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benchmark.html
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<!DOCTYPE html>
<html lang="ja">
<head>
<title>Geodesic Distance Formulae Benchmark</title>
<meta charset="utf-8"/>
</head>
<script src="https://cdn.jsdelivr.net/npm/chart.js"></script>
<script>
"use strict";
let ERR_BIN_START = 0;
let ERR_BIN_END = 0;
let ERR_BIN_DIV = 0;
let result = {};
let testdata = [];
let flag_graph_complete = false;
let distance_min = -1;
let distance_max = -1;
const worker = new Worker("benchmark_worker.js");
worker.onmessage = function(e){
document.getElementById("btn_benchmark").disabled = false;
document.getElementById("message").innerHTML = "";
distance_min = e.data.distance_min;
distance_max = e.data.distance_max;
ERR_BIN_DIV = Math.floor(30/(Math.log10(distance_max/distance_min)+1)+120);
ERR_BIN_START = Math.floor(Math.log10(distance_min)*ERR_BIN_DIV);
ERR_BIN_END = Math.floor(Math.log10(distance_max)*ERR_BIN_DIV);
testdata = e.data.testdata;
};
worker.postMessage({func: "loadTestData", args: []});
async function startBenchmark(){
document.getElementById("btn_benchmark").disabled = true;
document.getElementById("message").innerHTML = "executing benchmarks...";
result = await new Promise((resolve, reject) => {
worker.onmessage = function(e){
resolve(e.data);
};
worker.postMessage({
func: "startBenchmark",
args: [document.getElementById("benchmark_n_repeat_input").value - 0, result, ERR_BIN_START, ERR_BIN_END, ERR_BIN_DIV]
});
});
for(const f in result){
const avg = result[f].times.reduce((i, a) => i + a) / result[f].times.length;
}
showResultGraph();
showResultTable(result);
document.getElementById("btn_benchmark").disabled = false;
document.getElementById("message").innerHTML = "";
}
function showResultTable(){
const buf = []
buf.push("<font size=\"-1\"><table>");
buf.push("<table><tr><th>formula</th><th>mean calculation time [ms]</th></tr>");
for(const f in result){
buf.push("<tr><td class='center'>" + f + "</td>");
const avg = result[f].times.reduce((i, a) => i + a) / result[f].times.length;
buf.push("<td class='right'>" + avg.toFixed(2) + "</td>");
buf.push("</tr>");
}
buf.push("</table></font>");
document.getElementById("result").innerHTML = buf.join("");
}
function showResultGraph(){
const labels = [];
const datasets = [];
const colors = ["#3f3d99", "#993d70", "#998b3d", "#3d9955", "#3d5a99", "#993d8f", "#996c3d", "#43993d", "#3d7899", "#833d99", "#994e3d", "#61993d"];
const shapes = ["rect", "triangle", "rectRot"];
if(flag_graph_complete){
return;
}
setTimeout(() => {
for(let i = ERR_BIN_START; i <= ERR_BIN_END; i++){
labels.push(Math.pow(10,i/ERR_BIN_DIV));
}
let j = 0;
for(const f in result){
const dataset = {};
dataset.label = f;
dataset.backgroundColor = colors[j % colors.length];
dataset.pointStyle = shapes[Math.floor(j / 4) % shapes.length];
dataset.borderColor = dataset.backgroundColor;
dataset.data = [];
for(let i = 0; i <= ERR_BIN_END - ERR_BIN_START; i++){
if(result[f].errors.error_rel[i]){
dataset.data.push([
Math.pow(10,(i+ERR_BIN_START)/ERR_BIN_DIV),
Math.abs(result[f].errors.error_rel[i])
]);
}
}
j++;
datasets.push(dataset);
}
const margin_plot = (distance_min==distance_max)?2.0:Math.max(1.02, Math.pow(distance_max/distance_min, 0.03));
const chart = new Chart(document.getElementById("chart"), {
type: "line",
data: {
labels: labels,
datasets: datasets
},
options: {
