public static bool IntersectWith(this Circle _circle, Rectangle_AABB _rect)
{
var ex_rect = _rect.Expand(_circle.Radius, _circle.Radius);
//var coners = _rect.Corners;
if (ex_rect.ContainPoint(_circle.Center))
{ //圆心在扩展矩形内
//如果在四个角落，只有包含该加点才算相交，否则不算
var offsetStep = new Vector2(_rect.Witdh + _circle.Radius, _rect.Height + _circle.Radius) * 0.5f;
var size = new Vector2(_circle.Radius, _circle.Radius);
var leftTop_rect = new Rectangle_AABB(_rect.Center + offsetStep * new Vector2(-1, 1), size);
var rightTop_rect = new Rectangle_AABB(_rect.Center + offsetStep * new Vector2(1, 1), size);
var leftbottom_rect = new Rectangle_AABB(_rect.Center + offsetStep * new Vector2(-1, -1), size);
var rightbottom = new Rectangle_AABB(_rect.Center + offsetStep * new Vector2(1, -1), size);
if (leftTop_rect.ContainPoint(_circle.Center))
{
return(_circle.ContainPoint(_rect.LeftTop));
}
if (rightTop_rect.ContainPoint(_circle.Center))
{
return(_circle.ContainPoint(_rect.RightTop));
}
if (leftbottom_rect.ContainPoint(_circle.Center))
{
return(_circle.ContainPoint(_rect.LeftBottom));
}
if (rightbottom.ContainPoint(_circle.Center))
{
return(_circle.ContainPoint(_rect.RightBottom));
}
return(true);
}
else
{
return(false);//圆心在扩展矩形外，肯定不相交
}
}
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);
}