American Journal of Engineering, Science and Technology (AJEST) Volume 7, 2021

A New in Perspective New Technique Debating Old Hand-Drawing Perspective Methods Taught in Schools of Architecture

Yasser O. El-Gammal, Saudi Arabia

Abstract This paper introduces a new technique in hand-drawing perspective that is more convenient for students, instructors, and architectural design professionals - than the difficulties associated with old hand drawing methods taught in schools of architecture. The paper starts with an overview exploring origins and fundamental concepts of perspective drawing in an attempt to find a better approach in perspective drawing by investigating the works of ancient artists and painters, Afterwards; The paper proceeds with debating older perspective drawing methods taught in schools of architecture through exploring both students and instructors opinions about disadvantages of the old methods, and the recent trends in teaching perspective drawing. At the end, the paper introduces the concept of the suggested new method, its relationship with the magnification factor option in the AutoCAD universe, and its advantages, together with some early experimentation Keywords: Perspective Sketching, Perspective Drawing Method, Perspective Drawing Techniques

PROBLEM Students learning perspective hand drawing in schools of architecture find old drawing methods very tedious, time consuming, and end up with unsatisfactory results, not to mention the difficulty they experience when setting the building perspective scene measurements into scale, and from within too many drawing construction lines. Although both undergraduates and architects nowadays are heavily depending on 3Dimensional computer software for developing accurate perspective scenes; There will always still the need for using perspective hand-drawing; Since every architectural concept starts with a hand-drawn sketch. The cognitive design process works at brain speed is usually faster than drafting and designing simultaneously when using computer aided applications like AutoCAD and/or conventional 3D modeling software applications.

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On the other hand, instructors too have their own issues with these old methods, they find such techniques exhausting when trying to follow-up a students' work, never to mention the difficulty they experience in grading. As a whole, both students and instructors claim that once such old methods were learned, they never use them again in practice.

LITERATURE REVIEW Research findings expected to improve quality of the students' perspective drawings with respect to effort and time consumed in producing and grading their drawings

RESEARCH GOAL The goal of this paper is to investigate the possibility of introducing a perspective drawing technique that is more convenient for both students and instructors of architecture through suggesting a new perspective drawing technique called "The Scale Magnification Method" while keeping the resulted scene in proportion

RESEARCH SCOPE The research paper is focusing on debating the most two commonly known methods of perspective drawing among architects, which are: "The Proximity Method", and "The Building Plan (Footprint) Method", The research work introduced in this paper represents an attempt to investigate the possibility of creating a simpler new perspective drawing method that may reduce the complexities of these two methods. Exploring perspective drawing methods other than these two methods are not within the scope of this research paper

METHODOLOGY AND PHASES For the research paper to fulfill its goals; it starts with a quick overview exploring two of the most widely practiced perspective drawing techniques in ancient civilizations, and medieval times. The purpose of this section of the paper is to search for simpler perspective drawing techniques in older times that might be used instead of the debated complicated methods.

The second phase in this paper discusses both the "Proximity", and the "Building Plan (Footprint)" methods taught in schools of architecture, and introducing both the students and instructors opinions about such methods. The last section of the paper introduces the new suggested method.

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American Journal of Engineering, Science and Technology (AJEST) Volume 7, 2021

DISCUSSION OVERVIEW "Perspective" is originating from the Latin word: "Perspicere" which means "To see through". It is an approximate representation of the image seen by the human eyes on a flat surface such as a paper or a drawing board. The main characteristics of perspective drawing is that objects that are near to the eye of the observer are drawn in a scale that is larger than those that are at further distances from the same point of observation.

Fig. (1): Is a schematic explaining how real life objects are projected on 2Dimensional Surfaces and the eyes of an observer Source: (Researcher)

ANCIENT PERSPECTIVE DRAWING TECHNIQUES FORESHORTENING Is a simple technique for creating the illusion that the observed objects are extended into depth in space. To explain "Foreshortening"; Imagine there are some 3Dimensional objects in nature that are grouped at distances from each other, and that each of them is represented by a drawing in a separate board or a transparent sheet paper that is placed at the exact distance of its drawn object.