borderWidth: 1,
plugins: {
tooltip: {
enabled: false
},
legend: {
labels: {
usePointStyle: true
}
}
},
scales: {
x: {
display: true,
type: "logarithmic",
title: {
display: true,
text: "Distance [m]"
},
min: distance_min / margin_plot,
max: distance_max * margin_plot,
},
y: {
display: true,
type: "logarithmic",
title: {
display: true,
text: "Maximum Relative Error in Distance"
},
min: 1e-16,
max: 3e0,
ticks: {
callback: (val, index) => {
if(val.toExponential(1).startsWith("1")){
return val.toExponential(1);
}else{
return "";
}
}
}
}
}
}
});
flag_graph_complete = true;
}, 0);
}
</script>
<!-- Google tag (gtag.js) -->
<script async src="https://www.googletagmanager.com/gtag/js?id=G-4RTVKDCC9W"></script>
<script>
window.dataLayer = window.dataLayer || [];
function gtag(){dataLayer.push(arguments);}
gtag('js', new Date());
gtag('config', 'G-4RTVKDCC9W');
</script>
<style>
table {
border-collapse: collapse;
}
th, td {
padding: 2px;
border: 1px solid gray;
}
.left{
text-align: left;
}
.center{
text-align: center;
}
.right{
text-align: right;
}
</style>
<body bgcolor="#f0f0e8">
<h3>Benchmark of Geodesic Distance Formulae</h3>
<div>
Compared Formulae implemented in JavaScript:
<ul>
<li>Spherical: Menelaus of Alexandria (about 100); <a href="https://en.wikipedia.org/wiki/Great-circle_distance">Great-circle distance - Wikipedia</a>
<li>Flat-surface: Newton (?), Cassini (1713); <a href="https://en.wikipedia.org/wiki/Geographical_distance#Ellipsoidal_Earth_projected_to_a_plane">Geographical distance - Wikipedia</a>
<li>Hubeny: Hubeny (1954, 1959)
<li>Gauss-mid-latitude: Gauss (1843, 1846); Lambert and Swick (1935); <a href="https://kb.osu.edu/items/5cfd1585-a92a-5933-9469-366a5d6b6894">Rapp (1991)</a> §6.4; <a href="https://en.wikipedia.org/wiki/Geographical_distance#Gauss_mid-latitude_method_for_short_lines">Geographical distance - Wikipedia</a>
<li>Andoyer: <a href="https://doi.org/10.1007/BF03030136">Andoyer (1932)</a>; <a href="https://en.wikipedia.org/wiki/Marie_Henri_Andoyer#Publications">Marie Henri Andoyer - Wikipedia</a>
<li>Andoyer-Lambert: Lambert (1942); <a href="https://apps.dtic.mil/sti/tr/pdf/AD0627893.pdf">Thomas (1965)</a>; <a href="https://en.wikipedia.org/wiki/Geographical_distance#Lambert's_formula_for_long_lines">Geographical distance - Wikipedia</a>
<li>Andoyer-Lambert-Thomas: <a href="https://apps.dtic.mil/sti/tr/pdf/AD0703541.pdf">Thomas (1970)</a>
<!--<li>(Pittman: Pittman (1986);
<a href="https://www.researchgate.net/publication/280099320_GEODESICS_ON_AN_ELLIPSOID_-_PITTMAN'S_METHOD">Deakin and Hunter (2007, 2010)</a>; not tested) -->
<li>Vincenty: Vincentry (1975, 1976); <a href="https://dl.ndl.go.jp/info:ndljp/pid/11000306">回転楕円体上の測地線及び航程線の算出について（海洋情報部研究報告）</a> in Japanese
<li>Bowring: Bowring (1996); used by Geospatial Information Authority of Japan (GSI) based on this method, <a href="https://vldb.gsi.go.jp/sokuchi/surveycalc/surveycalc/algorithm/bl2st/bl2st.htm">経緯度を用いた2地点間の測地線長、方位角を求める計算（国土地理院）</a> in Japanese
<li>Karney: Karney (2011); <a href="https://geographiclib.sourceforge.io/">GeographicLib</a>
</ul>
</div>
<div>
n_repeat: <input id="benchmark_n_repeat_input" type="number" min="1" max="100" value="1">
<button id="btn_benchmark" onclick="startBenchmark()" disabled>Start Benchmark</button>
<span id="message">loading...</span>
<div id="result"></div>
<div><canvas id="chart"></canvas></div>
</div>
</body>
</html>