/// <summary>
/// 根据一种四参数模型的参数推导另一种四参数模型的参数
/// </summary>
/// <param name="inFour">输入四参数</param>
/// <param name="outMode">输出模型</param>
/// <returns></returns>
public static FourPara ChangeMode(FourPara inFour, enumFourMode outMode)
{
if (inFour is null)
{
return(null);
}
double dx2, dy2, r2, s2;
ChangeMode(inFour.DX, inFour.DY, inFour.R, inFour.S, inFour.Mode, out dx2, out dy2, out r2, out s2, outMode);
FourPara outFour = new FourPara
{
DX = dx2,
DY = dy2,
R = r2,
S = s2,
Mode = outMode,
};
return(outFour);
}
/// <summary>
/// 根据正算的四参数计算反算的四参数
/// </summary>
/// <param name="inFour">正算四参数</param>
/// <returns>反算四参数</returns>
public static FourPara GetInv(FourPara inFour)
{
if (inFour is null)
{
return(null);
}
string modeStr = Mode2Str(inFour.Mode);
double dx, dy, r, s;
GetInv(modeStr, inFour.DX, inFour.DY, inFour.R, inFour.S, out dx, out dy, out r, out s);
FourPara outFour = new FourPara
{
DX = dx,
DY = dy,
R = r,
S = s,
Mode = inFour.Mode,
};
return(outFour);
}
/// <summary>
/// 迭代计算四参数，剔除粗差(三倍中误差)的点
/// </summary>
/// <param name="x1">x坐标(米)</param>
/// <param name="y1">y坐标(米)</param>
/// <param name="x2">x坐标(米)</param>
/// <param name="y2">y坐标(米)</param>
/// <returns></returns>
public static FourPara CalParaIter(List <double> x1, List <double> y1,
List <double> x2, List <double> y2, string mode = "ors")
{
List <int> counts = new List <int> {
x1.Count, x2.Count, y1.Count, y2.Count
};
int minCount = counts.Min();
List <int> indexes = Enumerable.Range(0, minCount).ToList();
FourPara four = new FourPara();
Trans trans = new Trans();
List <double> x3 = new List <double>();
List <double> y3 = new List <double>();
List <double> xx1 = new List <double>();
List <double> yy1 = new List <double>();
List <double> xx2 = new List <double>();
List <double> yy2 = new List <double>();
while (indexes.Count > 3)
{
x3.Clear();
y3.Clear();
xx1.Clear();
yy1.Clear();
xx2.Clear();
yy2.Clear();
for (int i = 0; i < indexes.Count; i++)
{
xx1.Add(x1[indexes[i]]);
yy1.Add(y1[indexes[i]]);
xx2.Add(x2[indexes[i]]);
yy2.Add(y2[indexes[i]]);
}
//// 计算四参数
four = CalPara(xx1, yy1, xx2, yy2, mode);
//// 用得到的四参数进行转换
double x = 0d, y = 0d;
for (int i = 0; i < xx1.Count; i++)
{
trans.Four(xx1[i], yy1[i], out x, out y, four);
x3.Add(x);
y3.Add(y);
}
//// 计算点位误差
var diff = from i in Enumerable.Range(0, indexes.Count)
select new
{
Index = indexes[i],
Diff = Math.Sqrt(Math.Pow(x3[i] - x2[indexes[i]], 2) +
Math.Pow(y3[i] - y2[indexes[i]], 2)),
};
//// 计算验后中误差
double sigma = Math.Sqrt(diff.Sum(d => d.Diff * d.Diff) / indexes.Count);
var max = diff.OrderByDescending(d => d.Diff).First();
//// 剔除点
if (max.Diff < sigma * 3d)
{
break;
}
else
{
indexes.Remove(max.Index);
}
}
return(four);
}
/// <summary>
/// 计算四参数
/// </summary>
/// <param name="x1"></param>
/// <param name="y1"></param>
/// <param name="x2"></param>
/// <param name="y2"></param>
/// <param name="dx">平移量(米)</param>
/// <param name="dy">平移量(米)</param>
