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Active Forums => QB64 Discussion => Topic started by: lomalena on April 11, 2020, 09:11:42 am

Title: Math Question With Autocad Drawing Included
Post by: lomalena on April 11, 2020, 09:11:42 am
So, I have R = 3 - Cos (t)  equation.
I want this equation use as a base of a conic
How can I write this?

Title: Re: Math Question With Autocad Drawing Included
Post by: bplus on April 11, 2020, 10:06:29 am
Here are routines for drawing Ellipsii:
https://www.qb64.org/forum/index.php?topic=1069.0

Title: Re: Math Question With Autocad Drawing Included
Post by: bplus on April 11, 2020, 11:42:14 am
Well crap there is no simple ellipsii (though could use CIRCLE with aspect but it sucks) so here is TiltedEllipse simplified to Ellipse with a conic demo:

Code: QB64: [Select]
  2. _TITLE "Ellipsii No Fill" 'b+ 2020-04-11
  3. CONST xmax = 700, ymax = 700
  4. SCREEN _NEWIMAGE(xmax, ymax, 32)
  5. _DELAY .25
  7. DIM cx, cy, a, xRad, yRad, p, c~&, mx, my, dist, d
  8.  
  9. cx = xmax / 2: cy = ymax / 2
  10. xRad = 350: yRad = 50: c~& = &HFF0000FF
  12.     CLS
  14.     mx = _MOUSEX: my = _MOUSEY
  15.     dist = ((mx - cx) ^ 2 + (my - cy) ^ 2) ^ .5
  16.     FOR d = 0 TO dist STEP 15
  17.         p = 1 - d / dist
  18.         a = _ATAN2(my - cy, mx - cx)
  19.         Ellipse cx + d * COS(a), cy + d * SIN(a), p * xRad, p * yRad, c~&
  20.         Ellipse cx + d * COS(a), cy + d * SIN(a), p * yRad, p * xRad, &HFFFF0000
  21.     NEXT
  22.     _DISPLAY
  23.     _LIMIT 100
  25.  
  26. 'use this for regular ellipse  
  27. SUB Ellipse (CX, CY, xRadius, yRadius, C AS _UNSIGNED LONG)
  28.     '  CX = center x coordinate
  29.     '  CY = center y coordinate
  30.     '  xRadius = x axis radius
  31.     '  yRadius = y axis radius
  32.     '   C = fill color
  33.     DIM a, x, y, stepper
  34.     stepper = .001 '.025 ain't enough
  35.     FOR a = 0 TO 6.283185307179586 + stepper STEP stepper
  36.         x = CX + xRadius * COS(a)
  37.         y = CY + yRadius * SIN(a)
  38.         IF a <> 0 THEN LINE -(x, y), C ELSE PSET (x, y), C
  39.     NEXT
  41.  
  42.  

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Title: Re: Math Question With Autocad Drawing Included
Post by: STxAxTIC on April 11, 2020, 11:49:38 am
Quote
' major and minor axis is misleading as I already told Mr STx as major implies the bigger

say what?
Title: Re: Math Question With Autocad Drawing Included
Post by: bplus on April 11, 2020, 11:56:24 am
Quote from: STxAxTIC on April 11, 2020, 11:49:38 am
say what?

Referring to: https://www.qb64.org/forum/index.php?topic=1069.0

Code: QB64: [Select]
  1. SUB EllipseTilt (CX, CY, a, b, ang, C AS _UNSIGNED LONG)
  2.     '  CX = center x coordinate
  3.     '  CY = center y coordinate
  4.     '   a = semimajor axis  ' <<<<<<<<<<<<<<<<<< I said this is mislabeled
  5.     '   b = semiminor axis  ' <<<<<<<<<<<<<<<<<< I said this is mislabeled
  6.     ' ang = clockwise orientation of semimajor axis in radians (0 default)
  7.     '   C = fill color
  8.     FOR k = 0 TO 6.283185307179586 + .025 STEP .025
  9.         i = a * COS(k) * COS(ang) + b * SIN(k) * SIN(ang)
  10.         j = -a * COS(k) * SIN(ang) + b * SIN(k) * COS(ang)
  11.         i = i + CX
  12.         j = -j + CY
  13.         IF k <> 0 THEN
  14.             LINE -(i, j), C
  15.         ELSE
  16.             PSET (i, j), C
  17.         END IF
  18.     NEXT
  20.  
  21.  

