Point Axis To Axis Transformation

[madaxe]

I'm writing a simple geometry engine and I'm stuck on transforming points from one reference frame to another.

This code is working but i don't understand why i have to set "double T34 = - iTargetAxis.Origin.Z + iRefAxis.Origin.Z;" this to negative, and I'm sure this is mathematically wrong.



public static IPoint3D PointAxisToAxisTransformation(IPoint3D iRefPoint, IAxisSystem3D iRefAxis, IAxisSystem3D iTargetAxis)
{
IPoint3D ReturnPoint = null;
try
{
double T11 = (VectorMath.DotVectors(iRefAxis.XAxis.UnitVector, iTargetAxis.XAxis.UnitVector));
double T12 = (VectorMath.DotVectors(iRefAxis.XAxis.UnitVector, iTargetAxis.YAxis.UnitVector));
double T13 = (VectorMath.DotVectors(iRefAxis.XAxis.UnitVector, iTargetAxis.ZAxis.UnitVector));
double T14 = iTargetAxis.Origin.X + iRefAxis.Origin.X;

double T21 = (VectorMath.DotVectors(iRefAxis.YAxis.UnitVector, iTargetAxis.XAxis.UnitVector));
double T22 = (VectorMath.DotVectors(iRefAxis.YAxis.UnitVector, iTargetAxis.YAxis.UnitVector));
double T23 = (VectorMath.DotVectors(iRefAxis.YAxis.UnitVector, iTargetAxis.ZAxis.UnitVector));
double T24 = iTargetAxis.Origin.Y + iRefAxis.Origin.Y;

double T31 = (VectorMath.DotVectors(iRefAxis.ZAxis.UnitVector, iTargetAxis.XAxis.UnitVector));
double T32 = (VectorMath.DotVectors(iRefAxis.ZAxis.UnitVector, iTargetAxis.YAxis.UnitVector));
double T33 = (VectorMath.DotVectors(iRefAxis.ZAxis.UnitVector, iTargetAxis.ZAxis.UnitVector));
double T34 = -iTargetAxis.Origin.Z + iRefAxis.Origin.Z;

ReturnPoint = FactoryPoint3D.Point(
T11 * iRefPoint.X + T12 * iRefPoint.Y + T13 * iRefPoint.Z + T14,
T21 * iRefPoint.X + T22 * iRefPoint.Y + T23 * iRefPoint.Z + T24,
T31 * iRefPoint.X + T32 * iRefPoint.Y + T33 * iRefPoint.Z + T34
);
}
catch (Exception ex)
{
Console.WriteLine(ex.Message);
}
return ReturnPoint;
}

public static double DotVectors(IVector3D iFirstVector, IVector3D iSecondVector)
{
double ReturnDouble = 0;

// A.B = AxBx + AyBy + AzBz
double dblScalar;
dblScalar = 0;

dblScalar += iFirstVector.I * iSecondVector.UnitVector.I;
dblScalar += iFirstVector.J * iSecondVector.UnitVector.J;
dblScalar += iFirstVector.K * iSecondVector.UnitVector.K;

ReturnDouble = dblScalar;

return ReturnDouble;
}

 

[Cubist]

Hi madaxe

The process might make more sense if broken down into smaller parts. If I've understood the intent of your code then the steps might be:-

1. un-rotate the point from the iRefAxis axis directions to global axis directions (rotation around the iRefAxis origin)
2. shift the point from being relative to the iRefAxis origin to global, by adding vector ( iRefAxis.origin - [0,0,0] )
3. shift the point from being relative to the global origin to iTargetAxis, by adding vector ( [0,0,0] - iTargetAxis.origin )
4. rotate the point from global axis directions to iTargetAxis axis directions (around the iTargetAxis origin)

Be very careful if (when) combining these steps into a single rotation and offset, since the offset would need to be rotated. Having some matrix functions may be useful.