Wednesday, May 19, 2010

The eyes of a rectangle

Above is an illustration of our rectangle represented as a shark-shopping cart with a lantern. This concept has been illustrated so many times in design texts that I felt it necessary to distinguish my version from those that have preceded it. I believe this will probably be the authotiative version.

If a line is drawn from one corner of the rectangle to another, then intersected by another line dropped from an opposing corner so as to intersect it at a 90 degree angle, the intersection forms a power spot on that rectangle, which I have marked with a lambda. Four points on the canvas can be found using this method, one lower and one higher on each side. These points are called the eyes of the rectangle.

I am not sure if all the math is really necessary to find these spots. They are neither in the center horizontally nor in the corners of the composition. I figured out intuitively that there were four such spots on my canvas and saw this mathematical explanation many years later.

Many years ago in Rockport, I realized while looking at my work that I had become overly reliant on the power spot or eye idea in design, as I looked around my gallery every painting seemed to proceed from my nailing that power spot with a tree or the house or something. I made an effort to get away from that time honored design (Loraine used it extensively) as too old timey. I wanted a jazzier look. I began then to arrange patterns of interlocking shapes across my paintings. I still think about those spots but I try not to build my designs from them.

11 comments: said...

Question: Do you think these "power spots" are only effective for landscapes or would they work as well in figurative and still life work? Abstract?

Yes, it's a fine line between finding what works for an artists then making sure you don't become too formulaic or predictable. There is nothing like being in a room with all your art to give it a fair assessment. It tells all.

Bob Carter said...

Very interesting, Stape. On a canvas with the common 3:4 ratio (12x16, 18x24, etc.), the diagonal is 5 units. With a little trigonometry, you can figure out that the power spot is 1.8 units from the closer corner along the diagonal. In other words, the spots are at 0.36 of the diagonal length from each corner. If you drop a perpendicular from a power spot to the long dimension of the canvas (the 4 unit dimension), it is 1.44 units from the edge, which is 0.36 of the long dimension. Each spot is 1.08 units from the top or bottom, which is 0.36 of the short dimension (the 3 unit dimension). The recurrence of the fraction 0.36 in all these dimensions is fascinating -- I see the makings of a cult. The fraction 0.36 is roughly one third (0.33), so the spots lie very close to the intersections of lines that divide the canvas into thirds.
For many years I have routinely drawn pencil guidelines on my canvases, following a system used by the late watercolorist John Pike. He would draw a horizontal line across the middle and two vertical lines at the one-third and two-thirds points of the long dimension. This divides the canvas into six rectangles, which is just enough gridding to aid in placing elements of the design, either from the motif or a sketch. Ideally, points of interest lie close to the vertical lines. I regard the horizontal line as "the line of death". I never want the horizon there, but having that reference is a good check to get it horizontal, wherever above or below the mid-line it falls. From the geometry of the power spots (at least for a 3:4 format), it looks like Pike was getting to about the same placements by a different method. I might have to try moving the verticals to the 0.36 points to be in alignment with the universe.

billspaintingmn said...

Stape, I may be wrong, however this was refered to as "optic centers" where I went to school.
If you grid out the rectangle, 4 horizontal, 4 vertical your 'optic
centers' set comfortably off center
left or right, up or down from absolute center.
Your eye naturally seeks these areas out for information.
if you can grab the viewers eye at one of these optic centers, you can lead the eye through your picture and tell your story.
This is universal and can be used
in landscapes, figurative, still life or abstract.
It is used in advertising (TV & magazines) and is proven effective.
The military understands this well
and uses it to seek out its target.

Christine Walker said...

Ansel Adams used them in his prints. I am pritning and framing the shark

willek said...

I love using the "Eyes" and am not yet advanced enough to leave the system. I use the heck out of them combined with the steel yard and other systems putting a major event in one eye and lesser events in others. I never, however fill all 4 eyes. I have to re look at all of your pictures now to see what it is you do to obfuscate the eye thing. Enjoyed Bob's eye dissertation.

Kayla said...

Love your blog, Stape, but that sure doesn't look like a 90 degree angle in the illustration.

Stapleton Kearns said...

They work in any kind of painting and in architecture, furniture design and dog grooming as well.

Stapleton Kearns said...

I knew these posts wood bring you out. I will quote you on the frontside That is excellent. I hope you are well down there on the Cape.

Stapleton Kearns said...

I wonder what they are called in Japanese?

Stapleton Kearns said...

Be sure to use a water resistant mat.Seafoam green might be nice.

Stapleton Kearns said...

I am sure you can find plenty examples of me using it too.