少有人走的路1. 三点绘制圆
已知三点为（x1，y1)、（x2，y2)，（x3，y3)，求三点形成的圆的坐标，可以设求得的圆的原点为（X，Y），半径为R，这样可以得到方程组：
(x1-X)²-(y1-Y)²=R² (1)式
(x2-X)²-(y2-Y)²=R² (2)式
(x3-X)²-(y3-Y)²=R² (3)式
由上述方程组可以得到：
2(x1-x2)X +2(y1-y2)Y= x12-x22+y12-y22 (5)式
2(x1-x3)X +2(y1-y3)Y= x12-x32+y12-y32 (6)式
此时，设：
A= x1-x2
B = y1-y2
C= x1-x3
D = y1-y3
E= (x12-x22+y12-y22)/2
F= (x12-x32+y12-y32)/2
得到方程组：
AX+BY = E
CX+DY = F
求解，得到
X= -DE-BF）/ (BC-AD)
Y = -(AF-CE)/ (BC-AD)
经过计算，得到了圆心的坐标位置，也就得到了圆的半径计算公式
R = sqrt（（x1-X）（x1-X）+(y1-Y) (y1-Y)）;
2. 在圆上确定三点的角度
根据四个象限的坐标，选定cos作为角度的值，并利用sin值扩展到360度全象限，利用三个点的位置关系确定弧度为顺时针还是逆时针绘制弧线，其中某点（x0， y0）：
Sin = （y0-Y）/R
Cos= (x0-X）/R
3. 绘制弧线
在C#中，可以利用DrawArc()绘制弧线，其中最重要的要注意角度，绘制时角度要沿顺时针旋转，角度0度位于X轴的正方向上，在绘制弧度时，确定三个点的位置关系十分重要。
4．C#程序源码
void DrawArcFromThreePoint(Graphics mImgGraph, int x1, int y1, int x2, int y2, int x3, int y3)
{
var m_CurveColor = Color.Red;
double a = x1 - x2;
double b = y1 - y2;
double c = x1 - x3;
double d = y1 - y3;
double e = ((x1 * x1 - x2 * x2) + (y1 * y1 - y2 * y2)) / 2.0;
double f = ((x1 * x1 - x3 * x3) + (y1 * y1 - y3 * y3)) / 2.0;
double det = b * c - a * d;
if (Math.Abs(det) > 0.001)
{
//x0,y0为计算得到的原点
double x0 = -(d * e - b * f) / det;
double y0 = -(a * f - c * e) / det;
SolidBrush OriginBrush = new SolidBrush(Color.Blue);
mImgGraph.FillEllipse(OriginBrush, (int)(x0 - 3), (int)(y0 - 3), 6, 6);
double radius = Math.Sqrt((x1 - x0) * (x1 - x0) + (y1 - y0) * (y1 - y0));
double angle1;
double angle2;
double angle3;
double sinValue1;
double cosValue1;
double sinValue2;
double cosValue2;
double sinValue3;
double cosValue3;
sinValue1 = (y1 - y0) / radius;
cosValue1 = (x1 - x0) / radius;
if (cosValue1 >= 0.99999) cosValue1 = 0.99999;
if (cosValue1 <= -0.99999) cosValue1 = -0.99999;
angle1 = Math.Acos(cosValue1);
angle1 = angle1 / 3.14 * 180;
if (sinValue1 < -0.05) angle1 = 360 - angle1;
sinValue2 = (y2 - y0) / radius;
cosValue2 = (x2 - x0) / radius;
if (cosValue2 >= 0.99999) cosValue2 = 0.99999;
if (cosValue2 <= -0.99999) cosValue2 = -0.99999;
angle2 = Math.Acos(cosValue2);
angle2 = angle2 / 3.14 * 180;
if (sinValue2 < -0.05) angle2 = 360 - angle2;
sinValue3 = (y3 - y0) / radius;
cosValue3 = (x3 - x0) / radius;
if (cosValue3 >= 0.99999) cosValue3 = 0.99999;
if (cosValue3 <= -0.99999) cosValue3 = -0.99999;
angle3 = Math.Acos(cosValue3);
angle3 = angle3 / 3.14 * 180;
if (sinValue3 < -0.05) angle3 = 360 - angle3;
Pen CurvePen = new Pen(m_CurveColor);
Pen CurvePen1 = new Pen(Color.Green);
bool PosDown = false;
double Delta13;
if (angle1 < angle3)
{
Delta13 = angle3 - angle1;
}
else
Delta13 = angle3 - angle1 + 360;
double Delta12;
if (angle1 < angle2)
{
Delta12 = angle2 - angle1;
}
else
Delta12 = angle2 - angle1 + 360;
if (Delta13 > Delta12)
PosDown = true;
else
PosDown = false;
if (PosDown)
{
if (angle3 > angle1)
mImgGraph.DrawArc(CurvePen, (int)(x0 - radius), (int)(y0 - radius), (int)(2 * radius), (int)(2 * radius), (int)(angle1), (int)(angle3 - angle1));
else
mImgGraph.DrawArc(CurvePen, (int)(x0 - radius), (int)(y0 - radius), (int)(2 * radius), (int)(2 * radius), (int)(angle1), (int)(angle3 - angle1 + 360));
}
else
{
if (angle1 > angle3)
mImgGraph.DrawArc(CurvePen, (int)(x0 - radius), (int)(y0 - radius), (int)(2 * radius), (int)(2 * radius), (int)(angle3), (int)(angle1 - angle3));
else
mImgGraph.DrawArc(CurvePen, (int)(x0 - radius), (int)(y0 - radius), (int)(2 * radius), (int)(2 * radius), (int)(angle3), (int)(angle1 - angle3 + 360));
}
}
}————————————————
版权声明：本文为CSDN博主「mr_liyonghong」的原创文章，遵循 CC 4.0 BY-SA 版权协议，转载请附上原文出处链接及本声明。
原文链接：https://blog.csdn.net/mr_liyonghong/article/details/79557595
