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Messages - Zentek

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1
Programs / Re: Problem with Pseudo 3D Projection
« on: May 17, 2021, 04:10:02 pm »
Yeah excuse me, I did some errors.
I also already solved the problem by simply using my good ol' math skillz ;)
Its just the intersection with the y-axis and in fact this can be calculated by the slope (you calculate for a linear function y = mx+n the case x = 0 => n = intersection point)

You will find a first working demo. At the moment I implement PAINT to work correctly and then clipping, also sectors for different heights are implemented at the moment)
Code: QB64: [Select]
  1. SCREEN _NEWIMAGE(1280, 720, 256)
  4.  
  5. mdx = 1280 / 2: mdy = 720 / 2 ' The Middle of the screen
  6. wheight = 500 ' our wall height
  7. pheight = 0
  8.  
  9. ' lines start and end + player position
  10. px = 0: py = 0
  11. ' lines will be in an array
  12. DIM wall(5, 6) AS INTEGER
  13. wall(1, 1) = -10: wall(1, 2) = 10: wall(1, 3) = 10: wall(1, 4) = 10: wall(1, 5) = 10: wall(1, 6) = -1000
  14. wall(2, 1) = 10: wall(2, 2) = 10: wall(2, 3) = 10: wall(2, 4) = -10: wall(2, 5) = 20: wall(2, 6) = 0
  15. wall(3, 1) = 10: wall(3, 2) = -10: wall(3, 3) = 5: wall(3, 4) = -15: wall(3, 5) = -20: wall(3, 6) = 0
  16. wall(4, 1) = -5: wall(4, 2) = -15: wall(4, 3) = -10: wall(4, 4) = -10: wall(4, 5) = -5: wall(4, 6) = 0
  17. wall(5, 1) = -10: wall(5, 2) = -10: wall(5, 3) = -10: wall(5, 4) = 10: wall(5, 5) = 10: wall(5, 6) = 0
  18. ' players angle
  19. angle = 0
  20. scale = 100
  21. pi = 3.14159
  22. fwd = 0: bwd = 0: left = 0: right = 0: strafel = 0: strafer = 0: scaler = 0
  24.     FOR i = 1 TO 5
  25.         ' here goes the action now
  26.         ' transform the wall into players position
  27.         wx1 = wall(i, 1): wy1 = wall(i, 2): wx2 = wall(i, 3): wy2 = wall(i, 4)
  28.         tx1 = wx1 - px: ty1 = wy1 - py: tx2 = wx2 - px: ty2 = wy2 - py
  29.         ' rotate this
  30.         rx1 = tx1 * COS(-angle) - ty1 * SIN(-angle)
  31.         ry1 = tx1 * SIN(-angle) + ty1 * COS(-angle)
  32.         rx2 = tx2 * COS(-angle) - ty2 * SIN(-angle)
  33.         ry2 = tx2 * SIN(-angle) + ty2 * COS(-angle)
  34.         ' now we know the start and end point
  35.         PSET (mdx, mdy), 15
  36.         LINE (mdx + rx1, mdy + ry1)-(mdx + rx2, mdy + ry2), 15
  37.         ' draw the line around the player
  38.         ' now we have our static player and the rotated map
  39.         ' next thing to do is now project the 2d point to a 3d space
  40.  
  41.         REM ******************** 3D Projection ************************
  42.         REM Formula is quite simple
  43.         REM Use ry as scaling factor ... zx1 = rx1/ry1
  44.         REM upper and lower will be calculated with zu1 = wheight / ry1
  45.  
  46.  
  47.         ' render nothing behind us
  48.         IF rx1 <= 0 AND rx2 <= 0 THEN GOTO notrender
  49.         ' Clip the lines if one is partially behind the player
  50.         ' this will be done with intersection calculation
  51.  
