The concept of foreshortening is a very important one in axonometric projection. Let us take two orthographic views (first angle i.e elevation above, plan below) of a pencil which is parallel to the ground, and take a view perpendicular to its length. In its starting position the pencil is a true lenght in both plane and elevation. Holding the pointed end of the pencil steady move the opposite end away from you, ensuring the pencil remains parallel to the ground. Keep moving the pencil away from you until you are looking along the point of the pencil. A view along the point of the pencil (a point view) is a view parallel to the direction in which the pencil is pointing. The length of the pencil changed as you moved it from full length to a point view. Every time you moved the pencil away from you its length appeared to get shorter or it foreshortened. As the pencil rotates parallel to the Horizontal plane its elevation becomes foreshortened. The further you move the end of the pencil away from you the greater the foreshortening. This is known as the degree of foreshortening. For example, if you moved the pencil from its starting position (full length) 5? away from you (the 5? is relative to the vertical plane) then the degree of foreshortening is very small as the pencil appears only a little smaller than full size. However, if you moved it 85? from its initial position then it would appear very small (very near a point view). In this case there is a large degree of foreshortening.
Note: The pencil is initially parallel to both the Vertival and Horizontal planes. It is then rotated 5? . The pencil is now no longer parallel to the Vertical plane. The full 5? rotation can be seen in the plan view. When fully rotated the pencil is perpendicular to the Vertical plane and still parallel to the Horizontal plane.
Let us take the same cube as above to further illustrate this point. Starting with an elevation view of the cube we see a square. The LOS, in this view, is perpendicular to the front edges e.g. 'AB' and 'BC' and also to the back edges e.g. 'EF' and 'HG' ('G' is the lower corner right behind 'C' in the elevation). Because the LOS is perpendicular to these edges, they are true lengths. It is also important to note that in the elevation edges 'AE', 'BF', 'CG' and 'DH' all appear as point views. This is because we are looking parallel to these lines.
Let us now rotate the cube about 'AD' so that the elevation and end view are visible together. We are no longer looking perpendicular to the front face of the cube. What has happened to the edges 'AB' and 'AE'? The line 'AB' has been rotated just like the pencil above so it appears shorter in this view, i.e. 'AB' has foreshortened. However, the line 'AE' has gone from being a point view to a line view. This line still does not appear as a true length so it is still foreshortened. How about line 'AD'? We are still looking perpendicular to this line so it appears as a true length.
Finally let us rotate the cube vertically up about the line 'DG' while holding point 'D' on the ground. Now, what has happened to line 'AD'? Well, we are no longer looking perpendicular to it so it now also has foreshortened. If you watch the animation you will see the vertical height of line 'AD' decrease. In fact, all the edges of the cube now appear foreshortened. If the angles between the projection of the axes are equal, i.e. 120?, then all the edges foreshorten equally. This view is known as an isometric view. Also, when the angles between the projection of axes are equal the axonometric axes are known as isometric axes. When the cube has been fully rotated a point view of the body or long diagonal 'DG' results which only occurs in an isometric view of a cube.
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