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When looking from an angle of view that is almost perpendicular to all these transparent sheets together, they will appear as a collective of all images stacked behind each other, where objects at further distances are drawn in smaller scales while nearer ones are drawn in larger scales.

Fig. (2): Is a schematic explaining the "Foreshortening" drawing technique. Source: (Researcher)

"Foreshortening" has been widely practiced by medieval artists, this is clear in renaissance paintings, and the interior architecture in the churches of medieval Europe. The technique is also used by today's modern artists of comic arts.

Fig. (3): Left: Shows a Foreshortened painting of Christ, "The Mourning over the Dead Christ", The SCALA/Art. Middle: Shows use of foreshortening in comic arts. Right: Shows use of foreshortening in the interior architecture of a medieval church. Source: (Guerrero Tony, 2012), (Satyavrat Nirala, Blumberg Naomi, 2015), (Boundless, 2017)

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American Journal of Engineering, Science and Technology (AJEST) Volume 7, 2021

VERTICAL PERSPECTIVE Ancient civilizations like Egypt and many other communities in South America, and Africa draw major events, characters, and social practices through stacking the drawn topics in a vertical manner; by sizing royal, social, and community public figures hierarchically according to their spiritual, and social status, and not according to their distances from the viewer. Royal figures or masters are drawn in a larger scale and placed on top of their servants, slaves, and/or people that are lower in the social status. In General, most ancient civilizations were following the same drawing pattern instead of "Foreshortening", they developed the "Vertical perspective" technique. (Bowling Frank, Clark Ed, Pindell Howardena, 2016), (Edwards Amelia, 1891), (Edwards Amelia, 1891)

Fig. (4): Left: Is a wooden yellow Egyptian wall art canvas showing servants drawn in bottom, while their masters are drawn at a larger scale and on top. Right: Shows the ancient Egyptian "Procession of the negroes", from a wall- painting in the tomb of "HUI" at "EL KAB", reproduced from a photograph by Mr. W. M. Flinders Petrie. Source: (Bowling Frank, Clark Ed, Pindell Howardena, 2016), (Edwards Amelia, 1891)

DEBATING OLDER PERSPECTIVE DRAWING METHODS TAUGHT IN SCHOOLS OF ARCHITECTURE In architecture; most common perspective drawings fall between two "Sceneries"; The "Human level (Eye level)" scenes, and the "Arial level (Bird eye level)" scenes, regardless the type of perspective used or projection angles of the scenery. For a long time in architecture schools; some methods are practiced in perspective drawing yielding into what may be called a "Relative" expression of the drawn building figure. In general, the common characteristics of all these old techniques are "Approximation". The following argument is debating older perspective drawing methods used in the architecture design studio from both the students and instructors point of views

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FIRST: THE PROXIMITY METHOD In this method, the positions of the two vanishing points (V1), and (V2), were "Randomly" located on the "Horizon line", the distance between the two vanishing points is then "Equally" divided by a point (M1) that will be later used as a leader point for locating "Real measurements" on another horizontal line called "Ground line". Then, again; the distance between (M1) and (V2) is "Equally" divided by a "Vertical line". This vertical line, and according to this method is suggested to be fallen in a "Plane" where the final image will be generated. It is also suggesting that this "Plane" represents the image falling on the "Eyesight" of the observer. Then, the final division step is "Equally" dividing the distance between the vertical line and the (V2) by a point (M2) that will be also used as a leader point for locating "Real measurements" on the "Ground line"

Fig. (5): A schematic explaining old perspective drawing "Proximity Method", Source: (Researcher)

SECOND: THE BUILDING PLAN (FOOTPRINT) METHOD This method uses the projected plan of a building. The later is drawn with any "Scaled" dimensions and rotated at a specified angle of choice either (300/600 or 450) around a "Horizontal datum" touching the "Vertex" of the building plan, then; the two sides of the building plan are extended until intersecting with an "Imaginary Horizontal line". In this method, it is not clear whether this horizontal line represents the projection of the plane where the image will be generated or the plane of sight. It is also not clear whether the distance of this imaginary

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American Journal of Engineering, Science and Technology (AJEST) Volume 7, 2021 horizontal line represents the distance between the projected building and the eye of the observer. Afterwards; A rotation of both sides of the building is transformed up to the "Datum line" creating two points of measurements (M1) and (M2) that will be used as leader points for locating "Real measurements" on another horizontal line called "Ground line" that is falling at an "Unspecified Distance" between the datum line touching the plan of the building "Vertex", and the "Horizon line" of sight. Finally, two points generated from the extension of building sides, and another two points generated from the rotated building sides, all four are transformed to the "Horizon line" to be used as vanishing and measurement points respectively.

