For the Mathematicians.

[Roger Guay]

Hi François, 

My aim is to find a way to plot any and all implicit functions, not to plot only the lemniscate. But, that is a very interesting Wikipedia entry. Sorry I wasn’t clear!

Thanks,

Roger

> On Jan 22, 2022, at 4:37 PM, francois.chaplais via use-livecode <use-livecode at lists.runrev.com> wrote:
> 
> In
> https://en.wikipedia.org/wiki/Lemniscate_of_Bernoulli <https://en.wikipedia.org/wiki/Lemniscate_of_Bernoulli>
> use the formulation in polar coordinates.
> You sample theta, compute the corresponding radius r, convert the polar coordinates to usual cartesian coordinates, and draw a line between each point for successive angles theta.
> 
> This is an explicit formulation (up to the sign or r, but the figure is obviously symmetric with respect to the origin).
> 
> HTH
> François
> 
>> Le 22 janv. 2022 à 21:04, Roger Guay via use-livecode <use-livecode at lists.runrev.com> a écrit :
>> 
>> Thanks, Thomas. I’ve done some of that but you suggest some better keywords to search with. I will give it another go.
>> 
>> Roger
>> 
>>> On Jan 22, 2022, at 12:34 PM, Thomas von Fintel via use-livecode <use-livecode at lists.runrev.com> wrote:
>>> 
>>> I am not a mathematician, but this kind of equation is called implicit function, implicit equation or implicit curve. If you search for that combined with draw or plot, you might find explanations. But it seems to be complicated.
>>> 
>>> Hope this helps.
>>> Thomas
>>> 
>>> 
>>> 
>>>> Am 22.01.2022 um 17:56 schrieb Roger Guay via use-livecode <use-livecode at lists.runrev.com>:
>>>> 
>>>> This equation for the lemniscate, (x^2+y^2)^2 = 100*(x^2-y^2) is an example of a 2 variable function f(x,y). I am trying to figure how to plot such functions in LC. I can do simple functions like y = f(x) and x = f(t), y = f(t). Calculators such Good Grapher on the Mac do these f(x,y) functions with apparent ease. How? 
>>>> 
>>>> The only thing I’ve come up with so far is to imbed a y-repeat loop within an x-repeat loop where for each value of x (within a certain range), every value of y (within a certain range) is tested for the equation being true. If true, a point is generated in a point list of a polygon. I think, in principle, this should work and with persistence, I might be able make it work, but so far, no cigar. 
>>>> 
>>>> Is there a better way?
>>>> 
>>>> 
>>>> Thanks,
>>>> 
>>>> Roger
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