List of graphical methods
Encyclopedia
This is a list of graphical methods with a mathematical basis.
Included are diagram
techniques, chart
techniques, plot
techniques, and other forms of visualization
.
There is also a list of computer graphics and descriptive geometry topics.
Descriptive geometry
Engineering drawing
Systems analysis
Cartography
Included are diagram
Diagram
A diagram is a two-dimensional geometric symbolic representation of information according to some visualization technique. Sometimes, the technique uses a three-dimensional visualization which is then projected onto the two-dimensional surface...
techniques, chart
Chart
A chart is a graphical representation of data, in which "the data is represented by symbols, such as bars in a bar chart, lines in a line chart, or slices in a pie chart"...
techniques, plot
Plot (graphics)
A plot is a graphical technique for representing a data set, usually as a graph showing the relationship between two or more variables. The plot can be drawn by hand or by a mechanical or electronic plotter. Graphs are a visual representation of the relationship between variables, very useful for...
techniques, and other forms of visualization
Data visualization
Data visualization is the study of the visual representation of data, meaning "information that has been abstracted in some schematic form, including attributes or variables for the units of information"....
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There is also a list of computer graphics and descriptive geometry topics.
Simple displays
- Box plotBox plotIn descriptive statistics, a box plot or boxplot is a convenient way of graphically depicting groups of numerical data through their five-number summaries: the smallest observation , lower quartile , median , upper quartile , and largest observation...
- Graph of a functionGraph of a functionIn mathematics, the graph of a function f is the collection of all ordered pairs . In particular, if x is a real number, graph means the graphical representation of this collection, in the form of a curve on a Cartesian plane, together with Cartesian axes, etc. Graphing on a Cartesian plane is...
- Graph paperGraph paperGraph paper, graphing paper, grid paper or millimeter paper is writing paper that is printed with fine lines making up a regular grid. The lines are often used as guides for plotting mathematical functions or experimental data and drawing diagrams. It is commonly found in mathematics and...
- Logarithmic graph paper
- Heatmap
- HistogramHistogramIn statistics, a histogram is a graphical representation showing a visual impression of the distribution of data. It is an estimate of the probability distribution of a continuous variable and was first introduced by Karl Pearson...
- Bar chartBar chartA bar chart or bar graph is a chart with rectangular bars with lengths proportional to the values that they represent. The bars can be plotted vertically or horizontally....
- Bar chart
- Pie chartPie chartA pie chart is a circular chart divided into sectors, illustrating proportion. In a pie chart, the arc length of each sector , is proportional to the quantity it represents. When angles are measured with 1 turn as unit then a number of percent is identified with the same number of centiturns...
- PlottingPlot (graphics)A plot is a graphical technique for representing a data set, usually as a graph showing the relationship between two or more variables. The plot can be drawn by hand or by a mechanical or electronic plotter. Graphs are a visual representation of the relationship between variables, very useful for...
- ScatterplotScatterplotA scatter plot or scattergraph is a type of mathematical diagram using Cartesian coordinates to display values for two variables for a set of data....
- Skewplot
- SparklineSparklineA sparkline is a type of information graphic characterized by its small size and high data density. Sparklines present trends and variations associated with some measurement, such as average temperature or stock market activity, in a simple and condensed way...
- StemplotStemplotA stemplot , in statistics, is a device for presenting quantitative data in a graphical format, similar to a histogram, to assist in visualizing the shape of a distribution. They evolved from Arthur Bowley's work in the early 1900s, and are useful tools in exploratory data analysis...
- Radar chartRadar chartA radar chart is a graphical method of displaying multivariate data in the form of a two-dimensional chart of three or more quantitative variables represented on axes starting from the same point...
Descriptive geometryDescriptive geometryDescriptive geometry is the branch of geometry which allows the representation of three-dimensional objects in two dimensions, by using a specific set of procedures. The resulting techniques are important for engineering, architecture, design and in art...
- Isometric projectionIsometric projectionIsometric projection is a method for visually representing three-dimensional objects in two dimensions in technical and engineering drawings...
- Orthographic projectionOrthographic projectionOrthographic projection is a means of representing a three-dimensional object in two dimensions. It is a form of parallel projection, where all the projection lines are orthogonal to the projection plane, resulting in every plane of the scene appearing in affine transformation on the viewing surface...