Fig. (6): A schematic explaining old perspective drawing "Building Plan Method", Source: (Researcher) "" NOTES ON PERSPECTIVE DRAWING In his notes for the analysis of perspective distortions; "Leonardo Da Vinci" did not like the exaggerated apparent size of the perspective grid when it reaches the ground line of the image plane. He recommended drawing the object as it appears from a distance of (3 to 10) times its actual dimensions in order to eliminate distortion in the perspective scene. (Mcovey Bruce, 2015)

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Fig. (7): Is a schematic trying to explain the mathematical increment of selecting points (M1), and (M2) as they represent the intersection of the circular boundaries of an imaginary cone of vision with the plane of sight that is not exceeding the distortion limit of the Generated picture. Source: (Mcovey Bruce, 2015)

"ZEEMAN'S PARADOX" "Zeeman's Paradox" assumes that a perspective scene is viewed the same way as it is viewed by the retina of the human eye. That is; in the form of a two dimensional drawing. Renaissance and Baroque artists who adopted "Zeeman's" assumption understood that perspective drawings are effective even when they are not viewed from the center of projection. (Dixon R, 1991)

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American Journal of Engineering, Science and Technology (AJEST) Volume 7, 2021

Fig. (8): A Schematic explaining "Zeeman's paradox". Source: (Dixon R, 1991)

INSTRUCTORS OPINIONS ABOUT THE OLD METHODS ● These methods are very exhausting to the instructor when trying to follow-up a students' work. ● Instructors find some difficulty attaining the level of quality of one students' work compared to another which in terms leads in most cases to un-accurate grading due to many construction lines hiding the final sketch of the building subject matter. ● In terms of mathematics; There is no specific mathematical relationship or algorithm explaining the division increments between both vanishing and measurement points used in these methods, neither explaining how the distance between the "Ground line", and the "Horizon line" is defined, how the angle of vision is selected (Although the issue of the angle of vision is slightly solved in the building plan method - the distance between the eye of the observer or the observation plan and the building vertex is still not correctly defined), and/or how the height of the observer's eye is defined.

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● There is no guarantee that the "End-result" dimensions of the building in the perspective scene is relatively proportional to its real dimension in nature ● The scale of the building drawing in the generated perspective scene cannot be identified. ● Instructors claim that once students learn this method, they never use it again when creating hand drawn perspective sketching.

STUDENTS OPINIONS ABOUT THE OLD METHODS ● Students should go through too many steps until a single perspective sketch is finished ● Students find these methods difficult, exhausting, complicated, and have to draw many construction lines, until they finally manage to have the perspective of the building as an end result of their effort, which in most cases; turns to be unsatisfactory and cannot appear from down-under such too many construction lines ● Students find these methods very time consuming, it takes hours until the perspective sketch of the building is finished only, while "A sketch is a sketch"; Its main characteristics is that it is fast in nature and not inclined into details. And never to mention the extra time and effort that will be added to draw the entourage elements around the building ● Students expressed their preferring to save their time and effort for design thinking rather than consuming in creating a perspective sketch that should be done much faster and in a simpler manner. ● The worst thing that the students find (From their point of view) is the "Lack of magnification" in relation to sheet size and dimensions, in other words; the size and dimensions of the resulted perspective of the building is relatively small compared to the size and the dimensions of the rest of the wider area of the drawing sheet. Since the two vanishing points usually fall on the extreme opposite edges of the drawing sheet. Such problem requires that the student should take the drawn perspective and magnify the sheet over a photocopier machine in order to have an adequate capture of the building final scene on the final rendered drawing sheet ● Students admit that once they learn these methods they never use them again which makes them feel that learning such methods is useless, unpractical, and a great time waste

