public SpaceTransformationHandler(Point3D newCenter, Point3D newPtOnZAxis)
{
//Calculate the unit normals along the three direction for the new system
var n = new Vector3D
{
X = newPtOnZAxis.X - newCenter.X,
Y = newPtOnZAxis.Y - newCenter.Y,
Z = newPtOnZAxis.Z - newCenter.Z
};
n = n / n.Length;
var v = new Vector3D {
X = n.X, Y = n.Y + 10.0f, Z = n.Z
}; //A vector pointing a little higher than the first vector
var u = Vector3D.CrossProduct(v, n);
u = u / u.Length;
v = Vector3D.CrossProduct(n, u);
v = v / v.Length;
double[,] rotatXonMatrXx = { { u.X, u.Y, u.Z, 0.0f }, { v.X, v.Y, v.Z, 0.0f }, { n.X, n.Y, n.Z, 0.0f }, { 0.0f, 0.0f, 0.0f, 1.0f } };
double[,] translationMatrix = { { 1.0f, 0.0f, 0.0f, -newCenter.X }, { 0.0f, 1.0f, 0.0f, -newCenter.Y }, { 0.0f, 0.0f, 1.0f, -newCenter.Z }, { 0.0f, 0.0f, 0.0f, 1.0f } };
_transformationMatrix = MatrixDataProcessor.MultiplyMatrices(rotatXonMatrXx, translationMatrix);
}
public Point3D GetTransformedPoint(Point3D inP)
{
double[,] inputMatrix = { { inP.X }, { inP.Y }, { inP.Z }, { 1.0f } };
var resultantMatrix = MatrixDataProcessor.MultiplyMatrices(_transformationMatrix, inputMatrix);
var result = new Point3D
{
X = resultantMatrix[0, 0],
Y = resultantMatrix[1, 0],
Z = resultantMatrix[2, 0]
};
return(result);
}
/// <summary>
/// uses logic in Linear Regression.pdf to give a straight line based on the passed data points
/// see "calculate line equation using linear regression.pdf" for calculation parameters
/// </summary>
/// <param name="xYPts"></param>
/// <returns></returns>
public static LineEquation2D Get2DStraightLineFromDataConstants(List <Point> xYPts)
{
//eqn form y = a + bx
var n = xYPts.Count;
var sumX = (xYPts.Select(pt => pt.X)).Sum();
var sumY = (xYPts.Select(pt => pt.Y)).Sum();
var sumXx = (xYPts.Select(pt => pt.X * pt.X)).Sum();
var sumXy = (xYPts.Select(pt => pt.X * pt.Y)).Sum();
//n a + sumX b = sumY
//sumX a + sumXX b = sumXY
var coefficientMatrix = new[, ] {
{ n, sumX }, { sumX, sumXx }
};
var eqnConstants = new[] { sumY, sumXy };
var result = MatrixDataProcessor.SolveEquation(coefficientMatrix, eqnConstants);
return(new LineEquation2D {
M = result[1], C = result[0]
});
}