public static GLTK.Matrix Short3CoordToRotationMatrix(Chunks.Short3Coord xiCoord)
{
GLTK.Matrix lRotation = GLTK.Matrix.Rotation(-xiCoord.Z / 1024.0 * Math.PI / 2.0, GLTK.Vector.ZAxis);
lRotation *= GLTK.Matrix.Rotation(-xiCoord.Y / 1024.0 * Math.PI / 2.0, GLTK.Vector.YAxis);
lRotation *= GLTK.Matrix.Rotation(-xiCoord.X / 1024.0 * Math.PI / 2.0, GLTK.Vector.XAxis);
return(lRotation);
}
/// <summary>
/// Converts a GLTK rotation matrix into the MMs representation of a rotation.
///
/// The input matrix must be rotation-only, otherwise the output of this method
/// is not defined.
/// </summary>
public static Chunks.Short3Coord RotationMatrixToShort3Coord(GLTK.Matrix xiRotation)
{
// Algorithm is as follows:
//
// There are only two degrees of freedom, so one of the coordinates in the
// vector is redundant. Therefore we fix one of the coordinates at 0 and
// solve for the other 2.
//
// * First identify the axis that moves the furthest under the rotation;
// this will be the fixed coordinate i.e. we'll rotate about the other
// two.
// * Next see what effect the rotation has on the axis that moves furthest;
// since rotations are defined uniquely by their action on a single point
// on the unit ball (apart from the poles) we just need to solve the
// simultaneous equations generated by applying rotations of theta and phi
// around the two non-fixed axis to this vector. Note: it is sufficient
// to solve only two of the three equations as the third coordinate of the
// vector is determined by the other two.
// see what effect the rotation has on the x and y axes
GLTK.Vector lNewXAxis = xiRotation * GLTK.Vector.XAxis;
GLTK.Vector lNewYAxis = xiRotation * GLTK.Vector.YAxis;
GLTK.Vector lNewZAxis = xiRotation * GLTK.Vector.ZAxis;
double lXdist = Math.Abs(lNewXAxis * GLTK.Vector.XAxis);
double lYdist = Math.Abs(lNewYAxis * GLTK.Vector.YAxis);
double lZdist = Math.Abs(lNewZAxis * GLTK.Vector.ZAxis);
if (lXdist < lYdist && lXdist < lZdist)
{
// x axis has moved the furthest - use (0, y, z) format
// rotate about z by theta first, then y by phi
// need to solve cos(theta)*cos(phi) = newx.x; sin(theta) = newx.y
double lTheta = Math.Asin(-lNewXAxis.y);
// check which of the possible values for theta is correct
if (lNewXAxis.x < 0)
{
lTheta = Math.PI - lTheta;
}
double lPhi = Math.Acos(lNewXAxis.x / Math.Cos(lTheta));
// check which of the possible values for phi is correct
if (lNewXAxis.z < 0)
{
lPhi = -lPhi;
}
return(new Chunks.Short3Coord(
0,
(short)((lPhi / Math.PI) * 2 * 1024),
(short)((lTheta / Math.PI) * 2 * 1024)));
}
else if (lYdist < lZdist)
{
// y axis has moved the furthest - use (x, 0, z) format
// rotate about z by theta first, then x by phi
// need to solve -sin(theta) = newy.x; cos(theta)cos(phi) = newy.y
double lTheta = Math.Asin(lNewYAxis.x);
// check which of the possible values for theta is correct
if (lNewYAxis.y < 0)
{
lTheta = Math.PI - lTheta;
}
double lPhi = Math.Acos(lNewYAxis.y / Math.Cos(lTheta));
// check which of the possible values for phi is correct
if (lNewYAxis.z > 0)
{
lPhi = -lPhi;
}
return(new Chunks.Short3Coord(
(short)((lPhi / Math.PI) * 2 * 1024),
0,
(short)((lTheta / Math.PI) * 2 * 1024)));
}
else
{
// z axis has moved the furthest - use (x, y, 0) format
// rotate about y by theta first, then x by phi
// need to solve sin(theta) = newz.x; cos(phi)cos(theta) = newz.z
double lTheta = Math.Asin(lNewZAxis.x);
// check which of the possible values for theta is correct
if (lNewZAxis.z < 0)
{
lTheta = Math.PI - lTheta;
}
double lPhi = Math.Acos(lNewZAxis.z / Math.Cos(lTheta));
// check which of the possible values for phi is correct
if (lNewZAxis.y < 0)
{
lPhi = -lPhi;
}
return(new Chunks.Short3Coord(
(short)((lPhi / Math.PI) * 2 * 1024),
(short)((lTheta / Math.PI) * 2 * 1024),
0));
}
}
