53:
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45:
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223:). Thales also estimated the distances to ships at sea as seen from a clifftop by measuring the horizontal distance traversed by the line-of-sight for a known fall, and scaling up to the height of the whole cliff. Such techniques would have been familiar to the ancient Egyptians. Problem 57 of the
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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
52:
149:
and must be known. By determining the angles between the projection rays of the sensors and the basis, the intersection point, and thus the 3D coordinate, is calculated from the triangular relations.
913:
553:
282:(224–271) identified "measuring right angles and acute angles" as the fifth of his six principles for accurate map-making, necessary to accurately establish distances, while
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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
157:
929:
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921:
393:
255:. A detailed contemporary collection of constructions for the determination of lengths from a distance using this instrument is known, the
199:
The use of triangles to estimate distances dates to antiquity. In the 6th century BC, about 250 years prior to the establishment of the
513:
245:
the reciprocal of gradients as measured today. The slopes and angles were measured using a sighting rod that the Greeks called a
627:
219:. He measured the length of the pyramids' shadows and that of his own at the same moment, and compared the ratios to his height (
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Finding the position of a distant object B with the angles observed from points A and C and the baseline b between them
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293:) gives a version of the calculation above, for measuring perpendicular distances to inaccessible places.
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508:, Proceedings of a conference held July, 1997, Mathematisches Forschungsinstitut, Oberwolfach, Germany.
57:
468:
Science and
Civilization in China: Volume 3, Mathematics and the Sciences of the Heavens and the Earth
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270:–70 AD), which survived in Arabic translation; but the knowledge became lost in Europe until in 1615
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278:, reworked the technique for an attempt to measure the circumference of the earth. In China,
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and, in the military, the gun direction, the trajectory and distribution of fire power of
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measurements at known points, rather than measuring distances to the point directly as in
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This article is about measurement by the use of triangles. For other uses, see
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Thomas
Luhmann; Stuart Robson; Stephen Kyle; Jan Boehm (27 November 2013).
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119:; the use of both angles and distance measurements is referred to as
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367:[what is in the picture? (Answer: Triangulation Point)].
76:
is the process of determining the location of a point by forming
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Triangulation today is used for many purposes, including
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Geography and cartography in the medieval
Islamic world
48:
Estimating the height of a mountain using triangulation
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820:
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498:A Surveying Problem Travels from China to Paris
415:The Lives and Opinions of Eminent Philosophers
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8:
161:Measuring the height of a building with an
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531:
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385:Close-Range Photogrammetry and 3D Imaging
237:as the ratio of the run to the rise of a
227:, a thousand years earlier, defines the
365:"מה בתמונה? (תשובה: נקודת טריאנגולציה)"
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470:. Taipei: Caves Books Ltd. pp. 539–540
427:
7:
336:, covering a polygon with triangles
25:
628:Abu Muhammad al-Hasan al-Hamdani
80:to the point from known points.
27:Method of determining a location
251:, the forerunner of the Arabic
133:Triangulation (computer vision)
643:Khashkhash Ibn Saeed Ibn Aswad
211:to estimate the height of the
111:, triangulation involves only
32:Triangulation (disambiguation)
1:
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879:Mir Ahmed Nasrallah Thattvi
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931:Book of Roads and Kingdoms
923:Book of Roads and Kingdoms
130:
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36:
29:
496:Kurt Vogel (1983; 1997),
103:Triangulation (surveying)
828:Abd-al-Razzāq Samarqandī
434:: CS1 maint: location (
371:(in Hebrew). 2007-07-08.
203:, the Greek philosopher
37:Not to be confused with
324:Resection (orientation)
946:Kitab al-Rawd al-Mitar
833:Ghiyāth al-dīn Naqqāsh
502:Yvonne Dold-Samplonius
345:Wireless triangulation
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138:Computer stereo vision
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61:
49:
730:Abu'l Abbas al-Hijazi
207:is recorded as using
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58:triangulation station
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761:Ibn Said al-Maghribi
412:, "Life of Thales",
274:, after the work of
142:optical 3D measuring
1023:Elementary geometry
965:The Meadows of Gold
582:Abu Hanifa Dinawari
506:From China to Paris
369:Jeepolog.com forums
1028:Euclidean geometry
802:Hamdallah Mustawfi
725:Muhammad al-Idrisi
699:Mahmud al-Kashgari
623:Abu Zayd al-Balkhi
261:Hero of Alexandria
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127:In computer vision
94:
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60:signed by iron rod
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869:Sulaiman Al Mahri
689:Abu Saʿīd Gardēzī
668:Qudama ibn Ja'far
592:Sulaiman al-Tajir
410:Diogenes Laërtius
395:978-3-11-030278-3
303:Direction finding
221:intercept theorem
209:similar triangles
201:Ptolemaic dynasty
121:triangulateration
16:(Redirected from
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953:Mu'jam Al-Buldan
939:Tabula Rogeriana
933:(ibn Khordadbeh)
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613:Ahmad ibn Rustah
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18:Triangulating
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739:13th century
713:12th century
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658:Al-Muqaddasi
653:Ibn al-Faqih
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420:, retrieved
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276:Eratosthenes
256:
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163:inclinometer
146:
136:
106:
97:In surveying
84:Applications
73:
66:trigonometry
63:
807:Ibn Battuta
787:Al-Dimashqi
570:9th century
562:Geographers
453:In Euclidem
1012:Categories
987:Influences
925:(al-Bakrī)
792:Abu'l-Fida
746:Ibn Jubayr
648:Ibn Hawqal
422:2008-02-22
351:References
340:Trig point
329:Stereopsis
291: 263
182:astrometry
174:navigation
997:(Ptolemy)
995:Geography
884:Amīn Rāzī
874:Piri Reis
684:Al-Biruni
633:Al-Masudi
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170:surveying
109:surveying
78:triangles
843:Zheng He
720:al-Zuhri
694:Al-Bakri
638:Istakhri
466:(1986).
430:citation
319:Parallax
297:See also
272:Snellius
213:pyramids
70:geometry
853:Fei Xin
848:Ma Huan
704:Domiyat
587:Ya'qubi
504:(ed.),
480:Liu Hui
449:Proclus
418:, I, 27
284:Liu Hui
280:Pei Xiu
257:Dioptra
253:alidade
248:dioptra
194:weapons
153:History
812:Lin Nu
512:
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205:Thales
1018:Angle
959:Rihla
914:Works
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234:seked
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510:ISBN
436:link
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