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Offline Pete

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Re: elliptic hyperboloid
« Reply #15 on: April 17, 2020, 12:02:36 pm »
Quote from: Ashish on April 17, 2020, 11:07:24 am
It can be done in OpenGL easily BUT I will wait for @STxAxTIC
I think he is the only one who is going to help you and make you understand the things.

What? My equation needs Bill (STxAxTIC) to be explained? Oh wait, that's what I said. :D Yeah, it would be nice to have Bill chime in. What the hell though. I took 4 years of mechanical and architectural drawing in high school,  and never once did some dumbass instructor ask me to design a wormhole!

Pete
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Offline _vince

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Re: elliptic hyperboloid
« Reply #16 on: April 17, 2020, 01:12:12 pm »
parallel projection is easiest

Code: QB64: [Select]
  1. pi = 4*atn(1)
  2. sw = 640
  3. sh = 480
  4.  
  6.  
  8.         t = t + 0.05
  9.         a = 0
  10.         b = pi*cos(t)/3
  11.         ox = 120*cos(a - b)
  12.         oz = 120*sin(a - b)
  13.         oy = -150
  14.         oxx = 120*cos(a + b)
  15.         ozz = 120*sin(a + b)
  16.         oyy = 150
  17.         line (0,0)-(sw,sh),0,bf
  18.         for a=2*pi/30 to 2*pi step 2*pi/30
  19.                 x = 120*cos(a - b)
  20.                 z = 120*sin(a - b)
  21.                 y = -150
  22.                 line (sw/2 + ox + 0.707*oz, sh/2 + oy + 0.707*oz)-(sw/2 + x + 0.707*z, sh/2 + y + 0.707*z)
  23.                 ox = x
  24.                 oy = y
  25.                 oz = z
  26.  
  27.                 x = 120*cos(a + b)
  28.                 z = 120*sin(a + b)
  29.                 y = 150
  30.                 line -(sw/2 + x + 0.707*z, sh/2 + y + 0.707*z)
  31.                 line -(sw/2 + oxx + 0.707*ozz, sh/2 + oyy + 0.707*ozz)
  32.                 oxx = x
  33.                 oyy = y
  34.                 ozz = z
  35.         next
  36.  
  37.         _display
  38.         _limit 10
  39.  
  42.  
  43.  

Code: QB64: [Select]
  1. pi = 4*atn(1)
  2. sw = 640
  3. sh = 480
  4.  
  6.  
  8.         c = c + 0.05
  9.         t = t + 0.05
  10.         a = 0
  11.         b = pi*cos(t)/3
  12.         x = 250*cos(a - b)
  13.         z = 100*sin(a - b)
  14.         y = -150
  15.         yy = y*cos(c) - z*sin(c)
  16.         zz = y*sin(c) + z*cos(c)
  17.         y = yy
  18.         z = zz
  19.         ox = x
  20.         oz = z
  21.         oy = y
  22.  
  23.         x = 250*cos(a + b)
  24.         z = 100*sin(a + b)
  25.         y = 150
  26.         yy = y*cos(c) - z*sin(c)
  27.         zz = y*sin(c) + z*cos(c)
  28.         y = yy
  29.         z = zz
  30.         oxx = x
  31.         ozz = z
  32.         oyy = y
  33.         line (0,0)-(sw,sh),0,bf
  34.         for a=2*pi/30 to 2*pi step 2*pi/30
  35.                 x = 250*cos(a - b)
  36.                 z = 100*sin(a - b)
  37.                 y = -150
  38.  
  39.                 yy = y*cos(c) - z*sin(c)
  40.                 zz = y*sin(c) + z*cos(c)
  41.                 y = yy
  42.                 z = zz
  43.                 line (sw/2 + ox + 0.507*oz, sh/2 + oy + 0.507*oz)-(sw/2 + x + 0.507*z, sh/2 + y + 0.507*z)
  44.                 ox = x
  45.                 oy = y
  46.                 oz = z
  47.  
  48.                 x = 250*cos(a + b)
  49.                 z = 100*sin(a + b)
  50.                 y = 150
  51.  
  52.                 yy = y*cos(c) - z*sin(c)
  53.                 zz = y*sin(c) + z*cos(c)
  54.                 y = yy
  55.                 z = zz
  56.  
  57.                 line -(sw/2 + x + 0.507*z, sh/2 + y + 0.507*z)
  58.                 line -(sw/2 + oxx + 0.507*ozz, sh/2 + oyy + 0.507*ozz)
  59.                 oxx = x
  60.                 oyy = y
  61.                 ozz = z
  62.         next
  63.  
  64.         _display
  65.         _limit 10
  66.  
  69.  
  70.  
  71.  
« Last Edit: April 17, 2020, 01:38:51 pm by _vince »
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Offline Petr

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Re: elliptic hyperboloid
« Reply #17 on: April 17, 2020, 04:46:37 pm »
_vince, that's a great piece of code!
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Offline TerryRitchie

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Re: elliptic hyperboloid
« Reply #18 on: April 17, 2020, 05:52:20 pm »
I envy those of you (looking at you vince, static, bplus) that can whip out math equations like this. I'm stuck in Flatland I guess.
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Offline STxAxTIC

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Re: elliptic hyperboloid
« Reply #19 on: April 17, 2020, 06:43:02 pm »
Sorry I'm late to the party. Is solomon's question basically answered at this point? Nice work @_vince and @Ashish.

