/// <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);
}