vector maps
VERY INTERESTING!!! That is probably near to the idea of a meshgrid representation of tilings in Matlab I wrote about on Nov. 25 and something that is useful in my batch processing context.
What about the expected run time of such a representation compared to an original CRMT-pipeline? The run time of a CRMT-pipeline is proportional to the number of proto-tiles that are distributed over the background (14 with p3m1, 28 with p6m, …) and the background area but a grid representation is independent of the number of proto-tiles and only dependent on the number of output pixels (and the interpolation method).
If I am comparing the interpolation of conformal maps to a p3m1-CRMT-pipeline with a similar image area I estimate a 2-3x faster image generation. But perhaps the expected problems in the majority of cases with more than one type of proto-tile (C1, C2,…) could make this efficiency advantage disappear.
Interesting to see that in your first image example some edge artifacts vanishes, some were reduced or transformed but some remain unchanged. So the vector method have active influence on the edge artifacts which could lead to the hypothesis that there exists parameters of the warp/interpolation function (like interpolation method) that could also solve the edge problems (two birds with one stone).