/// <summary> /// 判断一个点是否是昂起直线的端点 /// </summary> /// <param name="line1"></param> /// <param name="source"></param> /// <returns></returns> private bool IsEndPoint(Line2D line1, Vector2D source) { if (source.IsAlmostEqualTo(line1.Start) || source.IsAlmostEqualTo(line1.End)) { return(true); } return(false); }
/// <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); } } }