private void mapToSphere(Point point, Vector3f vector)
{
Point2f tempPoint = new Point2f(point.X, point.Y);
//Adjust point coords and scale down to range of [-1 ... 1]
tempPoint.x = (tempPoint.x * this.adjustWidth) - 1.0f;
tempPoint.y = 1.0f - (tempPoint.y * this.adjustHeight);
//Compute square of the length of the vector from this point to the center
float length = (tempPoint.x * tempPoint.x) + (tempPoint.y * tempPoint.y);
//If the point is mapped outside the sphere... (length > radius squared)
if (length > 1.0f)
{
//Compute a normalizing factor (radius / sqrt(length))
float norm = (float)(1.0 / Math.Sqrt(length));
//Return the "normalized" vector, a point on the sphere
vector.x = tempPoint.x * norm;
vector.y = tempPoint.y * norm;
vector.z = 0.0f;
}
//Else it's inside
else
{
//Return a vector to a point mapped inside the sphere sqrt(radius squared - length)
vector.x = tempPoint.x;
vector.y = tempPoint.y;
vector.z = (float)System.Math.Sqrt(1.0f - length);
}
}
//Mouse drag, calculate rotation
public void drag(Point NewPt, Quat4f NewRot)
{
//Map the point to the sphere
this.mapToSphere(NewPt, EnVec);
//Return the quaternion equivalent to the rotation
if (NewRot != null)
{
Vector3f Perp = new Vector3f();
//Compute the vector perpendicular to the begin and end vectors
Vector3f.cross(Perp, StVec, EnVec);
//Compute the length of the perpendicular vector
if (Perp.length() > Epsilon)
//if its non-zero
{
//We're ok, so return the perpendicular vector as the transform after all
NewRot.x = Perp.x;
NewRot.y = Perp.y;
NewRot.z = Perp.z;
//In the quaternion values, w is cosine (theta / 2), where theta is the rotation angle
NewRot.w = Vector3f.dot(StVec, EnVec);
}
//if it is zero
else
{
//The begin and end vectors coincide, so return an identity transform
NewRot.x = NewRot.y = NewRot.z = NewRot.w = 0.0f;
}
}
}
/// <summary>
/// Cross Product of Two Vectors.
/// </summary>
/// <param name="Result">Resultant Vector</param>
/// <param name="v1">Vector 1</param>
/// <param name="v2">Vector 2</param>
public static void cross(Vector3f Result, Vector3f v1, Vector3f v2)
{
Result.x = (v1.y * v2.z) - (v1.z * v2.y);
Result.y = (v1.z * v2.x) - (v1.x * v2.z);
Result.z = (v1.x * v2.y) - (v1.y * v2.x);
}
/// <summary>
/// Dot Product of Two Vectors.
/// </summary>
/// <param name="v1">Vector 1</param>
/// <param name="v2">Vector 2</param>
/// <returns></returns>
public static float dot(Vector3f v1, Vector3f v2)
{
return (v1.x * v2.x) + (v1.y * v2.y) + (v1.z * v2.z);
}
private Vector3f StVec; //Saved click vector
#endregion Fields
#region Constructors
public arcball(float NewWidth, float NewHeight)
{
StVec = new Vector3f();
EnVec = new Vector3f();
setBounds(NewWidth, NewHeight);
}