Theprogrammersfirst: How to draw a spherical world?

2021-04-24

How to draw a spherical world?

I would like to create the following world with a WinForms application and a PictureBox: the observer stands in the middle and on the floor of this spherical world. He can turn his view 360°: North - East - South - West - North. He can also look up (from his point of view by max. 90° (zenith), so ϑ = 0°) and look at the horizon (0°, ϑ = 90°). So the observer always sees the ‘inner wall’ of the sphere. That's what I want to draw in the PictureBox.

The first goal is to get the whole thing working and see the world turning. The painted sky should have points so that you can see that there is turning something.

What do I need for this? What do I need to download from NuGet? Here is what I've tried.

FormMain.vb

Imports System.Windows.Media.Media3D
Public NotInheritable Class FormMain
    Private Sphere As New Class_Sphere
    Private Sub FormMain_Load(sender As Object, e As EventArgs) Handles MyBase.Load
        Me.BackColor = Color.FromArgb(180, 191, 183)
        PictureBox1.BackColor = Color.Black
        Me.Location = New Point(0, 0)
    End Sub

    Private Sub FormMain_KeyDown(sender As Object, e As KeyEventArgs) Handles MyBase.KeyDown
        Select Case e.KeyCode
            Case Keys.Up
                If Sphere.Theta > 0US Then
                    Sphere.Theta -= 1US
                End If
            Case Keys.Down
                If Sphere.Theta < 90US Then
                    Sphere.Theta += 1US
                End If
            Case Keys.Left
                If Sphere.Phi < 360US Then
                    Sphere.Phi += 1US
                End If
                If Sphere.Phi = 360US Then Sphere.Phi = 0US
            Case Keys.Right
                If Sphere.Phi > 0US Then
                    Sphere.Phi -= 1US
                End If
            Case Else
                Exit Select
        End Select

        Sphere.R_kart = Sphere.R_Polar * Math.Sin(CDbl(Sphere.Theta) * Math.PI / 180.0)
        Sphere.x_kart = Sphere.R_kart * Math.Cos(CDbl(Sphere.Phi) * Math.PI / 180.0)
        Sphere.y_kart = Sphere.R_kart * Math.Sin(CDbl(Sphere.Phi) * Math.PI / 180.0)
        Sphere.z_kart = Sphere.R_Polar * Math.Cos(CDbl(Sphere.Theta) * Math.PI / 180.0)
        Sphere.R_Polar_V = New Vector3D(Sphere.x_kart, Sphere.y_kart, Sphere.z_kart)
        'Debug.WriteLine("ϑ = " & Sphere.Theta & "    𝜑 = " & Sphere.Phi)
    End Sub

    Private Sub PictureBox1_Paint(sender As Object, e As PaintEventArgs) Handles PictureBox1.Paint

    End Sub

    Private Sub FormMain_FormClosing(sender As Object, e As FormClosingEventArgs) Handles MyBase.FormClosing
        If MessageBox.Show("Wirklich schließen?", "Programm", MessageBoxButtons.YesNo, MessageBoxIcon.Question) = DialogResult.No Then e.Cancel = True
    End Sub
End Class

Class_Sphere.vb

Imports System.Windows.Media.Media3D

Public NotInheritable Class Class_Sphere
    ''' <summary>
    ''' Höhenwinkel von 0° (oben) bis 90° (horizontal)
    ''' </summary>
    Public Theta As UInt16 = 90US
    ''' <summary>
    ''' Seitenwinkel von 0° bis 360°
    ''' </summary>
    Public Phi As UInt16 = 0US
    Public R_Polar As Double = 100.0R
    ''' <summary>
    ''' horizontale Entfernung
    ''' </summary>
    Public R_kart As Double = 0R
    Public x_kart As Double = 0R
    Public y_kart As Double = 0R
    Public z_kart As Double = 0R
    Public R_Polar_V As Vector3D
    Public alle_Punkte As List(Of Vector3D)
End Class

The axis names and variables are taken from the GET Lab video