public static bool IntersectWith(this Fan _fan, Circle _circle)
{
var a = _fan.LeftCorner; //向量a，即扇形的左边
var b = _fan.RightCorner; //向量b，即扇形的右边
var point = _circle.Center;
//条件一：扇形圆心 在 圆内
if (_circle.ContainPoint(_fan.Center))
{
return(true);
}
//条件二：,判断该点和圆心构成的向量是否在两条边之间
if (point.Between(_fan.Center, a, b))
{
//圆形的圆心 与 扇形的圆心 的距离 ，小于 “圆形的半径 + 扇形的半径”
var addRadius = _fan.Length + _circle.Radius;
//判断是否在扇形内
if (Vector2.SqrMagnitude(point - _fan.Center) <= Mathf.Pow(addRadius, 2))
{
return(true);
}
}
//条件三：扇形 的边与 圆形相交
if (IntersectWith(_circle, new Line(_fan.Center, _fan.LeftCorner)))
{
return(true);
}
if (IntersectWith(_circle, new Line(_fan.Center, _fan.RightCorner)))
{
return(true);
}
return(false);
}
public static bool IntersectWith(this Circle _circle, Fan _fan)
{
return(_fan.IntersectWith(_circle));
}
public static bool IntersectWith(this Fan _fan, Rectangle_AABB _rect)
{
//条件一：矩形四个角落的判断
var coners = _rect.Corners;
for (int i = 0; i < 4; i++)
{
if (_fan.ContainPoint(coners[i]))
{
return(true);
}
}
//条件二：扇形的两个边点落在矩形内
if (_rect.ContainPoint(_fan.LeftCorner))
{
return(true);
}
if (_rect.ContainPoint(_fan.RightCorner))
{
return(true);
}
//条件三：彼此中心点
if (_rect.ContainPoint(_fan.Center))
{
return(true);
}
if (_fan.ContainPoint(_rect.Center))
{
return(true);
}
//条件四，矩形的边和弧相交
var begin = _fan.Center;
var end = _rect.Center;
var v = end - begin;
//圆的方程（x - xc）^2 + ( y - yc ) ^ 2 = r^2
//线段的方程
// x = v.x * t + begin.x
// y = v.y * t + begin.y
//求扇形圆心和矩形的中心线段
//把线段方程代入可以得到一个二次方程
//把它化为形如 a * x^2 + 2 * b * x + c = 0
//如果 x 有解，说明相交，无解
//b^2 - a *c >= 0，有解
var dx = _fan.Center.x - begin.x;
var dy = _fan.Center.y - begin.y;
var sqr_r = _fan.Length * _fan.Length;
var a = v.x * v.x + v.y * v.y;
var b = -(dx * v.x + dy * v.y);
var c = dx * dx + dy * dy - sqr_r;
var d = b * b - a * c;
if (d >= 0) // 有解
{
var t = (-b + Mathf.Sqrt(d)) / a;
var x = v.x * t + begin.x;
var y = v.y * t + begin.y;
var point = new Vector2(x, y);
//扇形只会包含其中一个解
var left = _fan.LeftCorner;
var right = _fan.RightCorner;
if (_rect.ContainPoint(point) && point.Between(_fan.Center, left, right))
{
return(true);
}
//另一个方向
t = (-b + Mathf.Sqrt(d)) / a;
x = v.x * t + begin.x;
y = v.y * t + begin.y;
point = new Vector2(x, y);
if (_rect.ContainPoint(point) && point.Between(_fan.Center, left, right))
{
return(true);
}
}
else
{
//无解，说明要么扇形包含矩形中心，要么矩形包含扇形圆心，否则就不相交
}
return(false);
}
public static bool IntersectWith(this Rectangle_AABB _rect, Fan _fan)
{
return(_fan.IntersectWith(_rect));
}
