I am using a virtual sphere controller for an application rendering a globe. When using an orthogonal projection, I am able to grab a point on the globe and have it track with the mouse very tightly. When using a perspective projection, the point on the globe gets away from the cursor. I feel this is because my pointOnUnitSphere assumes an orthogonal projection. How would I go about using a perspective projection?

Here is the code I am using

P is a ground point, center is always 0,0,0 and radius is just the size of the virtual sphere I am using, in this case the radius of the globe.

private void pointOnUnitSphere(Point3d p, Vector3d v) {

double vx = (p.getX() - this.center.getX()) / this.radius;

double vy = (p.getY() - this.center.getY()) / this.radius;

double lengthSquared = vx * vx + vy * vy;

// Project the point onto the sphere, assuming orthognal projection.

// Points beyond the virtual sphere are normalized onto edge of the sphere (where z = 0)

double vz = 0.0;

if (lengthSquared < 1.0)

vz = Math.sqrt(1.0 - lengthSquared);

else {

// past the edge of the sphere. Normalize onto edge of

// the sphere

double length = Math.sqrt(lengthSquared);

vx /= length;

vy /= length;

}

v.setVector(vx, vy, vz);

}