- Perspective (graphical)Perspective (graphical)Perspective in the graphic arts, such as drawing, is an approximate representation, on a flat surface , of an image as it is seen by the eye...
Engineering drawingEngineering drawingAn engineering drawing, a type of technical drawing, is used to fully and clearly define requirements for engineered items.Engineering drawing produces engineering drawings . More than just the drawing of pictures, it is also a language—a graphical language that communicates ideas and information...
- Technical drawingTechnical drawingTechnical drawing, also known as drafting or draughting, is the act and discipline of composing plans that visually communicate how something functions or has to be constructed.Drafting is the language of industry....
- Mohr's circle
- PantographPantographA pantograph is a mechanical linkage connected in a special manner based on parallelograms so that the movement of one pen, in tracing an image, produces identical movements in a second pen...
- Circuit diagramCircuit diagramA circuit diagram is a simplified conventional graphical representation of an electrical circuit...
- Smith chartSmith chartThe Smith chart, invented by Phillip H. Smith , is a graphical aid or nomogram designed for electrical and electronics engineers specializing in radio frequency engineering to assist in solving problems with transmission lines and matching circuits...
- Sankey diagramSankey diagramSankey diagrams are a specific type of flow diagram, in which the width of the arrows is shown proportionally to the flow quantity. They are typically used to visualize energy or material or cost transfers between processes.-Application:...
Systems analysisSystems analysisSystems analysis is the study of sets of interacting entities, including computer systems analysis. This field is closely related to requirements analysis or operations research...
- Binary decision diagramBinary decision diagramIn the field of computer science, a binary decision diagram or branching program, like a negation normal form or a propositional directed acyclic graph , is a data structure that is used to represent a Boolean function. On a more abstract level, BDDs can be considered as a compressed...
- Control flow graphControl flow graphA control flow graph in computer science is a representation, using graph notation, of all paths that might be traversed through a program during its execution.- Overview :...
- Functional flow block diagramFunctional flow block diagramA Functional Flow Block Diagram is a multi-tier, time-sequenced, step-by-step flow diagram of a system’s functional flow.The FFBD notation was developed in the 1950s, and is widely used in classical systems engineering...
- IDEFIDEFIDEF, an abbreviation of Integration Definition, refers to a family of modeling languages in the field of systems and software engineering. They cover a wide range of uses, from functional modeling to data, simulation, object-oriented analysis/design and knowledge acquisition. These "definition...
- N2 chartN2 ChartThe N 2 chart, also referred to as N 2 diagram, N-squared diagram or N-squared chart, is a diagram in the shape of a matrix, representing functional or physical interfaces between system elements. It is used to systematically identify, define, tabulate, design, and analyze functional and...
- State diagramState diagramA state diagram is a type of diagram used in computer science and related fields to describe the behavior of systems. State diagrams require that the system described is composed of a finite number of states; sometimes, this is indeed the case, while at other times this is a reasonable abstraction...
- System context diagramSystem context diagramA System Context Diagram in software engineering and systems engineering is a diagram that represents the actors outside a system that could interact with that system. This diagram is the highest level view of a system. It is similar to a Block diagram...
CartographyCartographyCartography is the study and practice of making maps. Combining science, aesthetics, and technique, cartography builds on the premise that reality can be modeled in ways that communicate spatial information effectively.The fundamental problems of traditional cartography are to:*Set the map's...
- Map projectionMap projectionA map projection is any method of representing the surface of a sphere or other three-dimensional body on a plane. Map projections are necessary for creating maps. All map projections distort the surface in some fashion...
- Orthographic projection (cartography)Orthographic projection (cartography)An orthographic projection is a map projection of cartography. Like the stereographic projection and gnomonic projection, orthographic projection is a perspective projection, in which the sphere is projected onto a tangent plane or secant plane. The point of perspective for the orthographic...
- Robinson projectionRobinson projectionThe Robinson projection is a map projection of a world map, which shows the entire world at once. It was specifically created in an attempt to find a good compromise to the problem of readily showing the whole globe as a flat image....
- Stereographic projectionStereographic projectionThe stereographic projection, in geometry, is a particular mapping that projects a sphere onto a plane. The projection is defined on the entire sphere, except at one point — the projection point. Where it is defined, the mapping is smooth and bijective. It is conformal, meaning that it...
