When you want to use a reference of some sort (a sketch, a photo, even a reproduction in a book) but have to enlarge it, often the fastest way is to “square it up.” The end result will be squares on the original and the new blank support of different sizes but in the same proportions. Here is Ingres’ squaring of this sketch for a portrait.

Above is the “up” part of the squaring, the painting with subsequent changes that Ingres made in the final version like the tilt of the head in the Frick Gallery in New York.

OK, so how to you do this. There are two ways. One is to measure with a ruler and divide and multiple. That is the math way. The other is to use a geometric way. I find the geometric way the easiest. All you need is a ruler.

There are actually two separate problems:

1. THE OVERALL PROPORTIONS OF THE NEW SUPPORT.

2. MAKING PROPORTIONALLY THE SAME SQUARES ON EACH

**the over all proportion of the new support**

O.K. you have this great sketch in flimsy paper and you want to do a painting on good paper in a half sheet size. This blank support, on which you are going to paint, has to be in the same proportions as the original. In the above example the pencil sketch by Ingres and the canvas have to be proportionally similar, or more specifically the squares on the the sketch and the canvas have to have the same proportions.

You do this by putting the sketch in the lower right corner of the new support and drawing a diagonal line from the right bottom to the left top of the sketch and keep on going on the new support.

explanation of diagram:

1. You first draw the line DB through the corners of your sketch and continue on.

2. Any two perpendicular lines from the same spot on DB to the edge will create a box in the same proportion as the sketch. AB to EF are in proportion as is DC to DG.

To give you an example, I was using a square photograph from a magazine for an image on a quarter of a standard sheet of watercolor paper which is not square, so when I did this, I wound up with square outline on a larger rectangular sheet of paper. there was a band of paper left over on the right which I cut off.

**making proportionally similar squares on the sketch and the new paper**

this is what you have on your support, the paper you are going to work on (if you extend the line where the sketch was) and the sketch.

By placing a straight edge from the upper left corner to the bottom right corner, you can make a mark exactly in the middle of line AB. You are going to do this on both the sketch and the new support. No need to draw the line from corner to corner because you will have to erase it later. All you need is the center.

Now you draw lines perpendicular from the sides through the middle, and you have two squares. You are going to do this on both the sketch and the new support.

Now we repeat what we did on the whole support in one of the boxes we created. We draw line CD and bisect it like we did with line AB. You are going to do this on both the sketch and the new support.

We draw lines GH and EF. We can draw similar lines in the box below and the start on the other side. You are going to do this on both the sketch and the new support.

When you’re done you will have similar boxes on both the sketch and the final support (piece of paper, board, canvas, etc.)

That’s all there is to it.

on October 27, 2012 at 12:52 am |JohnAn easy method of creating proportionally equivalent grids is to use a long scale (a ruler). This is a drafting technique, really. Determine and draw outer boundary boxes on the original and on the new drawing in proportion, i.e., original is 5″, second is 10″ for 2x enlargement etc, or use the diagonal method you illustrate. Lay the scale diagonally across the first box intersecting top and bottom boundaries and pick a convenient and appropriate number of divisions. They can be whatever you like. It doesnt matter if the space is 1 inch, 3/4 inch, 2 cm or .5 in. You are just using the scale to define equal units. Move the scale around until the divisions come out to the right number and tick them off the diagonal scale with a pencil. Draw horizontal lines using a t-square and you have equal divisions. Make the same number of divisions using the same method on the second (the new) box and you have a proportional grid matching the first. Do the same thing for the vertical dimension and you are done. The grid “squares” do not have to be exactly square; eyeball what seems right. If you want them to be square you can do that but it takes a bit more fiddling around.

on December 2, 2013 at 3:41 am |Susan GaleVery clear and helpful. Thank you.

on December 16, 2013 at 3:26 am |Waterlogue– a great app for iphone/ipad | Channeling Winslow Homer[…] which will “square up” a photo so you can draw it on your paper. see here and here for my posts on the subject. It is really essential to get a good underdrawing. Sargent and […]

on April 26, 2015 at 1:45 pm |carlos barbonWonderful site, packed-full of insightful information and most valuable to those whom have been influenced by Homer and Sargent.