Marching Cubes: A High Resolution 3D Surface Construction Algorithm

Authors

William E. Lorensen, Harvey E. Cline

Year

1987

Journal Paper

Algorithm

Marching Cubes

Source

ACM SIGGRAPH Computer Graphics

Identifiers

DOI 10.1145/37402.37422

Abstract¶

We present a new algorithm, called marching cubes , that creates triangle models of constant density surfaces from 3D medical data. Using a divide-and-conquer approach to generate inter-slice connectivity, we create a case table that defines triangle topology. The algorithm processes the 3D medical data in scan-line order and calculates triangle vertices using linear interpolation. We find the gradient of the original data, normalize it, and use it as a basis for shading the models. The detail in images produced from the generated surface models is the result of maintaining the inter-slice connectivity, surface data, and gradient information present in the original 3D data. Results from computed tomography (CT), magnetic resonance (MR), and single-photon emission computed tomography (SPECT) illustrate the quality and functionality of marching cubes . We also discuss improvements that decrease processing time and add solid modeling capabilities.

Summary¶

Lorensen and Cline introduce Marching Cubes, a table-driven algorithm for extracting polygonal isosurfaces from volumetric scalar data. The paper became foundational in scientific visualization and medical imaging because it made high-resolution 3D surface construction practical from sampled volumes.