- Dymaxion mapDymaxion mapThe Dymaxion map or Fuller map is a projection of a world map onto the surface of a polyhedron, which can be unfolded and flattened to two dimensions. The projection depicts the earth's continents as "one island," or nearly contiguous land masses. The arrangement heavily interrupts the map in order...
- Topographic mapTopographic mapA topographic map is a type of map characterized by large-scale detail and quantitative representation of relief, usually using contour lines in modern mapping, but historically using a variety of methods. Traditional definitions require a topographic map to show both natural and man-made features...
- Craig retroazimuthal projectionCraig retroazimuthal projectionThe Craig retroazimuthal map projection was created by James Ireland Craig in 1909. It is a cylindrical projection preserving the direction from any place to another, predetermined place while avoiding some of the bizarre distortion of the Hammer retroazimuthal projection...
- Hammer retroazimuthal projection
Physical sciences
- Free body diagramFree body diagramA free body diagram, also called a force diagram, is a pictorial representation often used by physicists and engineers to analyze the forces acting on a body of interest. A free body diagram shows all forces of all types acting on this body. Drawing such a diagram can aid in solving for the unknown...
- Greninger chartGreninger chartIn crystallography, a Greninger chart is a chart that allows angular relations between zones and planes in a crystal to be directly read from an x-ray diffraction photograph....
- Phase diagramPhase diagramA phase diagram in physical chemistry, engineering, mineralogy, and materials science is a type of chart used to show conditions at which thermodynamically distinct phases can occur at equilibrium...
- Wavenumber-frequency diagramWavenumber-frequency diagramA wavenumber–frequency diagram is a plot displaying the relationship between the wavenumber and the frequency of certain phenomena...
- Bode plotBode plotA Bode plot is a graph of the transfer function of a linear, time-invariant system versus frequency, plotted with a log-frequency axis, to show the system's frequency response...
- Nyquist plotNyquist plotA Nyquist plot is a parametric plot of a transfer function used in automatic control and signal processing. The most common use of Nyquist plots is for assessing the stability of a system with feedback. In Cartesian coordinates, the real part of the transfer function is plotted on the X axis. The...
- Dalitz plotDalitz plotThe Dalitz plot is a scatterplot often used in particle physics to represent the relative frequency of various manners in which the products of certain three-body decays may move apart....
- Feynman diagramFeynman diagramFeynman diagrams are a pictorial representation scheme for the mathematical expressions governing the behavior of subatomic particles, first developed by the Nobel Prize-winning American physicist Richard Feynman, and first introduced in 1948...
Business methods
- FlowchartFlowchartA flowchart is a type of diagram that represents an algorithm or process, showing the steps as boxes of various kinds, and their order by connecting these with arrows. This diagrammatic representation can give a step-by-step solution to a given problem. Process operations are represented in these...
- WorkflowWorkflowA workflow consists of a sequence of connected steps. It is a depiction of a sequence of operations, declared as work of a person, a group of persons, an organization of staff, or one or more simple or complex mechanisms. Workflow may be seen as any abstraction of real work...
- Workflow
- Gantt chartGantt chartA Gantt chart is a type of bar chart that illustrates a project schedule. Gantt charts illustrate the start and finish dates of the terminal elements and summary elements of a project. Terminal elements and summary elements comprise the work breakdown structure of the project. Some Gantt charts...
- Growth-share matrixGrowth-share matrixThe BCG matrix is a chart that had been created by Bruce Henderson for the Boston Consulting Group in 1968 to help corporations with analyzing their business units or product lines...
(often called BCG chart) - Work breakdown structureWork breakdown structureA work breakdown structure , in project management and systems engineering, is a deliverable oriented decomposition of a project into smaller components. It defines and groups a project's discrete work elements in a way that helps organize and define the total work scope of the project.A work...
- Control chartControl chartControl charts, also known as Shewhart charts or process-behaviour charts, in statistical process control are tools used to determine whether or not a manufacturing or business process is in a state of statistical control.- Overview :...
