我正在尝试优化长距离远足小径的 Mapbox 视图，例如阿巴拉契亚小径或太平洋山脊小径。下面是一个例子，我已经手动定位，展示了西班牙的 Senda Pirenáica：
给出了感兴趣的区域、视口和间距。我需要找到正确的中心、方位和缩放。
该map.fitBounds方法在这里对我没有帮助，因为它假定pitch = 0和bearing = 0。
我做了一些探索，这似乎是最小周围矩形问题的变体，但我遇到了一些额外的复杂问题：
FWIW 我也在使用 turf-js，它可以帮助我获得线的凸包。
此解决方案导致路径显示在正确的方位上，洋红色梯形轮廓显示目标“最紧梯形”以显示计算结果。来自顶角的额外线显示 map.center() 值所在的位置。
方法如下：
结果如下所示：
在此之后，我们想要围绕路径旋转梯形并找到梯形与点的最紧密拟合。为了测试最紧密的配合，旋转路径而不是梯形更容易，所以我在这里采用了这种方法。我没有在路径上实现“凸包”以最小化要旋转的点数，但这可以作为优化步骤添加。
为了获得最紧密的拟合，第一步是移动 map.center() 以使路径位于视图的“后部”。这是截锥体中空间最多的地方，因此很容易在那里操作：
接下来，我们测量有角度的梯形墙与路径中每个点之间的距离，保存左侧和右侧最近的点。然后，我们通过基于这些距离水平平移视图来使路径居中，然后缩放视图以消除两侧的空间，如下面的绿色梯形所示：
用于获得这种“最合适”的比例为我们提供了这是否是路径的最佳视图的排名。然而，这个视图可能不是最好的视觉效果，因为我们将路径推到视图的后面来确定排名。相反，我们现在调整视图以将路径放置在视图的垂直中心，并相应地放大视图三角形。这为我们提供了所需的洋红色“最终”视图：
最后，这个过程是针对每个度数进行的，最小刻度值决定了获胜方位，我们从那里获取相关的刻度和中心位置。
mapboxgl.accessToken = 'pk.eyJ1IjoiZm1hY2RlZSIsImEiOiJjajJlNWMxenowNXU2MzNudmkzMndwaGI3In0.ALOYWlvpYXnlcH6sCR9MJg';
var map;
var myPath = [
[-122.48369693756104, 37.83381888486939],
[-122.48348236083984, 37.83317489144141],
[-122.48339653015138, 37.83270036637107],
[-122.48356819152832, 37.832056363179625],
[-122.48404026031496, 37.83114119107971],
[-122.48404026031496, 37.83049717427869],
[-122.48348236083984, 37.829920943955045],
[-122.48356819152832, 37.82954808664175],
[-122.48507022857666, 37.82944639795659],
[-122.48610019683838, 37.82880236636284],
[-122.48695850372314, 37.82931081282506],
[-122.48700141906738, 37.83080223556934],
[-122.48751640319824, 37.83168351665737],
[-122.48803138732912, 37.832158048267786],
[-122.48888969421387, 37.83297152392784],
[-122.48987674713133, 37.83263257682617],
[-122.49043464660643, 37.832937629287755],
[-122.49125003814696, 37.832429207817725],
[-122.49163627624512, 37.832564787218985],
[-122.49223709106445, 37.83337825839438],
[-122.49378204345702, 37.83368330777276]
];
var myPath2 = [
[-122.48369693756104, 37.83381888486939],
[-122.49378204345702, 37.83368330777276]
];
function addLayerToMap(name, points, color, width) {
map.addLayer({
"id": name,
"type": "line",
"source": {
"type": "geojson",
"data": {
"type": "Feature",
"properties": {},
"geometry": {
"type": "LineString",
"coordinates": points
}
}
},
"layout": {
"line-join": "round",
"line-cap": "round"
},
"paint": {
"line-color": color,
"line-width": width
}
});
}
function Mercator2ll(mercX, mercY) {
var rMajor = 6378137; //Equatorial Radius, WGS84
var shift = Math.PI * rMajor;
var lon = mercX / shift * 180.0;
var lat = mercY / shift * 180.0;
lat = 180 / Math.PI * (2 * Math.atan(Math.exp(lat * Math.PI / 180.0)) - Math.PI / 2.0);
return [ lon, lat ];
}
function ll2Mercator(lon, lat) {
var rMajor = 6378137; //Equatorial Radius, WGS84
var shift = Math.PI * rMajor;
var x = lon * shift / 180;
var y = Math.log(Math.tan((90 + lat) * Math.PI / 360)) / (Math.PI / 180);
y = y * shift / 180;
return [ x, y ];
}
function convertLL2Mercator(points) {
var m_points = [];
for(var i=0;i<points.length;i++) {
m_points[i] = ll2Mercator( points[i][0], points[i][1] );
}
return m_points;
}
function convertMercator2LL(m_points) {
var points = [];
