N-pointed star

[macalwen]

Code: (Select All)

Code: (Select All)

Screen 12
Window (-160, 120)-(160, -120)
Const pi = 3.1415926# / 180
Dim x(100) As Double, y(100) As Double, Nx(100) As Single, Ny(100) As Single, r1 As Double
Dim r As Integer, n As Integer, i As Integer, j As Integer, m As Integer
Input "number of N angles of N-pointed star:", n
If n < 3 Or n > 100 Then End
r = 100
m = 0
r1 = r * Sin(((360 / n) * (1 / 4)) * pi) / Cos((360 / (2 * n)) * pi)
For i = 0 To 360 Step 360 / n
    x(m) = r * Cos((i + 90) * pi)
    y(m) = r * Sin((i + 90) * pi)
    Nx(m) = r1 * Cos((126 + i) * pi)
    Ny(m) = r1 * Sin((126 + i) * pi)
    m = m + 1
Next i
If 360 Mod n <> 0 Then x(n) = x(0): y(n) = y(0)
For j = 0 To n - 1
    Line (x(j), y(j))-(Nx(j), Ny(j)), 4
    Line (Nx(j), Ny(j))-(x(j + 1), y(j + 1)), 4
Next j

[macalwen]

Code: (Select All)

Code: (Select All)

Screen 12
Const pi = 3.1415926#
a% = 20
b% = 10
Dim deg As Double
Dim Shared As Single x2, y2
Window (-30, 30)-(30, -30)
Circle (0, 0), 2, 10
For theta = 0 To 360 Step 0.5
    deg = theta * pi / 180
    x = a% * Cos(deg)
    y = b% * Sin(deg)
    ' PSet (x, y), 10
    u1 = 30 * pi / 180
    u2 = 90 * pi / 180
    u3 = 150 * pi / 180
    Call rote(x, y, u1)
    PSet (x2, y2), 10
    Call rote(x, y, u2)
    PSet (x2, y2), 10
    Call rote(x, y, u3)
    PSet (x2, y2), 10
Next theta
Sub rote (x1, y1, u)
    x2 = x1 * Cos(u) - y1 * Sin(u)
    y2 = y1 * Cos(u) + x1 * Sin(u)
End Sub

[bplus]

It's really radian = theta * pi / 180

and you take cos(radian) and sin(radian)

So the numbers are right but your words are misleading.

BTW QB64 has _Pi though uglier than just Pi you don't need the Pi = 3.14... line either.

Here is much more versatile routine with any inner and outer radius for star, any number of points, and color and you can fill it or not, demo of sub Star

This requires you to set color before calling Star to draw it.

Code: (Select All)

Sub Star (x, y, rInner, rOuter, nPoints, angleOffset, TFfill)
    ' x, y are same as for circle,
    ' rInner is center circle radius
    ' rOuter is the outer most point of star
    ' nPoints is the number of points,
    ' angleOffset = angle offset IN DEGREES, it will be converted to radians in sub
    ' this is to allow us to spin the polygon of n sides
    ' TFfill filled True or False (1 or 0)
    p_angle = Radians * (360 / nPoints): rad_angle_offset = Radians * angleOffset
    x1 = x + rInner * Cos(rad_angle_offset)
    y1 = y + rInner * Sin(rad_angle_offset)
    For i = 0 To nPoints - 1
        x2 = x + rOuter * Cos(i * p_angle + rad_angle_offset + .5 * p_angle)
        y2 = y + rOuter * Sin(i * p_angle + rad_angle_offset + .5 * p_angle)
        x3 = x + rInner * Cos((i + 1) * p_angle + rad_angle_offset)
        y3 = y + rInner * Sin((i + 1) * p_angle + rad_angle_offset)
        Line (x1, y1)-(x2, y2)
        Line (x2, y2)-(x3, y3)
        x1 = x3: y1 = y3
    Next
    If TFfill Then
        'Circle (x, y), 2, &HFFFFFFFF
        Paint (x, y), _DefaultColor, _DefaultColor
    End If
End Sub

Demo

Code: (Select All)

_Title "Even Better Stars" 'b+ 2021-11-18 trans of
'Better Stars.sdlbas (B+=MGA) 2016-05-16
' odd or even number of point, fat or skinny, better fills

Const Pi = _Acos(-1) 'cute way to get pi
'Print (Pi) 'check pi
'End
Const Radians = Pi / 180 'to convert an angle measured in degrees to and angle measure in radians, just mutiply by this
Const Xmax = 700
Const Ymax = 700
Const Cx = Xmax / 2
Const Cy = Ymax / 2

