Contents
What does marching cubes do?
Marching cubes is a computer graphics algorithm, published in the 1987 SIGGRAPH proceedings by Lorensen and Cline, for extracting a polygonal mesh of an isosurface from a three-dimensional discrete scalar field (the elements of which are sometimes called voxels).
Is marching cubes patented?
Marching cubes is a computer graphics algorithm for extracting a polygonal mesh of an isosurface from a 3-D volume. The marching cubes algorithm was published in the 1987 SIGGRAPH proceedings by William Lorensen and Harvey Cline.. A patent for the algorithm was applied for on June 5, 1985. The patent has now expired.
What is dual marching cubes?
The dual marching cubes algorithm presented by Nielson [30] is a different strategy to reconstruct an iso-surface from volume data. The intersection of the iso-surface with the cell can be approximated by a polygon on the cell faces. The DMC algorithm computes the dual of these MC polygons.
What is isosurface extraction?
Isosurface extraction is a powerful tool for investigating volumetric scalar fields and has been used extensively in medical imaging ever since the seminal paper by Lorensen and Kline on marching cubes [1, 2]. In medical imaging applications, isosurfaces permit the extraction of anatomical structures and tissues.
What is Isovalue?
In microeconomics, isovalue lines define a relationship between the production of two products in which the total market value is constant. For example: In a market that produces bread and wine, the market is willing to trade one bottle of wine for three breads.
What is isosurface value?
An isosurface is a 3D surface representation of points with equal values in a 3D data distribution. Is the 3D equivalent of a contour line. An isosurface can be used to represent, for example, all VoXels in an image with a given CoLocalization level. Those points are joined forming a 3D surface.
Is tetrahedron a pyramid?
The tetrahedron is a triangular pyramid having congruent equilateral triangles for each of its faces. The regular tetrahedron is a special case of the triangular pyramid.
Why are there discontinuities in a Marching cube?
However, due to the existence of ambiguities in the trilinear interpolant behavior in the cube faces and interior, the meshes extracted by the Marching Cubes presented discontinuities and topological issues. Given a cube of the grid, a face ambiguity occurs when its face vertices have alternating signs.
Is there an extended version of the Marching Cubes 33 algorithm?
In this paper, we present an extended version of the Marching Cubes 33 algorithm (a variation of the Marching Cubes algorithm which guarantees topological correctness), called Extended Marching Cubes 33.
What was the US patent for marching cubes?
An implementation of the marching cubes algorithm was patented as United States Patent 4,710,876. Another similar algorithm was developed, called marching tetrahedra, in order to circumvent the patent as well as solve a minor ambiguity problem of marching cubes with some cube configurations.
Who is the creator of the Marching cube?
The Marching Cubes 33, proposed by Chernyaev in 1995, is one of the first isosurface extraction algorithms intended to preserve the topology of the trilinear interpolant. In his work, Chernyaev extends to 33 the number of cases in the triangulation lookup table.