An isosurface is a three-dimensional analog of an isoline. It is a surface that represents points of a constant value (e.g. pressure, temperature, velocity, density) within a volume of space; in other words, it is a level set of a continuous function whose domain is 3-space.
The term isoline is also sometimes used for domains of more than 3 dimensions. [1]
Isosurfaces are normally displayed using computer graphics, and are used as data visualization methods in computational fluid dynamics (CFD), allowing engineers to study features of a fluid flow (gas or liquid) around objects, such as aircraft wings. An isosurface may represent an individual shock wave in supersonic flight, or several isosurfaces may be generated showing a sequence of pressure values in the air flowing around a wing. Isosurfaces tend to be a popular form of visualization for volume datasets since they can be rendered by a simple polygonal model, which can be drawn on the screen very quickly.
In medical imaging, isosurfaces may be used to represent regions of a particular density in a three-dimensional CT scan, allowing the visualization of internal organs, bones, or other structures.
Numerous other disciplines that are interested in three-dimensional data often use isosurfaces to obtain information about pharmacology, chemistry, geophysics and meteorology.
The marching cubes algorithm was first published in the 1987 SIGGRAPH proceedings by Lorensen and Cline, [2] and it creates a surface by intersecting the edges of a data volume grid with the volume contour. Where the surface intersects the edge the algorithm creates a vertex. By using a table of different triangles depending on different patterns of edge intersections the algorithm can create a surface. This algorithm has solutions for implementation both on the CPU and on the GPU.
The asymptotic decider algorithm was developed as an extension to marching cubes in order to resolve the possibility of ambiguity in it.
The marching tetrahedra algorithm was developed as an extension to marching cubes in order to solve an ambiguity in that algorithm and to create higher quality output surface.
The Surface Nets algorithm places an intersecting vertex in the middle of a volume voxel instead of at the edges, leading to a smoother output surface.
The dual contouring algorithm was first published in the 2002 SIGGRAPH proceedings by Ju and Losasso, [3] developed as an extension to both surface nets and marching cubes. It retains a dual vertex within the voxel but no longer at the center. Dual contouring leverages the position and normal of where the surface crosses the edges of a voxel to interpolate the position of the dual vertex within the voxel. This has the benefit of retaining sharp or smooth surfaces where surface nets often look blocky or incorrectly beveled. [4] Dual contouring often uses surface generation that leverages octrees as an optimization to adapt the number of triangles in output to the complexity of the surface.
Manifold dual contouring includes an analysis of the octree neighborhood to maintain continuity of the manifold surface [5] [6] [7]
Examples of isosurfaces are 'Metaballs' or 'blobby objects' used in 3D visualisation. A more general way to construct an isosurface is to use the function representation.
In geometry, a polyhedron is a three-dimensional shape with flat polygonal faces, straight edges and sharp corners or vertices.
In geometry, a tesseract is the four-dimensional analogue of the cube; the tesseract is to the cube as the cube is to the square. Just as the surface of the cube consists of six square faces, the hypersurface of the tesseract consists of eight cubical cells. The tesseract is one of the six convex regular 4-polytopes.
In 3D computer graphics, a voxel represents a value on a regular grid in three-dimensional space. As with pixels in a 2D bitmap, voxels themselves do not typically have their position explicitly encoded with their values. Instead, rendering systems infer the position of a voxel based upon its position relative to other voxels.
Scientific visualization is an interdisciplinary branch of science concerned with the visualization of scientific phenomena. It is also considered a subset of computer graphics, a branch of computer science. The purpose of scientific visualization is to graphically illustrate scientific data to enable scientists to understand, illustrate, and glean insight from their data. Research into how people read and misread various types of visualizations is helping to determine what types and features of visualizations are most understandable and effective in conveying information.
An octree is a tree data structure in which each internal node has exactly eight children. Octrees are most often used to partition a three-dimensional space by recursively subdividing it into eight octants. Octrees are the three-dimensional analog of quadtrees. The word is derived from oct + tree. Octrees are often used in 3D graphics and 3D game engines.
