C#關於圓與圓的交點問題
阿新 • • 發佈：2019-01-23
public Point[]
CircleInsect(Circle A,
Circle B,
Point[] points)
{
double x1 = A.Center.X;
double y1 = A.Center.Y;
double r1 = A.Radius;
double x2 = B.Center.X;
double y2 = B.Center.Y;
double r2 = B.Radius;
double
if (double_equals(x1, x2) && double_equals(y1, y2) && (double_equals(r1, r2))) // 兩圓重合
{
Console.WriteLine("The two circles are the same");
}
if ((Dis > r1 + r2) || Dis < Math
{
Console.WriteLine("The two circles have no intersection");
}
if (double_equals(Dis, r1 + r2) || double_equals(Dis, Math.Abs(r1 - r2))) // 兩圓有一個交點(即兩圓相切[內切和外切])
{
if (double_equals(Dis, r1 + r2))// 外切
{
if (double_equals(x1, x2) && !double_equals(y1, y2))
{
if (y1 > y2)
{
points[0].X = x1 = x2;
points[0].Y = y1 - r1;
}
else
{
points[0].X = x1 = x2;
points[0].Y = y1 + r1;
}
}
else if (!double_equals(x1, x2) && double_equals(y1, y2))
{
if (x1 > x2)
{
points[0].X = x1 - r1;
points[0].Y = y1 = y2;
}
else
{
points[0].X = x1 + r1;
points[0].Y = y1 = y2;
}
}
else if (!double_equals(x1, x2) && !double_equals(y1, y2))
{
// 外切情況，兩圓的交點在圓心AB連線上
double k1 = (y2 - y1) / (x2 - x1);
double k2 = -1 / k1;
points[0].X = x1 + (x2 - x1) * r1 / Dis;
//points[0].Y=y1+k2*(points[0].X-x1);
points[0].Y = y1 + (y2 - y1) * r1 / Dis;
}
}
else if (double_equals(Dis, Math.Abs(r1 - r2))) // 內切 (是否要考慮A包含B 還是B包含A，對結果是否有影響)
{
if (double_equals(x1, x2) && !double_equals(y1, y2))
{
if (r1 > r2) // A內含B
{
if (y1 > y2)
{
points[0].X = x1 = x2;
points[0].Y = y1 - r1;
}
else
{
points[0].X = x1 = x2;
points[0].Y = y1 + r1;
}
}
else // B 內含A
{
if (y1 > y2)
{
points[0].X = x1 = x2;
points[0].Y = y1 + r1;
}
else
{
points[0].X = x1 = x2;
points[0].Y = y1 - r1;
}
}
}
else if (!double_equals(x1, x2) && double_equals(y1, y2))
{
if (r1 > r2)
{
if (x1 > x2)
{
points[0].X = x1 - r1;
points[0].Y = y1 = y2;
}
else
{
points[0].X = x1 + r1;
points[0].Y = y1 = y2;
}
}
else
{
if (x1 > x2)
{
points[0].X = x1 + r1;
points[0].Y = y1 = y2;
}
else
{
points[0].X = x1 - r1;
points[0].Y = y1 = y2;
}
}
}
else if (!double_equals(x1, x2) && !double_equals(y1, y2)) // 是否要考慮內含關係(求座標時是否有影響)
{
// 內切情況，交點在AB連線的延長線上，要考慮切點的位置
double k1 = (y2 - y1) / (x2 - x1);
double k2 = -1 / k1;
points[0].X = x1 + (x1 - x2) * r1 / Dis;
//points[0].Y = y1 + k2 * (points[0].X - x1);
points[0].Y = y1 + (y1 - y2) * r1 / Dis;
}
}
}
if ((Dis < r1 + r2) && Dis > Math.Abs(r1 - r2)) // 兩圓有兩個交點(內交或者外交) 【內交與外交的情況是否一樣？】
{
