Buckminster Fuller’s triangle transformation / Fil

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Buckminster Fuller’s triangle transformation

Experimental two world projections Tobler’s hyperelliptical projection (1973)Jacques Bertin’s projection (1953)A map without Antarctica (Bertin1953 projection)Square Root Azimuthal projection The Log-Azimuthal projection Peirce Quincuncial Projection, centered on the South Pole Translucent Earth (Satellite projection)Lee’s conformal projection in a tetrahedron Airocean projection Cubic projections Cox conformal projection in a triangle Icosahedral projections Dodecahedral projection The Cahill-Keyes projection (1975)Polyhedral projections with d3-geo-polygon Wagner customizable projection Parametrized Equal Earth Projection The Hufnagel projection system Tissot's indicatrix An equal-area projection for the cubic Earth Base map

* Buckminster Fuller’s spherical triangle transformation procedure

* Based on Robert W. Gray’s formulae published in “Exact Transformation Equations

* For Fuller's World Map,” _Cartographica_, 32(3): 17-25 (1995).

* Implemented for D3.js by Philippe Rivière, 2018 (https://visionscarto.net/)

* To the extent possible under law, Philippe Rivière has waived all copyright

* and related or neighboring rights to this implementation. (Public Domain.)

function GrayFullerRaw() {

// standard symbols

var sqrt = Math.sqrt,

cos = Math.cos,

sin = Math.sin,

atan2 = Math.atan2,

SQRT_3 = sqrt(3);

// Gray’s constants

var Z = sqrt(5 + 2 * sqrt(5)) / sqrt(15),

el = sqrt(8) / sqrt(5 + sqrt(5)),

dve = sqrt(3 + sqrt(5)) / sqrt(5 + sqrt(5));

return function (lambda, phi) {

var cosPhi = cos(phi),

s = Z / (cosPhi * cos(lambda)),

x = cosPhi * sin(lambda) * s,

y = sin(phi) * s,

a1p = atan2((2 * y) / SQRT_3 + el / 3 - el / 2, dve),

a2p = atan2(x - y / SQRT_3 + el / 3 - el / 2, dve),

a3p = atan2(el / 3 - x - y / SQRT_3 - el / 2, dve);

return [SQRT_3 * (a2p - a3p), 2 * a1p - a2p - a3p];

};

}

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