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<title>Projections</title>
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<h1>Projections</h1>
<p>
Projections are used on the mapdata to translate coordinates to pixelpositions. There are various
projections that can be used. All implemented ones are showcased here.
</p>
<section id="mercator">
<h2>Mercator Projection</h2>
<p>The most commonly used projection is the mercator projection.</p>
<div class="center">
<div id="mercatorMap" class="map-wrapper">
<img src="../../assets/maps/osm/0/0/0.png" alt="" />
</div>
</div>
<script>
let boundaries = [
{ x: -90, y: -180 },
{ x: 90, y: 180 },
{ x: 0, y: 0 },
{ x: 90, y: -180 },
// Eastern Boundaries
{ x: -22, y: 180 },
{ x: -43, y: 180 },
{ x: -63, y: 180 },
{ x: -73, y: 180 },
{ x: -83, y: 180 },
{ x: -87, y: 180 },
{ x: 0, y: 180 },
{ x: 22, y: 180 },
{ x: 43, y: 180 },
{ x: 63, y: 180 },
{ x: 73, y: 180 },
{ x: 83, y: 180 },
{ x: 87, y: 180 },
{ x: -90, y: 180 },
// Western Boundaries
{ x: -22, y: -180 },
{ x: -43, y: -180 },
{ x: -63, y: -180 },
{ x: -73, y: -180 },
{ x: -83, y: -180 },
{ x: -87, y: -180 },
{ x: 0, y: -180 },
{ x: 22, y: -180 },
{ x: 43, y: -180 },
{ x: 63, y: -180 },
{ x: 73, y: -180 },
{ x: 83, y: -180 },
{ x: 87, y: -180 },
{ x: -90, y: -180 }
]
let capitals = {
abidjan: { x: 5, y: -5 },
canberra: { x: -35.312146, y: 149.121539 },
berlin: { x: 52.52543, y: 13.385291 },
capetown: { x: -33.925448, y: 18.416962 },
moscow: { x: 55.750892, y: 37.622799 },
washington: { x: 38.89565, y: -77.031407 },
rio: { x: -22.8714, y: -43.28049 },
tokio: { x: 35.696278, y: 139.731366 }
}
/**
*
*/
function createPointAtPoisition(position, className = '', style = {}) {
let point = document.createElement('div')
point.className = 'point ' + className
Object.assign(point.style, {
backgroundColor: "0xff0000"
}, style, {
left: position.x * 100 + '%',
top: position.y * 100 + '%'
})
return point
}
/**
* Draws a vertical line at the zero longitude of a map.
*/
function drawZeroLongitude(projection, parent) {
let element = document.createElement("div")
element.className = "long"
let position = projection.forward({ x: 0, y: 0 })
element.style.left = position.x * 100 + "%"
parent.appendChild(element)
}
/**
* Plots a point for a specific interval on the map. Distance defines that interval.
*/
function plotGridPoints(distance = 10, projection, parent) {
for (let lat = -90; lat <= 90; lat += distance) {
for (let lng = -180; lng <= 180; lng += distance) {
let color = "#0000ff"
let className = 'small'
if (lng == 180) {
color = '#ff0000'
lng = (lng == 180) ? 180 : lng
}
if (lng == -180) {
color = '#00ff00'
lng = (lng == 180) ? 180 : lng
className = "medium"
}
let relativePosition = projection.forward({ x: lat, y: lng })
let point = createPointAtPoisition(relativePosition, className, {
backgroundColor: color
})
robinsonMap.appendChild(point)
}
}
}
</script>
<script class="doctest" data-collapsible data-collapsed data-title="Test Data">
let mercatorTruth = {
abidjan: { x: 0.4861111111111111, y: 0.4860934491519468 },
canberra: { x: 0.9142264972222222, y: 0.6049626977761389 },
berlin: { x: 0.5371813638888889, y: 0.327930370913594 },
capetown: { x: 0.5511582277777778, y: 0.6002818272799257 },
moscow: { x: 0.604507775, y: 0.3126267957774014 },
washington: { x: 0.28602386944444447, y: 0.3825518808752881 },
rio: { x: 0.3797764166666667, y: 0.5652894059707362 },
tokio: { x: 0.8881426833333332, y: 0.39372656277794527 }
}
</script>
<script class="doctest">
; (function () {
//First we define the appropriate projection:
let mercatorProjection = new Projection.Mercator()
for (let [name, coordinates] of Object.entries(capitals)) {
// Every projection has a forward and a backward function.
// The forward function transforms coordinates in the form of
// {x: lat, y: lng} into relative screen coordinates in the form of {x,y}.
let relativePosition = mercatorProjection.forward(coordinates)
// Testcases for the forward transformation.
Doctest.expect(mercatorTruth[name], relativePosition)
// The backward function transforms relative positions on the screen
// to geographic coordinates.
let calculatedCoordinates = mercatorProjection.backward(relativePosition)
// Testcases for the backwards transformation.
Doctest.expectPointPrecision(coordinates, calculatedCoordinates)
let point = createPointAtPoisition(relativePosition)
mercatorMap.appendChild(point)
}
})()
</script>
</section>
<section id="robinson">
<h2>Robinson Projection</h2>
<p>
The robinson projection is a more 'artistic' approach, as it follows a table instead of a strict
formula. It has severe distortions at the poles, but that distortion declines rapidly heading towards
the equator.
</p>
<div class="center">
<div id="robinsonMap" class="map-wrapper">
<img src="../../assets/maps/wikimedia-world-robinson/2000px-BlankMap-World.png" alt="" width="512" />
</div>
</div>
<script class="doctest" data-collapsible data-collapsed data-title="Test Data">
let robinsonTruth = {
"abidjan": {
"x": 0.45839166666666664,
"y": 0.469
},
"canberra": {
"x": 0.8637961558795233,
"y": 0.71892906228
},
"berlin": {
"x": 0.5080051098978837,
"y": 0.17622420010000006
},
"capetown": {
"x": 0.522127677557207,
"y": 0.7103377776
},
"moscow": {
"x": 0.5636501036295355,
"y": 0.15721735316000007
},
"washington": {
"x": 0.27607293856102144,
"y": 0.25892488299999994
},
"rio": {
"x": 0.35541500995592845,
"y": 0.6418026800000001
},
"tokio": {
"x": 0.8386571387301243,
"y": 0.27869700196
}
}
</script>
<script class="doctest">
; (function () {
// Create the robinson projection.
let robinsonProjection = new Projection.Robinson(10)
// Note: The center on this map is at approximately latitude 10,
// therefore the projection must be shifted.
/**
* Create a point for each capital.
*/
for (let [key, position] of Object.entries(capitals)) {
let relativePosition = robinsonProjection.forward(position)
// Run Test Cases
Doctest.expectPointPrecision(robinsonTruth[key], relativePosition,0)
let point = createPointAtPoisition(relativePosition)
robinsonMap.appendChild(point)
}
})()
</script>
</section>
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