Re: For the Mathematicians.

2022-01-22 Thread Roger Guay via use-livecode 
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 
>  wrote:
> 
> In
> 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 
>>  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 
>>>  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 
 :
 
 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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Re: For the Mathematicians.

2022-01-22 Thread francois.chaplais via use-livecode 
In
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 
>  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 
>>  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 
>>> :
>>> 
>>> 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
>>> ___
>>> use-livecode mailing list
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>>> Please visit this url to subscribe, unsubscribe and manage your 
>>> subscription preferences:
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>> 
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> 
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Re: For the Mathematicians.

2022-01-22 Thread Roger Guay via use-livecode 
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 
>  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 
>> :
>> 
>> 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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>> preferences:
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Re: For the Mathematicians.

2022-01-22 Thread Thomas von Fintel via use-livecode 
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 
> :
> 
> 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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> preferences:
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For the Mathematicians.

2022-01-22 Thread Roger Guay via use-livecode 
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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