public Qauternion GetConjugate()
{
var result = new Qauternion(W, -X, -Y, -Z);
result.Normalize();
return(result);
}
private Vector3 RotateVector(Vector3 vector, Qauternion rotation)
{
var rotatedQ = new Qauternion(0, vector.X, vector.Y, vector.Z);
Qauternion result = rotation * rotatedQ;
result = result * rotation.GetConjugate();
return result.Axis;
}
private Vector3 RotateVector(Vector3 vector, Qauternion rotation)
{
var rotatedQ = new Qauternion(0, vector.X, vector.Y, vector.Z);
Qauternion result = rotation * rotatedQ;
result = result * rotation.GetConjugate();
return(result.Axis);
}
public Vector3 RotateVectorAroundAxis(Vector3 rotatingVector, Vector3 rotationVector, double angle)
{
if (Math.Abs(angle) < Consts.DoubleEqualityThreshold)
{
return new Vector3(rotatingVector.X, rotatingVector.Y, rotatingVector.Z);
}
var rotationQ = new Qauternion(rotationVector, angle);
return RotateVector(rotatingVector, rotationQ);
}
public Vector3 RotateVectorAroundAxis(Vector3 rotatingVector, Vector3 rotationVector, double angle)
{
if (Math.Abs(angle) < Consts.DoubleEqualityThreshold)
{
return(new Vector3(rotatingVector.X, rotatingVector.Y, rotatingVector.Z));
}
var rotationQ = new Qauternion(rotationVector, angle);
return(RotateVector(rotatingVector, rotationQ));
}
public Vector3[] GetLocalAxis(Vector3 vector, double adjustmentAngle, double referenceAngle)
{
double horizontalProjectionLength = Math.Sqrt(Math.Pow(vector.X, 2) + Math.Pow(vector.Y, 2));
bool isVertical = Math.Abs(horizontalProjectionLength) < Consts.DoubleEqualityThreshold;
var result = new Vector3[3];
var rotationVector = Vector3.Up;
if (isVertical)
{
// In this case up vector lies on X axis.
// We rotate X unit vector around vertical axis to get vertical result
double localXAxisAngle = referenceAngle + Math.PI / 2;
var rotation1 = new Qauternion(rotationVector, localXAxisAngle);
result[1] = RotateVector(Vector3.Right, rotation1);
result[0] = vector.Clone(); //No need for adjustment in this case.
}
else
{
//Construct horizontal projection vector.
var horizontalProjection = new Vector3(vector.X, vector.Y, 0);
horizontalProjection.Normalize();
// Now we have a projection on XY plane of the initial vector. We need to first rotate it 90 degrees around Z axis to find the right vector.
var rotation1 = new Qauternion(rotationVector, Math.PI / 2);
result[1] = RotateVector(horizontalProjection, rotation1);
// If adjustment is required we now rotate original vector by the required angle.
// We need to rotate it closer to the horizontal plane.
result[0] = AdjustVectorAsNeeded(vector, result[1], adjustmentAngle);
double adjustedAngle = GetAngleBetweenVectors(result[0], horizontalProjection) * 180 / Math.PI;
}
// And then we can rotate that vector by 90 degrees around the right vector to get our Up vector.
var rotation2 = new Qauternion(result[0], Math.PI / 2);
result[2] = RotateVector(result[1], rotation2);
if (Math.Abs(90 - GetAngleBetweenVectors(result[0], result[1]) * 180 / Math.PI) > Consts.DoubleEqualityThreshold ||
Math.Abs(90 - GetAngleBetweenVectors(result[1], result[2]) * 180 / Math.PI) > Consts.DoubleEqualityThreshold ||
Math.Abs(90 - GetAngleBetweenVectors(result[0], result[2]) * 180 / Math.PI) > Consts.DoubleEqualityThreshold)
{
throw new ArithmeticException("After trying to find local coordinate axes they were not 90 degrees away from the each other.");
}
return(result);
}
public Vector3[] GetLocalAxis(Vector3 vector, double adjustmentAngle, double referenceAngle)
{
double horizontalProjectionLength = Math.Sqrt(Math.Pow(vector.X, 2) + Math.Pow(vector.Y, 2));
bool isVertical = Math.Abs(horizontalProjectionLength) < Consts.DoubleEqualityThreshold;
var result = new Vector3[3];
var rotationVector = Vector3.Up;
if (isVertical)
{
// In this case up vector lies on X axis.
// We rotate X unit vector around vertical axis to get vertical result
double localXAxisAngle = referenceAngle + Math.PI / 2;
var rotation1 = new Qauternion(rotationVector, localXAxisAngle);
result[1] = RotateVector(Vector3.Right, rotation1);
result[0] = vector.Clone(); //No need for adjustment in this case.
}
else
{
//Construct horizontal projection vector.
var horizontalProjection = new Vector3(vector.X, vector.Y, 0);
horizontalProjection.Normalize();
// Now we have a projection on XY plane of the initial vector. We need to first rotate it 90 degrees around Z axis to find the right vector.
var rotation1 = new Qauternion(rotationVector, Math.PI / 2);
result[1] = RotateVector(horizontalProjection, rotation1);
// If adjustment is required we now rotate original vector by the required angle.
// We need to rotate it closer to the horizontal plane.
result[0] = AdjustVectorAsNeeded(vector, result[1], adjustmentAngle);
double adjustedAngle = GetAngleBetweenVectors(result[0], horizontalProjection) * 180 / Math.PI;
}
// And then we can rotate that vector by 90 degrees around the right vector to get our Up vector.
var rotation2 = new Qauternion(result[0], Math.PI / 2);
result[2] = RotateVector(result[1], rotation2);
if (Math.Abs(90 - GetAngleBetweenVectors(result[0], result[1]) * 180 / Math.PI) > Consts.DoubleEqualityThreshold ||
Math.Abs(90 - GetAngleBetweenVectors(result[1], result[2]) * 180 / Math.PI) > Consts.DoubleEqualityThreshold ||
Math.Abs(90 - GetAngleBetweenVectors(result[0], result[2]) * 180 / Math.PI) > Consts.DoubleEqualityThreshold)
{
throw new ArithmeticException("After trying to find local coordinate axes they were not 90 degrees away from the each other.");
}
return result;
}
protected bool Equals(Qauternion other)
{
return _w.Equals(other._w) && _x.Equals(other._x) && _y.Equals(other._y) && _z.Equals(other._z);
}
public Qauternion GetConjugate()
{
var result = new Qauternion(W, -X, -Y, -Z);
result.Normalize();
return result;
}
protected bool Equals(Qauternion other)
{
return(_w.Equals(other._w) && _x.Equals(other._x) && _y.Equals(other._y) && _z.Equals(other._z));
}