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@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@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@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 >>> _______________________________________________ >>> use-livecode mailing list >>> use-livecode@lists.runrev.com >>> Please visit this url to subscribe, unsubscribe and manage your >>> subscription preferences: >>> http://lists.runrev.com/mailman/listinfo/use-livecode >> >> _______________________________________________ >> use-livecode mailing list >> use-livecode@lists.runrev.com >> Please visit this url to subscribe, unsubscribe and manage your subscription >> preferences: >> http://lists.runrev.com/mailman/listinfo/use-livecode > > > _______________________________________________ > use-livecode mailing list > use-livecode@lists.runrev.com > Please visit this url to subscribe, unsubscribe and manage your subscription > preferences: > http://lists.runrev.com/mailman/listinfo/use-livecode _______________________________________________ use-livecode mailing list use-livecode@lists.runrev.com Please visit this url to subscribe, unsubscribe and manage your subscription preferences: http://lists.runrev.com/mailman/listinfo/use-livecode
