Is there a way to convert the optimized table to table with evenly spaced nodes without losing optimization perhaps using a preceding 1D shaper LUT?

This optimization technique works great to optimize 3D Look Up Tables (LUTs) and appropriately minimize errors due to interpolation. https://www.mathworks.com/matlabcentral/fileexchange/35194-table-breakpoint-optimization

Using this optimization tool, the nodes become unevenly spaced in order to best fit the input data, however, for my application, I need to have evenly spaced nodes within my lookup table. This is due to constraints of the LUT implementation where the nodes are specified as a min and max and assumed to be evenly spaced between those values. The following is an examples of such an implementation although it’s common for many lut formats to do the same thing. (<http://wwwimages.adobe.com/content/dam/Adobe/en/products/speedgrade/cc/pdfs/cube-lut-specification-1.0.pdf>)

I want to be able to utilize the optimization, but also create a uniformly spaced table. Is there a way to convert the optimized table to table with evenly spaced nodes without losing the optimization perhaps using a preceding 1D shaper LUT? Maybe by effectively shaping the data going into the uniformly spaced table 3D such that the results would match those of the optimized 3D alone.