/// <summary>
/// 利用4参数求新坐标系的坐标
/// </summary>
/// <param name="aPtSource">点的源坐标系的坐标</param>
/// <param name="sep">已经知道的4参数</param>
/// <param name="aPtTo">输出: 点的新坐标系的坐标</param>
public static XYZCoordinate Para4Convert(XYZCoordinate aPtSource, FourPara forPara)
{
double k = forPara.scale;
double a1 = k * Math.Cos(forPara.Ax);
double a2 = k * Math.Sin(forPara.Ax);
XYZCoordinate ToCoordinate = new XYZCoordinate();
ToCoordinate.X = forPara.deltaX + a1 * aPtSource.X + a2 * aPtSource.Y;
ToCoordinate.Y = forPara.deltaY + a1 * aPtSource.Y - a2 * aPtSource.X;
ToCoordinate.Z = aPtSource.Z;
return(ToCoordinate);
}
/// <summary>
/// 根据2个或者2个以上的点的两套坐标系的坐标计算4参数(最小二乘法)
/// </summary>
/// <param name="aPtSource">已知点的源坐标系的坐标</param>
/// <param name="aPtTo">已知点的新坐标系的坐标</param>
/// <param name="sep">输出: 4参数</param>
public static FourPara Calc4Para(List <XYZCoordinate> aPtSource, List <XYZCoordinate> aPtTo, out double rms)
{
#region 给A B 矩阵赋值
double[,] arrA = new double[aPtSource.Count * 2, 4]; // 如果是4个已知点， 8 * 4矩阵 A*X=B中的矩阵A
for (int i = 0; i <= arrA.GetLength(0) - 1; i++)
{
if (i % 2 == 0)
{
arrA[i, 0] = aPtSource[i / 2].X;
arrA[i, 1] = aPtSource[i / 2].Y;
arrA[i, 2] = 1;
arrA[i, 3] = 0;
}
else if (i % 2 == 1)
{
arrA[i, 0] = aPtSource[i / 2].Y;
arrA[i, 1] = -aPtSource[i / 2].X;
arrA[i, 2] = 0;
arrA[i, 3] = 1;
}
}
double[,] arrB = new double[aPtSource.Count * 2, 1]; // A * X = B 中的矩阵B, 如果有4个点，就是 8*1矩阵
for (int i = 0; i <= arrB.GetLength(0) - 1; i++)
{
if (i % 2 == 0)
{
arrB[i, 0] = aPtTo[i / 2].X;
}
else if (i % 2 == 1)
{
arrB[i, 0] = aPtTo[i / 2].Y;
}
}
#endregion
Matrix mtrA = new Matrix(arrA); // A矩阵
Matrix mtrAT = Matrix.Transpose(mtrA); // A的转置
Matrix mtrB = new Matrix(arrB); // B矩阵
Matrix mtrATmulA = Matrix.Multiply(mtrAT, mtrA); // A的转置×A
// 求(A的转置×A)的逆矩阵
mtrATmulA = Matrix.Inverse(mtrATmulA);
// A的转置 × B
Matrix mtrATmulB = Matrix.Multiply(mtrAT, mtrB); // A的转置 * B
// 结果
Matrix mtrResult = Matrix.Multiply(mtrATmulA, mtrATmulB);
FourPara forPara = new FourPara();
forPara.deltaX = mtrResult[2, 0];
forPara.deltaY = mtrResult[3, 0];
forPara.Ax = Math.Atan(mtrResult[1, 0] / mtrResult[0, 0]);
forPara.scale = mtrResult[1, 0] / Math.Sin(forPara.Ax);
//计算均方根误差rms
List <XYZCoordinate> pTo = new List <XYZCoordinate>();
for (int i = 0; i < aPtSource.Count; i++)
{
pTo.Add(Para4Convert(aPtSource[i], forPara));
}
rms = 0;
for (int i = 0; i < aPtTo.Count; i++)
{
double deltaX = aPtTo[i].X - pTo[i].X;
double deltaY = aPtTo[i].Y - pTo[i].Y;
double oneSigma = Math.Sqrt((Math.Pow(deltaX, 2) + Math.Pow(deltaY, 2)) / 2);
rms += oneSigma;
}
rms = rms / aPtTo.Count;
return(forPara);
}