Topic
Marching squares
About: Marching squares is a research topic. Over the lifetime, 163 publications have been published within this topic receiving 16467 citations.
Papers published on a yearly basis
Papers
1 Aug 1987
TL;DR: In this paper, a divide-and-conquer approach is used to generate inter-slice connectivity, and then a case table is created to define triangle topology using linear interpolation.
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.
14,549 citations
TL;DR: The paper’s primary aim is to survey the development of the marching cubes algorithm and its computational properties, extensions, and limitations (including the attempts to resolve its limitations).
603 citations
TL;DR: A full implementation of Chernyaev's technique to ensure a topologically correct result, i.e., a manifold mesh, for any input data is introduced, which completes the original paper for the ambiguity resolution and for the feasibility of the implementation.
Abstract: Marching Cubes methods first offered visual access to experimental and theoretical volumetric data. The implementation of this method usually relies on a small look-up table; many enhancements and optimizations of Marching Cubes still use it. However, this look-up table can lead to cracks and inconsistent topology. This paper introduces a full implementation of Chernyaev's technique to ensure a topologically correct result, i.e., a manifold mesh, for any input data. It completes the original paper for the ambiguity resolution and for the feasibility of the implementation. Moreover, the cube interpolation provided here can be used in a wider range of methods. The source code is available online.
596 citations
TL;DR: A new algorithm, regularised marching tetrahedra (RMT), is presented, which combines marching tetahedra and vertex clustering to generate iso-surfaces which are topologically consistent with the data and contain a number of triangles appropriate to the sampling resolution with significantly improved aspect ratios.
376 citations
TL;DR: A modification of the Marching Cubes algorithm for isosurfacing is proposed, with the intent of improving the representation of the surface in the interior of each grid cell, which correctly models the topology of the trilinear interpolant within the cell and which is robust under perturbations of the data and threshold value.
Abstract: This paper proposes a modification of the Marching Cubes algorithm for isosurfacing, with the intent of improving the representation of the surface in the interior of each grid cell. Our objective is to create a representation which correctly models the topology of the trilinear interpolant within the cell and which is robust under perturbations of the data and threshold value. To achieve this, we identify a small number of key points in the cell interior that are critical to the surface definition. This allows us to efficiently represent the different topologies that can occur, including the possibility of "tunnels." The representation is robust in the sense that the surface is visually continuous as the data and threshold change in value. Each interior point lies on the isosurface. Finally, a major feature of our new approach is the systematic method of triangulating the polygon in the cell interior.
199 citations
Related Topics (5)
Performance Metrics
| Year | Papers |
|---|---|
| 2021 | 5 |
| 2020 | 2 |
| 2019 | 2 |
| 2018 | 4 |
| 2017 | 2 |
| 2016 | 6 |