Convert rectangular 3D coordinates to cylindrical coordinates. : Math « Development « VB.Net Tutorial

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'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}