>>14128273you ask for the perimeter of some shape, which you have defined by your picture.
and by "defined by your picture" i think you assumed that we would know your intent, which is to find the equations you used to generate that picture.
but you really didn't give any indication that treating your curve as being defined by a few thousand pixels representing samples on a cartesian plan is wrong. i argue that dissecting your image and summing the distance between each adjacent sample (pixel, or because it's been anti-aliased, some other definition of describing where the samples lie), and doing something similar for the area, is just as or more valid than your original assumption.
you've since posted some equations and by now you should know about the arc length formula and solving piecewise
