30:T46c,{ const context = DOM.context2d(width, height); context.canvas.classList.add('draggable'); const path = d3.geoPath(projection, context); let land = land50; function render(x, y) { context.fillStyle = "#ffffff"; //"#f7f8fb"; context.fillRect(0, 0, width, height); context.fillStyle = "#fffffa"; context.beginPath(), path(sphere), context.fill(); context.strokeStyle = "#cdf"; context.lineWidth = 0.75; context.beginPath(), path(graticule2), context.stroke(); context.strokeStyle = "#7be"; context.lineWidth = 0.85; context.beginPath(), path(graticule), context.stroke(); context.fillStyle = 'rgba(10, 40, 24, .88)' context.beginPath(), path(land), context.fill(); context.lineWidth = 1.0; context.strokeStyle = "#999"; context.beginPath(), path(sphere), context.stroke(); } return d3.select(context.canvas) .call(drag(projection) .on("start.render", () => {land = land110; render();}) .on("drag.render", () => render()) .on("end.render", () => {land = land50; render();})) .call(() => render()) .node(); }31:T7ea,{ const height = Math.ceil(width * Math.sqrt(3)/2) const projection = butterfly(octoformal_octant, [-1]) .center([45, 50]) .angle(-90) .rotate([20,0,0]) .fitExtent([[1 , 1], [width - 1, height - 1]], sphere) .precision(0.05); const graticule = d3.geoGraticule() .extentMinor([[-180, -90], [180, 90]]) .stepMinor([10, 10])(); const graticule2 = d3.geoGraticule() .extentMajor([[-180, -90], [180, 90]]) .extentMinor([[-180, -90], [180, 90]]) .stepMajor([90, 90]) .stepMinor([90, 1])() const graticule3 = d3.geoGraticule() .extentMajor([[-180, -85 -1e-5], [180, 85 + 1e-5]]) .extentMinor([[-180, -60 -1e-5], [180, 60 + 1e-5]]) .stepMajor([2, 90]) .stepMinor([1, 90])() const context = DOM.context2d(width, height); context.canvas.classList.add('draggable'); const path = d3.geoPath(projection, context); let land = land50; function render(x, y) { context.fillStyle = "#ffffff"; //"#f7f8fb"; context.fillRect(0, 0, width, height); context.fillStyle = "#fffffa"; context.beginPath(), path(sphere), context.fill(); context.strokeStyle = "#cfdfff"; context.lineWidth = 0.75; context.beginPath(), path(graticule2), context.stroke(); context.strokeStyle = "#cfdfff"; context.lineWidth = 0.75; context.beginPath(), path(graticule3), context.stroke(); context.strokeStyle = "#9ce"; context.lineWidth = 0.85; context.beginPath(), path(graticule), context.stroke(); context.fillStyle = 'rgba(10, 40, 24, .80)' context.beginPath(), path(land), context.fill(); context.lineWidth = 0.85; context.strokeStyle = "#999"; context.beginPath(), path(sphere), context.stroke(); } return d3.select(context.canvas) .call(drag(projection) .on("start.render", () => {land = land110; render();}) .on("drag.render", () => render()) .on("end.render", () => {land = land50; render();})) .call(() => render()) .node(); }32:T595,{ const height = Math.ceil(width / Math.sqrt(3) * 3/4) const projection = butterfly(octoformal_octant, [-1, 3, 0, 7, 0, 1, 2, 6]) .center([180, -20]) .angle(-120) .rotate([22.5,0,0]) .fitExtent([[1 , 1], [width - 1, height - 1]], sphere) .precision(0.05); const context = DOM.context2d(width, height); context.canvas.classList.add('draggable'); const path = d3.geoPath(projection, context); let land = land50; function render(x, y) { context.fillStyle = "#ffffff"; //"#f7f8fb"; context.fillRect(0, 