projection. Thus, in the case of a cube oriented with a space's coordinate system, the primary views of the cube would be considered normal projections. Oblique projection In an oblique projection, the parallel projection rays are not perpendicular to the viewing plane, but strike the projection plane at an angle other than ninety degrees. 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 separating the coordinate axes as well as the foreshortening factors (scaling) 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, creating a truly-formed, full-size image of the chosen plane. Special types of oblique projections include military, cavalier and cabinet projection. Analytic representation If the image plane is given by equation and the direction of projection by , then the projection line through the point is parametrized by with . The image of is the intersection of line with plane ; it is given by the equation In several cases, these formulas can be simplified. (S1) If one can choose the vectors and such that , the formula for the image simplifies to (S2) In an orthographic projection, the vectors and are parallel. In this case, one can choose and one gets (S3) If one can choose the vectors and such that , and if the image plane contains the origin, one has and the parallel projection is a linear mapping: (Here is the identity matrix and the outer product.) From this analytic representation of a parallel projection one can deduce most of the properties stated in the previous sections. History Axonometry originated in China. Its function in Chinese art was unlike the linear perspective in European art since its perspective was not objective, or looking from the outside. Instead, its patterns used parallel projections within the painting that allowed the viewer to consider both the space and the ongoing progression of time in one scroll. According to science author and Medium journalist Jan Krikke, axonometry, and the pictorial grammar that goes with it, had taken on a new significance with the introduction of visual computing and engineering drawing. The concept of isometry had existed in a rough empirical