The jVectorMap world map uses the van der Grinten projection. The formula to convert from/to the map can be found this
Wikipedia and Wolfram article.
You'll need to scale it to your map's size & offset, given the above formula projects the long/lat (-180 to 180 deg) to a (-1 to +1) cartesian grid.
Also, the angles in the formula should be in radians, not in degrees.
function vanDerGrinten(lat, lng) {
lat = lat * Math.PI / 180;
lng = lng * Math.PI / 180;
var lng0 = 0;
var A1 = 0.5 * Math.abs((Math.PI / (lng - lng0) - (lng - lng0) / Math.PI));
var phi = Math.asin(Math.abs(2 * lat / Math.PI));
var G = Math.cos(phi) / (Math.sin(phi) + Math.cos(phi) - 1);
P = G * (2 / Math.sin(phi) - 1);
Q = A1 * A1 + G;
x0 = A1 * A1 * (G - P * P) * (G - P * P) - (P * P + A1 * A1) * (G * G - P * P);
x1 = (A1 * (G - P * P) + Math.sqrt(x0));
x2 = (P * P + A1 * A1);
x = sgn(lng - lng0) * Math.PI * x1 / x2;
y = sgn(lat) * Math.PI * Math.abs(P * Q - A1 * Math.sqrt((A1 * A1 + 1) * (P * P + A1 * A1) - Q * Q)) / (P * P + A1 * A1);
return { _x: x, _y: y };
}