meridian in degrees |
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*/ |
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merc_inv: function(x, y, c){ |
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return { |
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lat: (2 * Math.atan(Math.exp(y / this.radius)) - Math.PI / 2) * this.degRad, |
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lng: (c * this.radDeg + x / this.radius) * this.degRad |
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}; |
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}, |
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/** |
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* Converts point on sphere to the Cartesian coordinates using Albers Equal-Area Conic |
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* projection |
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* @see <a href="http://mathworld.wolfram.com/AlbersEqual-AreaConicProjection.html">Albers Equal-Area Conic projection</a> |
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* @param {Number} lat Latitude in degrees |
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* @param {Number} lng Longitude in degrees |
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* @param {Number} c Central meridian in degrees |
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*/ |
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aea: function(lat, lng, c){ |
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var fi0 = 0, |
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lambda0 = c * this.radDeg, |
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fi1 = 29.5 * this.radDeg, |
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fi2 = 45.5 * this.radDeg, |
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fi = lat * this.radDeg, |
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lambda = lng * this.radDeg, |
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n = (Math.sin(fi1)+Math.sin(fi2)) / 2, |
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C = Math.cos(fi1)*Math.cos(fi1)+2*n*Math.sin(fi1), |
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theta = n*(lambda-lambda0), |
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ro = Math.sqrt(C-2*n*Math.sin(fi))/n, |
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ro0 = Math.sqrt(C-2*n*Math.sin(fi0))/n; |
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return { |
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x: ro * Math.sin(theta) * this.radius, |
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y: - (ro0 - ro * Math.cos(theta)) * this.radius |
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}; |
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}, |
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/** |
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* Converts Cartesian coordinates to the point on sphere using Albers Equal-Area Conic |
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* projection |
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* @see <a href="http://mathworld.wolfram.com/AlbersEqual-AreaConicProjection.html">Albers Equal-Area Conic projection</a> |
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* @param {Number} x X of point in Cartesian system as integer |
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* @param {Number} y Y of point in Cartesian system as integer |
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* @param {Number} c Central meridian in degrees |
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*/ |
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aea_inv: function(xCoord, yCoord, c){ |
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var x = xCoord / this.radius, |
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y = yCoord / this.radius, |
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fi0 = 0, |
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lambda0 = c * this.radDeg, |
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fi1 = 29.5 * this.radDeg, |
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fi2 = 45.5 * this.radDeg, |
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n = (Math.sin(fi1)+Math.sin(fi2)) / 2, |
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C = Math.cos(fi1)*Math.cos(fi1)+2*n*Math.sin(fi1), |
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ro0 = Math.sqrt(C-2*n*Math.sin(fi0))/n, |
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ro = Math.sqrt(x*x+(ro0-y)*(ro0-y)), |
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theta = Math.atan( x / (ro0 - y) ); |
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return { |
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lat: (Math.asin((C - ro * ro * n * n) / (2 * n))) * this.degRad, |
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lng: (lambda0 + theta / n) * this.degRad |
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}; |
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}, |
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/** |
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* Converts point on sphere to the Cartesian coordinates using Lambert conformal |
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* conic projection |
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* @see <a href="http://mathworld.wolfram.com/LambertConformalConicProjection.html">Lambert Conformal Conic Projection</a> |
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* @param {Number} lat Latitude in degrees |
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* @param {Number} lng Longitude in degrees |
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* @param {Number} c Central meridian in degrees |
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*/ |
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lcc: function(lat, lng, c){ |
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var fi0 = 0, |
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lambda0 = c * this.radDeg, |
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lambda = lng * this.radDeg, |
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fi1 = 33 * this.radDeg, |
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fi2 = 45 * this.radDeg, |
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fi = lat * this.radDeg, |
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n = Math.log( Math.cos(fi1) * (1 / Math.cos(fi2)) ) / Math.log( Math.tan( Math.PI / 4 + fi2 / 2) * (1 / Math.tan( Math.PI / 4 + fi1 / 2) ) ), |
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F = ( Math.cos(fi1) * Math.pow( Math.tan( Math.PI / 4 + fi1 / 2 ), n ) ) / n, |
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ro = F * Math.pow( 1 / Math.tan( Math.PI / 4 + fi / 2 ), n ), |
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ro0 = F * Math.pow( 1 / Math.tan( Math.PI / 4 + fi0 / 2 ), n ); |
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return { |
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x: ro * Math.sin( n * (lambda - lambda0) ) * this.radius, |
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y: - (ro0 - ro * Math.cos( n * (lambda - lambda0) ) ) * this.radius |
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}; |
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}, |
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/** |
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* Converts Cartesian coordinates to the point on sphere using Lambert conformal conic |
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* projection |
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* @see <a href="http://mathworld.wolfram.com/LambertConformalConicProjection.html">Lambert Conformal Conic Projection</a> |
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* @param {Number} x X of point in Cartesian system as integer |
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* @param {Number} y Y of point in Cartesian system as integer |
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* @param {Number} c Central meridian in degrees |
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*/ |
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lcc_inv: function(xCoord, yCoord, c){ |
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var x = xCoord / this.radius, |
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y = yCoord / this.radius, |
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fi0 = 0, |
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lambda0 = c * this.radDeg, |
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fi1 = 33 * this.radDeg, |
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fi2 = 45 * this.radDeg, |
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n = Math.log( Math.cos(fi1) * (1 / Math.cos(fi2)) ) / Math.log( Math.tan( Math.PI / 4 + fi2 / 2) * (1 / Math.tan( Math.PI / 4 + fi1 / 2) ) ), |
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F = ( Math.cos(fi1) * Math.pow( Math.tan( Math.PI / 4 + fi1 / 2 ), n ) ) / n, |
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ro0 = F * Math.pow( 1 / Math.tan( Math.PI / 4 + fi0 / 2 ), n ), |
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ro = this.sgn(n) * Math.sqrt(x*x+(ro0-y)*(ro0-y)), |
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theta = Math.atan( x / (ro0 - y) ); |
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return { |
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lat: (2 * Math.atan(Math.pow(F/ro, 1/n)) - Math.PI / 2) * this.degRad, |
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lng: (lambda0 + theta / n) * this.degRad |
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}; |
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} |
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}; |