public static Dot2 CreateRandomDot(Random rand, Dot2 dot, double Radius, int maxWidth, int maxHeight)
{
Dot2 returndot;
//Dot2 nulls;
double radius = Radius + Radius * 1 * (rand.NextDouble() - 0.5);
//Vector top = new Vector(new Dot2(maxWidth,0));
//Vector left = new Vector(new Dot2(0,maxHeight));
//Vector buttom = new Vector(new Dot2(0,maxHeight),new Dot2(maxWidth,maxHeight));
//Vector right = new Vector(new Dot2(maxWidth,0),new Dot2(maxWidth,maxHeight));
Border border = new Border(new List <Dot2>()
{
new Dot2(0, 0), new Dot2(maxWidth, 0), new Dot2(maxWidth, maxHeight), new Dot2(0, maxHeight)
});
double theta = (rand.NextDouble() - 0.5) * 2 * System.Math.PI;
returndot = dot + new Dot2(radius * System.Math.Cos(theta), radius * System.Math.Sin(theta));
while (!Math.isInside(returndot, border)
//isIntersect(new Vector(dot, returndot), top, out nulls) || isIntersect(new Vector(dot, returndot), left, out nulls) || isIntersect(new Vector(dot, returndot), buttom, out nulls) || isIntersect(new Vector(dot, returndot), right, out nulls)
)
{
radius = Radius + Radius * 1 * (rand.NextDouble() - 0.5);
theta = (rand.NextDouble() - 0.5) * 2 * System.Math.PI;
returndot = dot + new Dot2(radius * System.Math.Cos(theta), radius * System.Math.Sin(theta));
}
return(returndot);
}
/// <summary>
/// 获取离边界最近的一条边（边可以不再边界上）
/// </summary>
/// <param name="origin"></param>
/// <param name="border"></param>
/// <returns></returns>
public static Vector getNearestVector(Dot2 origin, Border border)
{
if (border.DotCount < 2)
{
return(null);
}
int j1 = 0, j2 = 1;
double lengh1 = Math.Length(origin, border.get(j1)), lengh2 = Math.Length(origin, border.get(j2)), temp;
if (lengh1 > lengh2)
{
lengh1 = lengh1 + lengh2;
lengh2 = lengh1 - lengh2;
lengh1 = lengh1 - lengh2;
}
for (int i = 1; i < border.DotCount; i++)
{
temp = Math.Length(origin, border.get(i));
if (temp <= lengh1)
{
lengh2 = lengh1;
lengh1 = temp;
j2 = j1;
j1 = i;
}
else if (temp > lengh1 && temp <= lengh2)
{
lengh2 = temp;
j2 = i;
}
}
return(new Vector(border.get(j1), border.get(j2)));
}
/// <summary>
/// 判断点是否在边界内
/// </summary>
/// <param name="dot"></param>
/// <param name="border"></param>
/// <returns></returns>
public static bool isInside(Dot2 dot, Border border)
{
int num = 0;
//double minx, maxx;
for (int i = 0; i < border.DotCount - 1; i++)
{
if (dot.X <= (System.Math.Max(border.get(i).X, border.get(i + 1).X)) && (border.get(i).Y - dot.Y) * (border.get(i + 1).Y - dot.Y) < 0)
{
if (dot.X > System.Math.Min(border.get(i).X, border.get(i + 1).X))
{
if ((border.get(i).X *border.get(i + 1).Y - border.get(i).Y *border.get(i + 1).X + dot.Y * (border.get(i + 1).X - border.get(i).X)) / (border.get(i + 1).Y - border.get(i).Y) > dot.X)
{
num++;
}
}
else
{
num++;
}
}
}
if (num % 2 == 1)
{
return(true);
}
else
{
return(false);
}
}
public void putDot(Dot2 dot)
{
if (Dots.Contains(dot))
{
return;
}
Dots.Add(dot);
}
public void Insert(Dot2 dot, int index)
{
if (index == Dots.Count)
{
Add(dot);
}
else
{