'setdisplay(xmax, ymax, 32, 1)
Screen _NewImage(Xmax, Ymax, 32)
_ScreenMove 300, 40
'setcaption("Better Stars demo")
'autoback(-2)

'main
Const NS = 100
Dim Shared x(NS), y(NS), dx(NS), dy(NS), ri(NS), ro(NS), p(NS), a(NS), turn(NS), fill(NS), c(NS) As _Unsigned Long
loopcounter = 0
For i = 0 To NS
    NewStar i
Next
While _KeyDown(27) = 0
    Line (0, 0)-(Xmax, Ymax), _RGB32(0, 0, 0, 30), BF
    For i = 0 To NS
        If x(i) > 0 And x(i) < Xmax And y(i) > 0 And y(i) < Ymax Then
            'ink(colr(c(i)))
            Color c(i)
            Star x(i), y(i), ri(i), ro(i), p(i), a(i), fill(i)
            x(i) = x(i) + dx(i)
            y(i) = y(i) + dy(i)
            ri(i) = 1.015 * ri(i)
            ro(i) = 1.015 * ro(i)
            a(i) = a(i) + turn(i)
        Else
            NewStar i
        End If
    Next
    'screenswap
    _Display
    _Limit 100
    'wait(50)
    loopcounter = loopcounter + 1
Wend


Sub NewStar (nxt)
    angle = Rnd * 2 * Pi
    r = Rnd * 6 + 1
    dx(nxt) = r * Cos(angle)
    dy(nxt) = r * Sin(angle)
    r = Rnd * 300
    x(nxt) = Cx + r * dx(nxt)
    y(nxt) = Cy + r * dy(nxt)
    ri(nxt) = Rnd
    ro(nxt) = ri(nxt) + 1 + Rnd
    p(nxt) = 3 + Int(Rnd * 9)
    a(nxt) = Rnd * 2 * Pi
    turn(nxt) = Rnd * 6 - 3
    fill(nxt) = Int(Rnd * 2)
    c(nxt) = rndColor~&
End Sub

Function rndColor~& ()
    rndColor~& = _RGB32(Rnd * 255, Rnd * 255, Rnd * 255)
End Function

Sub Star (x, y, rInner, rOuter, nPoints, angleOffset, TFfill)
    ' x, y are same as for circle,
    ' rInner is center circle radius
    ' rOuter is the outer most point of star
    ' nPoints is the number of points,
    ' angleOffset = angle offset IN DEGREES, it will be converted to radians in sub
    ' this is to allow us to spin the polygon of n sides
    ' TFfill filled True or False (1 or 0)
    p_angle = Radians * (360 / nPoints): rad_angle_offset = Radians * angleOffset
    x1 = x + rInner * Cos(rad_angle_offset)
    y1 = y + rInner * Sin(rad_angle_offset)
    For i = 0 To nPoints - 1
        x2 = x + rOuter * Cos(i * p_angle + rad_angle_offset + .5 * p_angle)
        y2 = y + rOuter * Sin(i * p_angle + rad_angle_offset + .5 * p_angle)
        x3 = x + rInner * Cos((i + 1) * p_angle + rad_angle_offset)
        y3 = y + rInner * Sin((i + 1) * p_angle + rad_angle_offset)
        Line (x1, y1)-(x2, y2)
        Line (x2, y2)-(x3, y3)
        x1 = x3: y1 = y3
    Next
    If TFfill Then
        'Circle (x, y), 2, &HFFFFFFFF
        Paint (x, y), _DefaultColor, _DefaultColor
    End If
End Sub

Oh ha! I was using my own way to get Pi not using _Pi either

Oh and this was before using _D2R(degrees) ie radians = _D2R(degrees) and the reverse of course is degrees = _R2D(radians) so we used Pi/180 or 180/Pi to convert degrees to radians or vice versa.

