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First of all, I apologize since this is not strictly speaking a "mathematical" question but I could not find a better place for it.

For a work presentation I need a tool for accurate visualization of implicit algebraic curves in 2D. I tried ImplicitPlot function from Maple but for some complicated curves the results are not satisfiable. Also, it is not very convenient to zoom at certain locations along the curve.

I appreciate if someone can recommend me a good software tool for curve visualization thanks

PS. One of the equations I need to visualize is the following: (1-(1/5000000000000000)*x-(1/5000000000000000)*y-2*x^2+(1/5000000000000000)*x^3-(1/10000000000)*y^6+x^4-(1/10000000000000000)*y^5-(1/10000000000000000)*x^5+y^4-(1/10000000000)*x^6+(1/5000000000000000)*y^3-2*y^2+(1/1666666666666666)*x*y^2+(1/1666666666666666)*x^2*y+10*y^2*x^2-4*x*y+(5999999/1000000)*x*y^3+(5999999/1000000)*x^3*y+6*y^4*x^4+(3999999/1000000)*y^5*x^3+(499999/500000)*y^6*x^2-(3999999/500000)*y^4*x^2-(999999/500000)*y^5*x-(1/3333334444444814)*y^4*x-(1/1000000)*y^7*x+(3999999/1000000)*x^5*y^3-12*x^3*y^3-(1/2500000625000156)*x^2*y^3+(499999/500000)*y^2*x^6-(3999999/500000)*y^2*x^4-(1/2500000625000156)*y^2*x^3-(999999/500000)*x^5*y-(1/3333334444444814)*x^4*y-(1/1000000)*x^7*y)=0

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Have you tried SAGE? –  Derek Allums Aug 18 '12 at 15:01
1  
Even better: check out GrafEq. –  J. M. Aug 18 '12 at 15:20
    
You can improve Maple's output if you use numpoints=20000, for example. –  Sigur Aug 18 '12 at 15:24
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thanks for suggestions. I need to vizualise some "degenerate" algebraic curve which should look like two crossing lines ending abruptly. I just tried GrafEq on this equation and it hangs somewhere with Graph (82%). For implicit plot I tried up to numpoints=100000 and resolution=600 but it still does not produce any adequate image –  asm Aug 18 '12 at 15:51
    
Yes, and it's also freely available on the Internet: www.sagemath.org. –  Derek Allums Aug 18 '12 at 17:30

2 Answers 2

up vote 4 down vote accepted

Check out our xAlci curve renderer at: http://exacus.mpi-inf.mpg.de/cgi-bin/xalci.cgi. It has Flash interface and provides geometrically-correct rasterization of algebraic curves (i.e. guarantees a fixed Hausdorff distance). You can also save computed images in png format.

I took the liberty to visualize the equation you provided:

enter image description here

If you zoom in at one of the self-intersection points, you will see that each branch is composed of a pair of curve arcs:

enter image description here

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this looks great, thanks –  asm Aug 19 '12 at 8:15

Grapher is good:

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thanks but unfortunately I do not have Mac OS system –  asm Aug 18 '12 at 15:52

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