/// <summary> /// 获取有效的多边形 /// </summary> /// <param name="PG">多边形PG</param> /// <returns>返回多边形</returns> public static PolygonD?GetValidatePolygon(PolygonD PG) { List <PointD> pts = new List <PointD>(); for (Int32 i = 0; i < PG.Vertex.Count; ++i) { if (pts.Contains(PG.Vertex[i]) == false) { if (pts.Count > 2) { //斜率相等 if (LineAlgorithm.Gradient(new LineD(pts[pts.Count - 2], pts[pts.Count - 1])) == LineAlgorithm.Gradient(new LineD(pts[pts.Count - 1], PG.Vertex[i]))) { pts[pts.Count - 1] = PG.Vertex[i]; } else { pts.Add(PG.Vertex[i]); } } } } if (pts.Count < 3) { return(null); } return(new PolygonD(pts.ToArray())); }
/// <summary> /// 判断是否为凸多边形 /// </summary> /// <param name="PG">PG多边形</param> /// <returns>如果是凸多边形返回True,否则返回False。</returns> public static Boolean IsConvexPolygon(PolygonI PG) { if (PG.Vertex == null) { return(false); } if (PG.Vertex.Count < 4) { return(true); } for (Int32 i = 0; i < PG.Vertex.Count; ++i) { LineD line = new LineD(PG.Vertex[i], PG.Vertex[(i + 1) % PG.Vertex.Count]); Double flag = 0; for (Int32 j = 0; j < PG.Vertex.Count; ++j) { Double result = LineAlgorithm.Position(line, PG.Vertex[j]); if ((flag * result) < 0)//点在线的两侧则返回失败。 { return(false); } if (result != 0) { flag = result; } } } return(true); }
/// <summary> /// 获取线段L与圆C的交点集合 /// </summary> /// <param name="L">线段L</param> /// <param name="C">圆C</param> /// <returns>返回交点集合.</returns> public static PointD[] Intersection(LineI L, CircleI C) { List <PointD> result = new List <PointD>(); Int32? has = HasIntersection(L, C); if (has == 0 || has == null) { return(result.ToArray()); } //Points P (x,y) on a line defined by two points P1 (x1,y1,z1) and P2 (x2,y2,z2) is described by //P = P1 + u (P2 - P1) //or in each coordinate //x = x1 + u (x2 - x1) //y = y1 + u (y2 - y1) //z = z1 + u (z2 - z1) //A sphere centered at P3 (x3,y3,z3) with radius r is described by //(x - x3)2 + (y - y3)2 + (z - z3)2 = r2 //Substituting the equation of the line into the sphere gives a quadratic equation of the form //a u2 + b u + c = 0 //where: //a = (x2 - x1)2 + (y2 - y1)2 + (z2 - z1)2 //b = 2[ (x2 - x1) (x1 - x3) + (y2 - y1) (y1 - y3) + (z2 - z1) (z1 - z3) ] //c = x32 + y32 + z32 + x12 + y12 + z12 - 2[x3 x1 + y3 y1 + z3 z1] - r2 //The solutions to this quadratic are described by PointD PD = PointAlgorithm.Substract(L.Starting, L.End); Double a = PD.X * PD.X + PD.Y * PD.Y; Double b = 2 * ((L.End.X - L.Starting.X) * (L.Starting.X - C.Center.X) + (L.End.Y - L.Starting.Y) * (L.Starting.Y - C.Center.Y)); Double c = C.Center.X * C.Center.X + C.Center.Y * C.Center.Y + L.Starting.X * L.Starting.X + L.Starting.Y * L.Starting.Y - 2 * (C.Center.X * L.Starting.X + C.Center.Y * L.Starting.Y) - C.Radius * C.Radius; Double u1 = ((-1) * b + System.Math.Sqrt(b * b - 4 * a * c)) / (2 * a); Double u2 = ((-1) * b - System.Math.Sqrt(b * b - 4 * a * c)) / (2 * a); //交点 PointD P1 = new PointD(L.Starting.X + u1 * (L.End.X - L.Starting.X), L.Starting.Y + u1 * (L.End.Y - L.Starting.Y)); PointD P2 = new PointD(L.Starting.X + u2 * (L.End.X - L.Starting.X), L.Starting.Y + u2 * (L.End.Y - L.Starting.Y)); if (LineAlgorithm.OnLine(L, P1) == true) { result.Add(P1); } if (LineAlgorithm.OnLine(L, P2) == true && P1.Equals(P2) == false) { result.Add(P2); } return(result.ToArray()); }
