Oblique Perspectives and CAD Software

Oblique Perspectives and CAD Software

Pedro M. Cabezos-Bernal (Universidad Politécnica de Valencia, Spain) and Juan J. Cisneros-Vivó (Universidad Politécnica de Valencia, Spain)
DOI: 10.4018/978-1-5225-0029-2.ch013
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The great advances in the field of computer graphic design, have led to the development of more powerful applications, which have become an essential tool for the designer and have revolutionized the teaching of Descriptive Geometry. However, design software is not perfect, as there are some limitations that have to be overcome. This chapter focuses on solving the problem of obtaining oblique perspectives from a 3D model, as it is a common trouble in most of CAD software, since they only provide orthogonal projections and perspectives from a 3D model. This obstacle has led to the fact that the use of oblique projections, such as military and cavalier perspectives, has been drastically reduced.
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Oblique perspectives have been used with great success throughout history, particularly in their two most interesting cases: the cavalier perspective and the military one. Essentially, both are parallel oblique projections, differing only in the position of the projection plane regarding the projected object. In the case of a military perspective, the projection plane is horizontal, so the horizontal faces of the model are represented in true proportion, whereas in the case of a cavalier perspective, the projection plane is vertical, so only those vertical faces of the model that are parallel to the projection plane will be represented in true proportion (Figure 1).

Figure 1.

Parallel oblique projection of a cube to create a military and a cavalier perspective


The name military or cavalier can be followed by the appellative “perspective”, “axonometric” or even “projection”, being generally more extended in Latin countries the qualification “axonometry” and “perspective”, whereas “projection” is also used in English-speaking areas. Despite this, all of these adjectives are suitable and perfectly understandable. The “perspective” appellative may sound strange, since they are actually a parallel projection, not perspective, but we must take into account that a parallel projection can be considered as a perspective projection whose vertex is at infinite.


The Oblique Perspective Tradition

The theoretical concretion and the legitimization as a projection of military and cavalier perspectives did not come until the second half of the nineteenth century, by the statement and subsequent proof of Pohlke’s theorem. However, these representations have been used spontaneously and intuitively since ancient times, as in the case of a well-known Pompeian fresco of the first century A.D., depicting the dispute between the inhabitants of Nuceria and Pompeii in the Amphitheatre (Figure 2).

Figure 2.

Fresco of the first century A.D. found in a Pompeian Villa, showing the fight in the amphitheatre between the inhabitants of Pompeii and Nuceria. National Archaeological Museum of Naples


This primitive representation, intuitively painted, is a sort of cavalier perspective, in which the projection plane is parallel to the vertical planes that are represented in true proportion, while keeping the parallelism between edges in the foreshortened faces.

The advantages of this kind of representations are evident, since we can see some faces of the model in true proportion and its execution is quite simple, as only those faces that are not parallel to the projection plane are foreshortened. In that way, the designer can choose between a military or cavalier perspective, according to what is more interesting to represent in true proportion (plan or elevation).

These advantages fomented the use of military perspective in the treatises of military fortifications from the Renaissance, whose primary interest was to represent the fortifications plans in true proportion. This led to its designation as “military” perspective, while in the case of “cavalier” perspective, the origin of its name comes from its “resemblance” with the sight perceived by a cavalier on his horse, when he contemplated the facades frontally from that elevated position.

The first fortifications treatises to use oblique perspectives were those of Francesco Giorgio Martini, within Codex Saluzziano and Codex Senese, 1480 and 1490 respectively, containing unorthodox drawings, which can be assimilated to military and cavalier perspectives, see (Alonso & Calvo, 2014).

Key Terms in this Chapter

Cavalier Perspective: It is a particular case of oblique perspective in which the projection plane is vertical, so any shape contained in a vertical plan that is parallel to the projection plane, maintains its proportion after being projected.

Parallel Projection: It is a projection type in which the projection center is at infinity so the projection rays are parallel.

Oblique Perspective: It is a kind of representation that comes from a parallel projection whose projection rays are oblique in relation to the projection plane.

Chorography: The etymology of the term comes from the Greek choros , which means: ” country” and graphia , which means: “description”. It refers to the representations of the city made in the same way that an artist paints from life. Chorography, unlike cartography that is more abstract, eases the understanding of the represented cities. Initially, chorography had a purely literary character as it was referred to those textual descriptions of the territory included in the Laudes Civitatum of the first century A.D. During the Renaissance the term acquired a wider meaning to be understood also as a graphical urban representation.

Military Perspective: It is a particular case of oblique perspective in which the projection plane is horizontal, so any shape contained in a horizontal plan, maintains its proportion after being projected.

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