Oblique projection

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Oblique projection

In both orthographic and oblique projection, parallel lines in space appear parallel on the projected image. Because of its simplicity, oblique projection is used exclusively for pictorial purposes rather than for formal, working drawings.

In an oblique pictorial drawing, the displayed angles among the axes as well as the foreshortening factors scale are arbitrary. The distortion created thereby is usually attenuated by aligning one plane of the imaged object to be parallel with the plane of projection thereby creating a true shape, full-size image of the chosen plane.

Special types of oblique projections are: Cavalier projection[ edit ] In cavalier projection sometimes cavalier perspective or high view point a point of the object is represented by three coordinates, x, y and z. 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: The length of the third axis is not scaled.

Cabinet projection[ edit ] The term cabinet projection sometimes cabinet perspective stems from its use in illustrations by the furniture industry.

Unlike cavalier projection, where the third axis keeps its length, with Oblique projection projection the length of the receding lines is cut in half.

Military projection[ edit ] A variant of Oblique projection projection is called military projection. In this case the horizontal sections are isometrically drawn so that the floor plans are not distorted and the verticals are drawn at an angle.

The military projection is given by rotation in the xy-plane and a vertical translation an amount z. Impossible object An example of the limitations of isometric projection.

The height difference between the red and blue balls cannot be determined locally. The Penrose stairs depicts a staircase which seems to ascend anticlockwise or descend clockwise yet forms a continuous loop. Objects drawn with parallel projection do not appear larger or smaller as they extend closer to or away from the viewer.

While advantageous for architectural drawingswhere measurements must be taken directly from the image, the result is a perceived distortion, since unlike perspective projectionthis is not how our eyes or photography normally work.

It also can easily result in situations where depth and altitude are difficult to gauge, as is shown in the illustration to the right. In this isometric drawing, the blue sphere is two units higher than the red one.

However, this difference in elevation is not apparent if one covers the right half of the picture, as the boxes which serve as clues suggesting height are then obscured.

This visual ambiguity has been exploited in op artAs well as "impossible object" drawings.

References

Escher 's Waterfallwhile not strictly using parallel projection, is a well-known example, in which a channel of water seems to travel unaided along a downward path, only to then paradoxically fall once again as it returns to its source.

The water thus appears to disobey the law of conservation of energy. An extreme example is depicted in the film Inceptionwhere by a forced perspective trick an immobile stairway changes its connectivity. Perspective graphical Perspective of a geometric solid using two vanishing points.

In this case, the map of the solid orthogonal projection is drawn below the perspective, as if bending the ground plane. Axonometric projection of a scheme displaying the relevant elements of a vertical picture plane perspective.

The standing point P. The parallel lines through P. Perspective projection is a linear projection where three dimensional objects are projected on a picture plane. This has the effect that distant objects appear smaller than nearer objects. It also means that lines which are parallel in nature that is, meet at the point at infinity appear to intersect in the projected image, for example if railways are pictured with perspective projection, they appear to converge towards a single point, called vanishing point.

Photographic lenses and the human eye work in the same way, therefore perspective projection looks most realistic. The orthogonal projection of the eye point onto the picture plane is called the principal vanishing point P.

The principal vanishing point is the vanishing point of all horizontal lines perpendicular to the picture plane. The vanishing points of all horizontal lines lie on the horizon line.

Oblique projection

If, as is often the case, the picture plane is vertical, all vertical lines are drawn vertically, and have no finite vanishing point on the picture plane.

Various graphical methods can be easily envisaged for projecting geometrical scenes.The AP oblique cervical spine projections are supplementary views to the standard AP, odontoid and lateral c-spine series.

It can be taken either as an anterior oblique or posterior oblique projection. not straight or direct, as a course. indirectly stated or expressed; not straightforward: oblique remarks about the candidate's honesty.

indirectly aimed at or reached, as ends or results; deviously achieved. Other articles where Oblique projection is discussed: drafting: Pictorial views: the pictorial representation achieved by oblique projection, in which the principal surface of the object is considered to be in the plane of the paper and thus is represented in true size and shape.

Pathology Demonstrated: Pathologies, including possible fractures involving the distal tibiofibular joint, the distal fibula and lateral malleolus, and the base of the fifth metatasals, are demonstrated. Oblique Aerial Photograph Photograph taken from a non-perpendicular angle from a platform in the atmosphere.

Obliquity Tilt of the Earth's polar axis as measured from the perpendicular to the plane of the Earth's orbit around the Sun. The AP oblique cervical spine projections are supplementary views to the standard AP, odontoid and lateral c-spine series.

It can be taken either as an anterior oblique or posterior oblique projection.

Oblique projection - Wikipedia