/// <summary> /// 点P是否在多边形区域内 /// </summary> /// <param name="PG">多边形PL</param> /// <param name="P">点P</param> /// <returns>如果点P在区域内返回True,否则返回False.</returns> /// <remarks>此处不考虑平行边的情况</remarks> public static Boolean InPolygon(PolygonI PG, PointI P) { //count ← 0; //以P为端点,作从右向左的射线L; //for 多边形的每条边s // do if P在边s上 // then return true; // if s不是水平的 // then if s的一个端点在L上 // if 该端点是s两端点中纵坐标较大的端点 // then count ← count+1 // else if s和L相交 // then count ← count+1; //if count mod 2 = 1 // then return true; //else return false; Int32 count = 0; LineI L = new LineI(P, new PointI(Int32.MaxValue, P.Y)); foreach (LineI S in PG) { if (LineAlgorithm.OnLine(S, P) == true) { return(true); } if (LineAlgorithm.Gradient(S) != 0)//不是水平线段 { if (LineAlgorithm.OnLine(L, S.Starting) || LineAlgorithm.OnLine(L, S.End)) { if (LineAlgorithm.OnLine(L, S.Starting) && S.Starting.Y > S.End.Y) { ++count; } if (LineAlgorithm.OnLine(L, S.End) && S.End.Y > S.Starting.Y) { ++count; } } else if (LineAlgorithm.HasIntersection(S, L) > 0) { ++count; } } } //如果X的水平射线和多边形的交点数是奇数个则点在多边形内,否则不在区域内。 if (count % 2 == 0) { return(false); } return(true); }
/// <summary> /// 根据点P,Q,R三点确定一个圆,注意三点不能共线 /// </summary> /// <param name="P">点P</param> /// <param name="Q">点Q</param> /// <param name="R">点R</param> /// <returns>返回圆,如果圆不存在则返回null.</returns> public static CircleD?CreateCircle(PointI P, PointI Q, PointI R) { if (DoubleAlgorithm.Equals(LineAlgorithm.Position(P, Q, R), 0)) { return(null); //三点共线无法确定圆 } //formula //(x-a)^2+(y-b)^2=r^2 //f1:(x1-a)^2 + (y1-b)^2 = r^2 //f2:(x2-a)^2 + (y2-b)^2 = r^2 //f3:(x3-a)^2 + (y3-b)^2 = r^2 //f1=f2: x1^2-2ax1+y1^2-2by1= x2^2-2ax2+y2^2-2by2; //a=(((X(1)^2-X(2)^2+Y(1)^2-Y(2)^2)*(Y(2)-Y(3)))-((X(2)^2-X(3)^2+Y(2)^2-Y(3)^2)*(Y(1)-Y(2))))/(2*(X(1)-X(2))*(Y(2)-Y(3))-2*(X(2)-X(3))*(Y(1)-Y(2))) //b=(((X(1)^2-X(2)^2+Y(1)^2-Y(2)^2)*(X(2)-X(3)))-((X(2)^2-X(3)^2+Y(2)^2-Y(3)^2)*(X(1)-X(2))))/(2*(Y(1)-Y(2))*(X(2)-X(3))-2*(Y(2)-Y(3))*(X(1)-X(2))) Double a = (Double)(((P.X * P.X - Q.X * Q.X + P.Y * P.Y - Q.Y * Q.Y) * (Q.Y - R.Y)) - ((Q.X * Q.X - R.X * R.X + Q.Y * Q.Y - R.Y * R.Y) * (P.Y - Q.Y))) / (Double)(2 * (P.X - Q.X) * (Q.Y - R.Y) - 2 * (Q.X - R.X) * (P.Y - Q.Y)); Double b = (Double)(((P.X * P.X - Q.X * Q.X + P.Y * P.Y - Q.Y * Q.Y) * (Q.X - R.X)) - ((Q.X * Q.X - R.X * R.X + Q.Y * Q.Y - R.Y * R.Y) * (P.X - Q.X))) / (Double)(2 * (P.Y - Q.Y) * (Q.X - R.X) - 2 * (Q.Y - R.Y) * (P.X - Q.X)); Double r = PointAlgorithm.Distance(P, new PointD(a, b)); return(new CircleD(a, b, r)); }
/// <summary> /// 线段L是否在多边形区域内 /// </summary> /// <param name="PG">多边形PG</param> /// <param name="L">线段L</param> /// <returns>如果线段L在区域内返回True,否则返回False.</returns> public static Boolean InPolygon(PolygonI PG, LineI L) { //if 线端PQ的端点不都在多边形内 // then return false; //点集pointSet初始化为空; //for 多边形的每条边s // do if 线段的某个端点在s上 // then 将该端点加入pointSet; // else if s的某个端点在线段PQ上 // then 将该端点加入pointSet; // else if s和线段PQ相交 // 这时候已经可以肯定是内交了 // then return false; //将pointSet中的点按照X-Y坐标排序; //for pointSet中每两个相邻点 pointSet[i] , pointSet[ i+1] // do if pointSet[i] , pointSet[ i+1] 的中点不在多边形中 // then return false; //return true; List <PointI> PointList = new List <PointI>(); if (InPolygon(PG, L.Starting) == false) { return(false); } foreach (LineI S in PG) { if (LineAlgorithm.OnLine(S, L.Starting) == true) { PointList.Add(L.Starting); } else if (LineAlgorithm.OnLine(S, L.End) == true) { PointList.Add(L.End); } else if (LineAlgorithm.OnLine(L, S.Starting) == true) { PointList.Add(S.Starting); } else if (LineAlgorithm.OnLine(L, S.End) == true) { PointList.Add(S.End); } else if (LineAlgorithm.HasIntersection(L, S) > 0) { return(false); } } PointI[] OrderedPointList = PointList.ToArray(); for (Int32 i = 0; i < (OrderedPointList.Length - 1); ++i) { for (Int32 j = 0; j < (OrderedPointList.Length - i - 1); j++) { MinMax <PointI> MM = new MinMax <PointI>(OrderedPointList[j], OrderedPointList[j + 1]); OrderedPointList[j] = MM.Min; OrderedPointList[j + 1] = MM.Max; } } for (Int32 i = 0; i < (OrderedPointList.Length - 1); ++i) { if (false == InPolygon(PG, PointAlgorithm.MidPoint(OrderedPointList[i], OrderedPointList[i + 1]))) { return(false); } } return(true); }