0, width, height); context.fillStyle = "#fffffa"; context.beginPath(), path(sphere), context.fill(); context.strokeStyle = "#cdf"; context.lineWidth = 0.75; context.beginPath(), path(graticule2), context.stroke(); context.strokeStyle = "#7be"; context.lineWidth = 0.85; context.beginPath(), path(graticule), context.stroke(); context.fillStyle = 'rgba(10, 40, 24, .88)' context.beginPath(), path(land), context.fill(); context.lineWidth = 1.0; context.strokeStyle = "#999"; context.beginPath(), path(sphere), context.stroke(); } return d3.select(context.canvas) .call(drag(projection) .on("start.render", () => {land = land110; render();}) .on("drag.render", () => render()) .on("end.render", () => {land = land50; render();})) .call(() => render()) .node(); }33:T58e,{ const height = Math.ceil(width / Math.sqrt(3)) const projection = butterfly(octoformal_octant, [-1, 0, 0, 2, 5, 7, 4, 3]) .center([135, 0]) .angle(-120) .rotate([112.5,0,0]) .fitExtent([[1 , 1], [width - 1, height - 1]], sphere) .precision(0.05); const context = DOM.context2d(width, height); context.canvas.classList.add('draggable'); const path = d3.geoPath(projection, context); let land = land50; function render(x, y) { context.fillStyle = "#ffffff"; //"#f7f8fb"; context.fillRect(0, 0, width, height); context.fillStyle = "#fffffa"; context.beginPath(), path(sphere), context.fill(); context.strokeStyle = "#cdf"; context.lineWidth = 0.75; context.beginPath(), path(graticule2), context.stroke(); context.strokeStyle = "#7be"; context.lineWidth = 0.85; context.beginPath(), path(graticule), context.stroke(); context.fillStyle = 'rgba(10, 40, 24, .88)' context.beginPath(), path(land), context.fill(); context.lineWidth = 1.0; context.strokeStyle = "#999"; context.beginPath(), path(sphere), context.stroke(); } return d3.select(context.canvas) .call(drag(projection) .on("start.render", () => {land = land110; render();}) .on("drag.render", () => render()) .on("end.render", () => {land = land50; render();})) .call(() => render()) .node(); }34:T456,octoformal_octant = function octoformal_octant(face) { const {cos, sin, sign, atan2, hypot} = Math; const RADIANS = Math.PI / 180; let smz, smx, smy; { let [mlon, mlat] = d3.geoCentroid({type: "MultiPoint", coordinates: face}); mlon *= RADIANS; mlat *= RADIANS; smz = sign(sin(mlat)), smx = sign(cos(mlat)*cos(mlon)), smy = sign(cos(mlat)*sin(mlon)); } const project_octant = function (lon, lat) { let c = cos(lat), z = sin(lat), x = c*cos(lon), y = c*sin(lon); // truncate xyz coordinates falling outside this octant if (smz*z <= 0) z = smz * 0; if (smx*x <= 0) x = smx * 0; if (smy*y <= 0) y = smy * 0; return cartesian_octoformal(z, x, y); }; project_octant.invert = function (x, y) { y *= smz * smx * smy; // reflect alternate octants const w = cartesian_octoformal.invert(x, y); let z = w[0]; x = w[1]; y = w[2]; w.pop(); // reflect into appropriate output octant z *= smz; x *= smx; y *= smy; w[0] = atan2(y, x); w[1] = atan2(z, hypot(x, y)); return w; } return d3.geoProjection(project_octant); } 35:Tc0b,cartesian_octoformal = { const {sqrt, sign, round, cbrt, atan2, cos, sin} = Math; const TWOTHIRDS = 2/3; const SQRT3 = sqrt(3); const cartesian_octoformal = function cartesian_octoformal(z, x, y) { // ********** DOMAIN REDUCTION const sz = sign(z) || sign(1/z); // -0 -> -1; +0 -> +1 const sx = sign(x) || sign(1/x); const sy = sign(y) || sign(1/y); // reflect into positive octant z *= sz; x *= sx; y *= sy; // permute axes so that z >= x >= y const ygtx = y > x; if (ygtx) { const t = x; x = y; y = t; } const ygtz = y > z; if (ygtz) { const t = z; z = y; y = t; } const xgtz = x >= z; if (xgtz) { const t = z; z = x; x = t; } // stereographic projection z = 1 / (1 + z); x *= z; y *= z; // ********** MAP FUNDAMENTAL PIE SLICE const w = omap(x, y); // apply rational approximation x = w[0]; y = w[1]; // x + iy = (x + iy)^(2/3) { const r = cbrt(x*x + y*y); const angle = atan2(y, x) * TWOTHIRDS; x = r * cos(angle); y = r * sin(angle); } x -= 1; // put center of the triangle at the origin // ********** REFLECT ACCORDING TO EARLIER DOMAIN REDUCTIONS { const rot = SQRT3 * ((xgtz & ygtz) - (xgtz ^ ygtz)); const xrt3 = x * rot; const yrt3 = - y * rot; x += (xgtz | ygtz) * 0.5 * (yrt3 - 3 * x); // rotate y += (xgtz | ygtz) * 0.5 * (xrt3 - 3 * y); y *= (1 - 2 * (ygtx ^ ygtz ^ xgtz)); // flip y } y *= sz * sy * sx; // reflect odd octants w[0] = x; w[1] = y; // re-use array z return w; }; cartesian_octoformal.invert = function cartesian_octoformal(x, y) { // ********** DOMAIN REDUCTION const xgtz = (x * SQRT3 > y) | 0, ygtz = (x * SQRT3 > -y) | 0, ygtx = (y > 0) | 0; { const rot = SQRT3 * ((ygtz & ygtx) - (xgtz & (ygtx ^ 1))), xrt3 = x * rot, yrt3 = - y * rot; x += (xgtz | ygtz) * 0.5 * (yrt3 - 3 * x); // rotate y += (xgtz | ygtz) * 0.5 * (xrt3 - 3 * y); y *= (1 - 2 * (xgtz ^ ygtz ^ ygtx)); // flip y } x += 1; // move singularity to origin // ********** MAP FUNDAMENTAL TRIANGLE // x + iy = (x + iy)^(3/2), assuming y started <= 0 { const t = x, r = sqrt(x*x + y*y), x2 = sqrt(0.5 * (r + x)), // x2 + i*y2 = sqrt(x + iy) y2 = -sqrt(0.5 * (r - x)); x = x * x2 - y * y2; y = t * y2 + y * x2; } let w = oimap(x, y); // apply rational approximation x = w[0]; y = w[1]; // inverse stereographic projection let z; { const d = 1 / (0.5 + 0.5*(x*x + y*y)); z = (0.5 - 0.5*(x*x + y*y)) * d; x *= d; y *= d; } // ********** PERMUTE AXES ACCORDING TO EARLIER DOMAIN REDUCTIONS if (xgtz ^ ygtz ^ ygtx) { const t = x; x = y; y = t; } if (ygtz & ygtx) { const t = z; z = x; x = y; y = t; } else if (xgtz & (ygtx ^ 1)) { const t = z; z = y; y = x; x = t; } return [z, x, y]; } return cartesian_octoformal; }36:T761,omap = { const nodes = new Float64Array([ 4.100916630039677e-01, 1.078957919786730e-01, 1.446210672655586e-01, 1.446210672655586e-01, 1.234872078366100e-01, 0.000000000000000e+00, 3.880110914840966e-01, 2.709708654396763e-01, 3.682018550462841e-02, 3.682018550462841e-02, 3.216272607284061e-01, 3.216272607284061e-01, 3.213743061551601e-01, 0.000000000000000e+00, 2.419471033672143e-01, 2.419471033672143e-01, 3.662644231234737e-01, 3.651322036017664e-01, 2.171645054002400e-02, 0.000000000000000e+00, 4.141488339214348e-01, 1.353054022004537e-02 ]); const values = new Float64Array([ 7.128058932401936e-01, -4.139440993595627e-01, 3.970467265727428e-01, 0.000000000000000e+00, 1.695366102332019e-01, -1.695366102332019e-01, 9.026063887759997e-01, -1.582075029409894e-01, 1.010997427064757e-01, 0.000000000000000e+00, 8.804567105023327e-01, 0.000000000000000e+00, 4.415476272745202e-01, -4.415476272745202e-01, 6.636841839031136e-01, 0.000000000000000e+00, 9.991239427727002e-01, -1.516489767790573e-03, 