VB.Net Tutorial/Development/Math

Convert rectangular 3D coordinates to cylindrical coordinates.

"Convert cylindrical coordinates to rectangular 3D coordinates.
        " ----- Convert rectangular 3D coordinates to
        "       spherical coordinates.
        " ----- Convert spherical coordinates to
        "       rectangular 3D coordinates.
        " ----- Convert spherical coordinates to
        "       cylindrical coordinates.        
        " ----- Convert cylindrical coordinates to
        "       spherical coordinates.        
        
" Quote from
"Visual Basic 2005 Cookbook Solutions for VB 2005 Programmers
"by Tim Patrick (Author), John Craig (Author)
"# Publisher: O"Reilly Media, Inc. (September 21, 2006)
"# Language: English
"# ISBN-10: 0596101775
"# ISBN-13: 978-0596101770
Public Class Tester
    Public Shared Sub Main
        Dim result As New System.Text.StringBuilder
        Dim pointRec As New Point3D(3, 4, 5)
        Dim pointCyl As Point3D = RectToCylinder(pointRec)
        Dim pointSph As Point3D = RectToSphere(pointRec)
        Dim pointRecToCyl As Point3D = RectToCylinder(pointRec)
        Dim pointRecToSph As Point3D = RectToSphere(pointRec)
        Dim pointCylToRec As Point3D = CylinderToRect(pointCyl)
        Dim pointCylToSph As Point3D = CylinderToSphere(pointCyl)
        Dim pointSphToRec As Point3D = SphereToRect(pointSph)
        Dim pointSphToCyl As Point3D = SphereToCylinder(pointSph)
        result.AppendLine("Rec: " & pointRec.Tostring())
        result.AppendLine("Cyl: " & pointCyl.Tostring())
        result.AppendLine("Sph: " & pointSph.Tostring())
        result.AppendLine()
        result.AppendLine("Rec to Cyl: " & pointRecToCyl.Tostring())
        result.AppendLine("Rec to Sph: " & pointRecToSph.Tostring())
        result.AppendLine("Cyl to Rec: " & pointCylToRec.Tostring())
        result.AppendLine("Cyl to Sph: " & pointCylToSph.Tostring())
        result.AppendLine("Sph to Rec: " & pointSphToRec.Tostring())
        result.AppendLine("Sph to Cyl: " & pointSphToCyl.Tostring())
        Console.WriteLine(result.ToString())

    End Sub
    Public Shared Function RectToCylinder(ByVal pointA As Point3D) _
          As Point3D
        " ----- Convert rectangular 3D coordinates to
        "       cylindrical coordinates.
        Dim rho As Double
        Dim theta As Double
        rho = Math.Sqrt(pointA.X ^ 2 + pointA.Y ^ 2)
        theta = Math.Atan2(pointA.Y, pointA.X)
        Return New Point3D(rho, theta, pointA.Z)
    End Function
    Public Shared Function CylinderToRect(ByVal pointA As Point3D) _
          As Point3D
        " ----- Convert cylindrical coordinates to
        "       rectangular 3D coordinates.
        Dim x As Double
        Dim y As Double
        x = pointA.X * Math.Cos(pointA.Y)
        y = pointA.X * Math.Sin(pointA.Y)
        Return New Point3D(x, y, pointA.Z)
    End Function
    Public Shared Function RectToSphere(ByVal pointA As Point3D) _
          As Point3D
        " ----- Convert rectangular 3D coordinates to
        "       spherical coordinates.
        Dim rho As Double
        Dim theta As Double
        Dim phi As Double
        rho = Math.Sqrt(pointA.X ^ 2 + pointA.Y ^ 2 + _
           pointA.Z ^ 2)
        theta = Math.Atan2(pointA.Y, pointA.X)
        phi = Math.Acos(pointA.Z / Math.Sqrt( _
           pointA.X ^ 2 + pointA.Y ^ 2 + pointA.Z ^ 2))
        Return New Point3D(rho, theta, phi)
    End Function
    Public Shared Function SphereToRect(ByVal pointA As Point3D) _
          As Point3D
        " ----- Convert spherical coordinates to
        "       rectangular 3D coordinates.
        Dim x As Double
        Dim y As Double
        Dim z As Double
        x = pointA.X * Math.Cos(pointA.Y) * Math.Sin(pointA.Z)
        y = pointA.X * Math.Sin(pointA.Y) * Math.Sin(pointA.Z)
        z = pointA.X * Math.Cos(pointA.Z)
        Return New Point3D(x, y, z)
    End Function
    Public Shared Function CylinderToSphere(ByVal pointA As Point3D) _
          As Point3D
        " ----- Convert cylindrical coordinates to
        "       spherical coordinates.
        Dim rho As Double
        Dim theta As Double
        Dim phi As Double
        rho = Math.Sqrt(pointA.X ^ 2 + pointA.Z ^ 2)
        theta = pointA.Y
        phi = Math.Acos(pointA.Z / _
           Math.Sqrt(pointA.X ^ 2 + pointA.Z ^ 2))
        Return New Point3D(rho, theta, phi)
    End Function
    Public Shared Function SphereToCylinder(ByVal pointA As Point3D) _
          As Point3D
        " ----- Convert spherical coordinates to
        "       cylindrical coordinates.
        Dim rho As Double
        Dim theta As Double
        Dim z As Double
        rho = pointA.X * Math.Sin(pointA.Z)
        theta = pointA.Y
        z = pointA.X * Math.Cos(pointA.Z)
        Return New Point3D(rho, theta, z)
    End Function
    
