@mmcdara Thank you and Merry Christmas, but I still have some problems, You mean that when numpoints is specified, increasing the gridrefine may make the needed numpoints surpass the specified numpoints, as a result, making the figure is rougher? Only when the number of needed numpoints for gridrefine is less than the specified numpoints, can the figure is smooth?
By the way, how do you figure out that For gridrefine=3 F(x,y) is calculated at 515 points, while 4119 points are used for gridrefine=6. There's a formula that The highest grid level for gridrefine=l will be [2^l*m,2^l*n] , which may not help me to achieve the value of 515, and 4119.
Besides, how do you know "(Note these numbers are twice the numbers I obtained by examining the output of showstat(`plots/implicitplot`) )." the results of "showstat(`plots/implicitplot`) )" are too long, which confuses me a lot.
You also mention the "resolution", from the "HELP", I know that " The option resolution = r applies resolution-based smoothing of the output curve to reduce the size of the output data structure, but retain the visual features of the curve up to a resolution of r x r pixels", does this mean that command resolution increases the absolute error of implicitplot indeed?