for(var i=0;i<m_points.length;i++) {
points[i] = Mercator2ll( m_points[i][0], m_points[i][1] );;
}
return points;
}
function pointsTranslate(points,xoff,yoff) {
var newpoints = [];
for(var i=0;i<points.length;i++) {
newpoints[i] = [ points[i][0] + xoff, points[i][1] + yoff ];
}
return(newpoints);
}
// note [0] elements are lng [1] are lat
function getBoundingBox(arr) {
var ne = [ arr[0][0] , arr[0][1] ];
var sw = [ arr[0][0] , arr[0][1] ];
for(var i=1;i<arr.length;i++) {
if(ne[0] < arr[i][0]) ne[0] = arr[i][0];
if(ne[1] < arr[i][1]) ne[1] = arr[i][1];
if(sw[0] > arr[i][0]) sw[0] = arr[i][0];
if(sw[1] > arr[i][1]) sw[1] = arr[i][1];
}
return( [ sw, ne ] );
}
function pointsRotate(points, cx, cy, angle){
var radians = angle * Math.PI / 180.0;
var cos = Math.cos(radians);
var sin = Math.sin(radians);
var newpoints = [];
function rotate(x, y) {
var nx = cx + (cos * (x - cx)) + (-sin * (y - cy));
var ny = cy + (cos * (y - cy)) + (sin * (x - cx));
return [nx, ny];
}
for(var i=0;i<points.length;i++) {
newpoints[i] = rotate(points[i][0],points[i][1]);
}
return(newpoints);
}
function convertTrapezoidToPath(trap) {
return([
[trap.Tl.lng, trap.Tl.lat], [trap.Tr.lng, trap.Tr.lat],
[trap.Br.lng, trap.Br.lat], [trap.Bl.lng, trap.Bl.lat],
[trap.Tl.lng, trap.Tl.lat] ]);
}
function getViewTrapezoid() {
var canvas = map.getCanvas();
var trap = {};
trap.Tl = map.unproject([0,0]);
trap.Tr = map.unproject([canvas.offsetWidth,0]);
trap.Br = map.unproject([canvas.offsetWidth,canvas.offsetHeight]);
trap.Bl = map.unproject([0,canvas.offsetHeight]);
return(trap);
}
function pointsScale(points,cx,cy, scale) {
var newpoints = []
for(var i=0;i<points.length;i++) {
newpoints[i] = [ cx + (points[i][0]-cx)*scale, cy + (points[i][1]-cy)*scale ];
}
return(newpoints);
}
var id = 1000;
function convertMercator2LLAndDraw(m_points, color, thickness) {
var newpoints = convertMercator2LL(m_points);
addLayerToMap("id"+id++, newpoints, color, thickness);
}
function pointsInTrapezoid(points,yt,yb,xtl,xtr,xbl,xbr) {
var str = "";
var xleft = xtr;
var xright = xtl;
var yh = yt-yb;
var sloperight = (xtr-xbr)/yh;
var slopeleft = (xbl-xtl)/yh;
var flag = true;
var leftdiff = xtr - xtl;
var rightdiff = xtl - xtr;
var tmp = [ [xtl, yt], [xtr, yt], [xbr,yb], [xbl,yb], [xtl,yt] ];
// convertMercator2LLAndDraw(tmp, '#ff0', 2);
function pointInTrapezoid(x,y) {
var xsloperight = xbr + sloperight * (y-yb);
var xslopeleft = xbl - slopeleft * (y-yb);
if((x - xsloperight) > rightdiff) {
rightdiff = x - xsloperight;
xright = x;
}
if((x - xslopeleft) < leftdiff) {
leftdiff = x - xslopeleft;
xleft = x;
}
if( (y<yb) || (y > yt) ) {
console.log("y issue");
}
else if(xsloperight < x) {
console.log("sloperight");
}
else if(xslopeleft > x) {
console.log("slopeleft");
}
else return(true);
return(false);
}
for(var i=0;i<points.length;i++) {
if(pointInTrapezoid(points[i][0],points[i][1])) {
str += "1";
}
else {
str += "0";
flag = false;
}
}
if(flag == false) console.log(str);
return({ leftdiff: leftdiff, rightdiff: rightdiff });
}
var viewcnt = 0;
function calculateView(trap, points, center) {