/// <param name="r">旋转(弧度)</param>
/// <param name="s">尺度(ppm)</param>
/// <param name="mode">模型 ors或者rso o(ffset) s(cale) r(otate)</param>
/// <returns></returns>
public static bool CalPara(List <double> x1, List <double> y1,
List <double> x2, List <double> y2, out double dx, out double dy, out double r, out double s,
string mode = "ors")
{
dx = dy = r = s = 0;
if (x1 == null || y1 == null || x2 == null || y2 == null)
{
return(false);
}
//// 老板的算法
FourPara four = new FourPara();
if (!(x1.Count() == y1.Count() &&
x2.Count() == y2.Count() &&
x1.Count() == x2.Count()))
{
return(false);
}
int n = x1.Count();
if (n <= 2)
{
return(false);
}
List <double> xin = new List <double>(n);
List <double> yin = new List <double>(n);
List <double> xout = new List <double>(n);
List <double> yout = new List <double>(n);
for (int i = 0; i < x1.Count(); i++)
{
if (x1[i] >= 999999999 || y1[i] >= 999999999 ||
x2[i] >= 999999999 || y2[i] >= 999999999)
{
continue;
}
dx += x2[i] - x1[i];
dy += y2[i] - y1[i];
}
dx = dx / n;
dy = dy / n;
//Matrix<double> B = new DenseMatrix(n * 2, 4);
//Vector<double> L = new DenseVector(n * 2);
//Vector<double> xHat = new DenseVector(4);
double[,] B = new double[n * 2, 4];
double[] L = new double[n * 2];
double[] xHat = new double[4];
double[] w = new double[4];
xHat[0] = xHat[1] = xHat[2] = xHat[3] = 100;
int count = 0;
int num = 4;
while (count < 20 && Math.Abs(xHat[0]) > 1E-10 && Math.Abs(xHat[1]) > 1E-10 && Math.Abs(xHat[2]) > 1E-15 && Math.Abs(xHat[3]) > 1E-15)
{
count++;
for (int i = 0; i < n; i++)
{
B[i * 2, 0] = (1 + s) * Math.Cos(r);
B[i * 2, 1] = (1 + s) * Math.Sin(r);
B[i * 2, 2] = Math.Cos(r) * (x1[i] + dx) + Math.Sin(r) * (y1[i] + dy);
B[i * 2, 3] = -(1 + s) * Math.Sin(r) * (x1[i] + dx) + (1 + s) * Math.Cos(r) * (y1[i] + dy);
B[i * 2 + 1, 0] = -(1 + s) * Math.Sin(r);
B[i * 2 + 1, 1] = (1 + s) * Math.Cos(r);
B[i * 2 + 1, 2] = -Math.Sin(r) * (x1[i] + dx) + Math.Cos(r) * (y1[i] + dy);
B[i * 2 + 1, 3] = -(1 + s) * Math.Cos(r) * (x1[i] + dx) - (1 + s) * Math.Sin(r) * (y1[i] + dy);
L[i * 2] = (1 + s) * Math.Cos(r) * (x1[i] + dx) + (1 + s) * Math.Sin(r) * (y1[i] + dy) - x2[i];
L[i * 2 + 1] = -(1 + s) * Math.Sin(r) * (x1[i] + dx) + (1 + s) * Math.Cos(r) * (y1[i] + dy) - y2[i];
}
//xHat = -(B.Transpose() * B).Inverse() * (B.Transpose() * L);
double[] p = new double[num * num];
for (int i = 0; i < num; i++)
{
for (int j = i; j < num; j++)
{
p[i * num + j] = 0;
for (int k = 0; k < 2 * n; k++)
{
p[i * num + j] += B[k, j] * B[k, i];
}
p[j * num + i] = p[i * num + j];
}
}
for (int i = 0; i < num; i++)
{
w[i] = 0.0;
for (int j = 0; j < 2 * n; j++)
{
w[i] += B[j, i] * L[j];
}
}
inv(ref p, num);
for (int i = 0; i < num; i++)
{
xHat[i] = 0;
for (int j = 0; j < num; j++)
{
xHat[i] += -p[i * num + j] * w[j];
}
}
dx += xHat[0];
dy += xHat[1];
s += xHat[2];
r += xHat[3];
}
s *= 1e6;
//// 计算出参数的模型是ors，转换成rso
if (!mode.StartsWith("o"))
{
double dx2, dy2, r2, s2;
