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Performance minutiae #94

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Performance minutiae #94

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5477111
Add upstream source for ellipsoidal algorithms
James-E-A Jan 26, 2021
b19b59b
Refactor eq'n (6) to take full advantage of its performant design
James-E-A Jan 26, 2021
c844832
Fix embarassing typo
James-E-A Jan 26, 2021
c4a3012
Apply performance changes to the inverse formula, too
James-E-A Feb 11, 2021
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9 changes: 5 additions & 4 deletions latlon-ellipsoidal-vincenty.js
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Original file line number Diff line number Diff line change
@@ -1,6 +1,7 @@
/* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
/* Vincenty Direct and Inverse Solution of Geodesics on the Ellipsoid (c) Chris Veness 2002-2020 */
/* MIT Licence */
/* www.ngs.noaa.gov/PUBS_LIB/inverse.pdf */
/* www.movable-type.co.uk/scripts/latlong-ellipsoidal-vincenty.html */
/* www.movable-type.co.uk/scripts/geodesy-library.html#latlon-ellipsoidal-vincenty */
/* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
Expand Down Expand Up @@ -207,8 +208,8 @@ class LatLonEllipsoidal_Vincenty extends LatLonEllipsoidal {
const sinα = cosU1 * sinα1; // α = azimuth of the geodesic at the equator
const cosSqα = 1 - sinα*sinα;
const uSq = cosSqα * (a*a - b*b) / (b*b);
const A = 1 + uSq/16384*(4096+uSq*(-768+uSq*(320-175*uSq)));
const B = uSq/1024 * (256+uSq*(-128+uSq*(74-47*uSq)));
const A = (((uSq*-175 + 320)*uSq - 768)*uSq + 4096)*uSq/16384 + 1;
const B = (((uSq*-47 + 74)*uSq - 128)*uSq + 256)*uSq/1024;

let σ = s / (b*A), sinσ = null, cosσ = null, Δσ = null; // σ = angular distance P₁ P₂ on the sphere
let cos2σₘ = null; // σₘ = angular distance on the sphere from the equator to the midpoint of the line
Expand Down Expand Up @@ -301,8 +302,8 @@ class LatLonEllipsoidal_Vincenty extends LatLonEllipsoidal {
if (iterations >= 1000) throw new EvalError('Vincenty formula failed to converge');

const uSq = cosSqα * (a*a - b*b) / (b*b);
const A = 1 + uSq/16384*(4096+uSq*(-768+uSq*(320-175*uSq)));
const B = uSq/1024 * (256+uSq*(-128+uSq*(74-47*uSq)));
const A = (((uSq*-175 + 320)*uSq - 768)*uSq + 4096)*uSq/16384 + 1;
const B = (((uSq*-47 + 74)*uSq - 128)*uSq + 256)*uSq/1024;
const Δσ = B*sinσ*(cos2σₘ+B/4*(cosσ*(-1+2*cos2σₘ*cos2σₘ)-
B/6*cos2σₘ*(-3+4*sinσ*sinσ)*(-3+4*cos2σₘ*cos2σₘ)));

Expand Down