- Ishikawa diagramIshikawa diagramIshikawa diagrams are causal diagrams that show the causes of a certain event -- created by Kaoru Ishikawa . Common uses of the Ishikawa diagram are product design and quality defect prevention, to identify potential factors causing an overall effect...
- Pareto chart (often used to prioritise outputs of an Ishikawa diagramIshikawa diagramIshikawa diagrams are causal diagrams that show the causes of a certain event -- created by Kaoru Ishikawa . Common uses of the Ishikawa diagram are product design and quality defect prevention, to identify potential factors causing an overall effect...
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Conceptual analysis
- Mind mapping
- Concept mapping
- Conceptual graphConceptual graphConceptual graphs are a formalism for knowledge representation. In the first published paper on CGs, John F. Sowa used them to represent the conceptual schemas used in database systems...
- Entity-relationship diagram
Statistics
- Autocorrelation plot
- Bar chartBar chartA bar chart or bar graph is a chart with rectangular bars with lengths proportional to the values that they represent. The bars can be plotted vertically or horizontally....
- BiplotBiplotBiplots are a type of exploratory graph used in statistics, a generalization of the simple two-variable scatterplot. A biplot allows information on both samples and variables of a data matrix to be displayed graphically. Samples are displayed as points while variables are displayed either as...
- Box plotBox plotIn descriptive statistics, a box plot or boxplot is a convenient way of graphically depicting groups of numerical data through their five-number summaries: the smallest observation , lower quartile , median , upper quartile , and largest observation...
- Control chartControl chartControl charts, also known as Shewhart charts or process-behaviour charts, in statistical process control are tools used to determine whether or not a manufacturing or business process is in a state of statistical control.- Overview :...
- Forest plotForest plotA forest plot is a graphical display designed to illustrate the relative strength of treatment effects in multiple quantitative scientific studies addressing the same question. It was developed for use in medical research as a means of graphically representing a meta-analysis of the results of...
- Funnel plotFunnel plotA funnel plot is a useful graph designed to check the existence of publication bias in systematic reviews and meta-analyses. It assumes that the largest studies will be near the average, and small studies will be spread on both sides of the average...
- Galbraith plotGalbraith plotIn statistics, a Galbraith plot , is one way of displaying several estimates of the same quantity that have different standard errors....
- HistogramHistogramIn statistics, a histogram is a graphical representation showing a visual impression of the distribution of data. It is an estimate of the probability distribution of a continuous variable and was first introduced by Karl Pearson...
- Multidimensional scalingMultidimensional scalingMultidimensional scaling is a set of related statistical techniques often used in information visualization for exploring similarities or dissimilarities in data. MDS is a special case of ordination. An MDS algorithm starts with a matrix of item–item similarities, then assigns a location to each...
- np-chart
- p-chart
- Probability plotProbability plotIn statistics, a P-P plot is a probability plot for assessing how closely two data sets agree, which plots the two cumulative distribution functions against each other....
- Normal probability plotNormal probability plotThe normal probability plot is a graphical technique for normality testing: assessing whether or not a data set is approximately normally distributed....
- Normal probability plot
- Poincaré plotPoincaré plotA Poincaré plot, named after Henri Poincaré, is used to quantify self-similarity in processes, usually periodic functions. It is also known as a return map.Given a time series of the form...
- Probability plot correlation coefficient plotProbability plot correlation coefficient plotMany statistical analyses are based on distributional assumptions about the population from which the data have been obtained. However, distributional families can have radically different shapes depending on the value of the shape parameter. Therefore, finding a reasonable choice for the shape...
- Probability plot correlation coefficient plot
- Q-Q plotQ-Q plotIn statistics, a Q-Q plot is a probability plot, which is a graphical method for comparing two probability distributions by plotting their quantiles against each other. First, the set of intervals for the quantiles are chosen...
- RankitRankitIn statistics, rankits of a set of data are the expected values of the order statistics of a sample from the standard normal distribution the same size as the data. They are primarily used in the normal probability plot, a graphical technique for normality testing.-Example:This is perhaps most...
- Run chartRun ChartA run chart, also known as a run-sequence plot is a graph that displays observed data in a time sequence. Often, the data displayed represent some aspect of the output or performance of a manufacturing or other business process.- Overview :...
