計算太陽位置的方程：solar-calculator
計算太陽位置的方程：solar-calculator。
#<!DOCTYPE html> <meta charset="utf-8"> <style>
path { fill: none; stroke-linecap: round; stroke-linejoin: round; }
text { font: 10px sans-serif; }
.horizon { stroke: #000; stroke-width: 1.5px; }
.graticule { stroke: #000; stroke-opacity: .15; }
.analemmas path { stroke: #f00; stroke-width: 2px; }
.ticks line { stroke: #000; }
.ticks text { text-anchor: middle; }
.ticks--azimuth text:nth-of-type(9n + 1) { font-weight: bold; font-size: 14px; }
</style> <body> <script src="; <script src="solar-calculator.js"></script> <script>
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("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 + "°"; });svg.insert("g", ".sphere") .attr("class", "analemmas") .selectAll("path") .data(d3.range(24)) .enter().append("path") .datum(function(h) { return {type: "LineString", coordinates: d3.time.days.utc(start, end).map(function(d) { return solar.position(d3.time.hour.utc.offset(d, h)); })}; }) .attr("d", path);
d3.select(self.frameElement).style("height", height + "px");
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) ]; }
</script></pre>
solar-calculator.js#// 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); } })();</pre>