There are clearly two different approaches going on here. I can add a third (basically modifying Sanctum.bas to have the shape requested), but then the math behind the projection itself is harder to explain than any paraboloid.

What *exactly* is being asked, solomon? (I got your private message about this but lets carry on openly.)
« Last Edit: April 17, 2020, 08:41:06 pm by STxAxTIC »
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Offline solomon

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Re: elliptic hyperboloid
« Reply #20 on: April 18, 2020, 03:19:16 am »
I am trying to draw elliptical hyperboloid using ellipse code in this code. I tried to define two ellipses. I don't know how successful it is. I am trying. but I think these ellipses have to turn. as in the video I added. but I can't find how these ellipses will rotate in the code section.

I will also assign the scr file of this code to the AUTOCAD drawing program. and I'll see the shape there.






@STxAxTIC, @_vince, @Petr
« Last Edit: April 18, 2020, 04:56:15 am by solomon »
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Offline solomon

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Re: elliptic hyperboloid
« Reply #21 on: April 18, 2020, 03:26:06 am »
@STxAxTIC
I have beginner level knowledge and I have to draw this shape according to the code information I have.
also

Rotation algorithm:

Let there be a point P (x, y) in the plane. If we rotate this point counterclockwise around the origin by an angle of t (Theta), that point will come to the point Pt.
The coordinates of the Pt point are found as follows:
Pt.x = x * cos (t) - y * sin (t)
and
Pt.y = x * sin (t) + y * cos (t)

Code: QB64: [Select]
  1. TYPE point3d
  2.     x AS SINGLE
  3.     y AS SINGLE
  4.     z AS SINGLE
  6.  
  7. TYPE Elips
  8.     Center AS point3d
  9.     A AS SINGLE
  10.     B AS SINGLE
  12.  
  13. DIM elip AS Elips
  14. PRINT "please define elips:"
  15. INPUT "Elips Center (x, y): ", elip.Center.x, elip.Center.y
  16. INPUT "Elips 'A': ", elip.A
  17. INPUT "Elips 'B': ", elip.B
  18.  
  20. INPUT "Vertex number: ", n
  21.  
  22. OPEN "C:\scr\deneme2.scr" FOR OUTPUT AS #1
  23.  
  24.  
  25. CONST pi = 4 * ATN(1)
  27. dt = 2 * pi / n
  28.  
  29. DIM ElipsKoor(1 TO n) AS point3d
  32. FOR d = 1 TO n
  33.     t = (d - 1) * dt
  34.     r = Elips_R(elip.A, elip.B, t)
  35.  
  36.     DIM v AS point3d
  37.     v.z = 0
  38.     v.x = elip.Center.x + r * COS(t)
  39.     v.y = elip.Center.y + r * SIN(t)
  40.     ElipsKoor(d) = v
  42.  
  43.  
  45. INPUT "Elliptic hyperboloid height: ", h
  46.  
  47. DIM elip2 AS Elips
  48. PRINT "Please elip2 define:"
  49. INPUT "Elips2 Center (x, y): ", elip2.Center.x, elip2.Center.y
  50. INPUT "Elips 'A': ", elip2.A
  51. INPUT "Elips 'B': ", elip2.B
  52.  
  53. DIM Elips2Koor(1 TO n) AS point3d
  56. FOR k = 1 TO n
  57.     t2 = (k - 1) * dt
  58.     r2 = Elips_R(elip2.A, elip2.B, t)
  59.  
  60.     DIM v2 AS point3d
  61.     v2.z = h
  62.     v2.x = elip2.Center.x + r * COS(t2)
  63.     v2.y = elip2.Center.y + r * SIN(t2)
  64.  
  66.  
  67.  
  69. FOR d = 1 TO n
  70.     sv = d + 1
  71.     IF d = n THEN sv = 1
  72.     Write3DFace3 ElipsKoor(d), ElipsKoor(sv), Elip2Koor(k), Elip2Koor(sv)
  74.  
  76.  
  77. FUNCTION Elips_R (a AS SINGLE, b AS SINGLE, t AS SINGLE)
  78.     Elips_R = (a * b) / SQR((b * COS(t)) ^ 2 + (a * SIN(t)) ^ 2)
  80.  
  81.  
  82. SUB Write3DFace3 (v1 AS point3d, v2 AS point3d, v3 AS point3d)
  83.     PRINT #1, "3DFace"
  84.     WRITE #1, v1.x, v1.y, v1.z
  85.     WRITE #1, v2.x, v2.y, v2.z
  86.     WRITE #1, v3.x, v3.y, v3.z
  87.     PRINT #1, ""
  88.     PRINT #1, ""
  90.  
  91. SUB Write3DFace (v1 AS point3d, v2 AS point3d, v3 AS point3d, v4 AS point3d)
  92.     PRINT #1, "3DFace"
  93.     WRITE #1, v1.x, v1.y, v1.z
  94.     WRITE #1, v2.x, v2.y, v2.z
  95.     WRITE #1, v3.x, v3.y, v3.z
  96.     WRITE #1, v4.x, v4.y, v4.z
  97.     PRINT #1, ""
  98.     PRINT #1, ""
  100.  
  101. SUB WriteLine (v1 AS point3d, v2 AS point3d)
  102.     PRINT #1, "Line"
  103.     WRITE #1, v1.x, v1.y, v1.z
  104.     WRITE #1, v2.x, v2.y, v2.z
  105.     PRINT #1, ""
  107.  
  108.  
« Last Edit: April 18, 2020, 04:37:12 am by solomon »
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Offline Richard Frost

