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Triangulation
In trigonometry and geometry, triangulation is the process of determining the location of a point by forming triangles to the point from known points. Applications In surveying Specifically in surveying, triangulation involves only angle measurements at known points, rather than measuring distances to the point directly as in trilateration; the use of both angles and distance measurements is referred to as triangulateration. In computer vision Computer stereo vision and optical 3D measuring systems use this principle to determine the spatial dimensions and the geometry of an item. Basically, the configuration consists of two sensors observing the item. One of the sensors is typically a digital camera device, and the other one can also be a camera or a light projector. The projection centers of the sensors and the considered point on the object's surface define a (spatial) triangle. Within this triangle, the distance between the sensors is the base ''b'' and must be kn ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Triangle
A triangle is a polygon with three corners and three sides, one of the basic shapes in geometry. The corners, also called ''vertices'', are zero-dimensional points while the sides connecting them, also called ''edges'', are one-dimensional line segments. A triangle has three internal angles, each one bounded by a pair of adjacent edges; the sum of angles of a triangle always equals a straight angle (180 degrees or π radians). The triangle is a plane figure and its interior is a planar region. Sometimes an arbitrary edge is chosen to be the ''base'', in which case the opposite vertex is called the ''apex''; the shortest segment between the base and apex is the ''height''. The area of a triangle equals one-half the product of height and base length. In Euclidean geometry, any two points determine a unique line segment situated within a unique straight line, and any three points that do not all lie on the same straight line determine a unique triangle situated w ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Willebrord Snellius
Willebrord Snellius (born Willebrord Snel van Royen) (13 June 158030 October 1626) was a Dutch astronomer and mathematician, commonly known as Snell. His name is usually associated with the law of refraction of light known as Snell's law. The lunar crater Snellius (crater), Snellius is named after Willebrord Snellius. The Royal Netherlands Navy has named three survey ships after Snellius, including a HNLMS Snellius (A802), currently-serving vessel. Biography Willebrord Snellius was born in Leiden, Netherlands. In 1613 he succeeded his father, Rudolph Snellius, Rudolph Snel van Royen (1546–1613) as professor of mathematics at the University of Leiden. Surveying In 1615, Snellius, after the work of Eratosthenes in Ptolemaic Kingdom, Ptolemaic Egypt in the 3rd century BC, probably was the first to use triangulation (surveying), triangulation to do a large-scale arc measurement for determining the Earth radius, circumference of the earth. He was helped in his measureme ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Triangulation
In trigonometry and geometry, triangulation is the process of determining the location of a point by forming triangles to the point from known points. Applications In surveying Specifically in surveying, triangulation involves only angle measurements at known points, rather than measuring distances to the point directly as in trilateration; the use of both angles and distance measurements is referred to as triangulateration. In computer vision Computer stereo vision and optical 3D measuring systems use this principle to determine the spatial dimensions and the geometry of an item. Basically, the configuration consists of two sensors observing the item. One of the sensors is typically a digital camera device, and the other one can also be a camera or a light projector. The projection centers of the sensors and the considered point on the object's surface define a (spatial) triangle. Within this triangle, the distance between the sensors is the base ''b'' and must be kn ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Surveying
Surveying or land surveying is the technique, profession, art, and science of determining the land, terrestrial Plane (mathematics), two-dimensional or Three-dimensional space#In Euclidean geometry, three-dimensional positions of Point (geometry), points and the Euclidean distance, distances and angles between them. These points are usually on the surface of the Earth, and they are often used to establish maps and boundaries for ownership, locations, such as the designated positions of structural components for construction or the surface location of subsurface features, or other purposes required by government or civil law, such as property sales. A professional in land surveying is called a land surveyor. Surveyors work with elements of geodesy, geometry, trigonometry, regression analysis, physics, engineering, metrology, programming languages, and the law. They use equipment, such as total stations, robotic total stations, theodolites, Satellite navigation, GNSS receivers, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Optical 3D Measuring
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. Motivation and applications The research of 3D reconstruction has always been a difficult goal. By Using 3D reconstruction one can determine any object's 3D profile, as well as knowing the 3D coordinate of any point on the profile. The 3D reconstruction of objects is a generally scientific problem and core technology of a wide variety of fields, such as Computer Aided Geometric Design ( CAGD), computer graphics, computer animation, computer vision, medical imaging, computational science, virtual reality, digital media, etc. For instance, the lesion information of the patients can be presented in 3D on the computer, which offers a new and accurate approach in diagn ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Seked
Seked (or seqed) is an ancient Egyptian term describing the inclination of the triangular faces of a right pyramid. The system was based on the Egyptians' length measure known as the Cubit#Ancient Egyptian royal cubit, royal cubit. It was subdivided into seven ''palms'', each of which was sub-divided into four ''digits''. The inclination of measured slopes was therefore expressed as the number of horizontal palms and digits relative to each royal cubit rise. The seked is proportional to the reciprocal of our modern measure of slope or gradient, and to the Trigonometric functions, cotangent of the angle of elevation.Gillings: Mathematics in the Time of the Pharaohs 1982: pp 212 Specifically, if ''s'' is the seked, ''m'' the slope (rise over run), and \phi the angle of elevation from horizontal, then: :s = \frac = 7\cot(\phi). The most famous example of a seked slope is of the Great Pyramid of Giza in Egypt built around 2550 BC. Based on modern surveys, the faces of this monument ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Computer Stereo Vision
