旋转标定的数学公式
一 旋转中心标定
publicclassCircleFitter{/// <summary>/// 通过三个点计算圆心坐标/// </summary>/// <param name="point1">第一个点 (x1, y1)</param>/// <param name="point2">第二个点 (x2, y2)</param>/// <param name="point3">第三个点 (x3, y3)</param>/// <returns>圆心坐标 (cx, cy)</returns>publicstatic(doublecx,doublecy)FitCircleFromThreePoints((doublex,doubley)point1,(doublex,doubley)point2,(doublex,doubley)point3){// 解法基于三点确定一个圆的几何原理// 设圆心为 (cx, cy)，则有：// (x1-cx)² + (y1-cy)² = (x2-cx)² + (y2-cy)² = (x3-cx)² + (y3-cy)² = r²doublex1=point1.x,y1=point1.y;doublex2=point2.x,y2=point2.y;doublex3=point3.x,y3=point3.y;// 计算中间变量doubleA=x2-x1;doubleB=y2-y1;doubleC=x3-x1;doubleD=y3-y1;doubleE=A*(x1+x2)+B*(y1+y2);doubleF=C*(x1+x3)+D*(y1+y3);doubleG=2*(A*(y3-y1)-B*(x3-x1));// 避免除以零（三点共线的情况）if(Math.Abs(G)<1e-10){thrownewArgumentException("三点共线，无法确定唯一的圆");}// 计算圆心坐标doublecx=(D*E-B*F)/G;doublecy=(A*F-C*E)/G;return(cx,cy);}/// <summary>/// 计算圆的半径/// </summary>publicstaticdoubleCalculateRadius((doublex,doubley)center,(doublex,doubley)point){doubledx=point.x-center.x;doubledy=point.y-center.y;returnMath.Sqrt(dx*dx+dy*dy);}}
二 使用
publicpartialclassForm1:Form{publicForm1(){InitializeComponent();}privatevoidbutton1_Click(objectsender,EventArgse){try{// 拟合圆的三个点坐标varpoint1=(x:3332.24,y:1807.67);varpoint2=(x:3099.6,y:1922.86);varpoint3=(x:2838.07,y:2000.45);// 计算圆心varcenter=CircleFitter.FitCircleFromThreePoints(point1,point2,point3);MessageBox.Show($"圆心坐标: ({center.cx:F4},{center.cy:F4})");// 计算半径（使用第一个点）doubleradius=CircleFitter.CalculateRadius(center,point1);MessageBox.Show($"圆的半径:{radius:F4}");}catch(ArgumentExceptionex){Console.WriteLine($"错误:{ex.Message}");}}}
