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This is a C++ implementation of the Marching Cubes algorithm [1] adapted from [2].

The Marching Cubes algorithm is a computer graphics algorithm to extract a polygonal mesh (in this implementation, a triangular mesh) of an isosurface from a three-dimensional discrete scalar field.

A three-dimensional scalar field can be specified as a txt file in the format specified below and the triangular mesh is obtained in the Stanford PLY file format [3] which can be visualized using any mesh visualizer such as Paraview, Blender, etc.

The driver file is main_march.cpp. To run main_march.cpp, run the following commands:

make main_march
./main_march <inp_file_path> <out_file_path> <float_isovalue>

This command will read the scalar field specified in <inp_file_path> and extract an isosurface with functional value <float_isovalue> as a PLY file to <out_file_path>.

make main_march
./main_march data/txt_in/healthy_brain.txt data/ply_out/healthy_brain_72.ply 72.0

The input scalar field can be specified as a grid in a text file. The text file contains as many lines as there are number of points in the 3D grid. Each line of the text file is of the following format:

x y z value

where x,y,z specify the location in the grid and value assigns a functional value to that location.

The following images are obtained by running this implementation on a scalar field obtained from the MRI scan of the human brain.

[1] Lorensen, William E., and Harvey E. Cline. “Marching Cubes: A High Resolution 3D Surface Construction Algorithm.” Proceedings of the 14th Annual Conference on Computer Graphics and Interactive Techniques - SIGGRAPH '87, 1987, doi:10.1145/37401.37422.

[2] Brooke, Paul. “Polygonising a Scalar Field.” Polygonising a Scalar Field (Marching Cubes), paulbourke.net/geometry/polygonise/.

[3] Brooke, Paul. PLY - Polygon File Format, paulbourke.net/dataformats/ply/.