Gcode的G02|G03指令中A参数转换为IJ参数的方法

G00X5.0Y2.6
G03X6.0Y1.6A1.0

/// <summary>
/// 将G02|G03圆弧段R参数转换成IJ参数
/// </summary>
/// <param name="x0">起始点X坐标</param>
/// <param name="y0">起始点Y坐标</param>
/// <param name="x1">结束点X坐标</param>
/// <param name="y1">结束点Y坐标</param>
/// <param name="r">圆弧半径。如果半径大于0，则圆弧角度小于180度，否则大于180度</param>
/// <param name="clockwise">是否是顺时针，G02表示顺时针，G03表示逆时针，不需要考虑轴版本做调整</param>
/// <returns>参数(I,J)</returns>
public static (double, double) XYAToXYIJ(double x0, double y0, double x1, double y1, double r, bool clockwise)
{
    // 计算圆点中心坐标
    double centerX, centerY;
    if (Equals(y0, y1))
    {
        centerX = (x0 + x1) / 2;
        double w = centerX - x0;
        double h = Math.Sqrt(r * r - w * w);
        int sign = Math.Sign(x1 - x0) * Math.Sign(r);
        centerY = clockwise ? y0 - sign * h : y0 + sign * h;
    }
    else if (Equals(x0, x1))
    {
        centerY = (y0 + y1) / 2;
        double h = centerY - y0;
        double w = Math.Sqrt(r * r - h * h);
        int sign = Math.Sign(y1 - y0) * Math.Sign(r);
        centerX = clockwise ? x0 + sign * w : x0 - sign * w;
    }
    else
    {
        double mx = (x0 + x1) / 2;
        double my = (y0 + y1) / 2;
        double m = (x0 - x1) / (y1 - y0);
        double d = my - m * mx - y0;
        double a = 1 + m * m;
        double b = 2 * (m * d - x0);
        double c = d * d + x0 * x0 - r * r;
        d = Math.Sqrt(b * b - 4 * a * c);
        int sign = Math.Sign(x1 - x0) * Math.Sign(r);
        centerX = clockwise ? (-b - sign * d) / (2 * a) : (-b + sign * d) / (2 * a);
        centerY = m * (centerX - mx) + my;
    }
    return (centerX - x0, centerY - y0);
}