With its core symbolic paradigm and immediate access to sophisticated numerical, symbolic and geometric algorithms, Mathematica
is able to provide a uniquely flexible and unified framework for creating perceptually powerful graphics from functions and data—and for algorithmically highlighting features while maintaining aesthetic integrity.
styles for points, curves and surfaces
markers for discrete data points
whether to join points to make lines
what filling to add under points, curves and surfaces
a function for coloring curves or surfaces
what mesh lines, points, etc. to include
the style for mesh lines, points, etc.
array of shadings for mesh patches
functions to define families of mesh lines, etc.
range of values to include in the plot
general function to define the plotting region
how and where to check for discontinuities and excluded regions
how to render asymptotes, excluded regions, etc.
number of initial sample points for each variable
maximum level of recursive subdivision
whether to try to optimize for speed or for quality
how to join points in 2D and 3D (0 for steps, 1 for lines, etc.)