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BASIC PRINCIPLES

Parallelism

In images different but in regard of scale corresponding lines are parallel, a parallelism easily to demonstrate by holding a pencil in appropriate position while shifting it in-between two related lines. This parallelism does not only apply to lines defined by pairs of well characterized points, but also to lines defined by a single point and as a tangent to the contour of a structure (yellow) such as the scrub near the stair, or as a tangent to two contours (white) such as the structures of the two bushes in front of the house.

Keeping the pencil in firm position in regard of inclination while shifting the hand seems rather easy to accomplish, thus presenting as a procedure not only suitable to check on parallelism of corresponding lines, but also to create new lines (d*) parallel to already existing ones (d).

This method is of special use while sketching in the free nature, as it easily allows to pick up the inclination of line and transmit it on the drawing block (Fig 1d).

New Image

To make this procedure suitable to build up an entire new image, requests first to select a baseline (AB fig1a), then to establish a reference-line (A’B’ fig 1a), and thereafter to create points of repair as shown in fig 1b and c.

Baseline

Any line - even a virtual one - can serve as a baseline, as to derive from the examples provided. Most important is that this line is easy to recognize, and that the end points are clearly defined. First choice are for obvious reasons horizontal or vertical lines of appropriated length, located rather in the center of the image and being also an essential part of it, such as the line AB in Fig 1a.

Reference-line

The reference-line (A'B' in fig 1a) on the drawing plane corresponds to the baseline (AB) of the source image, and defines the position of the new image and the scale factor or size-relation involved in-between the two pictures.

Points of repair such as C’ are established as shown in fig 1b and 1c.

First a line p‘ is drawn as a parallel line to p passing through A‘ , followed by q’ as a parallel line to q passing through B, thus establishing C’ as the crossing-point of p’ and q’, and also defining A’C’ and B’C’.

All lines established in such a way can be used as a base to establish further points of repair.

The images below (Fig 3a - f ) demonstrate the consecutive built up of further points of repair. Fiig 3g illustrates the resulting outlay.

Note that the position of a single defined point of repair is independent of the pathway of its construction (Fig 4a) and similarly : a single point of repair  is always properly located in relation to all the other points (K, fig 4b).

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