PSET "hat" graphic from old ad in BYTE

[dcromley]

So this post will give the almost-original "PSET hat" drawing from an ad by Micro Technology Unlimited in Compute magazines of 1981.  The ad was for a Commodore PET upgrade to hi-res (320x200!).  The code has been modified to run under QB64, slowed down, and made able to be paused.  @CharlieJV got the key link to the thread ( https://atariage.com/forums/topic/218503.../#comments ) where Atari fans are running it -- on Ataris and many other old computers!  A lot of talk there how to speed it up.  We have to slow it down.  It's a BIG thread, but no mention of an author.

It was and is still stunning how such a few lines of code can create a complex drawing and even take care of hidden lines.  Here is a little info on the workings of the program (the programmer was working with a BASIC with 2-character name restrictions!).  I can understand only some of the code.  The hidden points in back are hidden by erasing them as the nearer points are drawn.  I did plot the math function they used:  Plug this function into my "FunctionPlot" program ( https://qb64phoenix.com/forum/showthread.php?tid=260 ).

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Function func1 (x)
  Dim r: r = Abs(x)
  func1 = (Sin(r) + 0.4 * Sin(3 * r)) * 4
  Line (zux(-4.71), 400)-(zux(-4.71), 700), 1 ' limits
  Line (zux(4.71), 400)-(zux(4.71), 700), 1 ' limits
End Function

Imagine the curve between the blue lines, rotated around the center -- it would look like a hat!  You can replace this one line in the original code and a get a different hat -- a dunce hat.

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'Replace this:
120 YY = (Sin(XT) + 0.4 * Sin(3 * XT)) * YF
'with this:
120 YY = 80 - Abs(XT) * 80
'Wait a few seconds for the hat to appear from below.

The almost-original code: ( @bplus - obviously I've spent too much time on this )

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' From Compute Magazine, 11/1/1981
' Ad by Micro Technology Unlimited, pg42
' The following has minimal changes to the original:
' o) to make it work in QB64
' o) to slow it down
' o) to be able to pause (ENTER), exit (ESC)
Dim Shared time0: time0 = Timer

' 10 VISMEM: CLEAR
10 Screen 7
20 P = 160: Q = 104
30 XP = 144: XR = 1.5 * 3.1415927
40 YP = 56: YR = 1: ZP = 64
50 XF = XR / XP: YF = YP / YR: ZF = XR / ZP
60 For ZI = -Q To Q - 1
  70 If ZI < -ZP Or ZI > ZP GoTo 150
  80 ZT = ZI * XP / ZP: ZZ = ZI
  90 XL = Int(.5 + (Sqr(XP * XP - ZT * ZT)))
  100 For XI = -XL To XL
    110 XT = Sqr(XI * XI + ZT * ZT) * XF: XX = XI
    120 YY = (Sin(XT) + 0.4 * Sin(3 * XT)) * YF
    130 GoSub 170
    sub1 (0) ' ck keyboard
  140 Next XI
150 Next ZI
' 160 Stop
160 sub1 (1) ' exit
170 X1 = XX + ZZ + P
180 Y1 = YY - ZZ + Q
' 190 GMODE 1: MOVE X1,Y1: WRPIX
190 PSet (X1, 199 - Y1), 15
200 If Y1 = 0 GoTo 220
' 210 GMODE 2: LINE X1,Y1-1,X1,0
210 Line (X1, 199 - Y1 + 1)-(X1, 199), 0
220 Return

Sub sub1 (swexit) ' ck keyboard, etc.
  _Limit 1000 ' slows it down (30 secs)
  If swexit Then s$ = Chr$(13): Locate 25, 1: _
   Print Timer - time0;: Else s$ = InKey$
  If s$ = Chr$(27) Then System ' exit
  If s$ = Chr$(13) Then
    While InKey$ = "": Wend
  End If
  If swexit Then System
End Sub

That Atari thread had another version, that drew front-to-back instead of back-to-front.  To do that and take care of hidden points, an
array(320) holds the y values drawn so far, and any point lower is not drawn.  Here is that code, from the same thread.

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' The "hat" - Front-to-back processing
' https://atariage.com/forums/topic/218503-graphics-8-fedora-hat/#comments
' Micro Tech Unlimited ad in Compute Magazine 11/1/81
Screen 7
100 Dim RR(320)
120 For I = 0 To 320: RR(I) = 193: Next I
150 XP = 144: XR = 4.71238905: XF = XR / XP
160 For ZI = 64 To -64 Step -1
  170 ZT = ZI * 2.25: ZS = ZT * ZT
  180 XL = Int(Sqr(20736 - ZS) + 0.5)
  190 For XI = 0 - XL To XL
    200 XT = Sqr(XI * XI + ZS) * XF
    210 YY = (Sin(XT) + Sin(XT * 3) * 0.4) * 56
    220 X1 = XI + ZI + 160: Y1 = 96 - YY + ZI
    223 If RR(X1) <= Y1 Then 250
    226 RR(X1) = Y1
    230 PSet (X1, Y1), 15
250 _Limit 2000: Next XI: Next ZI
260 While InKey$ = "": Wend: System

I could spend time on using that technique on a large screen, but I would rather study OpenGL.  With OpenGL, you (you) can create the surface in 3D and then move it and rotate it.  A great start into QB64 OpenGL is https://ashishkingdom.github.io/OpenGL-Tutorials/intro/ .  It covers basics, points, lines, triangles (key to all surfaces), circles, colors, textures, 2D translations, [oops, stop].  Very well done, but doesn't make it to 3D translations and 2D and 3D rotations, lights, cameras, etc. I will be asking how to get further into this.