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Last active Jan 16, 2020
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Solar Analemmas Anywhere

Hourly solar analemmas (ignoring daylight savings time) as seen from anywhere in the world in 2014.

.sun path {
fill: none;
stroke-linecap: round;
stroke-linejoin: round;
}
.sun text {
font: 10px sans-serif;
}
.sun .horizon {
stroke: #000;
stroke-width: 1.5px;
}
.sun .graticule {
stroke: #000;
stroke-opacity: .15;
}
.sun .analemmas path {
stroke: #f00;
stroke-width: 2px;
}
.sun .ticks line {
stroke: #000;
}
.sun .ticks text {
text-anchor: middle;
}
.sun .ticks--azimuth text:nth-of-type(9n + 1) {
font-weight: bold;
font-size: 14px;
}
var π = Math.PI,
τ = 2 * π,
radians = π / 180,
degrees = 180 / π;
var width = 960,
height = 960,
scale = width * .45;
var solar = solarCalculator([-122, 37]),
start = d3.time.year.utc.floor(new Date),
end = d3.time.year.utc.offset(start, 1);
var projection = d3.geo.projection(flippedStereographic)
.scale(scale)
.clipAngle(130)
.rotate([0, -90])
.translate([width / 2 + .5, height / 2 + .5])
.precision(.1);
var path = d3.geo.path()
.projection(projection);
var svg = d3.select('body').append('svg')
.attr('class', 'sun')
.attr('width', width)
.attr('height', height);
svg.append('path')
.datum(d3.geo.circle().origin([0, 90]).angle(90))
.attr('class', 'horizon')
.attr('d', path);
svg.append('path')
.datum(d3.geo.graticule())
.attr('class', 'graticule')
.attr('d', path);
var ticksAzimuth = svg.append('g')
.attr('class', 'ticks ticks--azimuth');
ticksAzimuth.selectAll('line')
.data(d3.range(360))
.enter().append('line')
.each(function(d) {
var p0 = projection([d, 0]),
p1 = projection([d, d % 10 ? -1 : -2]);
d3.select(this)
.attr('x1', p0[0])
.attr('y1', p0[1])
.attr('x2', p1[0])
.attr('y2', p1[1]);
});
ticksAzimuth.selectAll('text')
.data(d3.range(0, 360, 10))
.enter().append('text')
.each(function(d) {
var p = projection([d, -4]);
d3.select(this)
.attr('x', p[0])
.attr('y', p[1]);
})
.attr('dy', '.35em')
.text(function(d) {
return d === 0 ? 'N' :
d === 90 ? 'E' :
d === 180 ? 'S' :
d === 270 ? 'W' :
d + '°';
});
svg.append('g')
.attr('class', 'ticks ticks--elevation')
.selectAll('text')
.data(d3.range(10, 91, 10))
.enter().append('text')
.each(function(d) {
var p = projection([0, d]);
d3.select(this)
.attr('x', p[0])
.attr('y', p[1]);
})
.attr('dy', '.35em')
.text(function(d) { return d + '°'; });
function analemmaForHour(h) {
function pos(d) {
return solar.position(d3.time.hour.utc.offset(d, h));
}
return {
type: 'LineString',
coordinates: d3.time.days.utc(start, end).map(pos)
};
}
var analemmas = svg.insert('g', '.sphere')
.attr('class', 'analemmas')
.selectAll('path')
.data(d3.range(24))
.enter().append('path')
.datum(analemmaForHour)
.attr('d', path);
function setLocation(lat, lng) {
solar = solarCalculator([lng, lat]);
analemmas.remove();
analemmas = svg.select('g.analemmas')
.selectAll('path')
.data(d3.range(24))
.enter().append('path')
.datum(analemmaForHour)
.attr('d', path);
}
function flippedStereographic(λ, φ) {
var cosλ = Math.cos(λ),
cosφ = Math.cos(φ),
k = 1 / (1 + cosλ * cosφ);
return [
k * cosφ * Math.sin(λ),
-k * Math.sin(φ)
];
}
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<!DOCTYPE html>
<meta charset="utf-8">
<title>Solar Analemmas</title>
<style>
@import url(maps.css);
@import url(world.css);
@import url(analemmas.css);
</style>
<div id="map">
<h1>Solar Analemmas</h1>
</div>
<p class="caption">Drag to rotate the world. Scroll or pinch to zoom.</p>
<script src="d3.min.js"></script>
<script src="d3.geo.projection.min.js"></script>
<script src="topojson.min.js"></script>
<script src="d3.geo.zoom.min.js"></script>
<script src="nav.js"></script>
<script src="solar-calculator.js"></script>
<script src="analemmas.js"></script>
body {
margin-top: 0;
font-family: Georgia, serif;
text-align: center;
background: #fff;
}
p.caption {