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Re: elliptic hyperboloid
« Reply #22 on: April 18, 2020, 04:22:34 am »
It's a popular design for TV towers, like the Canton Tower. 
Also used for a lighthouse in 1910.

It also looks like the Holy Grail.  I offerred Ashish a shrubbery
for it.

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Offline Petr

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Re: elliptic hyperboloid
« Reply #23 on: April 18, 2020, 05:58:50 am »
Hi. Maybe this easy program help you.

Code: QB64: [Select]
  1. SCREEN _NEWIMAGE(1024, 768, 256)
  2. x = _WIDTH / 2
  3. y = _HEIGHT / 2
  4. radiusX = 50
  5. radiusY = 50
  6.  
  7. CIRCLE (x, y), 10
  8.  
  9.  
  10. DO UNTIL angle = 360
  11.  
  12.     angle = angle + 1
  13.     t = _D2R(angle)
  14.  
  15.     '    Pt.x = x * COS(t) - y * SIN(t)
  16.     '    Pt.y = x * SIN(t) + y * COS(t)
  17.  
  18.     Pt.x = x + COS(t) * radiusX
  19.     Pt.y = y + SIN(t) * radiusY
  20.  
  21.     CIRCLE (Pt.x, Pt.y), 10
  22.     _LIMIT 100
  24.  
  25.  
  26. PRINT "Press key..."
  28.  
  30. radiusX = 75
  31. radiusY = 25
  32.  
  33.  
  35.     angle = 0
  36.     DO UNTIL angle = 360
  37.         a2 = a2 + _D2R(15) 'rotate up to 15 degrees
  38.  
  39.         angle = angle + 360 / 20
  40.         t = _D2R(angle)
  41.         t2 = _D2R(angle + 360 / 20)
  42.         DO WHILE _MOUSEINPUT
  43.             an3 = an3 + _MOUSEWHEEL
  44.         LOOP
  45.         a3 = _D2R(an3)
  46.  
  47.         'ellipse 1
  48.         Pt.x = _MOUSEX + COS(t + a2) * radiusX
  49.         Pt.y = _MOUSEY + SIN(t + a2) * radiusY
  50.  
  51.         'ellipse 2
  52.         Pt.x2 = x + COS(t + a2 + a3) * radiusX
  53.         Pt.y2 = y + SIN(t + a2 + a3) * radiusY
  54.  
  55.  
  56.         '   PSET (Pt.x, Pt.y)
  57.         '   PSET (Pt.x2, Pt.y2), 14
  58.  
  59.         LINE (Pt.x, Pt.y)-(Pt.x2, Pt.y2)
  60.  
  61.  
  62.         'for ellipse1 circuit:
  63.         Pt.x3 = _MOUSEX + COS(t2 + a2) * radiusX
  64.         Pt.y3 = _MOUSEY + SIN(t2 + a2) * radiusY
  65.  
  66.  
  67.         'for ellipse2 circuit:
  68.         Pt.x4 = x + COS(t2 + a2 + a3) * radiusX
  69.         Pt.y4 = y + SIN(t2 + a2 + a3) * radiusY
  70.  
  71.         'draw elipses circuit
  72.         LINE (Pt.x3, Pt.y3)-(Pt.x, Pt.y), 9
  73.         LINE (Pt.x4, Pt.y4)-(Pt.x2, Pt.y2), 10
  74.  
  75.     LOOP
  76.     _DISPLAY
  77.     _LIMIT 25
  78.     CLS
  80.  

