//程序功能：利用最小二乘法拟合直线
//输入：二维点
//输出：拟合直线
line calLine(LinkedList <myPair> input)
{
matrix A = new matrix(input.Count, 2);
matrix AT = new matrix(2, input.Count);
matrix B = new matrix(input.Count, 1);
for (int i = 0; i < input.Count; ++i)
{
myPair cur = input.ElementAt(i);
A.a[i, 0] = cur.x;
A.a[i, 1] = cur.y;
AT.a[0, i] = cur.x;
AT.a[1, i] = cur.y;
B.a[i, 0] = 100;
}
matrix coef = AT.doMul(A);
matrix b = AT.doMul(B);
matrix mat = new matrix(2, 3);
for (int i = 0; i < 2; ++i)
{
for (int j = 0; j < 2; ++j)
{
mat.a[i, j] = coef.a[i, j];
}
}
mat.a[0, 2] = b.a[0, 0];
mat.a[1, 2] = b.a[1, 0];
double BB = (mat.a[0, 0] * mat.a[1, 2] - mat.a[1, 0] * mat.a[0, 2]) / (mat.a[1, 1] * mat.a[0, 0] - mat.a[0, 1] * mat.a[1, 0]);
double AA = (mat.a[0, 2] - mat.a[0, 1] * BB) / mat.a[0, 0];
return(new line(AA, BB, -100));
}
//计算圆的圆心，输入为自定义图片类input，输出为三元组(x,y,r)
//对input的限制：只包含单圆环
public circle doFind(myPicture input)
{
//从圆周上对称取10组点
int cnt = 0;
LinkedList <myPair> arr = new LinkedList <myPair>();
for (int i = 2; i < input.width; i += 8)
{
for (int j = 5; j < input.height; ++j)
{
if (input.grayDegree[i, j] == 255)
{
cnt++;
arr.AddLast(new myPair(i, j));
for (int k = input.height - 5; k >= 0; --k)
{
if (input.grayDegree[i, k] == 255)
{
arr.AddLast(new myPair(i, k));
break;
}
}
break;
}
}
if (cnt == 10)
{
break;
}
}
//最小二乘法求解圆心
A = new matrix(2 * cnt, 3);
AT = new matrix(3, 2 * cnt);
B = new matrix(2 * cnt, 1);
int cur = 0;
foreach (myPair p in arr)
{
int x = p.x;
int y = p.y;
A.a[cur, 0] = x;
A.a[cur, 1] = y;
A.a[cur, 2] = 1;
AT.a[0, cur] = x;
AT.a[1, cur] = y;
AT.a[2, cur] = 1;
B.a[cur, 0] = 1.0 * x * x + 1.0 * y * y;
cur++;
}
matrix coef = AT.doMul(A);
matrix b = AT.doMul(B);
matrix mat = new matrix(3, 4);
for (int i = 0; i < 3; ++i)
{
for (int j = 0; j < 3; ++j)
{
mat.a[i, j] = coef.a[i, j];
}
}
mat.a[0, 3] = b.a[0, 0];
mat.a[1, 3] = b.a[1, 0];
mat.a[2, 3] = b.a[2, 0];
return(cal(mat));
}