var bbox = getBoundingBox(points);
var bbox_height = Math.abs(bbox[0][1] - bbox[1][1]);
var view = {};
// move the view trapezoid so the path is at the far edge of the view
var viewTop = trap[0][1];
var pointsTop = bbox[1][1];
var yoff = -(viewTop - pointsTop);
var extents = pointsInTrapezoid(points,trap[0][1]+yoff,trap[3][1]+yoff,trap[0][0],trap[1][0],trap[3][0],trap[2][0]);
// center the view trapezoid horizontally around the path
var mid = (extents.leftdiff - extents.rightdiff) / 2;
var trap2 = pointsTranslate(trap,extents.leftdiff-mid,yoff);
view.cx = trap2[5][0];
view.cy = trap2[5][1];
var w = trap[1][0] - trap[0][0];
var h = trap[1][1] - trap[3][1];
// calculate the scale to fit the trapezoid to the path
view.scale = (w-mid*2)/w;
if(bbox_height > h*view.scale) {
// if the path is taller than the trapezoid then we need to make it larger
view.scale = bbox_height / h;
}
view.ranking = view.scale;
var trap3 = pointsScale(trap2,(trap2[0][0]+trap2[1][0])/2,trap2[0][1],view.scale);
w = trap3[1][0] - trap3[0][0];
h = trap3[1][1] - trap3[3][1];
view.cx = trap3[5][0];
view.cy = trap3[5][1];
// if the path is not as tall as the view then we should center it vertically for the best looking result
// this involves both a scale and a translate
if(h > bbox_height) {
var space = h - bbox_height;
var scale_mul = (h+space)/h;
view.scale = scale_mul * view.scale;
cy_offset = space/2;
trap3 = pointsScale(trap3,view.cx,view.cy,scale_mul);
trap3 = pointsTranslate(trap3,0,cy_offset);
view.cy = trap3[5][1];
}
return(view);
}
function thenCalculateOptimalView(path) {
var center = map.getCenter();
var trapezoid = getViewTrapezoid();
var trapezoid_path = convertTrapezoidToPath(trapezoid);
trapezoid_path[5] = [center.lng, center.lat];
var view = {};
//addLayerToMap("start", trapezoid_path, '#00F', 2);
// get the mercator versions of the points so that we can use them for rotations
var m_center = ll2Mercator(center.lng,center.lat);
var m_path = convertLL2Mercator(path);
var m_trapezoid_path = convertLL2Mercator(trapezoid_path);
// try all angles to see which fits best
for(var angle=0;angle<360;angle+=1) {
var m_newpoints = pointsRotate(m_path, m_center[0], m_center[1], angle);
var thisview = calculateView(m_trapezoid_path, m_newpoints, m_center);
if(!view.hasOwnProperty('ranking') || (view.ranking > thisview.ranking)) {
view.scale = thisview.scale;
view.cx = thisview.cx;
view.cy = thisview.cy;
view.angle = angle;
view.ranking = thisview.ranking;
}
}
// need the distance for the (cx, cy) from the current north up position
var cx_offset = view.cx - m_center[0];
var cy_offset = view.cy - m_center[1];
var rotated_offset = pointsRotate([[cx_offset,cy_offset]],0,0,-view.angle);
map.flyTo({ bearing: view.angle, speed:0.00001 });
// once bearing is set, adjust to tightest fit
waitForMapMoveCompletion(function () {
var center2 = map.getCenter();
var m_center2 = ll2Mercator(center2.lng,center2.lat);
m_center2[0] += rotated_offset[0][0];
m_center2[1] += rotated_offset[0][1];
var ll_center2 = Mercator2ll(m_center2[0],m_center2[1]);
map.easeTo({