2.981420000798688e-02, -2.981420000798688e-02, 5.885482041415332e-01, -5.509991640846738e-01 ]); const weights = new Float64Array([ -1.604010799036173e-01, 0.000000000000000e+00, 4.406932638137102e-01, -3.590142358058550e-01, -2.682474870656388e-01, 3.233841263826757e-01, -3.456311610501484e-02, 7.816337352508099e-02, 4.060412268290973e-01, -1.175759772628968e-01, -1.234674387645387e-01, 1.535188098943858e-02, 1.589851191228840e-02, 2.164613645838719e-01, -1.355901340191331e-01, -3.974410641906075e-01, 9.763735447473679e-03, 5.433180299326212e-03, -9.163015921366578e-02, 1.886629075998683e-01, -5.849732155961733e-02, 4.657443976479696e-02 ]); return reval(nodes, values, weights); }37:T62a,oimap = { const nodes = new Float64Array([ 7.121620036554932e-01, -4.147098356997996e-01, 4.026760197464420e-01, -0.000000000000000e+00, 1.676565322021649e-01, -1.676565322021649e-01, 1.111509242644564e-01, -0.000000000000000e+00, 8.173136328251600e-01, -0.000000000000000e+00, 9.219502964738188e-01, -1.283941485107439e-01, 4.152344775110253e-01, -4.152344775110253e-01, 5.865914838499277e-01, -5.529970199924502e-01, 9.936882763431703e-01, -1.088635423721026e-02 ]); const values = new Float64Array([ 4.101306536000851e-01, 1.073850072281838e-01, 1.466725531212872e-01, 1.466725531212872e-01, 1.221178836352449e-01, 0.000000000000000e+00, 4.048080174741815e-02, 4.048080174741815e-02, 2.983300885674245e-01, 2.983300885674245e-01, 3.843319729813929e-01, 2.891798550754255e-01, 3.022730272522167e-01, 0.000000000000000e+00, 4.141617509407632e-01, 1.210546059242303e-02, 3.677293652515539e-01, 3.596058723499682e-01 ]); const weights = new Float64Array([ 2.454639436696862e-01, 0.000000000000000e+00, -2.062366592193658e-01, 4.314467410113785e-01, -1.308918044184494e-01, -2.757937226001616e-01, -1.154451887326551e-01, 5.739532038113065e-02, -1.327290526250629e-01, 4.905901500513447e-01, 2.218695459619175e-01, -3.108343262633364e-01, -1.051671671849686e-01, -3.811564818299064e-01, 9.003881303601896e-02, -9.208213761650617e-02, 1.330976078818440e-01, 8.043443133079413e-02 ]); return reval(nodes, values, weights); }38:T4bf,reval = function reval(nodes, values, weights) { const n = nodes.length; return function reval(x, y) { // running total for numerator & denominator let px = 0, py = 0, qx = 0, qy = 0; for (let j = 0; j < n; j += 2) { // q += w_j / (z - z_j) // p += f_j * w_j / (z - z_j) const xj = x - nodes[j], yj = nodes[j+1] - y, wxj = weights[j], wyj = weights[j+1], fxj = values[j], fyj = values[j+1], dj = 1 / (xj*xj + yj*yj), qxj = dj * (wxj*xj - wyj*yj), qyj = dj * (wxj*yj + wyj*xj); px += fxj * qxj - fyj * qyj; py += fxj * qyj + fyj * qxj; qx += qxj, qy += qyj; } let d = 1 / (qx * qx + qy * qy), fx = (px * qx + py * qy) * d, fy = (py * qx - px * qy) * d; // Edge case where x + iy is one of the nodes; directly use value if (fx + fy !