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A 3D Sphere

by Boriza (1 Submission)
Category: Math/Dates
Compatability: Visual Basic 3.0
Difficulty: Unknown Difficulty
Date Added: Wed 3^rd February 2021
Rating: (16 Votes)

Draw a real 3D shpere using ONLY lines. This code can be easily modified to show other 3D objects. All you need to do is an array of coordinates. It does everything else for you (display, rotation, zoom etc) HAVE YOUR PERSONAL 3D ENGINE!!!

Inputs
'Try to change: ' number of angles and size of the polygon 'Also: Size of the sphere
Assumes
Just create form (form1), module and PASTE the code! This code rotates a polygon to create a sphere.
Side Effects
It does not always draw a full sphere, may be you can fix it...
API Declarations
Option Explicit
Public Const Pi = 3.1415926
'Number of angles of polygon
Public Const N_Angles = 5
'Diameter of the sphere
Public Const Sphere_Diam = 6000
Type Dot
X As Double
Y As Double
Z As Double
End Type
'polygon in array
Public Object(1 To N_Angles + 1) As Dot
Public H_Globe, V_Globe
Public X, Y, Z
Public Me_to_Obj
Public Obj_to_Me
Public Polygon_R
Public Turn_Angle As Double
Function CRad(Deg)
'convert deg to rad
CRad = Deg * Pi / 180
End Function
Function CDeg(Rad)
CDeg = Rad * 180 / Pi
End Function
Public Sub GenPolygon()
'generate polygon
Dim Angle
Dim n As Double
Angle = 360 / N_Angles
For n = 1 To UBound(Object())
Object(n).X = Sin(CRad(202.5 + (n - 1) * Angle)) * Polygon_R
Object(n).Y = Cos(CRad(202.5 + (n - 1) * Angle)) * Polygon_R
Object(n).Z = Sphere_Diam / 2
Next n
n = 1 - ((Polygon_R * 2) ^ 2) / (2 * ((Sphere_Diam / 2) ^ 2))
n = n ^ 2
n = Sqr(1 / n - 1)
Turn_Angle = Atn(n)
End Sub
Public Sub Rotate(Obj() As Dot, HAngle, VAngle)
'this function rotates dots in array around the axes
Dim X, Y, Z, c As Double
Dim Ha, Va As Double
Ha = HAngle + CRad(H_Globe)
Va = VAngle + CRad(V_Globe)
For c = 1 To UBound(Obj())
If Ha <> 0 Then
X = Obj(c).X
Y = Obj(c).Y
Z = Obj(c).Z

Obj(c).Z = Z * Cos(Ha) - X * Sin(Ha)
Obj(c).X = X * Cos(Ha) + Z * Sin(Ha)
End If

If Va <> 0 Then
X = Obj(c).X
Y = Obj(c).Y
Z = Obj(c).Z

Obj(c).Y = Y * Cos(Va) - Z * Sin(Va)
Obj(c).Z = Z * Cos(Va) + Y * Sin(Va)
End If
Next c
End Sub
Public Sub DrawArray(Obj() As Dot)
'display array of dots on the screen
'Note: all dots are connected by lines
On Error Resume Next

Dim n, d, dz
Dim R, X1, Y1, X2, Y2
d = Me_to_Obj
dz = d + Obj_to_Me
X2 = (Obj(1).X) * d / (Obj(1).Z + dz) + X
Y2 = (Obj(1).Y) * d / (Obj(1).Z + dz) + Y
For n = 0 To UBound(Obj()) - 1
X1 = X2
Y1 = Y2
X2 = (Obj(n + 1).X) * d / (Obj(n + 1).Z + dz) + X
Y2 = (Obj(n + 1).Y) * d / (Obj(n + 1).Z + dz) + Y
'Swap next 2 lines to get full sphere:
'Form1.Line (X1, Y1)-(X2, Y2)
If Obj(n + 1).Z < 0 Then Form1.Line (X1, Y1)-(X2, Y2)
Next n

End Sub
Public Sub Sphere()
'Displays polygons under different angles to construct a sphere
Form1.Cls
Dim H, V, A, n
A = Turn_Angle
n = Val(2 * Pi / Turn_Angle)
For H = 1 To n / 2
For V = 1 To n
DrawArray Object
Rotate Object, A, 0
Next V
Rotate Object, 0, A
Next H
End Sub

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