Use mousewheel to set points displacement in ellipse 2 and mouse.
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Offline Ashish

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Re: elliptic hyperboloid
« Reply #24 on: April 18, 2020, 09:54:26 am »
Amazing work @_vince and @Petr
Petr, when you have learned 3D maths?
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Offline Ashish

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Re: elliptic hyperboloid
« Reply #25 on: April 18, 2020, 10:06:29 am »
Here is my lazy approach.

Code: QB64: [Select]
  1. _TITLE "Elliptic Hyperboloid"
  2. SCREEN _NEWIMAGE(600, 600, 32)
  3.  
  5.     _LIMIT 30
  7.  
  8. SUB _GL ()
  9.     'using parametric equations
  10.     'x(u,v) = a*sqrt(1+u^2)*cos(v)
  11.     'y(u,v)=b*sqrt(1+u^2)*sin(v)
  12.     'z(u,v)=c*u
  13.     'for v in [0, 2ã]
  14.     'from https://mathworld.wolfram.com/EllipticHyperboloid.html
  15.  
  16.     _glMatrixMode _GL_PROJECTION
  17.     _gluPerspective 50, 1, 0.1, 100
  18.  
  19.     _glMatrixMode _GL_MODELVIEW
  20.     a = 1
  21.     b = 1
  22.     c = 1
  23.     STATIC rotY
  24.     _glTranslatef 0, 0, -10
  25.     _glRotatef rotY, 0, 1, 0
  26.     rotY = rotY + 1
  27.  
  28.     _glPointSize 2
  29.     _glBegin _GL_POINTS
  30.     FOR u = 0 TO 3 STEP 0.1
  31.         FOR v = 0 TO _PI(2) STEP 0.1
  32.             x = a * SQR(1 + u ^ 2) * COS(v)
  33.             y = c * u
  34.             z = b * SQR(1 + u ^ 2) * SIN(v) 'you see, I swap the expression for y and z 'cause in 3D graphics, Y-axis upward
  35.  
  36.             _glVertex3f x, y, z
  37.             _glVertex3f x, -y, z 'creating mirror image
  38.         NEXT
  39.     NEXT
  40.     _glEnd
  42.  
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Offline STxAxTIC

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Re: elliptic hyperboloid
« Reply #26 on: April 18, 2020, 10:46:58 am »
Solomon I see your private messages -

I still find the whole issue ambiguous, to be honest - because plotting general 3D shapes is not natural in QB64 without _GL tech. Do you need just a *particular* projection of the shape you need, or *any* projection? Is it required that you use QB64 for this? Why not gnuplot? We need specifics if you've got them. Also: can you give some feedback as to whether the good gentlemen above have gotten near the solution you need? Plenty of good code up there.
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Offline solomon

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Re: elliptic hyperboloid
« Reply #27 on: April 18, 2020, 10:57:16 am »
unfortunately the program I should use is qb64. I think it is not natural to limit it, but I have to come to the conclusion with the data I have. I'm sorry to say that I can't give feedback because I don't understand most of them. I really thank everyone who has worked. I try to reach the result around what I know. I think I cannot draw this form with the code I tried.

@Ashish and @_vince e thanx a lot, really good shape and turning :)
@Petr thanx :) I guess this shape is torus?

but what I want to tell before returning is
The ellipse forming the elliptical hyperboloid rotate and form the elliptic hyperboloid.
that is, the rotation in the formation of the shape.

When I run the shape, it doesn't need to rotate.
« Last Edit: April 18, 2020, 11:13:02 am by solomon »
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Offline bplus

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Re: elliptic hyperboloid
« Reply #28 on: April 18, 2020, 11:25:23 am »
Nice work _vince, Petr, Ashish. Petr seems really close to duplicating video so with _vince nice rotation but...

What is confusing to me is that it looks from video like the top and bottom are circles like Ashish has, not ellipse, this is made obvious when towards end the object is rotated on x axis so you see the circular face and the smaller circle of the "neck".
« Last Edit: April 18, 2020, 11:30:22 am by bplus »
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Offline _vince

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Re: elliptic hyperboloid
« Reply #29 on: April 18, 2020, 11:41:04 am »
Quote from: Richard Frost on April 18, 2020, 04:22:34 am
It's a popular design for TV towers, like the Canton Tower. 
Also used for a lighthouse in 1910.

It also looks like the Holy Grail.  I offerred Ashish a shrubbery
for it.

And 5G cooling towers as well!
https://en.wikipedia.org/wiki/Cooling_tower
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