Pre-processing to generate `*.mat' files.
-----------------------------------------

1. Execute `d6_export_invtets.m' which generates in `d6_invtets.mat'.
2. Execute `d6_export_cubes_filled.m' which generates in `d6_cubes_filled.mat'.
3. Execute `d6_export_bez_coeff.m' which generates `d6_bez_coeff_rat.mat'.
4. Execute `d6_find_lcm_denom.m' to find the smallest common denominator for the Bezier coefficients.
5. Execute `d6_convert_bez_coeff_to_integer.m' after setting `denom' variable to the denominator found in step 4. This script generates `d6_bez_coeff_int.mat'.
6. Check the result by executing `d6_compare_time.m'.

data file list
--------------

d6_bez_coeff_int.mat
	: Bezier coefficients in integer format (scaled by 24)
d6_bez_coeff_rat.mat
	: Bezier coefficients in rational format
d6_cubes_filled.mat
	: List of cube indices which contain (at least one) Bezier polynomial with non-zero coefficients.
d6_invtets.mat
	: Inverse matrices to be used as barycentric coordinate function.

script file list
----------------
d6_compare_time.m
	: Compares computation time among three packages. (de Boor's, Kobbelt's and Bezier form)
d6_compute_bez_coeff.m
	: Computes the Bezier coefficients for the polynomial defined on the given tetrahedron.
d6_convert_bez_coeff_to_integer.m
	: Converts Bezier coefficients in rational format to integer format by multiplying 24.
d6_convert_index.m
	: Converts a given pair of index vectors (icube,itet) to an integer index to access the Bezier coefficients table.
d6_convert_to_bez.m
	: Converts given volumetric data to Bezier polynomials by using the data as box spline coefficients.
d6_convert_to_quasi.m
	: Converts given volumetric data to quasi-interpolant form.
d6_eval_bez_basis.m
	: Evaluates the box spline using Bezier form at the input parameter.
d6_eval_bez.m
	: Evaluates the spline generated by input volumetric data as coefficients at the input parameter.
d6_eval_bez_bary.m
	: Same with `d6_eval_bez.m' but the input parameter is in barycentric coordinate.
d6_eval_grid_bez_basis.m
	: Evaluates the box spline in Bezier form on the given grid.
d6_eval_grid_bez.m
	: Evaluates the spline generated by the input volumetric data as coefficients on the given grid.
d6_export_bez_coeff.m
	: Computes and exports the coefficients of the Bezier polynomial pieces converted from the 6-direction box spline. The output file is `d6_bez_coeff_rat.mat'.
d6_export_cubes_filled.m
	: Exports the cubes overlapping the support of the 6-direction box spline which contains at least one Bezier polynomial tetrahedron. The output file is `d6_cubes_filled.mat'.
d6_export_invtets.m
	: Exports the inverse matrices of the tetrahedra in the unit cubes to be used for barycentric coordinate computation. The output file is `d6_invtets.mat'.
d6_export_povrat_bez_basis.m
	: Exports the Bezier polynomials converted from the 6-direction box spline in POV-Ray script format.
d6_export_povray.m
	: Exports the Bezier polynomials converted from quasi-interpolated volumetric data using 6-direction box spline. The volumetric data is assumed to be sampled on FCC lattice.
d6_find_lcm_denom.m
	: Find the smallest common denominator of the Bezier coefficients iterating `d6_bez_coeff_rat.mat'.
d6_find_tet.m
	: Finds the pair of indices (icube,itet) of the input parameter.
d6_hash_tet.m
	: Returns two tables required for the evaluation of the Bezier polynomials.
d6_setup.m
	: Initializes the global variables required for the evaluation of the Bezier polynomials.

demo script file list
---------------------
d6_demo_eval_plot_bez_basis.m
	: Evaluates and plots the level sets of the 6-direction box spline using Bezier form.
d6_demo_export_povray_bez_basis.m
	: Demo script for `d6_export_povray_bez_basis.m' script.
d6_demo_export_povray.m
	: Demo script for `d6_export_povray.m' script.
d6_demo_quasi.m
	: Demo script for `d6_convert_to_quasi.m' script.
d6_demo_reconstruct.m
	: Demo script for `d6_eval_bez.m' script. (Non-quasi-interpolant)  
d6_demo_symbolic_exp.m
	: Demo script generating symbolic expression of the Bezier polynomial pieces.

