相对的，椭圆的公式可以写为：
椭圆公式中的Y可以看做圆公式中的Y变换了倍之后得来。这里的公式中的X和Y对应的就是横纵坐标值。
OpenLayers的SimpleGeometry类及其子类提供了具有这种功能的函数scale，可以对横纵坐标进行按比例的拉伸变换。可以利用这个函数实现椭圆的绘制。
function genEllipseGeom(radiusMajor, radiusMinor, center, rotation) {
var circle = new Circle(center, radiusMinor);
var polygon = fromCircle(circle, 64);
polygon.scale(radiusMajor / radiusMinor, 1);
polygon.rotate(rotation, center);
return polygon;
}
参数radiusMajor, radiusMinor, center, rotation分别对应椭圆的长半轴、短半轴、重心和旋转角度。
算法的主要思想是：首先以短半轴为半径生成了一个Circle类型的几何，然后通过这个理想圆生成了一个正64边形多边形，拟合这个圆。再将这个多边形进行按比例变换，变换之后的结果再进行旋转，最后得到的就是使用多边形拟合的椭圆。
import { Map, View } from 'ol';
import TileLayer from 'ol/layer/Tile';
import OSM from 'ol/source/OSM';
import Circle from 'ol/geom/Circle';
import { fromCircle } from 'ol/geom/Polygon'
import VectorSource from 'ol/source/Vector';
import VectorLayer from 'ol/layer/Vector';
import Feature from 'ol/Feature';
let tileLayer = new TileLayer({
source: new OSM()
})
let map = new Map({
target: 'map',
layers: [
tileLayer
],
view: new View({
center: [11936406.337013, 3786384.633134],
zoom: 5,
constrainResolution: true
})
});
var vSource = new VectorSource()
var vLayer = new VectorLayer(
{
source: vSource,
}
)
function genEllipseGeom(radiusMajor, radiusMinor, center, rotation) {
var circle = new Circle(center, radiusMinor);
var polygon = fromCircle(circle, 64);
polygon.scale(radiusMajor / radiusMinor, 1);
polygon.rotate(rotation, center);
return polygon;
}
var elGeom = genEllipseGeom(600000, 400000, [11936406.337013, 3786384.633134], Math.PI / 4);
var ef = new Feature(elGeom);
vSource.addFeature(ef);
map.addLayer(vLayer)
draw交互组件绘制椭圆
使用draw交互组件绘制椭圆与绘制圆形是类似的，可以有两种思路：
两点法：第一个点确定重心，第二个点与重心的横坐标之差确定长半轴，纵坐标值差确定短半轴。这个方案的缺点是无法通过绘制来自由定义椭圆的旋转角度。
三点法：同样第一个点确定重心，第二个点与重心的连线确定长半轴，连线与横坐标轴的夹角确定旋转角度；第三个点到长半轴的距离确定短半轴。
本文使用三点法来实现椭圆的交互绘制。主要思路是通过自定义draw组件的geometryFunction来实现三点法绘制的逻辑。
import { Map, View } from 'ol';
import TileLayer from 'ol/layer/Tile';
import OSM from 'ol/source/OSM';
import Circle from 'ol/geom/Circle';
import Polygon from 'ol/geom/Polygon';
import { fromCircle } from 'ol/geom/Polygon'
import VectorSource from 'ol/source/Vector';
import VectorLayer from 'ol/layer/Vector';
import Feature from 'ol/Feature';
import Draw from 'ol/interaction/Draw';
import Style from 'ol/style/Style';
import Fill from 'ol/style/Fill';
import Stroke from 'ol/style/Stroke';
import CircleStyle from 'ol/style/Circle';
import GeometryType from 'ol/geom/GeometryType';
function createEditingStyle(feature) {
const styles = {};
const white = [255, 255, 255, 1];
const blue = [0, 0, 255, 1];
const width = 3;
styles[GeometryType.POLYGON] = [
new Style({
fill: new Fill({
color: [255, 255, 255, 0.3]
}),
stroke: new Stroke({
color: "#00FF00",
})
})
];
styles[GeometryType.MULTI_POLYGON] =
styles[GeometryType.POLYGON];
styles[GeometryType.LINE_STRING] = [
new Style({
stroke: new Stroke({
color: [0, 255, 0, 0.3],
width: width
})
})
];
styles[GeometryType.POINT] = [
new Style({
image: new CircleStyle({
radius: width * 2,
fill: new Fill({
color: blue
}),
stroke: new Stroke({
color: white,
width: width / 2
})
}),
zIndex: Infinity
})
];
return styles[feature.getGeometry().getType()]
}
let tileLayer = new TileLayer({
source: new OSM()
})
let map = new Map({
target: 'map',
layers: [
tileLayer
],
view: new View({
center: [11936406.337013, 3786384.633134],
zoom: 5,
constrainResolution: true
})
});
var vSource = new VectorSource()
var vLayer = new VectorLayer(
{
source: vSource,
}
)
function genEllipseGeom(radiusMajor, radiusMinor, center, rotation) {
var circle = new Circle(center, radiusMinor);
var polygon = fromCircle(circle, 64);
polygon.scale(radiusMajor / radiusMinor, 1);
polygon.rotate(rotation, center);
return polygon;
}
var elGeom = genEllipseGeom(600000, 400000, [11936406.337013, 3786384.633134], 0);
var ef = new Feature(elGeom);
vSource.addFeature(ef);
map.addLayer(vLayer)
var value = 'Polygon';
var geometryFunction;
var maxPoints = 3;
function geometryFunction(coordinates, geometry) {
let cArray = coordinates[0]
let center = cArray[0];
let startPoint = cArray[1];
let endPoint = cArray[2];
if (!geometry) {
geometry = new Polygon([]);
}
if (cArray.length == 3) {
let coordinatesRing = cArray.slice()
coordinatesRing.push(center)
let plg = new Polygon([coordinatesRing])
let plygArea = plg.getArea()
let radiusMajor = Math.sqrt(
Math.pow(center[0] - startPoint[0], 2) +
Math.pow(center[1] - startPoint[1], 2)
)
let radiusMinor = (plygArea * 2) / radiusMajor;
let dx = startPoint[0] - center[0];
let dy = startPoint[1] - center[1];
let rotation = Math.atan(dx / dy);
rotation = dy > 0 ? -rotation - Math.PI * 0.5 : -(Math.PI * 0.5 + rotation);
let f = genEllipseGeom(radiusMajor, radiusMinor, center, rotation)
geometry.setCoordinates(
f.getCoordinates()
)
}
return geometry
}
var draw = new Draw({
source: vSource,
type: value,
geometryFunction: geometryFunction,
maxPoints: maxPoints,
style: createEditingStyle
});
map.addInteraction(draw);