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American Journal of Engineering, Science and Technology (AJEST) Volume 7, 2021

Fig. (9): Left: Shows a simple staircase in perspective drawn with too many construction lines. Right: Shows lack of magnification of the produced perspective of the building in relation to sheet size and dimensions as a result of using the old perspective drawing methods. The artist had to draw a frame around the drawn building that is far from the sheet two extreme sides in order To focus the eye of the observer on the building and reduce the size and time consumed in the Work of entourage. Source: (Wikipedia, 2018), (Mcovey Bruce, 2015)

RECENT TRENDS IN TEACHING PERSPECTIVE DRAWING Recently, at the university and college education levels, instructors teaching perspective drawing tend to free themselves from applying classical approaches and using old methods due to the complications mentioned above.

For example; In "ARCH 202 Architectural Graphics and Elements of Design (6 credits)", and "ARCH 221 Architectural Drawing (2 credits)"; Two of the most recognized courses taught in the school of architecture at McGill University in Montreal, Canada, as part of both their Bachelor of Science (B.Sc.) and Masters of Science (M.Sc.) in Architecture.

Students are required to draw a perspective scene from a site visit to a building or a city- scape on their own, and by any means or methods they feel easy to use, and of comfort to them.

This is in addition to their practice of isometric, axonometric, and oblique projection drawings. (McGill Arch 202, 2012), (McGill Arch 221, 2015), (Jamilla, 2015) 11

Fig. (10): A schematic showing exercises of perspective drawing from the portfolio of a McGill University architecture student, where the two perspective scenes were fully drawn in a Very simple manner; by just using vanishing points only, Source: (Jamilla, 2015)

BIRTH OF THE IDEA, THE CONCEPT OF THE SUGGESTED NEW METHOD, AND ITS RELATIONSHIP WITH THE MAGNIFICATION FACTOR OPTION OF THE AUTOCAD UNIVERSE Whether perspective drawing instructors restrict to the old techniques with all its disadvantages and complications, or use more simple techniques; Both "Old" and "Free" methods generate an "Approximated - perspective drawing pattern" of the building scene with no defined drawing "Scale".

The suggested new method is based on combining two concepts; A much simpler derivation from the hand perspective drawing old methods, and the "Magnification factor function applied in perspective views generated inside the AutoCAD universe. The suggested new method is shifting the pattern of hand-drawn perspective to focus on resolving the two major disadvantages of the old methods which are: "Excessive drawing steps", and the "Magnification scale factor" of the drawn perspective. To create a perspective scene of a 3Dimensional object in AutoCAD, the (DVIEW) command is activated with the following argument:

"Select Objects": A command line string with the following parameters: [ ] "CAmera/TArget/Distance/POints/PAn/Zoom/TWist/CLip/Hide/Off/Undo/

Each of the above arguments sets a specific parameter of the perspective view, the most important of all are the "Camera", and the "Zoom" parameters. When the "Camera" option is activated; It opens a substring with camera parameters; (New camera/target distance <000.0000>:) for adding a new camera and specifying distance between the eye of the observer

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American Journal of Engineering, Science and Technology (AJEST) Volume 7, 2021 and the 3Dimenaional object in a perspective scene. "Changing the (Scale) of the drawn perspective according to the boundaries of the view", (Watson David, 2017), (Lynda, 2013)

Fig. (11): Showing how cameras are added to generate a perspective View of a building in AutoCAD. Source: (Lynda, 2013)

EXPLANATION OF THE NEW SUGGESTION: "THE SCALE MAGNIFICATION METHOD" The suggested method assumes that a cone of vision is radiating from a "Stationary point" with its circular base falling on an imaginary plane formed by two intersecting lines; The first line is a horizontal line (AB) where all measurements of the "Real widths of the building components" will be taken as a "True horizontal measurement", and the second line is a vertical line (CD) where all measurements of the "Real heights of the building components" will be taken as a "True vertical measurement".