if (double_equals(x1, x2) && !double_equals(y1, y2)) // 圓A和圓B 橫座標相等
{
double x0 = x1 = x2;
double y0 = y1 + (y2 - y1) * (r1 * r1 - r2 * r2 + Dis * Dis) / (2 * Dis * Dis);
double Dis1 = Math.Sqrt(r1 * r1 - (x0 - x1) * (x0 - x1) - (y0 - y1) * (y0 - y1));
points[0].X = x0 - Dis1;
points[0].Y = y0;
points[1].X = x0 + Dis1;
points[1].Y = y0;
}
else if (!double_equals(x1, x2) && double_equals(y1, y2)) // 圓A和圓B 縱座標相等
{
double y0 = y1 = y2;
double x0 = x1 + (x2 - x1) * (r1 * r1 - r2 * r2 + Dis * Dis) / (2 * Dis * Dis);
double Dis1 = Math.Sqrt(r1 * r1 - (x0 - x1) * (x0 - x1) - (y0 - y1) * (y0 - y1));
points[0].X = x0;
points[0].Y = y0 - Dis1;
points[1].X = x0;
points[1].Y = y0 + Dis1;
}
else if (!double_equals(x1, x2) && !double_equals(y1, y2)) // 橫縱座標都不等
{
double k1 = (y2 - y1) / (x2 - x1);//AB的斜率
double k2 = -1 / k1; // CD的斜率
double x0 = x1 + (x2 - x1) * (r1 * r1 - r2 * r2 + Dis * Dis) / (2 * Dis * Dis);
double y0 = y1 + k1 * (x0 - x1);
double Dis1 = r1 * r1 - (x0 - x1) * (x0 - x1) - (y0 - y1) * (y0 - y1); //CE的平方
double Dis2 = Math.Sqrt(Dis1 / (1 + k2 * k2));//EF的長，過C作過E點水平直線的垂線，交於F點
points[0].X = x0 - Dis2;
points[0].Y = y0 + k2 * (points[0].X - x0);
points[1].X = x0 + Dis2;
points[1].Y = y0 + k2 * (points[1].X - x0);
}
}
return points;
}
}
{
double x1 = A.Center.X;
double y1 = A.Center.Y;
double r1 = A.Radius;
double x2 = B.Center.X;
double y2 = B.Center.Y;
double r2 = B.Radius;
double
if (double_equals(x1, x2) && double_equals(y1, y2) && (double_equals(r1, r2))) // 兩圓重合
{
Console.WriteLine("The two circles are the same");
}
if ((Dis > r1 + r2) || Dis < Math
{
Console.WriteLine("The two circles have no intersection");
}
if (double_equals(Dis, r1 + r2) || double_equals(Dis, Math.Abs(r1 - r2))) // 兩圓有一個交點(即兩圓相切[內切和外切])
{
if (double_equals(Dis, r1 + r2))// 外切
{
if (double_equals(x1, x2) && !double_equals(y1, y2))
{
if (y1 > y2)
{
points[0].X = x1 = x2;
points[0].Y = y1 - r1;
}
else
{
points[0].X = x1 = x2;
points[0].Y = y1 + r1;
}
}
else if (!double_equals(x1, x2) && double_equals(y1, y2))
{
if (x1 > x2)
{
points[0].X = x1 - r1;
points[0].Y = y1 = y2;
}
else
{
points[0].X = x1 + r1;
points[0].Y = y1 = y2;
}
}
else if (!double_equals(x1, x2) && !double_equals(y1, y2))
{
// 外切情況，兩圓的交點在圓心AB連線上
double k1 = (y2 - y1) / (x2 - x1);
double k2 = -1 / k1;
points[0].X = x1 + (x2 - x1) * r1 / Dis;
//points[0].Y=y1+k2*(points[0].X-x1);
points[0].Y = y1 + (y2 - y1) * r1 / Dis;
}