== fx + fy) { // true if x or y is NaN for (let j = 0; j < n; j += 2) { const xj = x - nodes[j], yj = nodes[j+1] - y; if ((xj === 0) & (yj === 0)) { fx = values[j]; fy = values[j+1]; break; } } } const z = new Float64Array(2); z[0] = fx; z[1] = fy; return z; }; }39:Td83,md` * * * Below is Matlab code to generate the nodes, values, and weights used in this rational approximation. (Relies on Toby Driscoll’s [SC Toolbox](http://www.math.udel.edu/~driscoll/SC/) and Nick Trefethen & al.’s [Chebfun](http://www.chebfun.org), specifically the [AAA](https://github.com/chebfun/chebfun/blob/master/aaa.m) tool based on Nakatsukasa, Sète, & Trefethen (2018) [“The AAA Algorithm for Rational Approximation”](http://people.maths.ox.ac.uk/trefethen/AAAfinal.pdf). Also cf. Gopal & Trefethen (2019) [“Representation of Conformal Maps by Rational Functions”](https://arxiv.org/pdf/1804.08127.pdf).) * * * \`\`\`matlab % rational quadratic circle-arc interpolant, a function f % such that f(0) = a, f(1/2) = m, f(1) = b rerp = @(a, m, b) ... (@(z) ((b-m).*a.*(1-z) + (m-a).*b.*z) ... ./ ((b-m).*(1-z) + (m-a).*z)); lerp = @(a, b) ... (@(z) a.*(1-z) + b.*z); % midpoint between two points on the sphere, represented stereographically midpoint = @(w, z) ... (z + w + z.*w.*conj(z + w)) ./ ... ( abs(1 + z.*conj(w)) .* sqrt((1 + z.*conj(z)).* (1 + w.*conj(w))) + ... 1 - z .* conj(z) .* w .* conj(w)); spoke3 = rerp(0, ... midpoint(0, sqrt(2) / (1 + sqrt(3))), ... sqrt(2) / (1 + sqrt(3))); spoke2 = rerp(0, ... midpoint(0, 1 / (1 + sqrt(2))), ... 1 / (1 + sqrt(2))); arc23 = rerp( ... 1 / (1 + sqrt(2)), ... midpoint(1 / (1 + sqrt(2)), (1 + i) / (1 + sqrt(3))), ... (1 + i) / (1 + sqrt(3))); tri = hplmap( ... [-1 1 Inf], ... [1/3 1/2 1/6], ... scmapopt('Tolerance', 1e-16)); trimap = @(z) (tri(z) - tri(Inf)) ./ (tri(7) - tri(Inf)); sector_to_halfplane = @(z) -cosh(4 * log(z)); nf = 64; fz = chebpts(2*nf + 1); fz = fz(nf+2:end-1); % take points from 0 .. 1 fz = fz .* (sqrt(2) / (1 + sqrt(3))); fz = - sector_to_halfplane(fz); fz = real(trimap(fz)) .^ (3/2); fz = [-1; -flipud(fz); 0; fz; 1]; f = simplify(chebfun(fz, [ ... -sqrt(2) / (1 + sqrt(3)), ... sqrt(2) / (1 + sqrt(3))])); ng = 64; gz = chebpts(2*ng + 1); gz = gz(ng+2:end-1); % take points from 0 .. 1 gz = gz .* (1 / (1 + sqrt(2))); gz = sector_to_halfplane(gz); gz = real(trimap(gz) .^ (3/2)); gz = [-3^(3/4)/4; -flipud(gz); 0; gz; 3^(3/4)/4]; g = simplify(chebfun(gz, [ ... -1/(1 + sqrt(2)), ... 1/(1 + sqrt(2))])); nh = 64; hz = chebpts(2*nh + 1, [0 1]); hz = hz(2:end-1); hz = arc23(hz); hz = sector_to_halfplane(hz); hz = trimap(hz); hz = [((3 - sqrt(3)*1i)/4); hz; 1]; h = simplify(chebfun(4 * real(hz) - 3, [0 1])); % points to use per side n = 1024; p = chebpts(n+1, [0 1]); p = p(2:end-1); % input points around the boundary of the half-quadrant, % spaced to be packed closer near the corner with the % square root singularity zin = [ ... 0; ... spoke2(p.^2); ... 1/(1+sqrt(2)); ... arc23(p); ... (1+1i)/(1+sqrt(3)); ... ((1+1i)/sqrt(2)) * flipud(spoke3(p.^2)) ... ]; shortside = lerp(3/4 - 1i*sqrt(3)/4, 1); zout = [ ... 0; ... (1-1i) * g(spoke2(p.^2)); ... (1-1i) * 3^(3/4)/4; ... shortside(h(p)) .^ (3/2); ... 1; ... flipud(f(spoke3(p.^2))) ... ]; format longE; [r, rpol, ~, ~, rz, rf, rw] = aaa(zout(1:2:end), zin(1:2:end), 'tol', 3e-15) [s, spol, ~, ~, sz, sf, sw] = aaa(zin, zout, 'tol', 4e-15) % these approximations are pretty good! norm(zout - r(zin), inf) norm(s(zout) - zin, inf) figure; daspect([1 1 1]); hold on; plot(zin); plot(rz, 'ko'); plot(rpol, 'ro'); figure; daspect([1 1 1]); hold on; plot(zout); plot(sz, 'ko'); plot(spol, 'ro'); \`\`\` `3a:[] 2e:{"title":"Conformal octahedron","cells":[{"id":0,"value":"Title = md`\n# Conformal octahedron`","pinned":false,"hidden":false,"mode":"ojs"},{"id":56,"value":"$30","pinned":false,"hidden":false,"mode":"ojs"},{"id":2028,"value":"md`\n\nMake sure you try dragging the map above.