What is the usual method or algorithm used to construct the implicit equations of two variables?
I am talking about equations like
sin (x * y) * y = 20
x * x - y * y = 1
Etc.
Does anyone know how Maple or Matlab do this? My target language is C #.
Many thanks!
One way to do this is to try the function on a regular 2D grid. Then you can run an algorithm, for example, marching squares on the resulting 2D grid, to draw iso outlines.
- gnuplot. , , , . : http://www.gnuplot.info/
x , . x , bisection - ( , , ). y x. , , .
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y
, f(x) = 0, . , , : .. y x ).
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. , , : https://homepages.warwick.ac.uk/staff/David.Tall/pdfs/dot1986b-implicit-fns.pdf , .
, , , : https://academic.oup.com/comjnl/article/33/5/402/480353
,
matlab x.
x y.
x0, y0 x1, y1
x1, y1 x2, y2
...