/// <summary>
/// Calculates the four helmert transformation parameters {a,b,c,d} and the sum of the squares of the residuals (s0)
/// </summary>
/// <remarks>
/// <para>
/// a,b defines scale vector 1 of coordinate system, d,e scale vector 2.
/// c,f defines offset.
/// </para>
/// <para>
/// Converting from input (X,Y) to output coordinate system (X',Y') is done by:
/// X' = a*X + b*Y + c, Y' = -b*X + a*Y + d
/// </para>
/// <para>This is a transformation initially based on the affine transformation but slightly simpler.</para>
/// </remarks>
/// <returns>Array with the four transformation parameters, and sum of squared residuals: a,b,c,d,s0</returns>
public HelmertTransformationParameters GetHelmertTransformation()
{
throw new NotSupportedException("This method returns an incorrect transformation - do not use");
if (_inputs.Count < 2)
{
throw(new System.Exception("At least 2 measurements required to calculate helmert transformation"));
}
double b00 = 0;
double b02 = 0;
double b03 = 0;
double[] t = new double[4];
for (int i = 0; i < _inputs.Count; i++)
{
//Calculate summed values
b00 += Math.Pow(_inputs[i].X, 2) + Math.Pow(_inputs[i].Y, 2);
b02 -= _inputs[i].X;
b03 -= _inputs[i].Y;
t[0] += -(_inputs[i].X * _outputs[i].X) - (_inputs[i].Y * _outputs[i].Y);
t[1] += -(_inputs[i].Y * _outputs[i].X) + (_inputs[i].X * _outputs[i].Y);
t[2] += _outputs[i].X;
t[3] += _outputs[i].Y;
}
double frac = 1 / (-_inputs.Count * b00 + Math.Pow(b02, 2) + Math.Pow(b03, 2));
var result = new HelmertTransformationParameters();
result.A = (-_inputs.Count * t[0] + b02 * t[2] + b03 * t[3]) * frac;
result.B = (-_inputs.Count * t[1] + b03 * t[2] - b02 * t[3]) * frac;
result.C = (b02 * t[0] + b03 * t[1] - t[2] * b00) * frac;
result.D = (b03 * t[0] - b02 * t[1] - t[3] * b00) * frac;
//Calculate s0
double s0 = 0;
for (int i = 0; i < _inputs.Count; i++)
{
var tt = result.Transform(_outputs[i]);
s0 += Math.Pow(tt.X - _inputs[i].X, 2) + Math.Pow(tt.Y - _inputs[i].Y, 2);
}
result.s0 = Math.Sqrt(s0) / (_inputs.Count);
return(result);
}
/// <summary>
/// Calculates the four helmert transformation parameters {a,b,c,d} and the sum of the squares of the residuals (s0)
/// </summary>
/// <remarks>
/// <para>
/// a,b defines scale vector 1 of coordinate system, d,e scale vector 2.
/// c,f defines offset.
/// </para>
/// <para>
/// Converting from input (X,Y) to output coordinate system (X',Y') is done by:
/// X' = a*X + b*Y + c, Y' = -b*X + a*Y + d
/// </para>
/// <para>This is a transformation initially based on the affine transformation but slightly simpler.</para>
/// </remarks>
/// <returns>Array with the four transformation parameters, and sum of squared residuals: a,b,c,d,s0</returns>
public HelmertTransformationParameters GetHelmertTransformation()
{
throw new NotSupportedException("This method returns an incorrect transformation - do not use");
if (_inputs.Count < 2)
throw(new System.Exception("At least 2 measurements required to calculate helmert transformation"));
double b00=0;
double b02=0;
double b03=0;
double[] t = new double[4];
for (int i = 0; i < _inputs.Count; i++)
{
//Calculate summed values
b00 += Math.Pow(_inputs[i].X, 2) + Math.Pow(_inputs[i].Y, 2);
b02 -= _inputs[i].X;
b03 -= _inputs[i].Y;
t[0] += -(_inputs[i].X * _outputs[i].X) - (_inputs[i].Y * _outputs[i].Y);
t[1] += -(_inputs[i].Y * _outputs[i].X) + (_inputs[i].X * _outputs[i].Y);
t[2] += _outputs[i].X;
t[3] += _outputs[i].Y;
}
double frac = 1 / (-_inputs.Count * b00 + Math.Pow(b02, 2) + Math.Pow(b03, 2));
var result = new HelmertTransformationParameters();
result.A = (-_inputs.Count * t[0] + b02 * t[2] + b03 * t[3]) * frac;
result.B = (-_inputs.Count * t[1] + b03 * t[2] - b02 * t[3]) * frac;
result.C = (b02 * t[0] + b03 * t[1] - t[2] * b00) * frac;
result.D = (b03 * t[0] - b02 * t[1] - t[3] * b00) * frac;
//Calculate s0
double s0=0;
for (int i = 0; i < _inputs.Count; i++)
{
var tt = result.Transform(_outputs[i]);
s0 += Math.Pow(tt.X - _inputs[i].X, 2) + Math.Pow(tt.Y - _inputs[i].Y, 2);
}
result.s0 = Math.Sqrt(s0) / (_inputs.Count);
return result;
}
