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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
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 ...
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.
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.
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.
In mathematics, projective geometry is the study of geometric properties that are invariant with respect to projective transformations.This means that, compared to elementary Euclidean geometry, projective geometry has a different setting (projective space) and a selective set of basic geometric concepts.
The boundary of a cross-section in three-dimensional space that is parallel to two of the axes, that is, parallel to the plane determined by these axes, is sometimes referred to as a contour line; for example, if a plane cuts through mountains of a raised-relief map parallel to the ground, the result is a contour line in two-dimensional space ...