昨天看到某个公司招聘出的一道题目，题目是这样的：判断任意三个点是否构成三角形，以及某个点是否位于指定的三角形内。
关于这个问题，我给出了自己的答案，首先解决第一个问题：
///
<summary>
///
IsTriangle 判断集合中的头三个点PointF是否可以构成一个三角形
///
</summary>
public
static
bool
IsTriangle(ArrayList ptList)
{
PointF pt0
=
(PointF)ptList[
0
] ;
PointF pt1
=
(PointF)ptList[
1
] ;
PointF pt2
=
(PointF)ptList[
2
] ;
//如果有两个点相同
if
(pt0.Equals(pt1)
||
pt0.Equals(pt2)
||
pt1.Equals(pt2) )
{
return
false
;
}
float
length_01
=
(
float
)Math.Sqrt((pt0.X
-
pt1.X)
*
(pt0.X
-
pt1.X)
+
(pt0.Y
-
pt1.Y)
*
(pt0.Y
-
pt1.Y)) ;
float
length_02
=
(
float
)Math.Sqrt((pt0.X
-
pt2.X)
*
(pt0.X
-
pt2.X)
+
(pt0.Y
-
pt2.Y)
*
(pt0.Y
-
pt2.Y)) ;
float
length_12
=
(
float
)Math.Sqrt((pt2.X
-
pt1.X)
*
(pt2.X
-
pt1.X)
+
(pt2.Y
-
pt1.Y)
*
(pt2.Y
-
pt1.Y)) ;
bool
result0
=
(length_01
+
length_02
<=
length_12) ;
bool
result1
=
(length_01
+
length_12
<=
length_02) ;
bool
result2
=
(length_02
+
length_12
<=
length_01) ;
if
(result0
||
result1
||
result2)
{
return
false
;
}
return
true
;
}
该解答分为两步，首先判断是否有重点，接着以两边之和大于第三边作为构成三角形的依据。
关于第二个问题稍微复杂些，不过幸好我在早期研究过并解决了一个更常见的问题，那就是判断一个点是否位于某个多边形内，而且即使这个多边形是凹多边形。这个功能在EnterpriseServerBase.XMath.Geometry.Polygon类中实现。
对于问题二的解答，我封装了Triangle类，它不仅借助Polygon类解决了问题二，而且可以计算三角形的面积和各个边长。
public
class
Triangle
{
 private ArrayList vertextList = null ;
private ArrayList lengthList = null ;
private float myArea = 0 ;
  ctor#region ctor
public Triangle(ArrayList ptList)
 {
if(! GeometryHelper.IsTriangle(ptList))
{
throw new ArgumentException("The points in list can't construct a triangle !") ;
 }
this.vertextList = ptList ;
this.FillLengthList() ;
}
public Triangle(PointF pt0 ,PointF pt1 ,PointF pt2)
{
ArrayList ptList = new ArrayList() ;
ptList.Add(pt0) ;
ptList.Add(pt1) ;
ptList.Add(pt2) ;
if(! GeometryHelper.IsTriangle(ptList))
{
throw new ArgumentException("The points in list can't construct a triangle !") ;
}
this.vertextList = ptList ;
this.FillLengthList() ;
}
private void FillLengthList()
{
PointF pt0 = (PointF)this.vertextList[0] ;
PointF pt1 = (PointF)this.vertextList[1] ;
PointF pt2 = (PointF)this.vertextList[2] ;
float length_01 = (float)Math.Sqrt((pt0.X - pt1.X)*(pt0.X - pt1.X) + (pt0.Y - pt1.Y)*(pt0.Y - pt1.Y)) ;
float length_02 = (float)Math.Sqrt((pt0.X - pt2.X)*(pt0.X - pt2.X) + (pt0.Y - pt2.Y)*(pt0.Y - pt2.Y)) ;
float length_12 = (float)Math.Sqrt((pt2.X - pt1.X)*(pt2.X - pt1.X) + (pt2.Y - pt1.Y)*(pt2.Y - pt1.Y)) ;
this.lengthList = new ArrayList() ;
this.lengthList.Add(length_12) ;
this.lengthList.Add(length_02) ;
this.lengthList.Add(length_01) ;
}
 #endregion
Area ,GetEdgeLength#region Area ,GetEdgeLength
/**//// <summary>
/// Area 三角形的面积
/// </summary>
public float Area
{
get
{
if(this.myArea == 0)
{
this.myArea = this.GetArea() ;
}
return this.myArea ;
}
}
private float GetArea()
{
float len0 = (float)this.lengthList[0] ;
float len1 = (float)this.lengthList[1] ;
float len2 = (float)this.lengthList[2] ;
float p = (len0 + len1 + len2) * 0.5f ;
return (float)Math.Sqrt(p * (p-len0) * (p-len1) * (p-len2)) ;
}
public float GetEdgeLength(int index)//0<= index <=2
{
if((index <0) ||(index >2))
{
return 0 ;
}
return (float)this.lengthList[index] ;
}
#endregion
Contains#region Contains
/**//// <summary>
/// Contains 判断某点是否在三角形内部
/// </summary>
public bool Contains(PointF pt)
{
Polygon poly = new Polygon(this.vertextList) ;
return poly.Contains(pt) ;
}
#endregion
}
Polygon类的实现比较复杂，代码也比较多，源码就不列出来了，可以点击这里下载。 | 
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