/// <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);
}
