When Elodie Fourquet was a graduate student in computer science at the University of Waterloo in Canada, she was charged with creating a T-shirt for a computer graphics course. The idea was to put a number of 3-dimensional shapes designed by students in the class onto the shirt. No matter how she designed the shirt on the computer, however, the representation of the shapes in two dimensions seemed off. “I was unsatisfied trying to guess the numbers where things should be mathematically,” says Fourquet, assistant professor of computer science at Colgate. “Software still had this gap.”
That experience led her to look into how another group of designers solved the problem of representing 3-dimensional space on a flat surface: Renaissance painters. “They were representing depth before the mathematics that we developed for 3D graphics,” Fourquet says, “using only lines on a 2-dimensional canvas.” Studying their techniques, she has been developing her own techniques for creating 3-dimensional shapes using traditional sense of perspective in place of complex digital coding. She uses it to teach students to render artworks electronically in an introductory seminar called “From Painting to Pixels,” in which students leave with a new perspective on both art and computers.
Modern 3D graphics are based on photographic perspective, stemming from a single point — a so-called “pinhole camera” perspective. The farther one gets away from that point on the screen, however, the more images become distorted. “The pinhole camera model assumes you are looking straight and everything projects from one view,” Fourquet says. “We have come up with all of these fancy mathematics to correct the distortion on the side of the frame.” By contrast, Renaissance artists such as Leon Battista Alberti, Piero della Francesca, and Leonardo da Vinci, developed the principles of perspective by using geometry to create a grid, like a tile floor, that encompasses the entire plane of the wall or canvas, and then used that to place objects into the frame.
“The way Raphael worked, he created studies of different people in different positions, then glued all of these cartoons together into a collage of construction,” Fourquet says. “In the Renaissance, they just had basic geometry, they did not have an x, y, z coordinate system. They were guided by their perception of what looked right.” We lose that, Fourquet says, in 3D graphics software in which we push a button and then let the computer create images that may be mathematically correct, but may not look right to the eye.
Fourquet has continued to study how the brain perceives perspective in collaboration with Flip Phillips, a neuroscientist at Skidmore, supported by a two-year grant of $101,262 from Colgate’s Picker Interdisciplinary Science Institute. “We are going back to the essentials of how we understand depth perception, and what are the most important cues that help us read perspective in images,” Fourquet says.
“In the Renaissance, they just had basic geometry, they did not have an x, y, z coordinate system. They were guided by their perception of what looked right.”
In experiments they did last summer, the researchers showed a series of subtly manipulated images to participants to see whether they perceived them to be in two or three dimensions. Fourquet expected that the most important element in determining 3 dimensions would be how the ground was rendered to bring viewers into the space. Surprisingly, however, the horizon proved to be a more important attribute. “The horizon already has a lot of the components of what we end up believing the ground to be,” she explains. “When we did something to scramble the horizon, it distorted the image for people.” Eventually principles from their research could be incorporated into an illustration program such as Photoshop or Illustrator to help designers create a realistic image of space.
In her course, Fourquet starts by teaching students to throw away the computer mouse and pick up a graph pad and pencil, designing a plan based on geometrical principles of how they will render their chosen artwork in three dimensions on the computer. “There is a myth that computer programming is hard and if you are not mathematically strong, you cannot do it,” she says. “I show students that in order to program, you first need to have a plan.” Rather than creating images pixel by pixel, she guides them through the process of abstracting their artwork into geometrical shapes before figuring out how to represent them through code.
As no two artwork pieces are the same, every student confronts his or her own unique challenges. “I guide them through solving problems,” she says. “One student wanted to draw a train tank in the form of a cylinder; she came up with a way to draw a circle and layer it from back to front to create the appearance of three dimensions.” By solving those challenges, students learn the computer coding is more than just processing strings in a table, but can be more akin to making art. “Every student comes in with some piece that I don’t know how to render,” Fourquet says. “There are always new challenges, and they are always very satisfied in the end with what they can create.”