You are using the lousy named "a" variable as x axis radius when angle is 0 and calling it the "major axis" and calling b the y axis radius when ang = 0 the "minor axis", neither one is an axis of the ellipse and Major and Minor axis imply the size and in fact b can be larger than a with the code above.
Title: Re: Math Question With Autocad Drawing Included
Post by: STxAxTIC on April 11, 2020, 11:57:51 am
Oh right, this is because I'm one only one here who uses a sensible coordinate system, my mistake.
Title: Re: Math Question With Autocad Drawing Included
Post by: bplus on April 11, 2020, 12:02:07 pm
Quote from: STxAxTIC on April 11, 2020, 11:57:51 am
Oh right, this is because I'm one only one here who uses a sensible coordinate system, my mistake.

No it's not about coordinate system, the major axis of ellipse is the LONGER ONE and the minor axis of an ellipse is the shorter one and the variables a, b as you use them are neither.

https://www.google.com/search?client=opera&q=major+axis+of+an+ellipse&sourceid=opera&ie=UTF-8&oe=UTF-8
Title: Re: Math Question With Autocad Drawing Included
Post by: STxAxTIC on April 11, 2020, 12:03:51 pm
I'd say the smarter mathematician wouldn't lock himself in. Variables a and b have complete symmetry in the ellipse. I'm not sure what your complaint is now but honestly I'm not worried about it either. Let me know if you have any other questions about conic sections.

But seriously are you accusing me of calling "b" the semimajor axis? I haven't done that since 2003 and not publicly either.
Title: Re: Math Question With Autocad Drawing Included
Post by: bplus on April 11, 2020, 12:17:25 pm
Quote from: STxAxTIC on April 11, 2020, 12:03:51 pm
I'd say the smarter mathematician wouldn't lock himself in. Variables a and b have complete symmetry in the ellipse. I'm not sure what your complaint is now but honestly I'm not worried about it either. Let me know if you have any other questions about conic sections.

But seriously are you accusing me of calling "b" the semimajor axis? I haven't done that since 2003 and not publicly either.

The a variable effects the spread along the x axis.

The b variable effects the spread along the y axis.

They have no association with Major or Minor axis of Ellipse, not the way they are used in the SUB for drawing the eliipse.
Title: Re: Math Question With Autocad Drawing Included
Post by: STxAxTIC on April 11, 2020, 12:19:48 pm
Quote
The a variable effects the spread along the x axis.

The b variable effects the spread along the y axis.

They have no association with Major or Minor axis of Ellipse, not the way they are used in the SUB.

That is pure horse shit, sorry man. If you know you're right and I'm not reading you correctly then just carry on, its all good. All my math works on this end so idk man.
Title: Re: Math Question With Autocad Drawing Included
Post by: bplus on April 11, 2020, 12:25:05 pm
Quote from: STxAxTIC on April 11, 2020, 12:19:48 pm
That is pure horse shit, sorry man. If you know you're right and I'm not reading you correctly then just carry on, its all good. All my math works on this end so idk man.

I am talking about how this particular ellipse sub will draw the ellipse not math convention of calling a the major axis and b the minor.

If you want a tall skinny ellipse you better put the bigger length under the b variable.
Title: Re: Math Question With Autocad Drawing Included
Post by: STxAxTIC on April 11, 2020, 01:57:47 pm
Quote from: bplus on April 11, 2020, 12:25:05 pm
If you want a tall skinny ellipse you better put the bigger length under the b variable.

Oooooooooooooh I get you.

Nah man, that's a feature and nowhere near a bug or anything else. The parameter theta is locked with the "a" variable, even if its smaller. So to modify your statement above, if you want a tall skinny ellipse let a be the bigger side (as usual) and let theta=90 degrees. Good?
Title: Re: Math Question With Autocad Drawing Included
Post by: bplus on April 11, 2020, 02:08:34 pm
Quote from: STxAxTIC on April 11, 2020, 01:57:47 pm
Oooooooooooooh I get you.

Nah man, that's a feature and nowhere near a bug or anything else. The parameter theta is locked with the "a" variable, even if its smaller. So to modify your statement above, if you want a tall skinny ellipse let a be the bigger side (as usual) and let theta=90 degrees. Good?

