The adaptive = v option controls the algorithm used by the plot command to produce two-dimensional plots.

When plotting a function over an interval, the interval is sampled at a number of points, controlled by sample and numpoints.  Adaptive plotting, where necessary, subdivides these intervals to attempt to get a better representation of the function. This subsampling can be turned off by setting the adaptive option to false.  If this option is set to true, intervals are subdivided at most 6 times in trying to improve the plot.  By setting this option to a non-negative integer, you can control the maximum number of times that subintervals are divided.

The adaptive = geometric option is used for non-parametric plots in the Cartesian coordinate system. (For parametric plots and those using other coordinate systems, the option adaptive = true is the default.)  This causes plot to use an algorithm based on interval arithmetic together with an a posteriori geometric analysis based loosely on the RealBox object, which allows for the efficient recognition of many discontinuities. Moreover, the curve on-screen is often more accurate than with the other possible values of the adaptive option. While the adaptive = geometric option has higher overhead than the adaptive = true (or false) options, in most cases, the extra overhead is acceptable. However, for animations assembled manually, or for very large expressions, you may wish to use adaptive = true instead.

The adaptive = default option which is, as the name suggests, the default value for this option, uses a blended strategy that usually selects geometric plotting, when applicable, and selects adaptive plotting in some cases, such as for polynomials or for larger expressions.

If adaptive = true is used, the discont option must also be used for plot to detect discontinuities.

$\mathrm{plot}\left(\mathrm{floor}\left(x\right)-\mathrm{floor}\left(\frac{x}{3}\right)\,x\=-5..5\right)$

$\mathrm{plot}\left(\mathrm{floor}\left(x\right)-\mathrm{floor}\left(\frac{x}{3}\right)\,x\=-5..5\,\'\mathrm{adaptive}\'\=\mathrm{true}\right)$

$\mathrm{plot}\left(\mathrm{floor}\left(x\right)-\mathrm{floor}\left(\frac{x}{3}\right)\,x\=-5..5\,\'\mathrm{adaptive}\'\=\mathrm{false}\right)$

$\mathrm{plot}\left(\mathrm{floor}\left(x\right)-\mathrm{floor}\left(\frac{x}{3}\right)\,x\=-5..5\,\'\mathrm{adaptive}\'\=\mathrm{true}\,\'\mathrm{discont}\'\right)$

$\mathrm{plot}\left(\sin \left(100x\right)\+\cos \left(10x\right)\,x\=-2\mathrm{Pi}..2\mathrm{Pi}\,\'\mathrm{adaptive}\'\=\mathrm{true}\right)$

$\mathrm{plot}\left(\sin \left(100x\right)\+\cos \left(10x\right)\,x\=-2\mathrm{Pi}..2\mathrm{Pi}\right)$

$\mathrm{plot}\left(\sqrt{\sin \left(x^2\right)}\,x\=-5..5\,\'\mathrm{adaptive}\'\=\mathrm{false}\,\'\mathrm{numpoints}\'\=10\right)$

$\mathrm{plot}\left(\sqrt{\sin \left(x^2\right)}\,x\=-5..5\,\'\mathrm{adaptive}\'\=2\,\'\mathrm{numpoints}\'\=10\right)$

$\mathrm{plot}\left(\sqrt{\sin \left(x^2\right)}\,x\=-5..5\,\'\mathrm{adaptive}\'\=\mathrm{true}\,\'\mathrm{numpoints}\'\=10\right)$

$\mathrm{plot}\left(\sqrt{\sin \left(x^2\right)}\,x\=-5..5\right)$

$\mathrm{plot}\left(x^2\+1\+0.0125\ln \left(\left|1-3\left(x-1\right)\right|\right)\,x\=1..1.4\,\'\mathrm{adaptive}\'\=\mathrm{true}\right)$

$\mathrm{plot}\left(x^2\+1\+0.0125\ln \left(\left|1-3\left(x-1\right)\right|\right)\,x\=1..1.4\right)$

The adaptive option was updated in Maple 2022.