Operate.Add(new Operate(Type.Insert, dot, index));
Dots.Insert(index, dot.toDotx());
}
}
public void Insert(Dot2 dot, int index, DrawType type)
{
if (index == Dots.Count)
{
Operate.Add(new Operate(Type.Append, dot, index));
Dots.Add(dot.toDotx(type));
}
else
{
Operate.Add(new Operate(Type.Insert, dot, index));
Dots.Insert(index, dot.toDotx(type));
}
}
/// <summary>
/// 随机产生一个无交叉的边界
/// </summary>
/// <param name="number">3</param>
public Border(int number, int maxWidth, int maxHeight, out List <Dot2> dotss, Draw.Draw draw)
{
dotss = new List <Dot2>();
bool isIntersect = false;
Random rand = new Random();
Dot2 indot = null;
Dot2 dot = Math.CreateRandomDot(rand, maxWidth, maxHeight);
int i = 0;
Dot2 tempdot;
while (Dots.Count < number)
{
tempdot = Math.CreateRandomDot(rand, dot, 100, maxWidth, maxHeight);
if (i <= 2)
{
Add(tempdot);
dot = tempdot;
i++;
}
else
{
for (int j = 0; j < i - 2; j++)
{
if (Math.isIntersect(new Vector(tempdot, get(i - 1)), new Vector(get(j), get(j + 1)), out indot))
{
if (indot != null)
{
//draw.Lines(new List<Dot2>() { dot, Dots[i - 1], Dots[j], Dots[j + 1] });
dotss.Add(indot);
}
isIntersect = true;
break;
}
}
if (isIntersect == true)
{
isIntersect = false;
continue;
}
else
{
Add(tempdot);
dot = tempdot;
i++;
}
}
}
}
/// <summary>
/// 返回离点集最远的点
/// </summary>
/// <param name="origin"></param>
/// <param name="DotSet"></param>
/// <returns></returns>
public static Dot2 getFastestDot(Dot2 origin, List <Dot2> DotSet)
{
int j = 0;
double lengh = 0, temp;
for (int i = 0; i < DotSet.Count; i++)
{
temp = Math.Length(origin, DotSet[i]);
if (temp > lengh)
{
lengh = temp;
j = i;
}
}
return(DotSet[j]);
}
private void Reflesh_Click(object sender, RoutedEventArgs e)
{
Random rand = new Random();
Math.Dot2 dot = Test.Math.Math.CreateRandomDot(rand, (int)this.MineCanvas.Width - 10, (int)this.MineCanvas.Height - 10);
this.MineCanvas.Children.Clear();
//draw.Dots(new List<Math.Dot2>() { dot });
border.put(dot);
if (IsFill.IsChecked == true)
{
draw.Border(border);
}
else
{
draw.Lines(border);
}
//draw.Lines(border);
//draw.Appear(border.fetchLog().dot);
}
/// <summary>
/// 返回离点集最近的点
/// </summary>
/// <param name="origin"></param>
/// <param name="DotSet"></param>
/// <returns></returns>
public static Dot2 getNearestDot(Dot2 origin, List <Dot2> DotSet)
{
if (DotSet.Count == 0)
{
return(null);
}
int j = 0;
double lengh = Math.Length(origin, DotSet[j]), temp;
for (int i = 1; i < DotSet.Count; i++)
{
temp = Math.Length(origin, DotSet[i]);
if (temp < lengh)
{
lengh = temp;
j = i;
}
}
return(DotSet[j]);
}
/// <summary>
/// 将增加长度最小的点插入
/// </summary>
/// <param name="origin"></param>
/// <param name="border"></param>
public static void putMinLengthDotToBorder(Dot2 origin, Border border)
{
double temp, lengh = double.MaxValue;
if (border.DotCount <= 2)
{
border.Add(origin);
return;
}
int j = 0;
for (int i = 0; i < border.DotCount; i++)
{
temp = Math.Length(origin, border.get(i)) + Math.Length(origin, border.get(i + 1)) - border.getVecter(i).Length;