End Class

Public Class Point3D
    Public X As Double
    Public Y As Double
    Public Z As Double
    Public Sub New(ByVal xPoint As Double, _
          ByVal yPoint As Double, ByVal zPoint As Double)
        Me.X = xPoint
        Me.Y = yPoint
        Me.Z = zPoint
    End Sub
    Public Overrides Function Tostring() As String
        Return "{X=" & X & ",Y=" & Y & ",Z=" & Z & "}"
    End Function
End Class

Rec: {X=3,Y=4,Z=5}
Cyl: {X=5,Y=0.927295218001612,Z=5}
Sph: {X=7.07106781186548,Y=0.927295218001612,Z=0.785398163397448}
Rec to Cyl: {X=5,Y=0.927295218001612,Z=5}
Rec to Sph: {X=7.07106781186548,Y=0.927295218001612,Z=0.785398163397448}
Cyl to Rec: {X=3,Y=4,Z=5}
Cyl to Sph: {X=7.07106781186548,Y=0.927295218001612,Z=0.785398163397448}
Sph to Rec: {X=3,Y=4,Z=5}
Sph to Cyl: {X=5,Y=0.927295218001612,Z=5}

Generating random integers.

Module Tester
   Sub Main()
      Dim randomObject As Random = New Random()
      Dim randomNumber As Integer
      Dim output As String = ""
      Dim i As Integer
      For i = 1 To 20
         randomNumber = randomObject.Next(1, 7)
         output &= randomNumber & " "
         If i Mod 5 = 0 Then " is i a multiple of 5?
            output &= vbCrLf
         End If
      Next
      Console.WriteLine(output)
   End Sub 
End Module

4 1 3 4 3
5 6 2 6 5
5 3 6 4 1
6 6 3 6 3

Math. Cos and Sin

Public Class Tester
    Public Shared Sub Main
        Dim X As Single
        Dim Y As Single
        X = CSng( Math.Cos(100))
        Y = CSng( Math.Sin(100))
        Console.WriteLine(X)
        Console.WriteLine(Y)
        
    End Sub
End Class

0.8623189
-0.5063657

Math.Round

Public Class Tester
    Public Shared Sub Main
    
        Dim digits As Integer
        For digits = 0 To 5
            Console.WriteLine(Math.Round(Math.PI, digits))
        Next digits
     End Sub
End Class

3
3.1
3.14
3.142
3.1416
3.14159

Math.Sqrt and Atan2

Public Class Tester
    Public Shared Sub Main
        Dim magnitude As Single
        Dim radians As Single
        magnitude = CSng(Math.Sqrt(100 ^ 2 + 120 ^ 2))
        radians = CSng(Math.Atan2(100, 123))

        Console.WriteLine(magnitude)
        Console.WriteLine(radians)
        
    End Sub
End Class

156.205
0.6826226

Randomize

Option Strict On
Public Module RandomizeStatement
   Public Sub Main()
      Dim number As Double = 1.0325
      
      Rnd(-1)
      Randomize(number)                        " Number is any Double
      For ctr As Integer = 1 to 10
         Console.WriteLine(Rnd())
      Next
   End Sub
End Module

0.3610106
0.579608
0.2782471
0.05653632
0.2865489
0.33937
0.6398301
0.2991799
0.8264404
0.1662288