the shifting definition of my role in my artmaking

(and the skills i need to build.)

all art is arrangement, right? music = sound arranged through time, sculpture = form arranged in three dimensions, painting = color arranged in two dimensions, etc. and typically a painter will have a palette and a brush and a canvas, and recently many of us also use computers and video and so on, so now we've learned how to use some digital tools to go along with those in the brick-and-mortar universe. now, all of a sudden, unrelated to any brick-and-mortar-world or digital-world drawing tools, i need some math.

when i first started programming, i realized that math would start coming into it. but i never took to math classes, and i usually avoid math as much as possible. however i realized it will come in handy to start learning some as i was working on a new version of "color study."

"color study" consisted of stripes of painted color, with an image of that painting projected right back on top of itself, rotated ninety degrees, forming a grid. the grid shows every combination of primary and secondary additive and subtractive colors.

http://en.wikipedia.org/wiki/File:AdditiveColor.svg

http://en.wikipedia.org/wiki/File:SubtractiveColor.svg

http://en.wikipedia.org/wiki/Color_theory

for example, you see projected yellow on top of painted yellow, projected yellow on top of painted blue, projected blue on top of painted yellow. the plan was:

































http://www.eriksanner.com/2008_for_blog/080327_color_study_v5.pdf

here's the result of that, an image of a previous version of "color study" (picture of an egg tempera painting rotated ninety degrees and projected back onto that same painting):






































showing a new version soon and wanted to make some changes (improvements i think). first, added brown. next, wanted to change the order of the colors. i don't like that the white is on the edge (in the version shown above, painted white is left edge vertical stripe, projected white is bottom horizontal stripe). here's the new order:
































also i began toying with the idea of painting a pure painting and projecting a pure projection next to the projection-onto-the-painting grid - above in that same image you can see some possible layouts i was playing with.

so far, so good, role of the artist still "thinking about what to make" and "arranging the stuff to make it happen," all within the realm of what i expect to be doing when i'm working on a piece. realized that given time constraints and the scale of the piece (for the new version, i want to make it much bigger, but i won't have as much time as i'd like), it won't work to use egg tempera or oil paint. so, i went to the hardware store. it felt funny to let someone else mix the colors for me.








































































but "wanting to learn some math" is even weirder than "hey here i am asking other people to mix colors for me." the moment-where-i-thought-uh-oh-i-might-need-to-start-learning-more-math came after i decided to animate this version. at a crit several months ago, it was obvious that people understood the piece better if the projection was rotating. so, i wanted to rotate the projection (and back) continuously - simple enough. but i also didn't want any areas of the painting to be projectionless. this meant increasing and then decreasing the size of the projected stripes as they rotate - also no problem. however, i realized the rate of increase (and decrease) couldn't be uniform if i were both to avoid projectionless areas and keep as much of the projected color on the painted color as possible.

here are some illustrations of what i'm talking about. in each of these images, the 50% transparent square on top represents the projected square, and the 100% solid square beneath, always with perfectly vertical stripes, represents the painted square. when the actual piece is made, the projected square will be 100% solid, and the other square will be painted in the real world. this first image shows a square rotated, without increase, showing the projection gaps i want to be filled up, which is made possible only by enlarging the square.






































getting rid of the projected corners hanging off is no problem, i can just mask the projected square






































to get rid of the projectionless corners, i need to enlarge it, also no problem






































cropped, looks like this, exactly what i want, no problem so far right?






































the problem comes in the early stages of rotating the top (projected) square. the rate of increase of size can't be uniform, it has to increase sharply at first and then taper off as the rotation approaches forty-five degrees, otherwise there are projectionless gaps early on. so i can do it by hand, and it works, and you see the "artist's hand" in the work, no real problem. but i'd like to know how it makes sense, how to make it work, mathematically, so that i can program it. right now i don't even know what question to ask. when i google "how do i rotate and enlarge a square so that it continues to cover a square beneath it?" nothing too useful comes up. i think i need to find someone who is used to teaching geometry. i think i need to start learning math. this is not really something i anticipated when i realized that more than anything else, i want to spend my days making art. surprise!