if (temp < lengh)
{
lengh = temp;
j = i;
}
}
border.Insert(origin, j + 1, DrawType.Ignore);
}
/// <summary>
/// 计算三角形的面积
/// </summary>
/// <param name="A"></param>
/// <param name="B"></param>
/// <param name="C"></param>
/// <returns></returns>
public static double Area(Dot2 A, Dot2 B, Dot2 C)
{
return(0.5 * System.Math.Abs(A.X * B.Y + B.X * C.Y + A.Y * C.X - A.X * C.Y - A.Y * B.X - B.Y * C.X));
}
/// <summary>
/// 将一个点转为矢径
/// </summary>
/// <param name="D"></param>
public Vector(Dot2 D)
{
From = new Dot2(0, 0);
To = D;
}
/// <summary>
/// 创建单位向量
/// </summary>
public Vector()
{
From = new Dot2(0, 0);
To = new Dot2(1, 0);
}
/// <summary>
/// 判断两条边是否相交
/// </summary>
/// <param name="A"></param>
/// <param name="B"></param>
/// /// <param name="des">双方容差距离</param>
/// <returns></returns>
public static bool isIntersect(Vector A, Vector B, out Dot2 interdot, double des = 10)
{
interdot = null;
//第一步：盒子判断
double amin, amax, bmin, bmax;
if (A.From.X > A.To.X)
{
amin = A.To.X;
amax = A.From.X;
}
else
{
amin = A.From.X;
amax = A.To.X;
}
if (B.From.X > B.To.X)
{
bmin = B.To.X;
bmax = B.From.X;
}
else
{
bmin = B.From.X;
bmax = B.To.X;
}
if (amax - bmin < des || amin - bmax > des)
{
return(false);
}
if (A.From.Y > A.To.Y)
{
amin = A.To.Y;
amax = A.From.Y;
}
else
{
amin = A.From.Y;
amax = A.To.Y;
}
if (B.From.Y > B.To.Y)
{
bmin = B.To.Y;
bmax = B.From.Y;
}
else
{
bmin = B.From.Y;
bmax = B.To.Y;
}
if (amax - bmin < des || amin - bmax > des)
{
return(false);
}
//第二步同向判断
if (cross(A, new Vector(A.From, B.From)) * cross(A, new Vector(A.From, B.To)) > 0)
{
return(false);
}
//第三步位置判断
interdot = new Dot2(((A.To.Y * A.From.X - A.To.X * A.From.Y) * (B.To.X - B.From.X) - (B.To.Y * B.From.X - B.To.X * B.From.Y) * (A.To.X - A.From.X)) / ((B.To.X - B.From.X) * (A.To.Y - A.From.Y) - (B.To.Y - B.From.Y) * (A.To.X - A.From.X)),
-((B.To.Y * B.From.X - B.To.X * B.From.Y) * (A.To.Y - A.From.Y) - (B.To.Y - B.From.Y) * (A.To.Y * A.From.X - A.To.X * A.From.Y)) / ((B.To.X - B.From.X) * (A.To.Y - A.From.Y) - (B.To.Y - B.From.Y) * (A.To.X - A.From.X)));
if (dot(new Vector(interdot, A.From), new Vector(interdot, A.To)) > 0)
{
if (Length(interdot, A.From) > des || Length(interdot, A.To) > des)
{
return(false);
}
}
return(true);
}
/// <summary>
/// 将一个点插入到边界中，形成凸面体
/// </summary>
/// <param name="origin"></param>
/// <param name="border"></param>
/// <returns></returns>
public static void putDotToBorder(Dot2 origin, Border border)
{
Dot2 dot;
int i, j = 0, count = border.DotCount, tempj;
if (count <= 2)
{
border.Add(origin);
return;
}
double temp, lengh = double.MaxValue;
int isIntersects = 0;
for (i = 0; i < count; i++)
{
temp = Math.Length(origin, border.get(i));
if (temp < lengh)
{
lengh = temp;
j = i;
}
}
//判断是否相交
tempj = count + j;
for (i = 0; i < count; i++)
{
if (i == tempj % count || i == (tempj - 1) % count)
{
continue;
}
if (isIntersect(new Vector(origin, border.get(tempj)), border.getVecter(i), out dot))
{
isIntersects = 1;
break;
}
}
if (isIntersects == 1)
{
isIntersects = 4;
