[分享] 運算子的重載

呆呆

VB.2005 以上有一項不錯用的功能,叫運算子的重載
什麼是運算子的重載
其實就是運算符號的重新定義
這在數學上很常見
一般我們在數學上 + - * / 這些東西是指數字的 加減乘除
但如果到了向量,或矩陣,或是虛數,這些符號就重新定義了
因為向量的加減乘除法和純量顯然有很大的不同,所以
A向量+B向量的程式碼不會寫成 C = A+B
但我們為了要使程式碼簡單易明白,所以我們也很想要這樣寫,那就必需重新定義運算子

[ <attributes> ] Public [ Overloads ] Shared [ Shadows ] _
[ Widening | Narrowing ] Operator symbol ( operands ) As type
...
End Operator
那這個要怎麼用,我們可以新增一個WindowsForm 專案
然後在該專案中再新增一個 Vector3D 類別如下

1. Public Class Vector3D
   
2. 
   
3.     Private mXValue As Double
   
4.     Public Property XValue() As Double
   
5.         Get
   
6.             Return mXValue
   
7.         End Get
   
8.         Set(ByVal value As Double)
   
9.             mXValue = value
   
10.         End Set
    
11.     End Property
    
12. 
    
13.     Private mYvalue As Double
    
14.     Public Property YValue() As Double
    
15.         Get
    
16.             Return mYvalue
    
17.         End Get
    
18.         Set(ByVal value As Double)
    
19.             mYvalue = value
    
20.         End Set
    
21.     End Property
    
22. 
    
23.     Private mZvalue As Double
    
24.     Public Property ZValue() As Double
    
25.         Get
    
26.             Return mZvalue
    
27.         End Get
    
28.         Set(ByVal value As Double)
    
29.             mZvalue = value
    
30.         End Set
    
31.     End Property
    
32. 
    
33.     Public ReadOnly Property NormOfVector() As Double
    
34.         Get
    
35.             Return Math.Sqrt(XValue * XValue + YValue * YValue + ZValue * ZValue)
    
36.         End Get
    
37.     End Property
    
38. 
    
39.     Public Sub New(ByVal x As Double, ByVal y As Double, ByVal z As Double)
    
40. 
    
41.         mXValue = x
    
42.         mYvalue = y
    
43.         mZvalue = z
    
44. 
    
45.     End Sub
    
46. 
    
47.     Public Sub New()
    
48.         XValue = 0
    
49.         YValue = 0
    
50.         ZValue = 0
    
51.     End Sub
    
52. 
    
53.     Public Shared Operator +(ByVal A As Vector3D, ByVal B As Vector3D) As Vector3D
    
54. 
    
55.         Return New Vector3D(A.XValue + B.XValue, A.YValue + B.YValue, A.ZValue + B.ZValue)
    
56. 
    
57.     End Operator
    
58. 
    
59. 
    
60.     Public Shared Operator -(ByVal A As Vector3D, ByVal B As Vector3D) As Vector3D
    
61. 
    
62.         Return New Vector3D(A.XValue - B.XValue, A.YValue - B.YValue, A.ZValue - B.ZValue)
    
63. 
    
64.     End Operator
    
65. 
    
66.     '外積
    
67.     Public Shared Operator *(ByVal A As Vector3D, ByVal B As Vector3D) As Vector3D
    
68.         Dim tmpVector As New Vector3D
    
69. 
    
70.         With tmpVector
    
71.             .XValue = A.YValue * B.ZValue - A.ZValue * B.YValue
    
72.             .YValue = -(A.XValue * B.ZValue - A.ZValue * B.XValue)
    
73.             .ZValue = A.XValue * B.YValue - A.YValue * B.XValue
    
74.         End With
    
75.         Return tmpVector
    
76.     End Operator
    
77. 
    
78. 
    
79.     '內積
    
80.     Public Shared Operator ^(ByVal A As Vector3D, ByVal B As Vector3D) As Double
    
81.         Return A.XValue * B.XValue + A.YValue * +B.YValue + A.ZValue * B.ZValue
    
82.     End Operator
    
83. 
    
84. 
    
85.     Public Shared Function AngleBetweenTwoVector(ByVal A As Vector3D, ByVal B As Vector3D) As Double
    
86. 
    
87.         Return Math.Acos((A ^ B) / (A.NormOfVector * B.NormOfVector)) * 180 / Math.PI
    
88. 
    
89.     End Function
    
90. 
    
91. 
    
92.     Public Overrides Function ToString() As String
    
93. 
    
94.         If Me.YValue < 0 And Me.ZValue < 0 Then
    
95.             Return Me.XValue & "i - " & -Me.YValue & "j - " & -Me.ZValue & "k"
    
96.         End If
    
97. 
    
98.         If Me.YValue < 0 And Me.ZValue >= 0 Then
    
99.             Return Me.XValue & "i - " & -Me.YValue & "j + " & Me.ZValue & "k"
    
100.         End If
     
101. 
     
102.         If Me.YValue >= 0 And Me.ZValue < 0 Then
     
103.             Return Me.XValue & "i + " & Me.YValue & "j - " & -Me.ZValue & "k"
     
104.         End If
     
105. 
     
106.         Return Me.XValue & "i + " & Me.YValue & "j + " & Me.ZValue & "k"
     
107. 
     
108.     End Function
     
109. 
     
110. 
     
111. End Class

複製代碼

呆呆

上面的程式碼我們重定義了乘法的內外積和加減法
還有一個二向量的夾角分享方法
因為向量沒有除法所以不用定義,而乘法分為內外積二種
所以我們可以在 WindowsForm 上寫下以下程式碼

1. Public Class Form1
   
2. 
   
3.     Private A As New Vector3D(2, 3, 2)
   
4.     Private B As New Vector3D(1, 2, -1)
   
5.     Private C As New Vector3D
   
6.     Private D As Double
   
7.     Private H As Double
   
8. 
   
9.     Private fnt As Font
   
10. 
    
11.     Private Sub Form1_Load(ByVal sender As Object, ByVal e As System.EventArgs) Handles Me.Load
    
12. 
    
13.         fnt = New Font("新細明體", 30)
    
14. 
    
15.         C = A * B '外積
    
16.         D = A ^ B '內樍
    
17.         H = Vector3D.AngleBetweenTwoVector(A, B) '夾角
    
18. 
    
19.     End Sub
    
20. 
    
21. 
    
22.     Private Sub Form1_Paint(ByVal sender As Object, ByVal e As System.Windows.Forms.PaintEventArgs) Handles Me.Paint
    
23. 
    
24.         Dim g As Graphics = e.Graphics
    
25. 
    
26.         g.DrawString("二向量外積為   " & C.ToString, fnt, New SolidBrush(Color.Black), 10, 100)
    
27.         g.DrawString("二向量內積為   " & D.ToString, fnt, New SolidBrush(Color.Black), 10, 200)
    
28.         g.DrawString("二向量夾角為   " & H.ToString & " 度", fnt, New SolidBrush(Color.Black), 10, 300)
    
29. 
    
30.     End Sub
    
31. 
    
32. End Class

複製代碼

執行結果如下

呆呆

看起來是不是比較符合我們一般算數學的符號