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@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@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 _______________________________________________ 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