\n\n* * *\n\nOscar Sherman Adams, a senior geodetic computer for the U.S. Coast and Geodetic Survey, first constructed a conformal projection from the sphere to the octahedron circa 1925, under contract from Bernard Joseph Stanislaus Cahill. For historical details see [Gene Keyes’s website](http://www.genekeyes.com/CAHILL-VARIANTS/Cahill-Conformal.html).\n\nDecades later, Laurence Patrick Lee, chief geodetic computer for the the New Zealand Lands and Survey Department, described this and similar projections in a 1976 monograph, [*Conformal Projections Based on Elliptic Functions*](https://archive.org/details/conformalproject0000leel).\n\n* * *\n\nThanks to [Philippe Rivière](../@fil) for significant help understanding [d3-geo-polygon](https://github.com/d3/d3-geo-polygon).\n\n* * *\n\n`","pinned":false,"hidden":false,"mode":"ojs"},{"id":2157,"value":"md`\nHere’s a single octant, plotted with a 1° graticule near the equator and coarser longitudes toward the poles. Again, please try dragging the map:\n`","pinned":false,"hidden":false,"mode":"ojs"},{"id":2151,"value":"$31","pinned":false,"hidden":false,"mode":"ojs"},{"id":2229,"value":"md`\n@Fil also made a spinoff notebook including Cahill’s “M” and “Zigzag” arrangements, in addition to the butterfly map. We can reproduce Cahill’s maps with their characteristic 22°30′ (1/16 [turns][]) longitude rotation.\n\n [turns]: https://en.wikipedia.org/wiki/Turn_(angle)\n\n[

](http://www.genekeyes.com/CAHILL-VARIANTS/Cahill-Conformal.html)\n`","pinned":false,"hidden":false,"mode":"ojs"},{"id":2106,"value":"$32","pinned":false,"hidden":false,"mode":"ojs"},{"id":2223,"value":"md`\n[

](http://www.genekeyes.com/CAHILL-VARIANTS/Cahill-Conformal.html)\n`","pinned":false,"hidden":false,"mode":"ojs"},{"id":2197,"value":"$33","pinned":false,"hidden":false,"mode":"ojs"},{"id":1433,"value":"md`---`","pinned":false,"hidden":false,"mode":"ojs"},{"id":106,"value":"projection = {\n const {cos, sin, sign} = Math;\n const RADIANS = Math.PI / 180;\n \n return butterfly(octoformal_octant)\n .angle(-120)\n .rotate([20,0,0])\n .fitExtent([[1 , 1], [width - 1, height - 1]], sphere)\n .precision(0.05);\n}","pinned":true,"hidden":false,"mode":"ojs"},{"id":2267,"value":"octahedron = [0,1,2,3,4,5,6,7].map((i) => {\n const negz = i >> 2;\n const negx = (i >> 1) & 1;\n const negy = i & 1\n const zvertex = [[0, 90], [0, -90]][negz];\n const xvertex = [[0, 0], [180, 0]][negx];\n const yvertex = [[90, 0], [-90, 0]][negy];\n if (negz ^ negx ^ negy)\n return [zvertex, xvertex, yvertex];\n return [zvertex, yvertex, xvertex]\n})","pinned":true,"hidden":false,"mode":"ojs"},{"id":2062,"value":"octahedronExplicit = {\n var vertices = [\n [0, 90], [0, -90], // z+, z-\n [0, 0], [180, 0], // x+, x-\n [90, 0], [-90, 0] // y+, y-\n ];\n\n \n return [ // z x y\n [0, 4, 2], // + + +\n [0, 2, 5], // + + -\n [0, 3, 4], // + - +\n [0, 5, 3], // + - -\n [1, 2, 4], // - + +\n [1, 5, 2], // - + -\n [1, 4, 3], // - - +\n [1, 3, 5] // - - - \n ].map((face) => face.map((i) => vertices[i]));\n}","pinned":false,"hidden":false,"mode":"ojs"},{"id":2060,"value":"butterfly = function(faceProjection, layout) {\n const TWO_OVER_PI = 2/Math.PI;\n const faces = octahedron.map((face) => ({\n 