[bplus]

Thanks @macalwan I was impelled to update my own code for Star:

Code: (Select All)

 
' this sub requires fTri for Filling stars rev 2024-12-09 for FillTF option
Sub star (x, y, rInner, rOuter, nPoints, DegAngleOffset, K As _Unsigned Long, FillTF)
    ' x, y are same as for circle,
    ' rInner is center circle radius
    ' rOuter is the outer most point of star
    ' nPoints is the number of points,
    ' angleOffset = angle offset IN DEGREES, it will be converted to radians in sub
    ' this is to allow us to spin the polygon of n sides
    Dim pAngle, radAngleOffset, x1, y1, x2, y2, x3, y3, i As Long
 
    pAngle = _D2R(360 / nPoints): radAngleOffset = _D2R(DegAngleOffset)
    x1 = x + rInner * Cos(radAngleOffset)
    y1 = y + rInner * Sin(radAngleOffset)
    For i = 0 To nPoints - 1
        x2 = x + rOuter * Cos(i * pAngle + radAngleOffset + .5 * pAngle)
        y2 = y + rOuter * Sin(i * pAngle + radAngleOffset + .5 * pAngle)
        x3 = x + rInner * Cos((i + 1) * pAngle + radAngleOffset)
        y3 = y + rInner * Sin((i + 1) * pAngle + radAngleOffset)
        If FillTF Then
            fTri x1, y1, x2, y2, x3, y3, K
            Line (x3, y3)-(x1, y1), K ' need this ?? Yes!!! wo Paint leaks
            Line (x1, y1)-(x2, y2), K
            Line (x2, y2)-(x3, y3), K
        Else
            Line (x1, y1)-(x2, y2), K
            Line (x2, y2)-(x3, y3), K
        End If
        x1 = x3: y1 = y3
    Next
    If FillTF Then Paint (x, y), K, K
End Sub
 
Sub fTri (x1, y1, x2, y2, x3, y3, K As _Unsigned Long)
    Dim D As Long
    Static a&
    D = _Dest
    If a& = 0 Then a& = _NewImage(1, 1, 32)
    _Dest a&
    _DontBlend a& '  '<<<< new 2019-12-16 fix
    PSet (0, 0), K
    _Blend a& '<<<< new 2019-12-16 fix
    _Dest D
    _MapTriangle _Seamless(0, 0)-(0, 0)-(0, 0), a& To(x1, y1)-(x2, y2)-(x3, y3)
End Sub

And it's Demo:

Code: (Select All)

Option _Explicit
_Title "Better Stars 4" 'b+ 2024-12-09
' Even Better Stars 2 Arrow Steering" 'b+ 2021-11-23 try with arrow steering
' Better Stars.sdlbas (B+=MGA) 2016-05-16
' odd or even number of point, fat or skinny, better fills
 
' upgrade Star for FillTF and Color both why I didn't have this before ???
 
Const Xmax = 700
Const Ymax = 700
Const Cx = Xmax / 2
Const Cy = Ymax / 2
 
Screen _NewImage(Xmax, Ymax, 32)
_ScreenMove 300, 40
 
'main
Const NS = 100 ' number of stars (minus one because 0 based arrays)
Dim Shared x(NS), y(NS), dx(NS), dy(NS), ri(NS), ro(NS), p(NS), a(NS), turn(NS), fill(NS), c(NS) As _Unsigned Long
Dim As Long Loopcounter, i
 
Loopcounter = 0
For i = 0 To NS
    NewStar i
Next
While _KeyDown(27) = 0
    If _KeyDown(19200) Then '               turn left
        For i = 0 To NS
            x(i) = x(i) + 2 * ri(i) ^ 2
            dx(i) = dx(i) + 1
        Next
    End If
 
    If _KeyDown(19712) Then '              turn right
        For i = 0 To NS
            x(i) = x(i) - 2 * ri(i) ^ 2
            dx(i) = dx(i) - 1
        Next
    End If
 
    If _KeyDown(18432) Then '              turn up
        For i = 0 To NS
            y(i) = y(i) + 2 * ri(i) ^ 2
            dy(i) = dy(i) + 1
        Next
    End If
    If _KeyDown(20480) Then '               turn down
        For i = 0 To NS
            y(i) = y(i) - 2 * ri(i) ^ 2
            dy(i) = dy(i) - 1
        Next
    End If
 
    Line (0, 0)-(Xmax, Ymax), _RGB32(0, 0, 0, 10), BF
    For i = 0 To NS
        If x(i) > 0 And x(i) < Xmax And y(i) > 0 And y(i) < Ymax Then
            star x(i), y(i), ri(i), ro(i), p(i), a(i), c(i), fill(i)
            x(i) = x(i) + dx(i)
            y(i) = y(i) + dy(i)
            ri(i) = 1.015 * ri(i)
            ro(i) = 1.015 * ro(i)
            a(i) = a(i) + turn(i)
        Else
            NewStar i
        End If
    Next
    _Display
    _Limit 120
    Loopcounter = Loopcounter + 1
Wend
 
