tmc

Construction of Topologically Correct and Manifold Iso-surfaces
Author: Roberto Grosso

Different algorithms for computing topologically correct and manifold iso-surfaces from volume data (hexahedral meshes or voxel grids) were implemented. The output surfaces are represented using an indexed face set (shared vertex) and a halfedge data structure. The acronym tmc is intended to mean topologically correct and manifold iso-surface extraction by using a Marching Cubes like algorithm.

Folder matlab

In this folder there are some few MATLAB scripts which computes the intersection of a level set with one or two unit cells for different configurations.

Script t_mc_figs.m

This script generates the figures presented in the paper [1]. Just open the MATLAB script and press run. It will generate a set of MATLAB *.fig figures.

Scripts t_mc_gui.m and t_mc.m

These scripts compute the intersection of a level set with a unit cell for different configurations as described in the paper [1]. They contain a user interface to facilitate the usage and visualize different cases for different configurations. In order to run the script use MATLAB and run the script tmc_gui.m.

Scripts singular_gui.m and t_singular.m

These scripts implement the asymptotic decider presented in [2]. Some special cases handled by the asymptotic decider are demonstrated in this script. They can be executed by running the user interface in singular_gui.m

Folder mc

In this folder you find the main function in tmc.cpp and the classes in MarchingCubes.h and MarchingCubes.cpp which compute the topologically correct iso-surface from volume data as presented in [1]. Furthermore, a small data set used in the paper. The file format used for the volume data can be easily read from the method which overload the function operator. A shell script is provided to compile and execute the code.

Execution:

1. within the folder containing the sources just run the bash-script runtmc.sh.

2. Output are the files skull128.obj and skull128.off.

Folder cuda_tmc

This folder contains a CUDA implementation of the topologically correct iso-surface algorithm presented in [1]. This implementation optionally generates a halfedge or a shared vertex data structure for the triangle mesh. We do not include a main function to run the code. The class MarchingCubed implements two different methods to generate iso-surfaces from volume data: mc_halfedge() generates a halfedge data structure and mc_sharedvertex() generates a indexed face set (shared vertex) data structure.

Folder dmc

This folder contains a CUDA implementation of the Dual Marching Cubes method presented in [4],[3]. The main function kernel.cu demonstrates how to use the code. It can read volume data or alternatively generate a synthetic data set for demonstration purposes. The file format for volume data can be easily seen in the method readDataFromFile() implemented in the class UniformGrid. Data is artificially generated or read from file by the method init() main class DualMarchingCubes. Artificially generated data corresponds to implicit surfaces. Which surfaces can be obtained is listed in the main function kernel.cu.

Folder cpp_dmc

This folder contains a C++ implementation of the Dual Marching Cubes method presented in [4],[3]. The main function demonstrates how to use the code. It can read volume data or alternatively generate a synthetic data set for demonstration purposes. The class in charge of reading or generating a scalar field and save the data into a uniform grid is Volumes. The file format for volume data can be easily seen in the method readDataFromFile(). This class also implements different 3D scalar functions that can be used to synthetically generate iso-surfaces. Data generation, the computation of the DMC surface and the output into an obj file is carried out by the class ImplicitSurface by the method dmc(). The main.c file demonstrates how to use the code. This is a very first implementation in C++. Mesh simplification only removes elements with vertex valence pattern 3X3Y. The code can certainly be optimized. The simplification of elements with vertex valence pattern, which are not so common, will follows in a later version of the code.

Remark: The code was compiled in the Ubuntu 20.04 LTS terminal in Windows 10 with clang++ version 10.0.0-4. The simplest command line for compiling is clang++ -o dmc -std=c++17 -W *.cpp. Under this restrictions the code compiles with one warning. The code was developed with Visual Studio 2019 community. It is required to set the C++ Language Standard to ISO C++ 17 Standard.

References

[1]: Roberto Grosso: Construction of Topologically Correct and Manifold Isosurfaces. Computer Graphics Forum 35(5):187-196 · August 2016

[2]: Roberto Grosso: An asymptotic decider for robust and topologically correct triangulation of isosurfaces: topologically correct isosurfaces. CGI '17 Proceedings of the Computer Graphics International Conference. Japan, June 2017

[3]: Roberto Grosso, Daniel Zint: Parallel reconstruction of quad only meshes from volume data. In: Proceedings of the 15th International Joint Conference on Computer Vision, Imaging and Computer Graphics Theory and Applications - Volume 1: GRAPP,, pp. 102–112. INSTICC, SciTePress (2020).

[4]: Roberto Grosso, Daniel Zint: A parallel dual marching cubes approach to quad only surface reconstruction. The Visual Computer, (), 1-16. DOI 10.1007/s00371-021-02139-w