Twilight

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Equation

\[ (z^3-2)^2+(x^2+y^2-3)^3 \]

Properties:

degree 6
circular cusp singularity
smooth otherwise
bounded

Some story

Twilight, that time when dark and light are indistinguishable.

This surface is difficult to print, as it has a horizontal cusp singularity, which is hard to resolve as an overhang. Cool it!

input

%this is input file for surface `twilight` from Herwig Hauser's gallery.

CONFIG

tracktype: 1;


sharpendigits: 50; %sharpen nonsingular solutions to 50 digits or more using newton's method.
% this helps reduce the chance that two solutions which are supposed to be the same are marked as different.

randomseed: 4;  %fix the randomseed to eliminate changes run to run due to randseed.


odepredictor: 8;

endgamenum: 2;  %the cauchy endgame
numsamplepoints: 10;

finaltol: 1e-16;  %ask for at least 16 digits for all points, regardless of singularity;

condnumthreshold: 1e300;  % label no points as singular due to condition number.  only due to multiplicity

securitylevel: 1;  %track all paths to t=0, without truncating infinite paths.

endpointfinitethreshold: 1e12;  %in case nullspace elements are large.

maxnewtonits: 3;
maxstepsbeforenewton: 0;  %take a newton corrector step every single time step.

END;


INPUT

variable_group x, y, z;

function F;

F = (z^3-2)^2 +(x^2+y^2-3)^3;

END;

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