Sub NewStar (nxt)
    Dim angle, r
    angle = Rnd * 2 * _Pi
    r = Rnd * 6 + 1
    dx(nxt) = r * Cos(angle)
    dy(nxt) = r * Sin(angle)
    r = Rnd * 300
    x(nxt) = Cx + r * dx(nxt)
    y(nxt) = Cy + r * dy(nxt)
    ri(nxt) = Rnd
    ro(nxt) = ri(nxt) + 1 + Rnd
    p(nxt) = 3 + Int(Rnd * 9)
    a(nxt) = Rnd * 2 * _Pi
    turn(nxt) = Rnd * 6 - 3
    fill(nxt) = Int(Rnd * 2)
    c(nxt) = _RGB32(Rnd * 255, Rnd * 255, Rnd * 255)
End Sub
 
' this sub requires fTri for Filling stars rev 2024-12-09 for FillTF option
Sub star (x, y, rInner, rOuter, nPoints, DegAngleOffset, K As _Unsigned Long, FillTF)
    ' x, y are same as for circle,
    ' rInner is center circle radius
    ' rOuter is the outer most point of star
    ' nPoints is the number of points,
    ' angleOffset = angle offset IN DEGREES, it will be converted to radians in sub
    ' this is to allow us to spin the polygon of n sides
    Dim pAngle, radAngleOffset, x1, y1, x2, y2, x3, y3, i As Long
 
    pAngle = _D2R(360 / nPoints): radAngleOffset = _D2R(DegAngleOffset)
    x1 = x + rInner * Cos(radAngleOffset)
    y1 = y + rInner * Sin(radAngleOffset)
    For i = 0 To nPoints - 1
        x2 = x + rOuter * Cos(i * pAngle + radAngleOffset + .5 * pAngle)
        y2 = y + rOuter * Sin(i * pAngle + radAngleOffset + .5 * pAngle)
        x3 = x + rInner * Cos((i + 1) * pAngle + radAngleOffset)
        y3 = y + rInner * Sin((i + 1) * pAngle + radAngleOffset)
        If FillTF Then
            fTri x1, y1, x2, y2, x3, y3, K
            Line (x3, y3)-(x1, y1), K ' need this ?? Yes!!! wo Paint leaks
            Line (x1, y1)-(x2, y2), K
            Line (x2, y2)-(x3, y3), K
        Else
            Line (x1, y1)-(x2, y2), K
            Line (x2, y2)-(x3, y3), K
        End If
        x1 = x3: y1 = y3
    Next
    If FillTF Then Paint (x, y), K, K
End Sub
 
Sub fTri (x1, y1, x2, y2, x3, y3, K As _Unsigned Long)
    Dim D As Long
    Static a&
    D = _Dest
    If a& = 0 Then a& = _NewImage(1, 1, 32)
    _Dest a&
    _DontBlend a& '  '<<<< new 2019-12-16 fix
    PSet (0, 0), K
    _Blend a& '<<<< new 2019-12-16 fix
    _Dest D
    _MapTriangle _Seamless(0, 0)-(0, 0)-(0, 0), a& To(x1, y1)-(x2, y2)-(x3, y3)
End Sub

[SierraKen]

Awesome stuff guys! A couple days ago I found out how to make a 5 sided star. But I've also wanted to make the user be able to add as many points as they wish. I tried and tried but since I don't know a lot of math, I used Chat GPT and got this.
Macalwen, you might want to look at this code and see the explanations if you want to make pointed stars. I use this kind of math for different graphics and my clocks. But since I don't know how they actually work, I just copy the code to each thing I use. I also like experimenting with the numbers, variables, and equations. But I do like the way you did yours with the circles!  

B+, as usual, I am amazed.  

Code: (Select All)

 
'This was created using Chat GPT with a tiny bit added by SierraKen.    
 
