Information about Cavalier Perspective
The cavalier perspective, also called cavalier projection or high view point, is a way to represent a three dimensional object on a flat drawing, and more specifically, a type of oblique projection.
A point of the object is represented by three coordinates, x, y and z. On the drawing, it is represented by only two coordinates, x" and y". On the flat drawing, two axes, x and z on the figure, are perpendicular and the length on these axes are drawn with a 1:1 scale; it is thus similar to the dimetric projections, although it is not an orthographic projection, as the third axis, here y, is drawn in diagonal, making an arbitrary angle with the x" axis, usually 30 or 45°. The length of the third axis is not scaled[1][2].
This perspective does not try to give an illusion of what can be seen, but just tries to give an information about the depth.
It is very easy to draw, especially with pen and paper. It is thus often used when a figure must be drawn by hand, e.g. on a black board (lesson, oral examination).
The representation was initially used for military fortifications. In French, the « cavalier » (literally rider, horseman, see Cavalry) is an artificial hill behind the walls that allows to see the enemy above the walls [3]. The cavalier perspective was the way the things were seen from this high point. Some also explain the name by the fact that it was the way a rider could see a small object on the ground from his horseback [4].
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Pieces of fortification in cavalier perspective (Cyclopaedia vol. 1, 1728)
A point of the object is represented by three coordinates, x, y and z. On the drawing, it is represented by only two coordinates, x" and y". On the flat drawing, two axes, x and z on the figure, are perpendicular and the length on these axes are drawn with a 1:1 scale; it is thus similar to the dimetric projections, although it is not an orthographic projection, as the third axis, here y, is drawn in diagonal, making an arbitrary angle with the x" axis, usually 30 or 45°. The length of the third axis is not scaled[1][2].
This perspective does not try to give an illusion of what can be seen, but just tries to give an information about the depth.
It is very easy to draw, especially with pen and paper. It is thus often used when a figure must be drawn by hand, e.g. on a black board (lesson, oral examination).
The representation was initially used for military fortifications. In French, the « cavalier » (literally rider, horseman, see Cavalry) is an artificial hill behind the walls that allows to see the enemy above the walls [3]. The cavalier perspective was the way the things were seen from this high point. Some also explain the name by the fact that it was the way a rider could see a small object on the ground from his horseback [4].
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How the coordinates are used to place a point on a cavalier perspective
Mathematical aspects
If the plane that faces the reader is xz and the "vanishing direction" is the y axis and its angle is α, then a point in the space with coordinates (x, y, z) is represented on the flat figure by a (x", y") point, with:- x" = x + cos α·y ;
- y" = z + sin α·y.
- x" = x + 0.35·y ;
- y" = z + 0.61·y ;
- x" = x + 0,35·y ;
- y" = z + 0,35·y ;
References
1. ^ Illustrator Draftsman 3 & 2 - Volume 2 Standard Practices and Theory, page 67 from [1]
2. ^ Ingrid Carlbom, Joseph Paciorek, Planar Geometric Projections and Viewing Transformations, ACM Computing Surveys (CSUR), v.10 n.4, p.465-502, Dec. 1978
3. ^ Etymologie des maths, letter C (French)
4. ^ DES QUESTIONS D’ORIGINES (French)
2. ^ Ingrid Carlbom, Joseph Paciorek, Planar Geometric Projections and Viewing Transformations, ACM Computing Surveys (CSUR), v.10 n.4, p.465-502, Dec. 1978
3. ^ Etymologie des maths, letter C (French)
4. ^ DES QUESTIONS D’ORIGINES (French)
Further reading
- Foley, James (1997). Computer Graphics. Boston: Addison-Wesley. ISBN 0201848406.
Oblique projection is a simple type of graphical projection used for producing pictorial, two-dimensional images of three-dimensional objects.
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What it is
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perpendicular (or orthogonal) to each other if they form congruent adjacent angles. The term may be used as a noun or adjective. Thus, referring to Figure 1, the line AB is the perpendicular to CD through the point B.
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Dimetric projection is a form of axonometric projection, in which its direction of viewing is such that two of the three axes of space appear equally foreshortened, of which the attendant scale and angles of presentation are determined according to the angle of viewing; the scale
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Views
Graphical projections
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Graphical projections
- Perspective projection
- Parallel projection
- Orthographic projection
- Plan, or floor plan view
- Section
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Fortifications are military constructions and buildings designed for defense in warfare. Humans have constructed defensive works for many thousands of years, in a variety of increasingly complex designs.
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Cavalry (from French cavalerie) were soldiers or warriors who fought mounted on horseback in combat. The designation was not usually extended to any military force that used other animals, such as camels or mules.
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