text-align: center;
font-size: small;
font-style: italic;
width: 400px;
margin: 0 auto;
}
p, li {
line-height: 1.5em;
}
h1, h2, h3 {
font-weight: 300;
}
h1 {
font-size: 2.5em;
}
canvas {
cursor: move;
}
.wrapper {
width: 600px;
margin: 1em auto;
text-align: left;
}
.center {
text-align: center;
}
.clear {
clear: both;
}
if (frameElement) frameElement.style.height = '1600px';
var degrees = 180 / Math.PI,
w_width = 960,
w_height = 960,
loader = d3.dispatch('world'), id = -1;
d3.selectAll('#map')
.data([
orthographicProjection(w_width, w_height)
.scale(245)
.translate([w_width / 2, w_height * .56])
])
.append('svg')
.attr('class', 'world')
.attr('width', w_width)
.attr('height', w_height)
.each(function(projection) {
var path = d3.geo.path().projection(projection),
svg = d3.select(this).call(drawMap, path, true);
svg.selectAll('.foreground')
.call(d3.geo.zoom().projection(projection)
.scaleExtent([projection.scale() * .7, projection.scale() * 10])
.on('zoom.redraw', function() {
if (d3.event.sourceEvent.preventDefault)
d3.event.sourceEvent.preventDefault();
svg.selectAll('path').attr('d', path);
}));
loader.on('world.' + ++id, function() {
svg.selectAll('path').attr('d', path);
});
});
d3.json('world-110m.json', function(error, world) {
d3.selectAll('svg').insert('path', '.foreground')
.datum(topojson.feature(world, world.objects.land))
.attr('class', 'land');
d3.selectAll('svg').insert('path', '.foreground')
.datum(topojson.mesh(world, world.objects.countries))
.attr('class', 'mesh');
loader.world();
});
function drawMap(svg, path, mousePoint) {
var projection = path.projection();
svg.append('path')
.datum(d3.geo.graticule())
.attr('class', 'graticule')
.attr('d', path);
svg.append('path')
.datum({ type: 'Sphere' })
.attr('class', 'foreground')
.attr('d', path)
.on('mousedown.grab', function() {
var point;
if (mousePoint)
point = svg.insert('path', '.foreground')
.datum({
type: 'Point',
coordinates: projection.invert(d3.mouse(this))
})
.attr('class', 'point')
.attr('d', path);
var path = d3.select(this).classed('zooming', true),
w = d3.select(window).on('mouseup.grab', function() {
path.classed('zooming', false);
w.on('mouseup.grab', null);
if (mousePoint) point.remove();
});
})
.on('mousemove', function logCoords() {
var at = toLatLng.apply(this, projection.invert(d3.mouse(this)));
if (at) {
console.log(at.lat, at.lng);
setLocation(at.lat, at.lng);
}
});
}
function toLatLng(lng, lat) {
if (isNaN(lng) || isNaN(lat)) return null;
while (lng < 360) lng += 360;
lng = lng % 360;
if (lng > 180) lng -= 360;
return { lat: lat, lng: lng };
}
function orthographicProjection(width, height) {
return d3.geo.orthographic()
.precision(.5)
.clipAngle(90)
.clipExtent([[-1, -1], [width + 1, height + 1]])
.translate([width / 2, height / 2])
.scale(width / 2 - 10)
.rotate([0, -30]);
}
// Equations based on NOAA’s Solar Calculator; all angles in radians.
// http://www.esrl.noaa.gov/gmd/grad/solcalc/
(function() {
var J2000 = Date.UTC(2000, 0, 1, 12),
π = Math.PI,
τ = 2 * π,
radians = π / 180,
degrees = 180 / π;
solarCalculator = function(location) {
var longitude = location[0],
minutesOffset = 720 - longitude * 4,
λ = location[0] * radians,
φ = location[1] * radians,
cosφ = Math.cos(φ),
sinφ = Math.sin(φ);
function position(date) {
var centuries = (date - J2000) / (864e5 * 36525),
θ = solarDeclination(centuries),
cosθ = Math.cos(θ),
sinθ = Math.sin(θ),
azimuth = ((date - d3.time.day.utc.floor(date)) / 864e5 * τ + equationOfTime(centuries) + λ) % τ - π,
zenith = Math.acos(Math.max(-1, Math.min(1, sinφ * sinθ + cosφ * cosθ * Math.cos(azimuth)))),
azimuthDenominator = cosφ * Math.sin(zenith);
if (azimuth < -π) azimuth += τ;
if (Math.abs(azimuthDenominator) > 1e-6) azimuth = (azimuth > 0 ? -1 : 1) * (π - Math.acos(Math.max(-1, Math.min(1, (sinφ * Math.cos(zenith) - sinθ) / azimuthDenominator))));
if (azimuth < 0) azimuth += τ;
// Correct for atmospheric refraction.