Computer stereo vision is the extraction of 3D information from digital images, such as those obtained by a CCD camera. By comparing information about a scene from two vantage points, 3D information can be extracted by examining the relative positions of objects in the two panels. This is similar to the biological process of stereopsis. Outline In traditional stereo vision, two cameras, displaced horizontally from one another, are used to obtain two differing views on a scene, in a manner similar to human binocular vision. By comparing these two images, the relative depth information can be obtained in the form of a disparity map, which encodes the difference in horizontal coordinates of corresponding image points. The values in this disparity map are inversely proportional to the scene depth at the corresponding pixel location. For a human to compare the two images, they must be superimposed in a stereoscopic device, with the image from the right camera being shown to the obs ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Alidade
An alidade () (archaic forms include alhidade, alhidad, alidad) or a turning board is a device that allows one to sight a distant object and use the line of sight to perform a task. This task can be, for example, to Triangulation (surveying), triangulate a scale map on site using a plane table drawing of intersecting lines in the direction of the object from two or more points or to measure the angle and horizontal distance to the object from some reference point's Polar coordinate system, polar measurement. Angles measured can be horizontal, vertical or in any chosen plane. The alidade sighting ruler was originally a part of many types of scientific and astronomical instrument. At one time, some alidades, particularly using Graduation (instrument), circular graduations as on astrolabes, were also called ''diopters''. With modern technology, the name is applied to complete instruments such as the 'plane table alidade'. Origins The word in Arabic (, , ), signifies the same de ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Dioptra
A dioptra (sometimes also named dioptre or diopter, from ) is a classical astronomical and surveying instrument, dating from the 3rd century BC. The dioptra was a sighting tube or, alternatively, a rod with a sight at both ends, attached to a stand. If fitted with protractors, it could be used to measure angles. Use Greek astronomers used the dioptra to measure the positions of stars; both Euclid and Geminus refer to the dioptra in their astronomical works. It continued in use as an effective surveying tool. Adapted to surveying, the dioptra is similar to the theodolite, or surveyor's transit, which dates to the sixteenth century. It is a more accurate version of the groma. There is some speculation that it may have been used to build the Eupalinian aqueduct. Called "one of the greatest engineering achievements of ancient times," it is a tunnel long, excavated through a mountain on the Greek island of Samos during the reign of Polycrates in the sixth century B ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Slope
In mathematics, the slope or gradient of a Line (mathematics), line is a number that describes the direction (geometry), direction of the line on a plane (geometry), plane. Often denoted by the letter ''m'', slope is calculated as the ratio of the vertical change to the horizontal change ("rise over run") between two distinct points on the line, giving the same number for any choice of points. The line may be physical – as set by a Surveying, road surveyor, pictorial as in a diagram of a road or roof, or Pure mathematics, abstract. An application of the mathematical concept is found in the grade (slope), grade or gradient in geography and civil engineering. The ''steepness'', incline, or grade of a line is the absolute value of its slope: greater absolute value indicates a steeper line. The line trend is defined as follows: *An "increasing" or "ascending" line goes from left to right and has positive slope: m>0. *A "decreasing" or "descending" line goes from left to right ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Thales
Thales of Miletus ( ; ; ) was an Ancient Greek philosophy, Ancient Greek Pre-Socratic philosophy, pre-Socratic Philosophy, philosopher from Miletus in Ionia, Asia Minor. Thales was one of the Seven Sages of Greece, Seven Sages, founding figures of Ancient Greece. Beginning in eighteenth-century historiography, many came to regard him as the first philosopher in the Greek philosophy, Greek tradition, breaking from the prior use of mythology to explain the world and instead using natural philosophy. He is thus otherwise referred to as the first to have engaged in mathematics, History of science#Pre-socratics, science, and deductive reasoning. Thales's view that all of nature is based on the existence of a Arche, single ultimate substance, which he Theory, theorized to be Water (classical element), water, was widely influential among the philosophers of his time. Thales thought the Earth floated on water. In mathematics, Thales is the namesake of Thales's theorem, and the interc ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hero Of Alexandria
Hero of Alexandria (; , , also known as Heron of Alexandria ; probably 1st or 2nd century AD) was a Greek mathematician and engineer who was active in Alexandria in Egypt during the Roman era. He has been described as the greatest experimentalist of antiquity and a representative of the Hellenistic scientific tradition. Hero published a well-recognized description of a steam-powered device called an '' aeolipile'', also known as "Hero's engine". Among his most famous inventions was a windwheel, constituting the earliest instance of wind harnessing on land. In his work ''Mechanics'', he described pantographs. Some of his ideas were derived from the works of Ctesibius. In mathematics, he wrote a commentary on Euclid's ''Elements'' and a work on applied geometry known as the ''Metrica''. He is mostly remembered for Heron's formula; a way to calculate the area of a triangle using only the lengths of its sides. Much of Hero's original writings and designs have been lost, bu ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