All measurements taken on both the true horizontal and true vertical lines will be derivations of a common drawing scale factor; e.g. 1:50, 1:100, 1:200, etc. The formed (ABCD) plane is 13

"Perfectly parallel" to the plane of sight or the retinal plane of the eye of an observer facing the "Stationary point" but this time in its opposite direction like a mirror.

The intersection point of both (AB) and (CD) lying in the assumed plane represents the "True edge point" of the building "Touching" the (ABCD) plane. While according to this suggested visual formula; (ABCD) plane is the place in the overall scene where all "Real dimensions of both horizontal and vertical building components will be residing". Whilst, the generated perspective scene will exist in another imaginary plane residing behind such "True" (ABCD) plane.

The radius of the circular conical base (With its center point is the intersection between the true vertical line and the horizon line) - "Equally" divides both the "Horizon line", and the "True vertical line of measurement".

This basic division is suitable for generating (450) perspective sceneries. Adding an "Extension" (To the horizon line) that is "Equal" in length to the "Radius" of the circular base of the cone in either directions is the required extension for generating (300/600) perspective sceneries. For a (450) perspective scene; the two vanishing points are placed on the intersection points of the perimeter of the circle with the horizon line. For a (300/600) perspective scene; either of the vanishing points is moved to be placed at the end of the extended horizon line according to the above suggestion.

Distortion in the vertical direction will be falling beyond the points (C), and (D). And in this case; The "True horizontal measurement line" represents the datum where the vertex of the building base will be touching.

For shifting between a "Bird eye" and "Human eye" scenes, the height of the eye of the observer will be proportionally measured to scale from the intersection point of the "True horizontal and true vertical lines" together with all other real heights for the rest of the building components.

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American Journal of Engineering, Science and Technology (AJEST) Volume 7, 2021

Fig. (12): Explaining the (Scale Magnification) - new Method. Source: (Researcher)

All "Scaled" dimensions measured on the "True horizontal line" will create horizontal perspective grid(s) to be used for drawing footprints of all the building stories, while all "Scaled" dimensions measured on the "True vertical line" will create vertical perspective grid(s) to be used for drawing all the building facades and their details

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Fig. (13): Showing the measurement (Horizontal - base perspective grid) generated From the (Scale Magnification) - new Method. Source: (Researcher)

Fig. (14): Showing the measurement (Vertical - base perspective grid) generated From the (Scale Magnification) - new Method. Source: (Researcher)

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American Journal of Engineering, Science and Technology (AJEST) Volume 7, 2021

ADVANTAGES OF THE NEW METHOD ● Number of steps are minimized, and less time is consumed ● This method can be easily mastered and reused by students ● Less construction lines are created. This method creates two perspective grids; One horizontal and the other is vertical where illustrators will be able to generate the full perspective scene from the horizontal and the vertical profiles of the building only, and without the need to draw too many construction lines ● It facilitates Easy composition of the surrounding entourage in order to complete the scene ● Easy assessment of students' work by instructors ● Dimension proximities are based on direct scale factor conversions from real nature object proportions and dimensions to drawing sheet - mimicking AutoCAD behavior - where intermediate measuring points (M1), and (M2) are no longer required, since measurement rulers are directly transformed to a "True horizontal" and a "True vertical" lines that are in terms falling in a "True plane" which is typically parallel to the observer's eye and plane of vision; thus creating less errors. ● However, Illustrators who will be using this method should keep in mind that for generating perspective scenes with scaling factors proportional to object dimensions; It is assumed that the "Projection" of the eye of the observer should stay moving inside the plane formed by points (ABCD) of the true lines of dimensions, and that they are in fact imitating the effect of changing between different camera lenses - (When shifting between 300/600 and 450 scenes) - while the distance between the eye of the observer (Or the camera in this case) - and the edge of the object falling on the true plane of dimension remains fixed ● This method agrees with "Leonardo Da Vinci's" dislikes about the perspective distortions created by the classical methods including painter foreshortening techniques. As he also recommended painting an object according to its magnification factor and not based on derivative dimensions of the projected object parts. ● This method is also compatible with "Zeeman's Paradox", since he excludes all the dynamic aspects of visual experience and limits the problem to a "Stationary point". The viewer takes in visual rays only from a fixed location in space, in a fixed posture (Including both body position and orientation of the head), and facing in a fixed direction (With a fixed position of the eye or eyes), where "Zeeman" sees a "Stationary point" as the fundamental premise of a perspective drawing.

