Previously in Understanding Loomis, I have shown several ways of determining depth by diagonals.  The method explained today is another method of finding depth by diagonal, but this one is a more accurate method than those previously covered.  Today’s method should be used when the illustrator is seeking to draw to scale; i.e. when he must divide the vertical and horizontal planes into square units for measurement in perspective.  The previously outlined methods are fine when the illustrator is seeking to represent visually realistic perspective, but when mathematical precision is necessary -as in the cases of scale drawings-  a more precise method is needed.

Today’s post will explain the method of laying out the precise division of vertical planes.  How this is used in the creation of scale drawings will be covered in the next posting.

1. First establish the horizon and the V.P. for the first plane.  Cast perspective lines back from the VP to establish the height of the plane.  Determine height by eye.
2. Establish the First Unit depth also by eye. This establishes a Base Unit Plane, which will be cloned in perspective.  Next, cast a new line from the centre point on the nearest edge of the Base Unit Plane to the VP.  This will bisect the plane perfectly in half.  We shall call this new line the Middle Line. 
3. When the first unit is established, it is cloned by using diagonals.  Create a Vertical Line by bisecting the horizon at the original VP.  Make certain to draw the Vertical Line long enough to accommodate the diagonals which you will draw in the next step.  
4.  Cast the first diagonal (green in this example) from the near bottom corner through the far top corner to the Vertical Line (the pink line in this example).  At the place where the (green) diagonal line crosses the (pink) vertical, make a secondary VP. 
5. This step is where the method tightens up the measurement.  Cast a downward diagonal (yellow in this example) from the top near corner of the plane, through the point where the bisecting Middle Line (from step 2) crosses the midpoint on the far edge of the plane.  This line does not go corner to corner. Extend this downward diagonal far enough for it to meet the (pink) Vertical Line.  Mark a tertiary VP at the low crossing point.  
6. Again, as in step 4, cast a new ascending  diagonal from the next bottom corner (where the next plane will be) up to the secondary VP marked on the Vertical Line in step 4.
7. Where the ascending diagonal (green) and the descending diagonal (yellow) both cross the original perspective lines (red), draw a vertical line to indicate the depth of the second plane.  This will be a more accurate representation of the First Unit Plane’s width in perspective, than that which was shown in previous postings. 
8. Repeat the procedure by casting ascending lines corner to corner, and descending lines from corner through the Centre Line to establish the further planar depths. 
9. Erase the guide lines to reveal the four planes receding into the distance, with more precise perspectival depth.

Conclusion

Readers will have noticed that with the introduction of a secondary guiding point, i.e. the bisecting Middle Line, the illusion of correct perspective is tightened.  For the sake of interest, compare the planes of today’s post with the divisions of depth created with the earlier methods in previous postings.  You will be able to see the subtle difference by eye, and how this method creates a more accurate representation of repeating planar depth in perspective.  This is especially true in the perspectival plane sections which are shown far off in distance.  The previous methods tend to shorten the depth incrementally, such that the distant planar sections become much too close together.

Next week, we will investigate how to use this method of depth by diagonal to set up for the creating of scale drawings.