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Descriptive geometry is the branch of geometry which allows the representation of three-dimensional objects in two dimensions by using a specific set of procedures. The resulting techniques are important for engineering, architecture, design and in art. [1]
Parallel lines are mapped on parallel lines, or on a pair of points (if they are parallel to ). The ratio of the length of two line segments on a line stays unchanged. As a special case, midpoints are mapped on midpoints. The length of a line segment parallel to the projection plane remains unchanged. The length of any line segment is shortened ...
Classification of Axonometric projection and some 3D projections "Axonometry" means "to measure along the axes". In German literature, axonometry is based on Pohlke's theorem, such that the scope of axonometric projection could encompass every type of parallel projection, including not only orthographic projection (and multiview projection), but also oblique projection.
ISO 406:1987 Technical drawings — Tolerancing of linear and angular dimensions ISO 1660:2017 Geometrical product specifications (GPS) — Geometrical tolerancing — Profile tolerancing ISO 2203:1973 Technical drawings — Conventional representation of gears
The maximum dimension may also be determined in a similar fashion. For the lowest dimensions, they take on the following forms. A projective space is of: (M1) at most dimension 0 if it has no more than 1 point, (M2) at most dimension 1 if it has no more than 1 line, (M3) at most dimension 2 if it has no more than 1 plane, and so on.
Example mechanical drawing. Here is an example of an engineering drawing (an isometric view of the same object is shown above). The different line types are colored for clarity. Black = object line and hatching; Red = hidden line; Blue = center line of piece or opening; Magenta = phantom line or cutting plane line
Isometric projection is a method for visually representing three-dimensional objects in two dimensions in technical and engineering drawings. It is an axonometric projection in which the three coordinate axes appear equally foreshortened and the angle between any two of them is 120 degrees.
An example of a multiview orthographic drawing from a US Patent (1913), showing two views of the same object. Third angle projection is used. In third-angle projection , the object is conceptually located in quadrant III, i.e. it is positioned below and behind the viewing planes, the planes are transparent , and each view is pulled onto the ...