center:[ll_center2[0],ll_center2[1]],
zoom : map.getZoom() });
console.log("bearing:"+view.angle+ " scale:"+view.scale+" center: ("+ll_center2[0]+","+ll_center2[1]+")");
// draw the tight fitting trapezoid for reference purposes
var m_trapR = pointsRotate(m_trapezoid_path,m_center[0],m_center[1],-view.angle);
var m_trapRS = pointsScale(m_trapR,m_center[0],m_center[1],view.scale);
var m_trapRST = pointsTranslate(m_trapRS,m_center2[0]-m_center[0],m_center2[1]-m_center[1]);
convertMercator2LLAndDraw(m_trapRST,'#f0f',4);
});
}
function waitForMapMoveCompletion(func) {
if(map.isMoving())
setTimeout(function() { waitForMapMoveCompletion(func); },250);
else
func();
}
function thenSetPitch(path,pitch) {
map.flyTo({ pitch:pitch } );
waitForMapMoveCompletion(function() { thenCalculateOptimalView(path); })
}
function displayFittedView(path,pitch) {
var bbox = getBoundingBox(path);
var path_cx = (bbox[0][0]+bbox[1][0])/2;
var path_cy = (bbox[0][1]+bbox[1][1])/2;
// start with a 'north up' view
map = new mapboxgl.Map({
container: 'map',
style: 'mapbox://styles/mapbox/streets-v9',
center: [path_cx, path_cy],
zoom: 12
});
// use the bounding box to get into the right zoom range
map.on('load', function () {
addLayerToMap("path",path,'#888',8);
map.fitBounds(bbox);
waitForMapMoveCompletion(function() { thenSetPitch(path,pitch); });
});
}
window.onload = function(e) {
displayFittedView(myPath,60);
}body { margin:0; padding:0; }
#map { position:absolute; top:0; bottom:0; width:100%; }<script src='https://api.tiles.mapbox.com/mapbox-gl-js/v0.37.0/mapbox-gl.js'></script>
<link href='https://api.tiles.mapbox.com/mapbox-gl-js/v0.37.0/mapbox-gl.css' rel='stylesheet' />
<div id='map'></div>最小的周围矩形将特定于 pitch=0（直接向下看）。
一种选择是继续使用最小环绕矩形方法并计算目标区域的变换 - 就像 3d 引擎一样。如果这是您所做的，则可以浏览统一文档以更好地了解查看截锥体的机制
我觉得这不适合您的问题，因为您必须从不同角度重新计算目标区域的 2d 渲染，这是一种相对昂贵的蛮力。
标准化计算的另一种方法是将视口投影渲染到目标区域平面中。你自己看：
然后你所要做的就是“只是”找出你的原始凸包可以适合该形状的梯形的最大尺寸（特别是凸等腰梯形，因为我们不操纵相机胶卷）。
这是我有点不了解的地方，不知道在哪里指向你进行计算。我认为在这个 2D 空间中迭代可能的解决方案至少更便宜。
PS：要记住的另一件事是视口投影形状会根据 FOV（视场）而有所不同。
当您调整浏览器视口的大小时，这种情况会发生变化，但该属性似乎没有在 mapbox-gl-js 中公开。
编辑：
经过一番思考，我觉得最好的数学解决方案在现实中会感觉有点“枯燥”。没有跨越用例，并且可能做出一些错误的假设，我会问这些问题：
也许按船体形状对不同类型的路线进行分类并创建平移预设会很方便？
希望这可以通过一些调整为您指明正确的方向。
首先我设置了我们要展示的两个点
let pointA = [-70, 43]
let pointB = [-83, 32]
然后我找到了这两点的中间。我为此做了自己的功能，但看起来草皮可以做到这一点。
function middleCoord(a, b){
let x = (a - b)/2
return _.min([a, b]) + x
}
let center = [middleCoord(pointA[0], pointB[0]), middleCoord(pointA[1], pointB[1])]
我使用草皮轴承功能从第二点看第一点
let p1 = turf.point(pointA)
let p2 = turf.point(pointB)
let points = turf.featureCollection([p1, p2])
let bearing = turf.bearing(p2, p1)
然后我调用地图并运行 fitBounds 函数：
var map = new mapboxgl.Map({
container: 'map', // container id
style: 'mapbox://styles/mapbox/outdoors-v10', //hosted style id
center: center, // starting position
zoom: 4, // starting zoom
pitch: 60,
bearing: bearing
})
map.fitBounds([pointA, pointB], {padding: 0, offset: 0})
这是一个代码笔： https ://codepen.io/thejoshderocher/pen/BRYGXq
调整方位以最好地利用屏幕尺寸是获取窗口的大小并调整方位以充分利用可用的屏幕空间。如果是竖屏的手机屏幕，这个轴承就完美了。如果您在视野开阔的桌面上，则需要旋转以使 A 点位于顶角之一。