Yes that will work too.
Title: Re: Math Question With Autocad Drawing Included
Post by: bplus on April 11, 2020, 03:56:07 pm
This might be faster ellipse because the loop is much shorter and there is no guessing as to increment steps:
( ie try the EllipseTilt with 400)
Code: QB64: [Select]
  2. _TITLE "Ellipse No Fill" 'b+ 2020-04-11
  3. CONST xmax = 700, ymax = 700
  4. SCREEN _NEWIMAGE(xmax, ymax, 32)
  5. _DELAY .25
  7. DIM cx, cy, a, xRad, yRad, p, c~&, mx, my, dist, d
  8.  
  9. cx = xmax / 2: cy = ymax / 2
  10. xRad = 10: yRad = 300: c~& = &HFF0000FF
  12.     CLS
  14.     mx = _MOUSEX: my = _MOUSEY
  15.     dist = ((mx - cx) ^ 2 + (my - cy) ^ 2) ^ .5
  16.     FOR d = 0 TO dist STEP 20
  17.         p = 1 - d / dist
  18.         a = _ATAN2(my - cy, mx - cx)
  19.         Ellipse cx + d * COS(a), cy + d * SIN(a), p * xRad, p * yRad, c~&
  20.         'Ellipse cx + d * COS(a), cy + d * SIN(a), p * yRad, p * xRad, &HFFFF0000
  21.     NEXT
  22.     _DISPLAY
  23.     _LIMIT 100
  25.  
  26.  
  27. 'there is a better way so there is no guessing the stepper size
  28. SUB Ellipse (CX, CY, xRadius AS INTEGER, yRadius AS INTEGER, C AS _UNSIGNED LONG)
  29.     '  CX = center x coordinate
  30.     '  CY = center y coordinate
  31.     '  xRadius = x axis radius
  32.     '  yRadius = y axis radius
  33.     '   C = fill color
  34.     DIM a, x, y, sq, delta, lastDelta
  35.     IF xRadius = 0 AND yRadius = 0 THEN EXIT SUB
  36.     IF xRadius = 0 THEN
  37.         LINE (CX, CY + yRadius)-(CX, CY - yRadius), C
  38.     ELSEIF yRadius = 0 THEN
  39.         LINE (CX + xRadius, CY)-(CX - xRadius, CY), C
  40.     ELSE
  41.         IF xRadius >= yRadius THEN
  42.             a = yRadius / xRadius: sq = xRadius * xRadius
  43.             FOR x = 0 TO xRadius
  44.                 IF x = 0 THEN
  45.                     lastDelta = SQR(sq - x * x) * a
  46.                     PSET (CX + x, CY + lastDelta), C
  47.                     PSET (CX + x, CY - lastDelta), C
  48.                     PSET (CX - x, CY + lastDelta), C
  49.                     PSET (CX - x, CY - lastDelta), C
  50.                 ELSE
  51.                     delta = SQR(sq - x * x) * a
  52.                     LINE (CX + (x - 1), CY + lastDelta)-(CX + x, CY + delta), C
  53.                     LINE (CX + (x - 1), CY - lastDelta)-(CX + x, CY - delta), C
  54.                     LINE (CX - (x - 1), CY + lastDelta)-(CX - x, CY + delta), C
  55.                     LINE (CX - (x - 1), CY - lastDelta)-(CX - x, CY - delta), C
  56.                     lastDelta = delta
  57.                 END IF
  58.             NEXT
  59.         ELSE
  60.             a = xRadius / yRadius: sq = yRadius * yRadius
  61.             FOR y = 0 TO yRadius
  62.                 IF y = 0 THEN
  63.                     lastDelta = SQR(sq - y * y) * a
  64.                     PSET (CX + lastDelta, CY + y), C
  65.                     PSET (CX - lastDelta, CY + y), C
  66.                     PSET (CX + lastDelta, CY - y), C
  67.                     PSET (CX - lastDelta, CY - y), C
  68.                 ELSE
  69.                     delta = SQR(sq - y * y) * a
  70.                     LINE (CX + lastDelta, CY + (y - 1))-(CX + delta, CY + y), C
  71.                     LINE (CX - lastDelta, CY + (y - 1))-(CX - delta, CY + y), C
  72.                     LINE (CX + lastDelta, CY - (y - 1))-(CX + delta, CY - y), C
  73.                     LINE (CX - lastDelta, CY - (y - 1))-(CX - delta, CY - y), C
  74.                     lastDelta = delta
  75.                 END IF
  76.  
  77.             NEXT
  78.         END IF
  79.     END IF
  81.  
  82.  
  83.  
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