Screen _NewImage(800, 600, 32) ' Set graphics mode
 
start:
Clear
Cls ' Clear screen
 
' Get user input for the number of spikes
Input "Enter the number of spikes for the star (5 or more): "; numSpikes
 
If numSpikes > 10000 Then
    Print "The number of spikes cannot be more than 10000, using 10000 spikes instead"
    numSpikes = 10000
End If
 
' Validate the input to ensure it's at least 5
If numSpikes < 5 Then
    Print "The number of spikes must be at least 5. Using 5 spikes instead."
    numSpikes = 5
End If
 
' Define the center of the star
cx = 400
cy = 300
 
'Define Pi
Pi = _Pi
 
' Define the size of the star
size = 200
 
' Calculate the angle between each point
angleStep = 360 / numSpikes
 
' Initialize an array to store the points of the star
Dim pointsX(numSpikes)
Dim pointsY(numSpikes)
 
' Loop to calculate the coordinates of each point
For i = 0 To numSpikes - 1
    angle = i * angleStep
    pointsX(i) = cx + size * Cos(angle * Pi / 180)
    pointsY(i) = cy - size * Sin(angle * Pi / 180)
Next
 
' Draw the lines connecting the points to form the star
For i = 0 To numSpikes - 1
    ' Connect the current point to the next one, wrapping around at the end
    Line (pointsX(i), pointsY(i))-(pointsX((i + 2) Mod numSpikes), pointsY((i + 2) Mod numSpikes)), _RGB32(255, 255, 255)
Next
 
Locate 35, 5: Input "Again (Y/N): ", ag$
If Left$(ag$, 1) = "y" Or Left$(ag$, 1) = "Y" Then GoTo start:
 
End

[James D Jarvis]

I did this a while back.  Every once in a while it doesn't make a complete star (not sure why). Someone might find this useful.   

Code: (Select All)

Screen _NewImage(600, 500, 256)
Dim st(100, 10)
Const sx = 1: Const sy = 2: Const pnts = 3: Const sr1 = 4: Const sr2 = 5: Const klr = 6: Const styl = 7
Const hdg = 8: Const mr = 9: Const rtn = 10
Randomize Timer
For st = 0 To 9
    Print "starpoly: a variation of the polygon drawing routine I've posted earlier"
    Print
    Print "Style "; st
    Print "(press any key to continue)"
 
    starpoly 300, 250, 160, 82, 5, 180, 12, st
 
    any$ = Input$(1)
    Cls
Next
For s = 1 To 100
    st(s, sr1) = Int(Rnd * 100) + 20
    st(s, sr2) = Int(st(s, sr1) / (1.5 + Rnd * 4))
    st(s, klr) = Int(Rnd * 256)
    st(s, pnts) = Int(5 + Rnd * 10)
    st(s, sx) = Int(Rnd * 700) + 50
    st(s, sy) = Int(Rnd * 400) + 50
    st(s, styl) = Int(Rnd * 13) - 3
    If st(s, styl) < 1 Then st(s, styl) = 0
    st(s, hdg) = Int(Rnd * 360)
    st(s, rtn) = Int(1 + Rnd * 360)
    st(s, mr) = Rnd * 4
Next
Do
    Cls
    _Limit 60
 
    For s = 1 To 100
        starpoly st(s, sx), st(s, sy), st(s, sr1), st(s, sr2), st(s, pnts), st(s, rtn), st(s, klr), st(s, styl)
        st(s, sx) = st(s, sx) + st(s, mr) * Sin(0.01745329 * st(s, hdg))
        st(s, sy) = st(s, sy) + st(s, mr) * Cos(0.01745329 * st(s, hdg))
        st(s, rtn) = st(s, rtn) + Int(Rnd * 3) + Int(Rnd * 3)
        If st(s, sx) < -50 Or st(s, sx) > 850 Or st(s, sy) < -50 Or st(s, sy) > 550 Then
            st(s, sr1) = Int(Rnd * 100) + 20
            st(s, sr2) = Int(st(s, sr1) / (1.5 + Rnd * 4))
            st(s, klr) = Int(Rnd * 256)
            st(s, pnts) = Int(5 + Rnd * 10)
            st(s, sx) = Int(Rnd * 700) + 50
            st(s, sy) = Int(Rnd * 400) + 50
            st(s, styl) = Int(Rnd * 13) - 3
            If st(s, styl) < 1 Then st(s, styl) = 0
 
            st(s, hdg) = Int(Rnd * 360)
            st(s, rtn) = Int(1 + Rnd * 360)
            st(s, mr) = Rnd * 4
        End If
        st(s, mr) = st(s, mr) + 0.001
    Next s
    Locate 1, 1: Print "<ESC> to exit"
    _Display
    kk$ = InKey$
Loop Until kk$ = Chr$(27)
End
 