var atmosphere = 90 - zenith * degrees;
if (atmosphere <= 85) {
var te = Math.tan(atmosphere * radians);
zenith -= (atmosphere > 5 ? 58.1 / te - .07 / (te * te * te) + .000086 / (te * te * te * te * te)
: atmosphere > -.575 ? 1735 + atmosphere * (-518.2 + atmosphere * (103.4 + atmosphere * (-12.79 + atmosphere * .711)))
: -20.774 / te) / 3600 * radians;
}
// Note: if zenith > 108°, it’s dark.
return [azimuth * degrees, 90 - zenith * degrees];
}
function noon(date) {
var centuries = (d3.time.day.utc.floor(date) - J2000) / (864e5 * 36525),
minutes = (minutesOffset - (equationOfTime(centuries + (minutesOffset - (equationOfTime(centuries - longitude / (360 * 365.25 * 100)) * degrees * 4)) / (1440 * 365.25 * 100)) * degrees * 4) - date.getTimezoneOffset()) % 1440;
if (minutes < 0) minutes += 1440;
return new Date(+d3.time.day.floor(date) + minutes * 60 * 1000);
}
return {
position: position,
noon: noon
};
};
function equationOfTime(centuries) {
var e = eccentricityEarthOrbit(centuries),
m = solarGeometricMeanAnomaly(centuries),
l = solarGeometricMeanLongitude(centuries),
y = Math.tan(obliquityCorrection(centuries) / 2);
y *= y;
return y * Math.sin(2 * l)
- 2 * e * Math.sin(m)
+ 4 * e * y * Math.sin(m) * Math.cos(2 * l)
- 0.5 * y * y * Math.sin(4 * l)
- 1.25 * e * e * Math.sin(2 * m);
}
function solarDeclination(centuries) {
return Math.asin(Math.sin(obliquityCorrection(centuries)) * Math.sin(solarApparentLongitude(centuries)));
}
function solarApparentLongitude(centuries) {
return solarTrueLongitude(centuries) - (0.00569 + 0.00478 * Math.sin((125.04 - 1934.136 * centuries) * radians)) * radians;
}
function solarTrueLongitude(centuries) {
return solarGeometricMeanLongitude(centuries) + solarEquationOfCenter(centuries);
}
function solarGeometricMeanAnomaly(centuries) {
return (357.52911 + centuries * (35999.05029 - 0.0001537 * centuries)) * radians;
}
function solarGeometricMeanLongitude(centuries) {
var l = (280.46646 + centuries * (36000.76983 + centuries * 0.0003032)) % 360;
return (l < 0 ? l + 360 : l) / 180 * π;
}
function solarEquationOfCenter(centuries) {
var m = solarGeometricMeanAnomaly(centuries);
return (Math.sin(m) * (1.914602 - centuries * (0.004817 + 0.000014 * centuries))
+ Math.sin(m + m) * (0.019993 - 0.000101 * centuries)
+ Math.sin(m + m + m) * 0.000289) * radians;
}
function obliquityCorrection(centuries) {
return meanObliquityOfEcliptic(centuries) + 0.00256 * Math.cos((125.04 - 1934.136 * centuries) * radians) * radians;
}
function meanObliquityOfEcliptic(centuries) {
return (23 + (26 + (21.448 - centuries * (46.8150 + centuries * (0.00059 - centuries * 0.001813))) / 60) / 60) * radians;
}
function eccentricityEarthOrbit(centuries) {
return 0.016708634 - centuries * (0.000042037 + 0.0000001267 * centuries);
}
})();
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#map {
width: 960px;
margin: 0 auto;
}
#map h1 {
position: absolute;
width: 960px;
}
.foreground {
fill: none;
stroke: #000;
stroke-width: 1px;
pointer-events: all;
cursor: -webkit-grab;
cursor: -moz-grab;
}
.foreground.zooming {
cursor: -webkit-grabbing;
cursor: -moz-grabbing;
}
.graticule {
fill: none;
stroke: #636B62;
stroke-width: .5px;
stroke-dasharray: 2,2;
}
.land {
fill: #69D2E7;
stroke: none;
}
.mesh {
stroke: #50576A;
stroke-width: .5px;
fill: none;
}
.point {
fill: #f00;
}
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