向量及其运算(一)：二维向量的基本运算

Public Class Vector2D
    Public Property x As Double ‘x分量
    Public Property y As Double ‘y分量
    ‘‘‘ <summary>
    ‘‘‘ 二维向量类，能够实现平面向量的表示与运算
    ‘‘‘ </summary>
    ‘‘‘ <param name="nX">向量的X初始值,不填写默认为0</param>
    ‘‘‘ <param name="nY">向量的Y初始值,不填写默认为0</param>
    Public Sub New(Optional nX As Double = 0, Optional nY As Double = 0)
        x = nX
        y = nY
    End Sub
End Class

    ‘‘‘ <summary>
    ‘‘‘ 加上一个向量
    ‘‘‘ </summary>
    ‘‘‘ <param name="aVector">要加的向量</param>
    ‘‘‘ <remarks></remarks>
    Public Sub Add(ByVal aVector As Vector2D)
        x += aVector.x
        y += aVector.y
    End Sub

    ‘‘‘ <summary>
    ‘‘‘ 减去一个向量
    ‘‘‘ </summary>
    ‘‘‘ <param name="mVector">要减的向量</param>
    ‘‘‘ <remarks></remarks>
    Public Sub Minus(ByVal mVector As Vector2D)
        x -= mVector.x
        y -= mVector.y
    End Sub

    ‘‘‘ <summary>
    ‘‘‘ 乘以一个标量
    ‘‘‘ </summary>
    ‘‘‘ <param name="mNum">要乘的标量</param>
    ‘‘‘ <remarks></remarks>
    Public Sub Multiply(ByVal mNum As Double)
        x *= mNum
        y *= mNum
    End Sub

    ‘‘‘ <summary>
    ‘‘‘ 除以一个标量
    ‘‘‘ </summary>
    ‘‘‘ <param name="dNum">要除的标量</param>
    ‘‘‘ <remarks></remarks>
    Public Sub Divide(ByVal dNum As Double)
        x /= dNum
        y /= dNum
    End Sub

    ‘重载向量与向量加法运算符
    Public Overloads Shared Operator +(ByVal LeftVector As Vector2D, ByVal RightVector As Vector2D) As Vector2D
        Return New Vector2D(LeftVector.x + RightVector.x, LeftVector.y + RightVector.y)
    End Operator
    ‘重载向量与向量减法运算符
    Public Overloads Shared Operator -(ByVal LeftVector As Vector2D, ByVal RightVector As Vector2D) As Vector2D
        Return New Vector2D(LeftVector.x - RightVector.x, LeftVector.y - RightVector.y)
    End Operator
    ‘重载向量与标量乘法运算符
    Public Overloads Shared Operator *(ByVal LeftVector As Vector2D, ByVal RightNum As Double) As Vector2D
        Return New Vector2D(LeftVector.x * RightNum, LeftVector.y * RightNum)
    End Operator
    ‘重载标量与向量乘法运算符(交换律)
    Public Overloads Shared Operator *(ByVal LeftNum As Double, ByVal RightVector As Vector2D) As Vector2D
        Return New Vector2D(RightVector.x * LeftNum, LeftNum.y * RightVector)
    End Operator
    ‘重载向量与标量除法运算符
    Public Overloads Shared Operator /(ByVal LeftVector As Vector2D, ByVal RightNum As Double) As Vector2D
        Return New Vector2D(LeftVector.x / RightNum, LeftVector.y / RightNum)
    End Operator

    ‘‘‘ <summary>
    ‘‘‘ 返回向量的模长
    ‘‘‘ </summary>
    ‘‘‘ <returns></returns>
    Public Function Magnitude() As Double
        Return Math.Sqrt(x * x + y * y)
    End Function

    ‘‘‘ <summary>
    ‘‘‘ 指定向量的模长
    ‘‘‘ </summary>
    ‘‘‘ <param name="sPutNum">指定的长度</param>
    Public Sub SetMag(ByVal sPutNum As Double)
        Dim tempMag As Double = Me.Magnitude
            x = x * (sPutNum / tempMag)
            y = y * (sPutNum / tempMag)
    End Sub

    ‘‘‘ <summary>
    ‘‘‘ 限制向量模长,小于或等于某一值
    ‘‘‘ </summary>
    ‘‘‘ <param name="lUponNum">指定的最大值</param>
    Public Sub LimitMag(ByVal lUponNum As Double)
        Dim tempMag As Double = Me.Magnitude
        If tempMag > lUponNum Then
            x = x * (lUponNum / tempMag)
            y = y * (lUponNum / tempMag)
        End If
    End Sub

    ‘‘‘ <summary>
    ‘‘‘ ‘求向量的方向角
    ‘‘‘ </summary>
    ‘‘‘ <param name="gVector">指定的向量</param>
    ‘‘‘ <returns></returns>
    Public Shared Function GetHeading(ByVal gVector As Vector2D) As Double
        Dim Angle As Double
        Angle = Math.Asin(gVector.x / Math.Sqrt(gVector.x * gVector.x + gVector.y * gVector.y)) * (180 / Math.PI)
        Return Angle
    End Function

    ‘‘‘ <summary>
    ‘‘‘  ‘求两向量的夹角
    ‘‘‘ </summary>
    ‘‘‘ <param name="gLeftVector">第一个向量</param>
    ‘‘‘ <param name="gRightVector">第二个向量</param>
    ‘‘‘ <returns></returns>
    Public Shared Function GetAngleBetween(ByVal gLeftVector As Vector2D, ByVal gRightVector As Vector2D) As Double
        Dim Angle As Double
        Angle = Math.Asin((gLeftVector.x * gRightVector.x + gLeftVector.y * gRightVector.y) /
                          (Math.Sqrt(gLeftVector.x * gLeftVector.x + gLeftVector.y * gLeftVector.y) *
                           Math.Sqrt(gRightVector.x * gRightVector.x + gRightVector.y * gRightVector.y))) *
                          (180 / Math.PI)
        Return Angle
    End Function

    ‘‘‘ <summary>
    ‘‘‘ 向量旋转
    ‘‘‘ </summary>
    ‘‘‘ <param name="gAngle">指定旋转的角度，弧度制</param>
    Public Sub Rotate(ByVal gAngle As Double)
        Dim x1, y1 As Double
        x1 = x * Math.Cos(gAngle) - y * Math.Sin(gAngle)
        y1 = y * Math.Cos(gAngle) + x * Math.Sin(gAngle)
        x = x1
        y = y1
    End Sub