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A parallel projection is a particular case of projection in mathematics and graphical projection in technical drawing. Parallel projections can be seen as the limit of a central or perspective projection, in which the rays pass through a fixed point called the center or viewpoint, as this point is moved towards
Establishing a parallel projection of a translation surface one 1) has to produce projections of the two generatrices, 2) make a jig of curve and 3) draw with help of this jig copies of the curve respecting the rules of a translation surface. The contour of the surface is the envelope of the curves drawn with the jig.
Given the X, Y and Z coordinates of P, R, S and U, projections 1 and 2 are drawn to scale on the X-Y and X-Z planes, respectively. To get a true view (length in the projection is equal to length in 3D space) of one of the lines: SU in this example, projection 3 is drawn with hinge line H 2,3 parallel to S 2 U 2 .
Snyder [6] describes generating formulae for the projection, as well as the projection's characteristics. Coordinates from a spherical datum can be transformed into Albers equal-area conic projection coordinates with the following formulas, where is the radius, is the longitude, the reference longitude, the latitude, the reference latitude and and the standard parallels:
Cylindrical equal-area projection with standard parallels at 30°N/S and an aspect ratio of (3/4)π ≈ 2.356. 2002 Hobo–Dyer: Cylindrical Equal-area Mick Dyer: Cylindrical equal-area projection with standard parallels at 37.5°N/S and an aspect ratio of 1.977. Similar are Trystan Edwards with standard parallels at 37.4° and Smyth equal ...
1. Projections of two sets of parallel lines lying in some plane π A appear to converge, i.e. the vanishing point associated with that pair, on a horizon line, or vanishing line H formed by the intersection of the image plane with the plane parallel to π A and passing through the pinhole.
The projection of the point C itself is not defined. The projection parallel to a direction D, onto a plane or parallel projection: The image of a point P is the intersection of the plane with the line parallel to D passing through P. See Affine space § Projection for an accurate definition, generalized to any dimension. [citation needed]
Because a parallel projection and a scaling preserves ratios one can map an arbitrary point = (,,) by the axonometric procedure below. Pohlke's theorem can be stated in terms of linear algebra as: Any affine mapping of the 3-dimensional space onto a plane can be considered as the composition of a similarity and a parallel projection.