/// <summary>
/// 两个圆形的相交
/// </summary>
/// <param name="circle2D"></param>
/// <returns></returns>
public List <Vector2D> Intersect(Circle2D source)
{
List <Vector2D> intersects = null;
//假如两个圆形重合,或者一个圆在另外一个内部，则返回不会有交点
if (this.IsAlmostEqualTo(source))
{
return(intersects);
}
//获取圆点之间的距离
var c_d = source.Central.Distance(source.Central);
//获取半径的总长度
var r_d = this.Radius + source.Radius;
//获取两个半径的差值
var r_ans = Math.Abs(this.Radius - source.Radius);
//假如圆点之间的距离，要大于半径，则说明相离
if (c_d.AreCompare(r_d) == 1)
{
return(intersects);
}
//两个原点的距离要小于半径的差值，说明一定是包含
else if (c_d.AreCompare(r_ans) == -1)
{
return(intersects);
}
else
{
double a, b, c, p, q, r, cos, sin;
a = 2 * this.Radius * (this.Central.X - source.Central.X);
b = 2 * this.Radius * (this.Central.Y - source.Central.Y);
c = Math.Pow(source.Radius, 2) - Math.Pow(this.Radius, 2) - Math.Pow(this.Central.X - source.Central.X, 2) - Math.Pow(this.Central.Y - source.Central.Y, 2);
p = Math.Pow(a, 2) + Math.Pow(b, 2);
q = -2 * a * c;
r = Math.Pow(c, 2) - Math.Pow(b, 2);
//说明是相切,那么只有一个解
if (r_d.AreCompare(c_d) == 0 || c_d.AreCompare(r_ans) == 0)
{
cos = -q / p / 2;
sin = Math.Sqrt(1 - Math.Pow(cos, 2));
Vector2D intersect = new Vector2D();
intersect.X = this.Radius * cos + this.Central.X;
intersect.Y = this.Radius * sin + this.Central.Y;
intersects = new List <Vector2D>();
//由于sin可能有正负两种情况，则先计算的交点是否正确
if (source.Central.Distance(intersect).AreCompare(source.Radius) == 0)
{
intersects.Add(intersect);
}
else
{
intersect.Y = -this.Radius * sin + this.Central.Y;
intersects.Add(intersect);
}
return(intersects);
}
//说明两个多边形相交
else
{
intersects = new List <Vector2D>();
cos = (Math.Sqrt(Math.Pow(q, 2) - 4 * p * r) - q) / 2 * p;
sin = Math.Sqrt(1 - Math.Pow(cos, 2));
//第一个点
Vector2D intersect1 = new Vector2D();
intersect1.X = this.Radius * cos + this.Central.X;
intersect1.Y = this.Radius * sin + this.Central.Y;
if (source.Central.Distance(intersect1).AreCompare(source.Radius) == 0)
{
intersects.Add(intersect1);
}
else
{
intersect1.Y = -this.Radius * sin + this.Central.Y;
intersects.Add(intersect1);
}
cos = (-Math.Sqrt(Math.Pow(q, 2) - 4 * p * r) - q) / 2 * p;
sin = Math.Sqrt(1 - Math.Pow(cos, 2));
Vector2D intersect2 = new Vector2D();
intersect2.X = this.Radius * cos + this.Central.X;
intersect2.Y = this.Radius * sin + this.Central.Y;
if (source.Central.Distance(intersect2).AreCompare(source.Radius) == 0)
{
intersects.Add(intersect2);
}
else
{
intersect2.Y = -this.Radius * sin + this.Central.Y;
intersects.Add(intersect2);
}
//特殊情况，两个点计算到同一点，如圆形坐标对称，正好是互相反转关系，则需要对其中一个坐标进行调整
if (intersect1.IsAlmostEqualTo(intersect2))
{
intersect2.Y = -intersect2.Y;
}
return(intersects);
}
}
}