 
Sub starpoly (cx, cy, rr, r2, points, turn, klr As _Unsigned Long, style)
    'rr is outer radius
    'r2 is inner radius
    'points= how many points the star has
    'turn is how many degrees to rotate the sta, a turn of 0 will result in a stabdard star point "down"
    'style 0 = star outline
    'style 1 = star outline with line from center to outer radius
    'style 2 = star outline with  line from center to inner radius
    'style 3 = star outline with lines from center to oouter and inner radius
    'styles 4 and up will double the number of points
    'style 4 and up will created variated starbursts , mode 5 and up adding accent lines.
    shapedeg = 360 / points
    Select EveryCase style
        Case 0 To 3
            n = 0
            x = rr * Sin(0.01745329 * turn)
            y = rr * Cos(0.01745329 * turn)
            Line (cx + x, cy + y)-(cx + x, cy + y), klr
            For deg = turn To turn + 360 Step shapedeg / 2
                If n = 0 Then
                    x2 = rr * Sin(0.01745329 * deg)
                    y2 = rr * Cos(0.01745329 * deg)
                End If
                If n = 1 Then
                    x2 = r2 * Sin(0.01745329 * deg)
                    y2 = r2 * Cos(0.01745329 * deg)
                End If
                Line -(cx + x2, cy + y2), klr
                n = n + 1
                If n = 2 Then n = 0
            Next
        Case 1, 3
            n = 0
            For deg = turn To turn + 360 Step shapedeg / 2
                If n = 0 Then
                    x2 = rr * Sin(0.01745329 * deg)
                    y2 = rr * Cos(0.01745329 * deg)
                    Line (cx, cy)-(cx + x2, cy + y2), klr
                End If
                n = n + 1
                If n = 2 Then n = 0
            Next
        Case 2, 3
            n = 0
            For deg = turn To turn + 360 Step shapedeg / 2
                If n = 0 Then
                Else
                    x2 = r2 * Sin(0.01745329 * deg)
                    y2 = r2 * Cos(0.01745329 * deg)
                    Line (cx, cy)-(cx + x2, cy + y2), klr
                End If
                n = n + 1
                If n = 2 Then n = 0
            Next
        Case 4 To 9
            shapedeg = shapedeg / 2
            x = rr * Sin(0.01745329 * turn)
            y = rr * Cos(0.01745329 * turn)
            Line (cx + x, cy + y)-(cx + x, cy + y), klr
            n = 0
            For deg = turn To turn + 360 Step shapedeg / 2
                If n = 0 Then
                    x2 = rr * Sin(0.01745329 * deg)
                    y2 = rr * Cos(0.01745329 * deg)
                End If
                If n = 2 Or n = 4 Then
                    x2 = ((r2 + rr) / 2) * Sin(0.01745329 * deg)
                    y2 = ((r2 + rr) / 2) * Cos(0.01745329 * deg)
                End If
                If n = 1 Or n = 3 Then
                    x2 = r2 * Sin(0.01745329 * deg)
                    y2 = r2 * Cos(0.01745329 * deg)
                End If
                Line -(cx + x2, cy + y2), klr
                n = n + 1
                If n = 4 Then n = 0
            Next
        Case 5, 8, 9
            n = 0
            For deg = turn To turn + 360 Step shapedeg / 2
                If n = 0 Then
                    x2 = rr * Sin(0.01745329 * deg)
                    y2 = rr * Cos(0.01745329 * deg)
                    Line (cx, cy)-(cx + x2, cy + y2), klr
                End If
 
                n = n + 1
                If n = 4 Then n = 0
            Next
        Case 6, 9
            n = 0
            For deg = turn To turn + 360 Step shapedeg / 2
                If n = 1 Or n = 3 Then
                    x2 = r2 * Sin(0.01745329 * deg)
                    y2 = r2 * Cos(0.01745329 * deg)
                    Line (cx, cy)-(cx + x2, cy + y2), klr
                End If
                n = n + 1
                If n = 4 Then n = 0
            Next
        Case 7, 8, 9
            n = 0
            For deg = turn To turn + 360 Step shapedeg / 2
                If n = 2 Or n = 4 Then
                    x2 = ((r2 + rr) / 2) * Sin(0.01745329 * deg)
                    y2 = ((r2 + rr) / 2) * Cos(0.01745329 * deg)
                    Line (cx, cy)-(cx + x2, cy + y2), klr
                End If
                n = n + 1
                If n = 4 Then n = 0
            Next
    End Select
End Sub

[NakedApe]

Very cool stars, @bplus and @James D Jarvis! I could get lost in those multi-verses...

[macalwen]

thanks for @bplus and @James D Jarvis @SierraKen，My variable name “DEG” wasn't quite right. “RAD” would be more accurate. Your fireworks were beautiful.