7. 15. 3. 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 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
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
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}
