In geometry, a Cartesian coordinate system in a plane is a coordinate system that specifies each point uniquely by a pair of real numbers called coordinates, which are the signed distances to the point from two fixed perpendicular oriented lines, called coordinate lines, coordinate axes or just axes of the system. The point where they meet is called the origin and has (0, 0) as coordinates.
Vector graphics are a form of computer graphics in which visual images are created directly from geometric shapes defined on a Cartesian plane, such as points, lines, curves and polygons. The associated mechanisms may include vector display and printing hardware, vector data models and file formats, as well as the software based on these data models. Vector graphics are an alternative to raster or bitmap graphics, with each having advantages and disadvantages in specific situations.
In geometry, two geometric objects are perpendicular if their intersection forms right angles at the point of intersection called a foot. The condition of perpendicularity may be represented graphically using the perpendicular symbol, ⟂. Perpendicular intersections can happen between two lines, between a line and a plane, and between two planes.
In geometry, a coordinate system is a system that uses one or more numbers, or coordinates, to uniquely determine the position of the points or other geometric elements on a manifold such as Euclidean space. The order of the coordinates is significant, and they are sometimes identified by their position in an ordered tuple and sometimes by a letter, as in "the x-coordinate". The coordinates are taken to be real numbers in elementary mathematics, but may be complex numbers or elements of a more abstract system such as a commutative ring. The use of a coordinate system allows problems in geometry to be translated into problems about numbers and vice versa; this is the basis of analytic geometry.
In mathematics, a stereographic projection is a perspective projection of the sphere, through a specific point on the sphere, onto a plane perpendicular to the diameter through the point. It is a smooth, bijective function from the entire sphere except the center of projection to the entire plane. It maps circles on the sphere to circles or lines on the plane, and is conformal, meaning that it preserves angles at which curves meet and thus locally approximately preserves shapes. It is neither isometric nor equiareal.
In vector computer graphics, CAD systems, and geographic information systems, geometric primitive is the simplest geometric shape that the system can handle. Sometimes the subroutines that draw the corresponding objects are called "geometric primitives" as well. The most "primitive" primitives are point and straight line segment, which were all that early vector graphics systems had.
A 3D projection is a design technique used to display a three-dimensional (3D) object on a two-dimensional (2D) surface. These projections rely on visual perspective and aspect analysis to project a complex object for viewing capability on a simpler plane.
In geometry and topology, the line at infinity is a projective line that is added to the real (affine) plane in order to give closure to, and remove the exceptional cases from, the incidence properties of the resulting projective plane. The line at infinity is also called the ideal line.
In mathematics, the real projective plane is an example of a compact non-orientable two-dimensional manifold; in other words, a one-sided surface. It cannot be embedded in standard three-dimensional space without intersecting itself. It has basic applications to geometry, since the common construction of the real projective plane is as the space of lines in R3 passing through the origin. The real projective plane is then an extension of the (ordinary) plane — to every point (v1,v2) of the ordinary plane, the line spanned by (v1,v2,1) is associated (i.e., the real projective plane is the projective completion of the ordinary plane, cf. also the homogeneous coordinates below) while there are also some “points in the infinity”.
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.
In geometry, a straight line, usually abbreviated line, is an infinitely long object with no width, depth, or curvature, an idealization of such physical objects as a straightedge, a taut string, or a ray of light. Lines are spaces of dimension one, which may be embedded in spaces of dimension two, three, or higher. The word line may also refer, in everyday life, to a line segment, which is a part of a line delimited by two points.
In geometry and science, a cross section is the non-empty intersection of a solid body in three-dimensional space with a plane, or the analog in higher-dimensional spaces. Cutting an object into slices creates many parallel cross-sections. The boundary of a cross-section in three-dimensional space that is parallel to two of the axes, that is, parallel to the plane determined by these axes, is sometimes referred to as a contour line; for example, if a plane cuts through mountains of a raised-relief map parallel to the ground, the result is a contour line in two-dimensional space showing points on the surface of the mountains of equal elevation.
Point plotting is an elementary mathematical skill required in analytic geometry. Invented by René Descartes and originally used to locate positions on military maps, this skill is now assumed of everyone who wants to locate grid 7A on any map.
The shapefile format is a geospatial vector data format for geographic information system (GIS) software. It is developed and regulated by Esri as a mostly open specification for data interoperability among Esri and other GIS software products. The shapefile format can spatially describe vector features: points, lines, and polygons, representing, for example, water wells, rivers, and lakes. Each item usually has attributes that describe it, such as name or temperature.
In geometry, a three-dimensional space is a mathematical space in which three values (coordinates) are required to determine the position of a point. Most commonly, it is the three-dimensional Euclidean space, that is, the Euclidean space of dimension three, which models physical space. More general three-dimensional spaces are called 3-manifolds. The term may also refer colloquially to a subset of space, a three-dimensional region, a solid figure.
A 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. The relative position and angle of the axes is typically uninformative, but various heuristics, such as algorithms that plot data as the maximal total area, can be applied to sort the variables (axes) into relative positions that reveal distinct correlations, trade-offs, and a multitude of other comparative measures.
The pinhole camera model describes the mathematical relationship between the coordinates of a point in three-dimensional space and its projection onto the image plane of an ideal pinhole camera, where the camera aperture is described as a point and no lenses are used to focus light. The model does not include, for example, geometric distortions or blurring of unfocused objects caused by lenses and finite sized apertures. It also does not take into account that most practical cameras have only discrete image coordinates. This means that the pinhole camera model can only be used as a first order approximation of the mapping from a 3D scene to a 2D image. Its validity depends on the quality of the camera and, in general, decreases from the center of the image to the edges as lens distortion effects increase.
In mathematics, a Euclidean plane is a Euclidean space of dimension two, denoted or . It is a geometric space in which two real numbers are required to determine the position of each point. It is an affine space, which includes in particular the concept of parallel lines. It has also metrical properties induced by a distance, which allows to define circles, and angle measurement.
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 computer. In the past, sometimes mechanical or electronic plotters were used. Graphs are a visual representation of the relationship between variables, which are very useful for humans who can then quickly derive an understanding which may not have come from lists of values. Given a scale or ruler, graphs can also be used to read off the value of an unknown variable plotted as a function of a known one, but this can also be done with data presented in tabular form. Graphs of functions are used in mathematics, sciences, engineering, technology, finance, and other areas.
A motion chart is a dynamic bubble chart which allows efficient and interactive exploration and visualization of longitudinal multivariate data. Motion charts provide mechanisms for mapping ordinal, nominal and quantitative variables onto time, 2D coordinate axes, size, colors, glyphs and appearance characteristics, which facilitate the interactive display of multidimensional and temporal data.