In scientific visualization and computer graphics, volume rendering is a set of techniques used to display a 2D projection of a 3D discretely sampled data set, typically a 3D scalar field.
In computer graphics, metaballs are organic-looking n-dimensional isosurfaces, characterised by their ability to meld together when in close proximity to create single, contiguous objects.
In 3D computer graphics and solid modeling, a polygon mesh is a collection of vertices, edges and faces that defines the shape of a polyhedral object. The faces usually consist of triangles, quadrilaterals (quads), or other simple convex polygons (n-gons), since this simplifies rendering, but may also be more generally composed of concave polygons, or even polygons with holes.
Non-photorealistic rendering (NPR) is an area of computer graphics that focuses on enabling a wide variety of expressive styles for digital art, in contrast to traditional computer graphics, which focuses on photorealism. NPR is inspired by other artistic modes such as painting, drawing, technical illustration, and animated cartoons. NPR has appeared in movies and video games in the form of cel-shaded animation as well as in scientific visualization, architectural illustration and experimental animation.
In geometry, a triangulation is a subdivision of a planar object into triangles, and by extension the subdivision of a higher-dimension geometric object into simplices. Triangulations of a three-dimensional volume would involve subdividing it into tetrahedra packed together.
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 applications of this algorithm are mainly concerned with medical visualizations such as CT and MRI scan data images, and special effects or 3-D modelling with what is usually called metaballs or other metasurfaces. The marching cubes algorithm is meant to be used for 3-D; the 2-D version of this algorithm is called the marching squares algorithm.
In 3D computer graphics, polygonal modeling is an approach for modeling objects by representing or approximating their surfaces using polygon meshes. Polygonal modeling is well suited to scanline rendering and is therefore the method of choice for real-time computer graphics. Alternate methods of representing 3D objects include NURBS surfaces, subdivision surfaces, and equation-based representations used in ray tracers.
Marching tetrahedra is an algorithm in the field of computer graphics to render implicit surfaces. It clarifies a minor ambiguity problem of the marching cubes algorithm with some cube configurations. It was originally introduced in 1991.
Mesh generation is the practice of creating a mesh, a subdivision of a continuous geometric space into discrete geometric and topological cells. Often these cells form a simplicial complex. Usually the cells partition the geometric input domain. Mesh cells are used as discrete local approximations of the larger domain. Meshes are created by computer algorithms, often with human guidance through a GUI, depending on the complexity of the domain and the type of mesh desired. A typical goal is to create a mesh that accurately captures the input domain geometry, with high-quality (well-shaped) cells, and without so many cells as to make subsequent calculations intractable. The mesh should also be fine in areas that are important for the subsequent calculations.
In computer graphics, marching squares is an algorithm that generates contours for a two-dimensional scalar field. A similar method can be used to contour 2D triangle meshes.
In computer science a level set data structure is designed to represent discretely sampled dynamic level sets functions.
Simplicial continuation, or piecewise linear continuation, is a one-parameter continuation method which is well suited to small to medium embedding spaces. The algorithm has been generalized to compute higher-dimensional manifolds by and.
In computer vision and computer graphics, 3D reconstruction is the process of capturing the shape and appearance of real objects. This process can be accomplished either by active or passive methods. If the model is allowed to change its shape in time, this is referred to as non-rigid or spatio-temporal reconstruction.
The Point Cloud Library (PCL) is an open-source library of algorithms for point cloud processing tasks and 3D geometry processing, such as occur in three-dimensional computer vision. The library contains algorithms for filtering, feature estimation, surface reconstruction, 3D registration, model fitting, object recognition, and segmentation. Each module is implemented as a smaller library that can be compiled separately. PCL has its own data format for storing point clouds - PCD, but also allows datasets to be loaded and saved in many other formats. It is written in C++ and released under the BSD license.
In scientific visualization the asymptotic decider is an algorithm developed by Nielson and Hamann in 1991 that creates isosurfaces from a given scalar field. It was proposed as an improvement to the marching cubes algorithm, which can produce some "bad" topology, but can also be considered an algorithm in its own right.
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