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Projection Drawings of Cubic Models


Overview

A three-dimensional object can be represented in two dimensions by a projection (or perspective) drawing:


This page shows some projection drawings of collections of cubes. Although the drawings look different (in each case the cubes are arranged in a different pattern) they all have one thing in common. The perimeter of all of the drawings is the same. Each arrangement of cubes projects onto the same two-dimensional shape:




Projection Drawings of Collections of Cubes





Programming Notes

The underlying programming tools used are Javascript, HTML tables and .gif images built with Paint. The projection drawing was divided into a 7 by 7 array as follows:

For each unique cell pattern in the array, a .gif was built and a two character code assigned:

BB BT FF FT SB SF SS ST TB TS TT

The code for a cell pattern represents the orientation of cube faces that appear in that cell: F=Front, S=Side, T=Top and B for Background. So BT codes for a cell that contains background and the top of a cube and SS codes for a cell that contains just cube sides.

The perspective from which a cubic model is viewed will determine what cell patterns can be present. For example in the above drawing BS is not possible but SB is.

A complete drawing such as the one above is coded by the string

BBBBBTTTTSBBBB..BBBBFFFFSSTSBB..BTTTFFFFSTTTTS..FFFTTTTSFFFFSS..FFFFFFSSFFFFSB..BBFFFFSFSSBBBB..BBBBFFFFSBBBBB

The string is passed to a Javascript routine which then translates each two-character code into the corresponding .gif and populates a 7*7 table ready for display. The special .. code is used to tell the routine to start a new table row.

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