  52.         IF rx1 <= 0 OR rx2 <= 0 THEN
  53.             ' clip the line at y-axis
  54.             iy = ry1 - (ry1 - ry2) / (rx1 - rx2) * rx1 ' line intersection calculation with simple linear function y = 0
  55.             IF rx1 <= 0 THEN rx1 = 0.01: ry1 = iy
  56.             IF rx2 <= 0 THEN rx2 = 0.01: ry2 = iy
  57.         END IF
  58.  
  59.         ' Calculations here
  60.         zx1 = -ry1 * scale / rx1
  61.         zd1 = -wheight / rx1 - wall(i, 5) / rx1 - pheight
  62.         zu1 = wheight / rx1 - wall(i, 6) / rx1 - pheight
  63.         zx2 = -ry2 * scale / rx2
  64.         zd2 = -wheight / rx2 - wall(i, 5) / rx2 - pheight
  65.         zu2 = wheight / rx2 - wall(i, 6) / rx2 - pheight
  66.  
  67.         ' draw the lines
  68.         'LINE (mdx * zx1 / 2 + mdx, mdy * zu1 / 2 + mdy)-(mdx * zx2 / 2 + mdx, mdy * zu2 / 2 + mdy), 14
  69.         'LINE (mdx * zx1 / 2 + mdx, mdy * zd1 / 2 + mdy)-(mdx * zx2 / 2 + mdx, mdy * zd2 / 2 + mdy), 14
  70.         'LINE (mdx * zx1 / 2 + mdx, mdy * zu1 / 2 + mdy)-(mdx * zx1 / 2 + mdx, mdy * zd1 / 2 + mdy), 6
  71.         'LINE (mdx * zx2 / 2 + mdx, mdy * zu2 / 2 + mdy)-(mdx * zx2 / 2 + mdx, mdy * zd2 / 2 + mdy), 6
  72.         ' draw the lines
  73.         LINE (zx1 + mdx, zu1 + mdy)-(zx2 + mdx, zu2 + mdy), 14
  74.         LINE (zx1 + mdx, zd1 + mdy)-(zx2 + mdx, zd2 + mdy), 14
  75.         LINE (zx1 + mdx, zu1 + mdy)-(zx1 + mdx, zd1 + mdy), 6
  76.         LINE (zx2 + mdx, zu2 + mdy)-(zx2 + mdx, zd2 + mdy), 6
  77.  
  78.         notrender:
  79.     NEXT i
  80.     LOCATE 1, 1: PRINT "Scale factor = "; scale
  81.  
  82.     ' modified key input to detect several keypresses
  83.     _LIMIT 20
  84.     kpress = _KEYHIT
  85.     IF kpress = 18432 THEN fwd = 1
  86.     IF kpress = -18432 THEN fwd = 0
  87.     IF kpress = 20480 THEN bwd = 1
  88.     IF kpress = -20480 THEN bwd = 0
  89.     IF kpress = 19200 THEN left = 1
  90.     IF kpress = -19200 THEN left = 0
  91.     IF kpress = 19712 THEN right = 1
  92.     IF kpress = -19712 THEN right = 0
  93.     IF kpress = 97 THEN strafel = 1
  94.     IF kpress = -97 THEN strafel = 0
  95.     IF kpress = 100 THEN strafer = 1
  96.     IF kpress = -100 THEN strafer = 0
  97.     IF kpress = 27 THEN END
  98.     IF kpress = 43 THEN scaler = 1
  99.     IF kpress = -43 THEN scaler = 0
  100.     IF kpress = 45 THEN scaler = -1
  101.     IF kpress = -45 THEN scaler = 0
  102.     IF fwd = 1 THEN px = px + 0.2 * COS(angle): py = py + 0.2 * SIN(angle): CLS
  103.     IF bwd = 1 THEN px = px - 0.2 * COS(angle): py = py - 0.2 * SIN(angle): CLS
  104.     IF left = 1 THEN angle = angle + 0.05: CLS
  105.     IF right = 1 THEN angle = angle - 0.05: CLS
  106.     IF strafel = 1 THEN px = px + 0.2 * COS(angle + 0.5 * pi): py = py + 0.2 * SIN(angle + 0.5 * pi): CLS
  107.     IF strafer = 1 THEN px = px - 0.2 * COS(angle + 0.5 * pi): py = py - 0.2 * SIN(angle + 0.5 * pi): CLS
  108.     IF scaler > 0 THEN scale = scale + 50: CLS
  109.     IF scaler < 0 THEN scale = scale - 50: CLS
  111.  
  112. REM  (rx1 * ry2 - rx2 * ry1)/(rx1 - rx2)
  113.  
  114.  

