Isosurface
Encyclopedia
An isosurface is a three-dimensional
Dimension
In physics and mathematics, the dimension of a space or object is informally defined as the minimum number of coordinates needed to specify any point within it. Thus a line has a dimension of one because only one coordinate is needed to specify a point on it...
analog of an isoline
Contour line
A contour line of a function of two variables is a curve along which the function has a constant value. In cartography, a contour line joins points of equal elevation above a given level, such as mean sea level...
. It is a surface that represents points of a constant value (e.g. pressure, temperature, velocity, density) within a volume
Volume
Volume is the quantity of three-dimensional space enclosed by some closed boundary, for example, the space that a substance or shape occupies or contains....
of space; in other words, it is a level set
Level set
In mathematics, a level set of a real-valued function f of n variables is a set of the formthat is, a set where the function takes on a given constant value c....
of a continuous function whose domain is 3D-space.
Isosurfaces are normally displayed using computer graphics
Computer graphics
Computer graphics are graphics created using computers and, more generally, the representation and manipulation of image data by a computer with help from specialized software and hardware....
, and are used as data visualization methods in computational fluid dynamics
Computational fluid dynamics
Computational fluid dynamics, usually abbreviated as CFD, is a branch of fluid mechanics that uses numerical methods and algorithms to solve and analyze problems that involve fluid flows. Computers are used to perform the calculations required to simulate the interaction of liquids and gases with...
(CFD), allowing engineers to study features of a fluid flow (gas or liquid) around objects, such as aircraft wing
Wing
A wing is an appendage with a surface that produces lift for flight or propulsion through the atmosphere, or through another gaseous or liquid fluid...
s. An isosurface may represent an individual shock wave
Shock wave
A shock wave is a type of propagating disturbance. Like an ordinary wave, it carries energy and can propagate through a medium or in some cases in the absence of a material medium, through a field such as the electromagnetic field...
in supersonic
Supersonic
Supersonic speed is a rate of travel of an object that exceeds the speed of sound . For objects traveling in dry air of a temperature of 20 °C this speed is approximately 343 m/s, 1,125 ft/s, 768 mph or 1,235 km/h. Speeds greater than five times the speed of sound are often...
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
Medical imaging is the technique and process used to create images of the human body for clinical purposes or medical science...
, isosurfaces may be used to represent regions of a particular density
Density
The mass density or density of a material is defined as its mass per unit volume. The symbol most often used for density is ρ . In some cases , density is also defined as its weight per unit volume; although, this quantity is more properly called specific weight...
in a three-dimensional CT
Computed tomography
X-ray computed tomography or Computer tomography , is a medical imaging method employing tomography created by computer processing...
scan, allowing the visualization of internal organ
Organ (anatomy)
In biology, an organ is a collection of tissues joined in structural unit to serve a common function. Usually there is a main tissue and sporadic tissues . The main tissue is the one that is unique for the specific organ. For example, main tissue in the heart is the myocardium, while sporadic are...
s, bone
Bone
Bones are rigid organs that constitute part of the endoskeleton of vertebrates. They support, and protect the various organs of the body, produce red and white blood cells and store minerals. Bone tissue is a type of dense connective tissue...
s, or other structures.
Numerous other disciplines that are interested in three-dimensional data often use isosurfaces to obtain information about pharmacology
Pharmacology
Pharmacology is the branch of medicine and biology concerned with the study of drug action. More specifically, it is the study of the interactions that occur between a living organism and chemicals that affect normal or abnormal biochemical function...
, chemistry
Chemistry
Chemistry is the science of matter, especially its chemical reactions, but also its composition, structure and properties. Chemistry is concerned with atoms and their interactions with other atoms, and particularly with the properties of chemical bonds....
, geophysics
Geophysics
Geophysics is the physics of the Earth and its environment in space; also the study of the Earth using quantitative physical methods. The term geophysics sometimes refers only to the geological applications: Earth's shape; its gravitational and magnetic fields; its internal structure and...
and meteorology
Meteorology
Meteorology is the interdisciplinary scientific study of the atmosphere. Studies in the field stretch back millennia, though significant progress in meteorology did not occur until the 18th century. The 19th century saw breakthroughs occur after observing networks developed across several countries...
.
A popular method of constructing an isosurface from a data
Data (computing)
In computer science, data is information in a form suitable for use with a computer. Data is often distinguished from programs. A program is a sequence of instructions that detail a task for the computer to perform...
volume is the marching cubes
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 scalar field...
algorithm, and another, very similar method is the marching tetrahedrons
Marching Tetrahedrons
Marching tetrahedrons is an algorithm in the field of computer graphics to render implicit surfaces. It clarifies a minor ambiguity problem of marching cubes with some cube configurations....
algorithm.
Examples of isosurfaces are 'Metaballs
Metaballs
Metaballs are, in computer graphics, organic-looking n-dimensional objects. The technique for rendering metaballs was invented by Jim Blinn in the early 1980s....
' or 'blobby objects' used in 3D visualisation. A more general way to construct an isosurface is to use the function representation
Function representation
Function Representation is used in solid modeling, volume modeling and computer graphics. FRep was introduced in "Function representation in geometric modeling: concepts, implementation and applications" as a uniform representation of multidimensional geometric objects...
and the HyperFun
HyperFun
HyperFun is a programming language and software used to create, visualize, and fabricate volumetric 3D and higher dimensional models. Unlike other modeling packages, it can easily model objects of the quality found in reality and nature...
language.