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Re: [Maxima-discuss] Problem with draw2d(implicit(...))
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From: Sidney M. <si...@fr...> - 2020-03-25 00:23:44
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Just for fun I ran this example through an implicit polynomial plotting program I wrote in Java. Attached is the result. You will note that the area around (0,0) is a little confused as there are multiple "roots" there. The idea of the program is simple. To see if there is any curve of f(x, y) in the rectangle [-1 < x < 1, -1 < y < 1] one adds the absolute values of the coefficients (except the constant term) and checks if this is sum less than the absolute value of the constant term. If so, there is no possibility that there is any part of the curve in the rectangle. Otherwise, subdivide the rectangle into 4 quarters and for each quarter check the function f(x/2 +- 1/2, y/2 +- 1/2) for each quarter in the same way. Continue recursively until down to one pixel and plot it. Scaling and translating the curve is easy. The actual code is fairly short - the main length of the code is the parsing of the formula and other Java stuff. If there is any interest I can post the code. --Sidney Marshall -------------------------------------- At 08:05 AM 3/21/2020 +0100, Gunter Königsmann wrote: >On 20.03.20 23:38, Thomas D. Dean wrote: > On >2020-03-20 15:34, Robert Dodier wrote: >> On >Fri, Mar 20, 2020 at 3:10 PM Michel Talon ><ta...@lp...> >> wrote: >> >>> You >are right, this is closer to what the plot >should look like. I >>> have also tried with >maple >>> as said by Thomas, it gives a very >poor plot which looks quite the >>> same as your >own. >>> Apparently this is a very difficult >problem for those plotters since >>> the "rabbit >ears" should >>> extend to (0,0) as shown by the >plot of the Puiseux series. Now i >>> understand >how the Puiseux >>> developments are to be >connected, precisely by these rabbit ears. >>> >You can see that on some range of >>> x there >are 5 solutions to f(x,y)=0 and less in other >ranges >>> because some solutions become >imaginary. >> >> I don't understand why some >methods for plotting this function work >> >better than others. In addition to the ones >already mentioned, there >> is also >implicit_plot which yields yet another picture. >Can someone >> explain why different methods >give different results here? >> > I think the >number of points in the plot makes a >difference. Varying > the number pf plots in >Maple, I can make the plot not show the rabbit > >ears or to through 0,0. > > In gnuplot, I >believe bins=xxx controls the number of points >used in > the plot. How can this be passed >through from Maxima? > draw3d(   > xu_grid=500,    yv_grid=500,   > contour='map,   > contour_levels=10,key="test",   > explicit(       > 2*x^5-x^3*y+2*x^2*y^2-x*y^3+2*y^5,      >  x,-.2,.2,        y,-.2,.2    ), >   grid=true )$ >_______________________________________________ >Maxima-discuss mailing list >Max...@li... >https://lists.sourceforge.net/lists/listinfo/maxima-discuss |