'face': face,\n 'project': faceProjection(face)\n }));\n\n layout = layout || [-1, 0, 0, 2, 0, 1, 2, 3];\n\n layout.forEach((d, i) => {\n var node = faces[d];\n node && (node.children || (node.children = [])).push(faces[i]);\n });\n \n const pickFace = function(longitude, latitude) {\n longitude *= TWO_OVER_PI;\n const zneg = latitude < 0,\n yneg = longitude < 0,\n xneg = longitude * longitude > 1;\n return faces[(zneg << 2) + (xneg << 1) + yneg];\n }\n \n return d3.geoPolyhedral(faces[0], pickFace)\n .angle(-30)\n .scale(100)\n .center([90, 45]);\n}","pinned":true,"hidden":false,"mode":"ojs"},{"id":1855,"value":"$34","pinned":true,"hidden":false,"mode":"ojs"},{"id":1691,"value":"$35","pinned":true,"hidden":false,"mode":"ojs"},{"id":1694,"value":"$36","pinned":true,"hidden":false,"mode":"ojs"},{"id":1700,"value":"$37","pinned":true,"hidden":false,"mode":"ojs"},{"id":1011,"value":"$38","pinned":true,"hidden":false,"mode":"ojs"},{"id":2055,"value":"$39","pinned":false,"hidden":false,"mode":"ojs"},{"id":62,"value":"md`---`","pinned":false,"hidden":false,"mode":"ojs"},{"id":23,"value":"height = Math.ceil(width / Math.sqrt(3))","pinned":false,"hidden":false,"mode":"ojs"},{"id":21,"value":"sphere = ({ type: \"Sphere\" })","pinned":false,"hidden":false,"mode":"ojs"},{"id":18,"value":"graticule = d3.geoGraticule()\n .extentMinor([[-180, -85], [180, 85]])\n .stepMinor([30, 30])();","pinned":false,"hidden":false,"mode":"ojs"},{"id":969,"value":"graticule2 = d3.geoGraticule()\n .extentMajor([[-180, -85 -1e-5], [180, 85 + 1e-5]])\n .extentMinor([[-180, -80], [180, 80]])\n .stepMajor([10, 5])\n .stepMinor([5, 5])()","pinned":false,"hidden":false,"mode":"ojs"},{"id":15,"value":"land50 = topojson.feature(world50, world50.objects.land)","pinned":false,"hidden":false,"mode":"ojs"},{"id":1542,"value":"land110 = topojson.feature(world110, world110.objects.land)","pinned":false,"hidden":false,"mode":"ojs"},{"id":1657,"value":"world50 = fetch(\"https://cdn.jsdelivr.net/npm/world-atlas@2/land-50m.json\").then(response => response.json())","pinned":false,"hidden":false,"mode":"ojs"},{"id":1535,"value":"world110 = fetch(\"https://cdn.jsdelivr.net/npm/world-atlas@2/land-110m.json\").then(response => response.json())","pinned":false,"hidden":false,"mode":"ojs"},{"id":2,"value":"topojson = require(\"topojson-client@3\")","pinned":false,"hidden":false,"mode":"ojs"},{"id":7,"value":"d3 = require(\"d3-geo@1\", \"d3-selection@1\", \"d3-drag@1\", \"d3-geo-projection@2\", \"d3-geo-polygon@1\")","pinned":false,"hidden":false,"mode":"ojs"},{"id":556,"value":"function drag(projection) {\n let v0, q0, r0;\n \n function dragstarted() {\n v0 = versor.cartesian(projection.invert([d3.event.x, d3.event.y]));\n q0 = versor(r0 = projection.rotate());\n }\n \n function dragged() {\n const v1 = versor.cartesian(projection.rotate(r0).invert([d3.event.x, d3.event.y]));\n const q1 = versor.multiply(q0, versor.delta(v0, v1));\n projection.rotate(versor.rotation(q1));\n }\n \n return d3.drag()\n .on(\"start\", dragstarted)\n .on(\"drag\", dragged);\n}","pinned":false,"hidden":false,"mode":"ojs"},{"id":558,"value":"versor = require(\"versor@0.0.3\")","pinned":false,"hidden":false,"mode":"ojs"},{"id":1584,"value":"html`\n`","pinned":false,"hidden":false,"mode":"ojs"}],"files":"$W3a","stdlib":"1","titling":"auto"}