An isosurface is a three-dimensional analog of an isoline. It is a

surface A surface, as the term is most generally used, is the outermost or uppermost layer of a physical object or space. It is the portion or region of the object that can first be perceived by an observer using the senses of sight and touch, and is ...

that represents points of a constant value (e.g.

pressure Pressure (symbol: ''p'' or ''P'') is the force applied perpendicular to the surface of an object per unit area over which that force is distributed. Gauge pressure (also spelled ''gage'' pressure)The preferred spelling varies by country and eve ...

temperature Temperature is a physical quantity that quantitatively expresses the attribute of hotness or coldness. Temperature is measurement, measured with a thermometer. It reflects the average kinetic energy of the vibrating and colliding atoms making ...

velocity Velocity is a measurement of speed in a certain direction of motion. It is a fundamental concept in kinematics, the branch of classical mechanics that describes the motion of physical objects. Velocity is a vector (geometry), vector Physical q ...

density Density (volumetric mass density or specific mass) is the ratio of a substance's mass to its volume. The symbol most often used for density is ''ρ'' (the lower case Greek letter rho), although the Latin letter ''D'' (or ''d'') can also be u ...

) within a

volume Volume is a measure of regions in three-dimensional space. It is often quantified numerically using SI derived units (such as the cubic metre and litre) or by various imperial or US customary units (such as the gallon, quart, cubic inch) ...

of space; in other words, it is a

level set In mathematics, a level set of a real-valued function of real variables is a set where the function takes on a given constant value , that is: : L_c(f) = \left\~. When the number of independent variables is two, a level set is call ...

of a continuous function whose domain is 3-space. The term ''isoline'' is also sometimes used for domains of more than 3 dimensions. CFD simulation showing vorticity isosurfaces behind propeller

CFD simulation showing vorticity isosurfaces behind propeller

Applications

Isosurfaces are normally displayed using

computer graphics Computer graphics deals with generating images and art with the aid of computers. Computer graphics is a core technology in digital photography, film, video games, digital art, cell phone and computer displays, and many specialized applications. ...

, and are used as data visualization methods in

computational fluid dynamics Computational fluid dynamics (CFD) is a branch of fluid mechanics that uses numerical analysis and data structures to analyze and solve problems that involve fluid dynamics, fluid flows. Computers are used to perform the calculations required ...

(CFD), allowing engineers to study features of a

fluid flow In physics, physical chemistry and engineering, fluid dynamics is a subdiscipline of fluid mechanics that describes the flow of fluids – liquids and gases. It has several subdisciplines, including (the study of air and other gases in motion ...

(gas or liquid) around objects, such as aircraft

wing A wing is a type of fin that produces both Lift (force), lift and drag while moving through air. Wings are defined by two shape characteristics, an airfoil section and a planform (aeronautics), planform. Wing efficiency is expressed as lift-to-d ...

s. An isosurface may represent an individual

shock wave In physics, a shock wave (also spelled shockwave), or shock, is a type of propagating disturbance that moves faster than the local speed of sound in the medium. Like an ordinary wave, a shock wave carries energy and can propagate through a me ...

supersonic Supersonic speed is the speed of an object that exceeds the speed of sound (Mach 1). For objects traveling in dry air of a temperature of 20 °C (68 °F) at sea level, this speed is approximately . Speeds greater than five times ...

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 Medical imaging is the technique and process of imaging the interior of a body for clinical analysis and medical intervention, as well as visual representation of the function of some organs or tissues (physiology). Medical imaging seeks to revea ...

, isosurfaces may be used to represent regions of a particular

in a three-dimensional CT scan, allowing the visualization of internal organs,

bone A bone is a rigid organ that constitutes part of the skeleton in most vertebrate animals. Bones protect the various other organs of the body, produce red and white blood cells, store minerals, provide structure and support for the body, ...

s, or other structures. Numerous other disciplines that are interested in three-dimensional data often use isosurfaces to obtain information about

pharmacology Pharmacology is the science of drugs and medications, including a substance's origin, composition, pharmacokinetics, pharmacodynamics, therapeutic use, and toxicology. More specifically, it is the study of the interactions that occur betwee ...

chemistry Chemistry is the scientific study of the properties and behavior of matter. It is a physical science within the natural sciences that studies the chemical elements that make up matter and chemical compound, compounds made of atoms, molecules a ...

geophysics Geophysics () is a subject of natural science concerned with the physical processes and Physical property, properties of Earth and its surrounding space environment, and the use of quantitative methods for their analysis. Geophysicists conduct i ...

and

meteorology Meteorology is the scientific study of the Earth's atmosphere and short-term atmospheric phenomena (i.e. weather), with a focus on weather forecasting. It has applications in the military, aviation, energy production, transport, agricultur ...

Implementation algorithms

Marching cubes

The

marching cubes 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 somet ...

algorithm was first published in the 1987 SIGGRAPH proceedings by Lorensen and Cline, and it creates a surface by intersecting the edges of a

data Data ( , ) are a collection of discrete or continuous values that convey information, describing the quantity, quality, fact, statistics, other basic units of meaning, or simply sequences of symbols that may be further interpreted for ...

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.

Asymptotic decider

The asymptotic decider algorithm was developed as an extension to

in order to resolve the possibility of ambiguity in it.

Marching tetrahedra

The marching tetrahedra algorithm was developed as an extension to

in order to solve an ambiguity in that algorithm and to create higher quality output surface.

Surface nets

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.

Dual contouring

The dual contouring algorithm was first published in the 2002 SIGGRAPH proceedings by Ju and Losasso, developed as an extension to both surface nets and marching cubes. It retains a dual vertex within the

voxel In computing, a voxel is a representation of a value on a three-dimensional regular grid, akin to the two-dimensional pixel. Voxels are frequently used in the Data visualization, visualization and analysis of medical imaging, medical and scient ...

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. Dual contouring often uses surface generation that leverages

octree An octree is a tree data structure in which each internal node has exactly eight child node, children. Octrees are most often used to partition a three-dimensional space by recursive subdivision, recursively subdividing it into eight Octant (geo ...

s as an optimization to adapt the number of triangles in output to the complexity of the surface.

Manifold dual contouring

Manifold dual contouring includes an analysis of the octree neighborhood to maintain continuity of the manifold surface

Examples

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.

Gallery

File:NREL 10secs.png, Surface of constant pressure. File:Katrina 28aug05 isosurface.gif, Surface with shading information varying across it to convey rain column height. File:Heat rose.jpg, Multiple surfaces of constant temperature, with normal vectors added to each surface. File:Gauss Laguerre TEM Mode P2L8.png, Surfaces of constant intensity, with color shading linked to intensity to permit conveying information about the contours of varying intensity fields.

References

* {{cite book, author1=Charles D. Hansen, author2=Chris R. Johnson, title=Visualization Handbook, url=https://books.google.com/books?id=ZFrlULckWdAC&pg=PA7, year=2004, publisher=Academic Press, isbn=978-0-12-387582-2, pages=7–11

External links

Isosurface PolygonizationThe contourist package for numeric python
generates triangulations of isosurfaces for arbitrary 3 dimensional functions which can be displayed using HTML5 as illustrated in thi
jsfiddle
3D computer graphics Medical imaging Surfaces Implicit surface modeling