EARLY EXPERIMENTATIONS The following figures are showing different examples of both Exterior-bird eye, and Interior-human eye perspective sketches generated by using the suggested "Scale Magnification method". Drawings obtained from the researcher undergraduate old architecture student sketchbook of perspective exercises

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Fig. (15): A Schematic of an "Exterior bird eye perspective" generated by using the suggested "Scale Magnification method". Source: (Researcher)

Fig. (16): A Schematic of an "Exterior bird eye perspective" generated by using the suggested "Scale Magnification method". Source: (Researcher)

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American Journal of Engineering, Science and Technology (AJEST) Volume 7, 2021

Fig. (17): A Schematic of an "Interior perspective" generated by using the suggested "Scale Magnification method". Source: (Researcher)

CONCLUSION

Both architecture students and instructors find old perspective drawing methods tedious, time consuming, and inefficient. Seeking more simplified drawing methods with less steps, and more efficient, while keeping the generated perspective scene of the building in reasonable proportions with its self, and with the size of the drawing sheet.

RECOMMENDATIONS

Populating the use of the suggested "Scale Magnification Method" in perspective courses as a better substitute and more efficient technique than the older ones Expanding teaching and practicing hand drawn perspective and free hand sketching in architectural course maps

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12) Watson David, (2017), "Perspectives, Slides and Scripts", The (DVIEW) command,. Published in: Cad tutor Net, retrieved October 2017 from: http://www.cadtutor.net/tutorials/autocad/perspectives-slides-scripts.php 13) Wikipedia, (2017), "Perspective (Graphical)", published in "Wikipedia", retrieved October 2017 from: https://en.wikipedia.org/wiki/Perspective_(graphical) 14) Andersen, Kirsti (2007). The Geometry of an Art: The History of the Mathematical Theory of Perspective from Alberti to Monge. Springer. Close, C. F. Text-Book of Topographical and Geographical Surveying, 2nd ed. London: H. M. Stationary Office, 1913. Craig, T. A Treatise on Projections. Washington, DC: U.S. Government Printing Office, 1882. 15) Cucker, Felix (2013). Manifold Mirrors: Crossing Paths of Arts & Mathematics. Cambridge University Press. pp. 269–278/ISBN 978-0-521-728768. 16) Dana, P. H, (1921) "Map Projections." http://www.colorado.edu/geography/gcraft/notes/mapproj/mapproj_f.html. Hinks, A. R. Map Projections, 2nd rev. ed. Cambridge, England: Cambridge University Press, 1921. 17) El-Bizri, Nader (2010). "Classical Optics and the Perspectiva Traditions Leading to the Renaissance". In Hendrix, John Shannon; Carman, Charles H. Renaissance Theories of Vision (Visual Culture in Early Modernity). Farnham, Surrey: Ashgate. pp. 11–30. ISBN 1-409400-24-7. 18) O'Connor, J. J.; Robertson, E. F. (2015). "". University of St Andrews. 23 September 2015. 19) Plato's Republic, Book X, 602d. http://etext.library.adelaide.edu.au/mirror/classics.mit.edu/Plato/republic.11.x.html 20) Panofsky, Erwin (1960). Renaissance and Renascences in Western Art. Stockholm: Almqvist & Wiksell. p. 122, note 1. ISBN 0-06-430026-9. "Linear Perspective: Brunelleschi's Experiment". Smart history at Khan Academy. Retrieved 12 May 2013 21) Savetz, (2008), "Perspective Grid", in "Printable Paper", By Publishing 2008, Source: https://www.printablepaper.net/category/perspective 22) Weisstein, Eric W, (2018), "Vertical Perspective Projection - Mathworld notebook", publisher: wolfram inc. retrieved October 2017 from: http://mathworld.wolfram.com/VerticalPerspectiveProjection.html

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