lengh = double.MaxValue;
//采用面积最小方式
for (i = 0; i < border.DotCount; i++)
{
temp = Math.Area(origin, border.get(i), border.get((i + 1)));
if (temp < lengh)
{
lengh = temp;
j = i;
}
}
//判断是否相交,若相交，取最近的相交的线段插入
temp = double.MaxValue;
tempj = count + j;
for (i = 0; i < count; i++)
{
if (i == tempj % count || i == (tempj - 1) % count)
{
continue;
}
if (isIntersect(new Vector(origin, border.get(tempj)), border.getVecter(i), out dot))
{
temp = Math.Length(origin, dot);
if (temp < lengh)
{
isIntersects = 5;
lengh = temp;
j = i;
}
}
}
//if (isIntersects == 5)
//{
//}
//tempj = count + i+1;
//for (i = 0; i < count; i++)
//{
// if (i == tempj % count || i == (tempj - 1) % count)
// {
// continue;
// }
// if (isIntersect(new Vector(origin, border.get(tempj)), border.getVecter(i), out dot))
// {
// isIntersects = 5;
// break;
// }
//}
}
else
{
tempj = count + j - 1;
for (i = 0; i < count; i++)
{
if (i == tempj % count || i == (tempj - 1) % count)
{
continue;
}
if (isIntersect(new Vector(origin, border.get(tempj)), border.getVecter(i), out dot))
{
isIntersects = 1;
break;
}
}
tempj = count + j + 1;
for (i = 0; i < count; i++)
{
if (i == tempj % count || i == (tempj - 1) % count)
{
continue;
}
if (isIntersect(new Vector(origin, border.get(tempj)), border.getVecter(i), out dot))
{
if (isIntersects == 1)
{
isIntersects = 2;
}
else
{
isIntersects = 3;
}
break;
}
}
}
switch (isIntersects)
{
case 0: //两线段都无交点
if (Math.Length(origin, border.get(j - 1)) + border.getVecter(j).Length > Math.Length(origin, border.get(j + 1)) + border.getVecter(j - 1).Length)
{
border.Insert(origin, j + 1, DrawType.normal);
}
else
{
border.Insert(origin, j, DrawType.normal);
}
break;
case 1: //仅左线段相交
border.Insert(origin, j + 1, DrawType.Ignore);
break;
case 2: //左右线段都相交
break;
case 3: //仅右线段相交
border.Insert(origin, j, DrawType.Ignore);
break;
case 4: //采用面积最小方式,无相交
border.Insert(origin, j + 1, DrawType.Ignore);
break;
case 5: //采用面积最小方式,有相交,插入相交线段
border.Insert(origin, j + 1, DrawType.Ignore);
break;
default:
break;
}
}
public Operate(Type type, Dot2 dot, int index)
{
this.type = type;
this.dot = dot;
this.index = index;
}
public Dotx(Dot2 dot, DrawType type)
{
this.X = dot.X;
this.Y = dot.Y;
this.type = type;
}
public Dotx(Dot2 dot)
{
this.X = dot.X;
this.Y = dot.Y;
this.type = DrawType.normal;
}
/// <summary>
/// 获取两个点的长度
/// </summary>
/// <returns></returns>
public static double Length(Dot2 D1, Dot2 D2)
{
return(System.Math.Sqrt(System.Math.Pow((D1.X - D2.X), 2) + System.Math.Pow((D1.Y - D2.Y), 2)));
}
/// <summary>
/// 根据两个点生成向量
/// </summary>
public Vector(Dot2 from, Dot2 to)
{
From = from;
To = to;
}
public void put(Dot2 dot)
{
Math.putMinLengthDotToBorder(dot, this);
//Math.putDotToBorder(dot, this);
//getNearestVector
}
public void Modify(Dot2 dot, int index)
{
Dots[index].X = dot.X;
Dots[index].Y = dot.Y;
Operate.Add(new Operate(Type.Modify, dot, index));
}
public void Add(Dot2 dot)
{
Operate.Add(new Operate(Type.Append, dot, Dots.Count));
Dots.Add(dot.toDotx());
}