}
else if (double_equals(Dis, Math.Abs(r1 - r2))) // 內切 (是否要考慮A包含B 還是B包含A，對結果是否有影響)
{
if (double_equals(x1, x2) && !double_equals(y1, y2))
{
if (r1 > r2) // A內含B
{
if (y1 > y2)
{
points[0].X = x1 = x2;
points[0].Y = y1 - r1;
}
else
{
points[0].X = x1 = x2;
points[0].Y = y1 + r1;
}
}
else // B 內含A
{
if (y1 > y2)
{
points[0].X = x1 = x2;
points[0].Y = y1 + r1;
}
else
{
points[0].X = x1 = x2;
points[0].Y = y1 - r1;
}
}
}
else if (!double_equals(x1, x2) && double_equals(y1, y2))
{
if (r1 > r2)
{
if (x1 > x2)
{
points[0].X = x1 - r1;
points[0].Y = y1 = y2;
}
else
{
points[0].X = x1 + r1;
points[0].Y = y1 = y2;
}
}
else
{
if (x1 > x2)
{
points[0].X = x1 + r1;
points[0].Y = y1 = y2;
}
else
{
points[0].X = x1 - r1;
points[0].Y = y1 = y2;
}
}
}
else if (!double_equals(x1, x2) && !double_equals(y1, y2)) // 是否要考慮內含關係(求座標時是否有影響)
{
// 內切情況，交點在AB連線的延長線上，要考慮切點的位置
double k1 = (y2 - y1) / (x2 - x1);
double k2 = -1 / k1;
points[0].X = x1 + (x1 - x2) * r1 / Dis;
//points[0].Y = y1 + k2 * (points[0].X - x1);
points[0].Y = y1 + (y1 - y2) * r1 / Dis;
}
}
}
if ((Dis < r1 + r2) && Dis > Math.Abs(r1 - r2)) // 兩圓有兩個交點(內交或者外交) 【內交與外交的情況是否一樣？】
{
if (double_equals(x1, x2) && !double_equals(y1, y2)) // 圓A和圓B 橫座標相等
{
double x0 = x1 = x2;
double y0 = y1 + (y2 - y1) * (r1 * r1 - r2 * r2 + Dis * Dis) / (2 * Dis * Dis);
double Dis1 = Math.Sqrt(r1 * r1 - (x0 - x1) * (x0 - x1) - (y0 - y1) * (y0 - y1));
points[0].X = x0 - Dis1;
points[0].Y = y0;
points[1].X = x0 + Dis1;
points[1].Y = y0;
}
else if (!double_equals(x1, x2) && double_equals(y1, y2)) // 圓A和圓B 縱座標相等
{
double y0 = y1 = y2;
double x0 = x1 + (x2 - x1) * (r1 * r1 - r2 * r2 + Dis * Dis) / (2 * Dis * Dis);
double Dis1 = Math.Sqrt(r1 * r1 - (x0 - x1) * (x0 - x1) - (y0 - y1) * (y0 - y1));
points[0].X = x0;
points[0].Y = y0 - Dis1;
points[1].X = x0;
points[1].Y = y0 + Dis1;
}
else if (!double_equals(x1, x2) && !double_equals(y1, y2)) // 橫縱座標都不等
{
double k1 = (y2 - y1) / (x2 - x1);//AB的斜率
double k2 = -1 / k1; // CD的斜率
double x0 = x1 + (x2 - x1) * (r1 * r1 - r2 * r2 + Dis * Dis) / (2 * Dis * Dis);
double y0 = y1 + k1 * (x0 - x1);
double Dis1 = r1 * r1 - (x0 - x1) * (x0 - x1) - (y0 - y1) * (y0 - y1); //CE的平方
double Dis2 = Math.Sqrt(Dis1 / (1 + k2 * k2));//EF的長，過C作過E點水平直線的垂線，交於F點
points[0].X = x0 - Dis2;
points[0].Y = y0 + k2 * (points[0].X - x0);
points[1].X = x0 + Dis2;
points[1].Y = y0 + k2 * (points[1].X - x0);
}
}
return points;
}
}