/// <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> /// 计算点P到多边形PG的最近距离 /// </summary> /// <param name="P">点P</param> /// <param name="PG">多边形PG</param> /// <returns>返回最近距离</returns> public static Double ClosestDistance(PointI P, PolygonI PG) { Double result = Double.MaxValue; foreach (LineI S in PG) { result = System.Math.Min(result, ClosestDistance(P, S)); } return(result); }
/// <summary> /// 计算偏移多边形PG /// </summary> /// <param name="PG">多边形PG</param> /// <param name="velocity">偏移速度</param> /// <returns>返回偏移多边形</returns> public static PolygonI Offset(PolygonI PG, PointI velocity) { List <PointI> list = new List <PointI>(); for (Int32 i = 0; i < PG.Vertex.Count; ++i) { list.Add(PG.Vertex[i] + velocity); } return(new PolygonI(list.ToArray())); }
/// <summary> /// 计算多边形PG面积 /// </summary> /// <param name="PG">多边形PG</param> /// <returns>返回面积。</returns> public static Double Area(PolygonI PG) { //formula (1/2) *( (Xi*Yi+1 -Xi+1*Yi) +...) Double result = 0; for (Int32 i = 0; i < PG.Vertex.Count; ++i) { result += PointAlgorithm.Multiple(PG.Vertex[i % PG.Vertex.Count], PG.Vertex[(i + 1) % PG.Vertex.Count]); } return(System.Math.Abs(0.5 * result)); }
/// <summary> /// 判断矩形R是否在多边形内 /// </summary> /// <param name="PG">PG多边形</param> /// <param name="R">R矩形</param> /// <returns>如果R矩形在区域内返回True,否则返回False.</returns> public static Boolean InPolygon(PolygonI PG, RectangleI R) { foreach (LineD L in R) { if (InPolygon(PG, L) == false) { return(false); } } return(true); }
/// <summary> /// 判断多边形PL是否在多边形内 /// </summary> /// <param name="PG">PG多边形</param> /// <param name="PL">PL多边形</param> /// <returns>如果PL多边形在区域内返回True,否则返回False.</returns> public static Boolean InPolygon(PolygonI PG, PolygonI PL) { foreach (LineI L in PL) { if (InPolygon(PG, L) == false) { return(false); } } return(true); }
/// <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> /// 判断圆C是否在多边形PG内 /// </summary> /// <param name="PG">PG多边形</param> /// <param name="C">圆C</param> /// <returns>如果圆C在区域内返回True,否则返回False.</returns> public static Boolean InPolygon(PolygonI PG, CircleI C) { //如果圆心不在多边形内则返回不在多边形内 if (false == InPolygon(PG, C.Center)) { return(false); } Double D = PointAlgorithm.ClosestDistance(C.Center, PG); if (D > C.Radius || DoubleAlgorithm.Equals(D, C.Radius)) { return(true); } return(false); }
/// <summary> /// 判断多边形PG是否在圆内 /// </summary> /// <param name="C">圆C</param> /// <param name="PG">多边形PG</param> /// <returns>如果在圆内返回True,否则返回False。</returns> public static Boolean InCircle(CircleI C, PolygonI PG) { if (PG.Vertex == null) { return(false); } for (Int32 i = 0; i < PG.Vertex.Count; ++i) { if (PointAlgorithm.Distance(PG.Vertex[i], C.Center) > C.Radius) { return(false); } } return(true); }
/// <summary> /// 多边形是否在区域内 /// </summary> /// <param name="Rect">矩形区域</param> /// <param name="PL">多边形PL</param> /// <returns> /// 返回True表示多边形PL在区域内,返回False则不在区域内. /// </returns> public static Boolean InRectangle(RectangleI Rect, PolygonI PL) { if (PL.Vertex == null) { return(false); } for (Int32 i = 0; i < PL.Vertex.Count; ++i) { if (false == InRectangle(Rect, PL.Vertex[i])) { return(false); } } return(true); }
/// <summary> /// 获取线段L与多边形PG的交点集合 /// </summary> /// <param name="L">线段L</param> /// <param name="PG">多边形PG</param> /// <returns>返回交点集合,如果有无数个交点则返回null.</returns> public static PointD[] Intersection(LineI L, PolygonI PG) { List <PointD> result = new List <PointD>(); foreach (LineI S in PG) { PointD[] P = Intersection(L, S); if (P == null) { return(null); } if (P.Length == 0) { continue; } if (result.Contains(P[0]) == false) { result.Add((PointD)P[0]); } } return(result.ToArray()); }
/// <summary> /// 判断多边形PG与线段L的交点个数 /// </summary> /// <param name="L">线段L</param> /// <param name="PG">多边形PG</param> /// <returns>相交返回交点数目,否则返回0</returns> public static Int32?HasIntersection(LineI L, PolygonI PG) { Int32 count = 0; foreach (LineI S in PG) { Int32?result = HasIntersection(L, S); if (result == null) { return(null); } count += (Int32)result; } foreach (PointI P in PG.Vertex) { if (OnLine(L, P) == true) { count--; } } return(count); }
/// <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 PolygonI?GetValidatePolygon(PolygonI PG) { return((PolygonI)GetValidatePolygon((PolygonD)PG)); }
/// <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); }
private void CastEdgeShadow(SSVector2I mPoint1, SSVector2I mPoint2) { var polygon = new PolygonI(mPoint1, GetProjection(mPoint1), GetProjection(mPoint2), mPoint2); Polygons.Add(polygon); }