3D Drawing – Moving Your Drawing to the Distorted and Flattened View

I had Jen, someone who had purchased my book, Sidewalk Canvas, email with a question a few days ago about gridding a drawing.  At first I thought she meant gridding in general, but as I started to answer her I realized she meant the specific question of taking a perspective drawing and transferring it to being a flattened (and thereby showing the distortion) drawing for anamorphicly created depth.  On pages 48-51 in the book I described how to create the correct grid, in perspective, and then take that grid by hand and flatten it, transferring the correct appearing drawing to the distorted state it needs to be in for the drawing to read correctly.

I went through it pretty step by step in the book and am trying to figure out another way of explaining it that would be easier to understand – But I think the simpler concept to apply first is that when you look at that grid in fig. 8 p 49,
Image (fig8)
you are seeing it drawn in perspective, instead of flat, as you would need it to draw it.  So, the concept I’m trying to explain on pages 50 and 51 is how to transfer that grid into a flat grid.  The basic idea is that you need to take each one of those grid squares, seen in perspective, and you need to draw them in their flattened state.  So, the way I show in the book is a precise, but somewhat tedious, way of doing this.  Essentially what you are trying to do is take each one of the points where the drawing is crossing a grid line and transpose it onto the flattened grid in the exact same place.  The compass and ruler allow you to get that to the correct point very precisely.  While the vertical lines of the drawing are not so difficult to place accurately without the ruler method, the horizontal lines can be a bit trickier as you are dealing with flattened perspective in your measurements.  
Okay, so let’s look at figure 5-7 on page 51.  
Image(fig 5-7)
What I am trying to show (though it’s not being done very well!) is that the place that the left side of the rope-tied piling crosses the grid line in the perspective grid lines up, using the ruler and compass at the bottom, to hit the precise point on the flattened grid where you see the side of the piling being drawn in.  Same with the eyeball, fish’s mouth, etc.  So, if you were to go through your line drawing, which is drawn in perspective, and transfer it point by point using the ruler to your flattened grid, it would give you a way to take your drawing and distort it correctly in the flattened view.  
 As I said, this is very tedious and very precise.  There are easier ways of doing it if you’re familiar with photoshop or another photo editing program.  
 Now, in looking through all of this information there is one fact you need to understand – using this traditional method of anamorphic perspective will not render a perfect illusion of distortion.  Why is that? Well, first off, this geometric equation is based on the idea of flat planes but, let’s face it, nothing we are doing is flat – not the surface we draw on (a globe, the earth), nor the surface we view it with (our eyeball or the curvature of a camera lens) – so even as we transpose this perfect drawing, you will look at it as a large painting after and various portions will not appear quite right.  There are various ways of tackling this issue – some people try just using a projector and shooting the image onto the ground – this works to some extent, but the vertical perspective isn’t really correct and it causes some significant proportionate issues within the larger painting  – but if you don’t get math, it’s a semi-successful crutch.  There are adjusted geometric equations that allow for this curvature – Kurt Wenner has developed one, though it is more of his own “master’s secret” and not really available for the public at this point.  And there are lots of artists who use a bit of geometry and a bit of good old fashioned work ethic in making the adjustments by hand as they develop the image, correcting along the way to make a better painting.  
IMHO, it’s valuable to understand the math and to learn how to use it – think of it like learning foundation skills of any sort – skipping the foundation is less about “cheating” and much more about really understanding our craft from the ground up so that we make whatever adjustments necessary out of knowledge, not out of accidental guessing.  Take the time, figure it out, apply it, and learn what needs to be adjusted – better to make mistakes and learn how to be better then to stay mediocre :o)

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