Sunday, 16 June 2013

03.10 Quadrilaterals - symmetrical and asymmetrical

Rectangles and their perfect forms, squares, are easily found as literal forms in man-made environments. They are highly unusual, implied or literal, in the natural world.

Just as ellipses have a special relationship with circles, where ellipses are commonly interpreted as circles viewed at an angle not perpendicular to their plane; so do members in the group of symmetrical quadrilaterals.

Rectangles (including squares)
These are only seen as such when viewed along the central axis: a line passing through the exact centre of the shape running perpendicular to its plane.

These are observed when rectangles are viewed on a perpendicular plane passing through the diagonal corners.

These are observed when rectangles are viewed on a perpendicular plane bisecting two opposite sides.

Asymmetric quadrilaterals
These are seen when rectangles are viewed along axes not passing through a point of symmetry. They would likely be resolved as two triangles.

Thus not only are the points of a rectangle highly constrained in composition, but the angle of its viewing is too. Precision is of utmost importance when taking an image of a rectangle, as misalignments with the image frame are glaringly obvious. As a possible consequence of the due care required, deployment of rectangular elements lend a sense of formality, of controlled structure; and slightly less so with trapezoids and parallelograms.

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