ChangeMode(dx, dy, r, s, "ors", out dx2, out dy2, out r2, out s2, "rso");
dx = dx2;
dy = dy2;
r = r2;
s = s2;
}
return(true);
}
/// <summary>
/// 计算四参数
/// </summary>
/// <param name="x1"></param>
/// <param name="y1"></param>
/// <param name="x2"></param>
/// <param name="y2"></param>
/// <param name="mode">默认是"ors",即o(ffset)-r(otate)-s(cale)</param>
/// <returns></returns>
public static FourPara CalPara(List <double> x1, List <double> y1,
List <double> x2, List <double> y2, string mode = "rso")
{
if (x1 == null || y1 == null || x2 == null || y2 == null)
{
return(null);
}
//// 模型,默认是 旋转-缩放-平移
if (mode is null)
{
mode = "ors";
}
#region 自己的算法
//int minCnt = Min(Min(x1.Count, y1.Count), Min(x2.Count, y2.Count));
//if (minCnt < 2) return null;
//Matrix<double> B = new DenseMatrix(minCnt * 2, 4);
//Vector<double> L = new DenseVector(minCnt * 2);
//for (int i = 0; i < minCnt; i++)
//{
// B[i * 2, 0] = y1[i];
// B[i * 2, 1] = x1[i];
// B[i * 2, 2] = 1;
// B[i * 2, 3] = 0;
// B[i * 2 + 1, 0] = -x1[i];
// B[i * 2 + 1, 1] = y1[i];
// B[i * 2 + 1, 2] = 0;
// B[i * 2 + 1, 3] = 1;
// L[i * 2] = x2[i];
// L[i * 2 + 1] = y2[i];
//}
//Vector<double> xHat = (B.Transpose() * B).Inverse() * (B.Transpose() * L);
//double a = xHat[0]; // m*sin(θ)
//double b = xHat[1]; // m*cos(θ)
//double c = xHat[2]; // Δx
//double d = xHat[3]; // Δy
//FourPara four = new FourPara
//{
// Mode = enumFourMode.RSO,
// R = Math.Atan2(a, b),
// S = (Math.Sqrt(a * a + b * b) - 1) * 1e6,
// DX = c,
// DY = d
//};
//try
//{
// //// 将模型改为 平移-旋转-缩放
// if (mode.ToLower().StartsWith("o"))
// {
// four.Mode = enumFourMode.ORS;
// double dx = four.DX;
// double dy = four.DY;
// four.DX = (1/(1 + four.S * 1e-6)) * (Math.Cos(four.R) * dx - Math.Sin(four.R) * dy);
// four.DY = (1/(1 + four.S * 1e-6)) * (Math.Sin(four.R) * dx + Math.Cos(four.R) * dy);
// }
//}
//catch (Exception ex)
//{
//}
#endregion
double dx, dy, r, s;
CalPara(x1, y1, x2, y2, out dx, out dy, out r, out s, mode);
FourPara four = new FourPara
{
Mode = Str2Mode(mode),
DX = dx,
DY = dy,
R = r,
S = s,
};
return(four);
}
/// <summary>
/// 四参数转仿射参数
/// </summary>
/// <param name="four"></param>
/// <param name="A"></param>
/// <param name="B"></param>
/// <param name="C"></param>
/// <param name="D"></param>
/// <param name="E"></param>
/// <param name="F"></param>
public static void Four2Affine(FourPara four, out double A, out double B, out double C, out double D, out double E, out double F)
{
Four2Affine(four.DX, four.DY, four.R, four.S, out A, out B, out C, out D, out E, out F, Mode2Str(four.Mode));
}
public static void Four2d(ref double x, ref double y, FourPara four)
{
Four2d(ref x, ref y, four.DX, four.DY, four.R, four.S, FourPara.Mode2Str(four.Mode));
}
public void Four(double x1, double y1, out double x2, out double y2,
FourPara four)
{
Four(x1, y1, out x2, out y2, four.DX, four.DY, four.R, four.S, FourPara.Mode2Str(four.Mode));
}