Entering functions

[SRB_Math]

Is it possible to enter a function / equation to define a line / edge?

[pendean]

Can you elaborate please?

[SRB_Math]

Can I enter an equation like y = 2x^3 + 3x +15, with a restricted domain to define a line, so that I can then rotate it on an axis to create a solid?

[doni49]

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@SRB_Math wrote:

Can I enter an equation like y = 2x^3 + 3x +15, with a restricted domain to define a line, so that I can then rotate it on an axis to create a solid?

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I still have no idea what you mean by "with a restricted domain".  But you can perform calculations using the QUICKCALC command which should help you.

[Kent1Cooper]

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@SRB_Math wrote:

Can I enter an equation like y = 2x^3 + 3x +15, with a restricted domain to define a line, so that I can then rotate it on an axis to create a solid?

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As far as I know, the answer is no, but one could pretty easily convert a function like that into an AutoLISP expression in a routine that would ask for the domain [minimum and maximum values for X] and a precision [how closely spaced in the X direction you want points calculated], calculate the Y values for each X position, and draw for example a Spline or Polyline along the calculated route; the Polyline version could then be smoothed with PEDIT's Fit or Spline option if desired.  Does that sound like it would work for you?

[By the way, an equation like that certainly wouldn't define a "Line" in AutoCAD's use of the word, but I think I know what you mean.]

For instance [minimally tested, and taking the default end tangent directions, without the usual controls, etc.]:

(defun C:EQUATION3 (/ mult3 mult2 mult1 const minX maxX inc n)
  (setq
    mult3 (getreal "\nMultiplier on X^3: ")
    mult2 (getreal "\nMultiplier on X^2: ")
    mult1 (getreal "\nMultiplier on X: ")
    const (getreal "\nConstant: ")
    minX (getreal "\nMinimum X value: ")
    maxX (getreal "\nMaximum X value: ")
    inc (getreal "\nPrecision [increment between X values]: ")
    n -1
  ); setq
  (command "_.spline")
  (repeat (1+ (fix (/ (- maxX minX) inc)))
    (command ; feed out to Spline command
      (list
        (setq x (+ minX (* inc (setq n (1+ n)))))
        (+
          (* mult3 (expt x 3))
          (* mult2 (expt x 2))
          (* mult1 x)
          const
        ); +
      ); list
    ); command
  ); repeat
  (command "" "" "")
); defun

In your example case, answer 0 for the multiplier on X^2.  All supplied answers can be positive or negative, whole or decimal numbers, etc.

[JDMather · Accepted solution]

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@SRB_Math wrote:

Can I enter an equation like y = 2x^3 + 3x +15, with a restricted domain to define a line, so that I can then rotate it on an axis to create a solid?

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You can do this in Autodesk Inventor with Equation Curves.

Here is an example (but not with your equation).

http://help.autodesk.com/view/INVNTOR/2015/ENU/?guid=GUID-8BF2EEB8-3A64-43F1-BA75-5ECBE357F08C

Students can download Inventor from http://www.autodesk.com/edcommunity

[kasperwuyts · Accepted solution]

How Autodesk would recommend doing it:
http://knowledge.autodesk.com/support/autocad/troubleshooting/caas/sfdcarticles/sfdcarticles/Draw-po...

[Kent1Cooper · Accepted solution]

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@Kent1Cooper wrote:

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....  All supplied answers can be positive or negative, whole or decimal numbers, etc.

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...except that, of course I should have said, 'inc' can't be zero or negative -- it would be better done this way:

....

    inc (getdist "\nPrecision [increment between X values]: ")

....

[Kent1Cooper · Accepted solution]

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@kasperwuyts wrote:
How Autodesk would recommend doing it: ....

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Wow -- that's pretty cumbersome, especially considering that you'd need to go through that entire rigmarole, including making a complete and distinct set of Excel and Word and .scr files separately for every such equation with different multipliers and constant and bounds that you want to draw.  If a Polyline such as that would make will do for you instead of a Spline, just take mine and remove the s from "_.spline" and the last two "" Enters from the (command) function that has three of them.

[SRB_Math]

Thank you.

[SRB_Math]

Cheers. Like it.

[Kent1Cooper]

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@SRB_Math wrote:

Is it possible to enter a function / equation to define a line / edge?

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I came up with a more sophisticated routine for AutoCAD, PolynomialFunction.lsp with its PF command, to draw a Polynomial Function in the form Y = a series of descending powers of X with coefficient multipliers, and a constant.

It gives you the following choices:

A. whether to draw a Spline or a Polyline;
B. the X-Y axis intersection origin point to build it around [it puts a Point entity there for reference];

C. the degree [highest exponent on X -- I tried it even up to X^17];

D. the coefficient applied to each power of X [positive, negative or 0];

E. the constant number [positive, negative or 0];

F. the bounds [either as numbers relative to the origin or by picking points from which it will take their X coordinates];

G. the precision [increment in X direction between calculated values of Y].

And it remembers all your choices, and offers them as defaults on subsequent use.  See a few additional things to know, in the comments at the top of the file.