- Seasonal subseries plotSeasonal subseries plotSeasonal subseries plots are a tool for detecting seasonality in a time series. This plot allows one to detect both between-group and within-group patterns. This plot is only useful if the period of the seasonality is already known. In many cases, this will in fact be known. For example, monthly...
- Scatter plot
- Scree plot
- Ternary plotTernary plotA ternary plot, ternary graph, triangle plot, simplex plot, or de Finetti diagram is a barycentric plot on three variables which sum to a constant. It graphically depicts the ratios of the three variables as positions in an equilateral triangle...
- Recurrence plotRecurrence plotIn descriptive statistics and chaos theory, a recurrence plot is a plot showing, for a given moment in time, the times at which a phase space trajectory visits roughly the same area in the phase space...
- Waterfall chartWaterfall chartWaterfall Chart is a form of data visualization which helps in determining the cumulative effect of sequentially introduced positive or negative values. The waterfall chart is also known as a Flying Bricks Chart or Mario Chart due to the apparent suspension of columns in mid-air...
Other
- Ulam spiralUlam spiralThe Ulam spiral, or prime spiral is a simple method of visualizing the prime numbers that reveals the apparent tendency of certain quadratic polynomials to generate unusually large numbers of primes...
- NomogramNomogramA nomogram, nomograph, or abac is a graphical calculating device developed by P.E. Elyasberg, a two-dimensional diagram designed to allow the approximate graphical computation of a function: it uses a coordinate system other than Cartesian coordinates...
- Fitness landscapeFitness landscapeIn evolutionary biology, fitness landscapes or adaptive landscapes are used to visualize the relationship between genotypes and reproductive success. It is assumed that every genotype has a well-defined replication rate . This fitness is the "height" of the landscape...
- Weather mapWeather mapA weather map displays various meteorological features across a particular area at a particular point in time. Such maps have been in use since the mid-19th century and are used for research and weather forecasting purposes. Maps using isotherms show temperature gradients, which can help locate...
- Predominance diagramPredominance diagramthumb|200px|Predominance diagram for chromateA predominance diagram purports to show the conditions of concentration and pH where a chemical species has the highest concentration in solutions in which there are multiple acid-base equilibria. The lines on a predominance diagram indicate where...
- One-line diagramOne-line diagramIn power engineering, a one-line diagram or single-line diagram is a simplified notation for representing a three-phase power system. The one-line diagram has its largest application in power flow studies. Electrical elements such as circuit breakers, transformers, capacitors, bus bars, and...
- AutostereogramAutostereogramAn autostereogram is a single-image stereogram , designed to create the visual illusion of a three-dimensional scene from a two-dimensional image in the human brain...
- Edgeworth boxEdgeworth boxIn economics, an Edgeworth box, named after Francis Ysidro Edgeworth, is a way of representing various distributions of resources. Edgeworth made his presentation in his book Mathematical Psychics: An Essay on the Application of Mathematics to the Moral Sciences, 1881...
- Lineweaver-Burke diagram
- Eadie-Hofstee diagramEadie-Hofstee diagramIn biochemistry, an Eadie–Hofstee diagram is a graphical representation of enzyme kinetics in which reaction velocity is plotted as a function of the velocity vs...
- Population pyramidPopulation pyramidA population pyramid, also called an age structure diagram, is a graphical illustration that shows the distribution of various age groups in a population , which forms the shape of a pyramid when the population is growing...
- Parametric plot
- Causality loop diagram
- Ramachandran plotRamachandran plot-Introduction and early history:A Ramachandran plot , originally developed in 1963 by G. N. Ramachandran C. Ramakrishnan and V...
- V model
- Sentence diagramSentence diagramIn pedagogy, a sentence diagram is a pictorial representation of the grammatical structure of a natural-language sentence. A sentence diagram is a form of a parse tree.- History :...
- Tree diagramTree diagramThe term tree diagram refers to a specific type of diagram that has a unique network topology. It can be seen as a specific type of network diagram, which in turn can be seen as a special kind of cluster diagram.-Applications:...
- TreemappingTreemappingIn information visualization and computing, treemapping is a method for displaying hierarchical data by using nested rectangles.- Main idea :...
- Airfield traffic pattern diagramAirfield traffic patternAn airfield traffic pattern is a standard path followed by aircraft when taking off or landing, while maintaining visual contact with the airfield....