Currently grids are a mess.
The old SCT way of doing things was to define a grid as sets of orthogonal curves. Each curve was discretized separately, as a way of getting smooth results without wasting (1994-era) computing time on well resolved regions.
The Carleson grids, as far as I can figure, rely on standardly discretized curves. Each curve's discretization size depends on its radius, though.
Wegert's phase plots, which are beautiful, rely on just a meshgrid style array of point values.
Any of the plots are easy to produce, as long as you don't insist on an evenly spaced grid in the user domain. How you would visualize a map from, say, one polygon to another is open to question.
Phase plots seem to be better than SCT plots, though exponential crowding may change that tune. In a sense Carleson plots produce the most information, but they are an acquired taste and much more complicated to support. The @ehkropf implementation has overridden the adaptive capacity of gridcurves in order to make them work.
It may be that we need a factory class for grids that can produce different types of plots for different types of data. Visualization is so important to the package that we have to get this right.
Currently grids are a mess.
The old SCT way of doing things was to define a grid as sets of orthogonal curves. Each curve was discretized separately, as a way of getting smooth results without wasting (1994-era) computing time on well resolved regions.
The Carleson grids, as far as I can figure, rely on standardly discretized curves. Each curve's discretization size depends on its radius, though.
Wegert's phase plots, which are beautiful, rely on just a meshgrid style array of point values.
Any of the plots are easy to produce, as long as you don't insist on an evenly spaced grid in the user domain. How you would visualize a map from, say, one polygon to another is open to question.
Phase plots seem to be better than SCT plots, though exponential crowding may change that tune. In a sense Carleson plots produce the most information, but they are an acquired taste and much more complicated to support. The @ehkropf implementation has overridden the adaptive capacity of gridcurves in order to make them work.
It may be that we need a factory class for grids that can produce different types of plots for different types of data. Visualization is so important to the package that we have to get this right.