But obviously there are some problems with PAINT as when something is off the screen, it won't be rendered correctly ...

Have fun and stay tuned :)

2
Programs / Problem with Pseudo 3D Projection
« on: May 10, 2021, 01:12:39 pm »
Hello to all of you,
I am new here and wanted to ask something specific in this forum about my code in QB64.
So my code for a simple pseudo 3D projection is the following:
Code: QB64: [Select]
  1. REM 3D Test Suite
  2. REM (C) Christoph Petsch
  3. REM TODO: clipping of lines
  4.  
  8.  
  9. mdx = 160: mdy = 100 ' The Middle of the screen
  10. wheight = 80 ' our wall height
  11.  
  12. ' lines start and end + player position
  13. px = 0: py = 0
  14. ' lines will be in an array
  15. DIM wall(5, 4) AS INTEGER
  16. wall(1, 1) = -10: wall(1, 2) = 10: wall(1, 3) = 1: wall(1, 4) = 10
  17. wall(2, 1) = 10: wall(2, 2) = 10: wall(2, 3) = 10: wall(2, 4) = -10
  18. wall(3, 1) = 10: wall(3, 2) = -10: wall(3, 3) = 5: wall(3, 4) = -15
  19. wall(4, 1) = -5: wall(4, 2) = -15: wall(4, 3) = -10: wall(4, 4) = -10
  20. wall(5, 1) = -10: wall(5, 2) = -10: wall(5, 3) = -10: wall(5, 4) = 10
  21. ' players angle
  22. angle = 0
  23. scale = 5
  24. pi = 3.14159
  25.  
  27.     FOR i = 1 TO 5
  28.         ' here goes the action now
  29.         ' transform the wall into players position
  30.         wx1 = wall(i, 1): wy1 = wall(i, 2): wx2 = wall(i, 3): wy2 = wall(i, 4)
  31.         tx1 = wx1 - px: ty1 = wy1 - py: tx2 = wx2 - px: ty2 = wy2 - py
  32.         ' rotate this
  33.         rx1 = tx1 * COS(-angle) - ty1 * SIN(-angle)
  34.         ry1 = tx1 * SIN(-angle) + ty1 * COS(-angle)
  35.         rx2 = tx2 * COS(-angle) - ty2 * SIN(-angle)
  36.         ry2 = tx2 * SIN(-angle) + ty2 * COS(-angle)
  37.         ' now we know the start and end point
  38.         PSET (mdx, mdy), 15
  39.         LINE (mdx + rx1, mdy + ry1)-(mdx + rx2, mdy + ry2), 15
  40.         ' draw the line around the player
  41.         ' now we have our static player and the rotated map
  42.         ' next thing to do is now project the 2d point to a 3d space
  43.  
  44.         REM ******************** 3D Projection ************************
  45.         REM Formula is quite simple
  46.         REM Use ry as scaling factor ... zx1 = rx1/ry1
  47.         REM upper and lower will be calculated with zu1 = wheight / ry1
  48.  
  49.  
  50.         ' render nothing behind us
  51.         IF rx1 <= 0 AND rx2 <= 0 THEN GOTO notrender
  52.         ' Clip the lines if one is partially behind the player
  53.         ' this will be done with intersection calculation
  54.  
  55.         IF rx1 <= 0 OR rx2 <= 0 THEN
  56.             ' clip the line at y-axis
  57.             iy = (rx1 * ry2 - rx2 * ry1) / (rx1 - rx2)
  58.             IF rx1 <= 0 THEN rx1 = 0.01: ry1 = iy
  59.             IF rx2 <= 0 THEN rx2 = 0.01: ry2 = iy
  60.         END IF
  61.  
  62.         ' Calculations here
  63.         zx1 = -ry1 * scale / rx1
  64.         zu1 = wheight / rx1
  65.         zd1 = -zu1
  66.         zx2 = -ry2 * scale / rx2
  67.         zu2 = wheight / rx2
  68.         zd2 = -zu2
  69.  
  70.         ' draw the lines
  71.         LINE (mdx + zx1, mdy + zu1)-(mdx + zx2, mdy + zu2), 14
  72.         LINE (mdx + zx1, mdy + zd1)-(mdx + zx2, mdy + zd2), 14
  73.         LINE (mdx + zx1, mdy + zu1)-(mdx + zx1, mdy + zd1), 6
  74.         LINE (mdx + zx2, mdy + zu2)-(mdx + zx2, mdy + zd2), 6
  75.  
  76.         notrender:
  77.     NEXT i
  78.     a$ = INKEY$
  79.     SELECT CASE a$
  80.         CASE "q"
  81.             END
  82.         CASE "w"
  83.             CLS
  84.             px = px + 0.2 * COS(angle)
  85.             py = py + 0.2 * SIN(angle)
  86.         CASE "s"
  87.             CLS
  88.             px = px - 0.2 * COS(angle)
  89.             py = py - 0.2 * SIN(angle)
  90.         CASE "a"
  91.             CLS
  92.             angle = angle + 0.01
  93.         CASE "d"
  94.             CLS
  95.             angle = angle - 0.01
  96.         CASE "j"
  97.             ' Strafe
  98.             CLS
  99.             px = px - 0.2 * COS(-angle + 0.5 * pi)
  100.             py = py - 0.2 * SIN(-angle + 0.5 * pi)
  101.         CASE "l"
  102.             CLS
  103.             px = px + 0.2 * COS(-angle + 0.5 * pi)
  104.             py = py + 0.2 * SIN(-angle + 0.5 * pi)
  105.         CASE ELSE
  106.             'do nothing
  107.     END SELECT
  108.  
  110.  
  111.  

So this little program just projects a 2d map with some sense of depth onto the screen. It works in fact but it renders a terrible picture...
It seems like some warp effect I can't get rid of (you will see it yourself) also the intersection calculation is just a snipped from github and I don't really understand what it does... (if someone has an idea, what this actually does in terms of math (it just calculates the intersection point with the y axis))

So thank you if you find the time to answer my (maybe stupid) question.

Greetings

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