Drawing Ellipse with OpenLayers

Question

I am trying to draw ellipse on the client side using openlayers with some mathematical functions from drawing ellipse with svg. I have achieved drawing it but not rotation what I have written for parameter and I am not sure about axis length too.

When I measure semi-major or semi-minor axis length, I am not getting the true length what I have given for 4.8 * 1000 meter.

I know PostGIS 2.1 has ST_MakeEllipse function for this but I want it on the client side.

I am sharing javascript code, reference image and result image with you. Any help would be appreciated.

Reference Image:

Codes:

var radiusX= 4,8 * 2 // Semi-major axis length - km
var radiusY= 2,5 * 2 // Semi-minor axis length -km 
var rot = 125 //Rotation


var xCent = 14.7495;
var yCent = 47.4640;

var z = [];
var list = [];

for (var i = 0 * Math.PI; i < 2 * Math.PI; i += 0.01 ) {
    xPos = xCent - (radiusX* Math.sin(i)) * Math.sin(rot * Math.PI) + (radiusY* Math.cos(i)) * Math.cos(rot * Math.PI);
    yPos = yCent + (radiusY* Math.cos(i)) * Math.sin(rot * Math.PI) + (radiusX* Math.sin(i)) * Math.cos(rot * Math.PI);

    if(i == 0 ) {
        z.push( new OpenLayers.Geometry.Point(xPos, yPos).transform(map.displayProjection, map.projection)); 
    } else {
        list.push(new OpenLayers.Geometry.Point(xPos, yPos).transform(map.displayProjection, map.projection));
    }
};


var linear_ring = new OpenLayers.Geometry.LinearRing(list);
var polygonFeature = new OpenLayers.Feature.Vector(new OpenLayers.Geometry.Polygon([linear_ring]), null, null);
vector.addFeatures([polygonFeature ])

Result:

Answer 1

I've done similar work before, for rotation, there is rotate function for polygons. In your case, add following line before adding feature to the layer:

var originPoint = new OpenLayers.Geometry.Point(xCent, yCent).transform(map.displayProjection, map.projection); //center point for rotation
polygonFeature.geometry.rotate(rot, originPoint);

You can find full documentation about rotate function here

I'm not sure about your calculation for the ellipses(you might have used some mathematical transformations), but I would suggest to use the polar system to get those points coordinates.

Get the distance from the point on ellipse at direction θ to the origin using following formula:

The coordinates of the point are:

x = r(θ) * cos(θ)
y = r(θ) * sin(θ)