Editing Descriptive geometry (section)

{{Short description|Branch of geometry which allows the representation of three-dimensional objects in two dimensions}}
{{Multiple issues|
{{technical|date=January 2017}}
{{More citations needed|date=February 2011}}
}}
[[File:DALLA.GIF|thumb|Example of four different 2D representations of the same 3D object]]
{{multiple image
 | align = right | total_width=310
 | image1 = Raytraced JF compound.png
 | image2 = JF cube net.svg
 | footer = Example object and its six principal views
}}
{{multiple image
 | align = right | perrow = 1
 | image1 = Shed with conic dormer.png | width1 = 150
 | image2 = Shed with conic dormer.svg | width2 = 300
 | footer = Different [[orthographic projection]]s of a house. The file below shows three principal views and one that shows the true lengths in the plane of the roof. <small>(The [[cone|conic]] [[dormer]] shows parts of an [[ellipse]] and a [[hyperbola]].)</small>
}}
'''Descriptive 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]].<ref>{{Citation
|author=Joseph Malkevitch
|publisher=[[American Mathematical Society]]
|title=Mathematics and Art
|date=April 2003
|journal=Feature Column Archive
|url=https://www.ams.org/featurecolumn/archive/art1.html
}}
</ref>   The theoretical basis for descriptive geometry is provided by [[graphical projection|planar geometric projections]].  The earliest known publication on the technique was "Underweysung der Messung mit dem Zirckel und Richtscheyt" (''Observation of the measurement with the compass and spirit level''), published in Linien, Nuremberg: 1525, by [[Albrecht Dürer]]. Italian architect [[Guarino Guarini]] was also a pioneer of projective and descriptive geometry, as is clear from his ''Placita Philosophica'' (1665), ''Euclides Adauctus'' (1671) and ''Architettura Civile'' (1686—not published until 1737), anticipating the work of [[Gaspard Monge]] (1746–1818), who is usually credited with the invention of descriptive geometry.<ref>{{cite encyclopedia|title=Guarini, Guarino|encyclopedia=A Dictionary of Architecture|year=2015|publisher=[[Oxford University Press]]|editor=[[James Stevens Curl]]|isbn=9780198606789|url=https://books.google.com/books?id=jIWr0IO9dYIC&pg=PA337|page=337}}</ref><ref>{{cite journal|title=Stereotomy Role in Guarino Guarini's Space Research|last=Bianchini|first=Carlo|year=2012|journal=Nuts and Bolts of Construction History|volume=1|pages=257–263|isbn=978-2-7084-0929-3}}</ref> Gaspard Monge is usually considered the "father of descriptive geometry" due to his developments in geometric problem solving. His first discoveries were in 1765 while he was working as a draftsman for military fortifications, although his findings were published later on.<ref>{{Citation
|author=Ingrid Carlbom, Joseph Paciorek
|title=Planar Geometric Projections and Viewing Transformations
|volume=10
|pages=465–502
|date=December 1978
|doi=10.1145/356744.356750
|journal=[[ACM Computing Surveys]]
|issue=4
|citeseerx=10.1.1.532.4774
|s2cid=708008
}}</ref>

Monge's protocols allow an imaginary object to be drawn in such a way that it may be modeled in three dimensions.  All geometric aspects of the imaginary object are accounted for in true size/to-scale and shape, and can be imaged as seen from any position in space.  All images are represented on a two-dimensional surface.

Descriptive geometry uses the image-creating technique of imaginary, parallel projectors emanating from an imaginary object and intersecting an imaginary plane of projection at right angles. The cumulative points of intersections create the desired image.