Axonometric projection

Axonometric projection is a type of orthographic projection used for creating a pictorial drawing of an object, where the lines of sight are perpendicular to the plane of projection, and the object is rotated around one or more of its axes to reveal multiple sides.Optical-grinding engine model (1822), drawn in 30° isometric perspectiveExample of a dimetric perspective drawing from a US Patent (1874)Example of a trimetric projection showing the shape of the Bank of China Tower in Hong Kong.Example of dimetric projection in Chinese art in an illustrated edition of the Romance of the Three Kingdoms, China, c. 15th century CE.Detail of the original version of Along the River During the Qingming Festival attributed to Zhang Zeduan (1085–1145). Note that the picture switches back and forth between axonometric and perspective projection in different parts of the image, and is thus inconsistent. Axonometric projection is a type of orthographic projection used for creating a pictorial drawing of an object, where the lines of sight are perpendicular to the plane of projection, and the object is rotated around one or more of its axes to reveal multiple sides. 'Axonometry' means 'to measure along axes'. In German literature, axonometry is based on Pohlke's theorem, so that the scope of axonometric projection encompasses every type of parallel projection, including not only oblique projection, but also orthographic projection and therefore multiview projection. However, outside of German literature, the term 'axonometric' is often used to make an explicit distinction from multiview projection, because axonometric projection allows for the depiction of more than one 'side' of an object, whereas a multiview projection allows for the depiction of only one 'side' of an object: Furthermore, in English literature, the term 'axonometric projection' typically implies an orthographic projection, such as an isometric projection. With an axonometric projection, the scale of an object does not depend on its location along any particular axis (an object in the 'foreground' has the same scale as an object in the 'background'); consequently, such pictures look distorted, because human vision or photography uses perspective projection, in which the scale of an object depends on its location along one of the axes (e.g., the z or 'depth' axis). This distortion, the direct result of a presence or absence of foreshortening, is especially evident if the object is mostly composed of rectangular features. Despite this limitation, axonometric projection can be useful for purposes of illustration, especially because it allows for simultaneously relaying precise measurements. The three types of axonometric projection are isometric projection, dimetric projection, and trimetric projection, depending on the exact angle at which the view deviates from the orthogonal. Typically in axonometric drawing, as in other types of pictorials, one axis of space is shown as the vertical. In isometric projection, the most commonly used form of axonometric projection in engineering drawing, the direction of viewing is such that the three axes of space appear equally foreshortened, and there is a common angle of 120° between them. As the distortion caused by foreshortening is uniform, the proportionality between lengths is preserved, and the axes share a common scale; this eases the ability to take measurements directly from the drawing. Another advantage is that 120° angles are easily constructed using only a compass and straightedge. In dimetric projection, the 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 of the third direction is determined separately. Dimensional approximations are common in dimetric drawings. In trimetric projection, the direction of viewing is such that all of the three axes of space appear unequally foreshortened. The scale along each of the three axes and the angles among them are determined separately as dictated by the angle of viewing. Dimensional approximations in trimetric drawings are common, and trimetric perspective is seldom used in technical drawings. The concept of isometry had existed in a rough empirical form for centuries, well before Professor William Farish (1759–1837) of Cambridge University was the first to provide detailed rules for isometric drawing.