# Non-Euclidean Geometry in Pattern Making

The “inspiration pic” for the costume.

Not so long ago, my sister came home from work quite frustrated.  In her line of work she is responsible for costume productions for Hale Centre Theatre in West Valley.  For the upcoming production, the costume designer wanted to recreate a dress she found while doing her research.  The research image was passed off to one of the pattern makers, whose attempt to craft the pattern followed none of the principles of aesthetics, pattern making, or the basic principles of geometry, Euclidean, and non-Euclidean.

After she related this portion of her story, I asked my sister how it should have been done.  So she began explaining some of the concepts in pattern making, and how to create different effects in clothing using what I later learned to be principles of hyperbolic and spherical/elliptic geometries.

The image in [Fig 1a] is a technical sketch of the original pattern created to emulate the skirt from the research image, as can be seen, each section has a triangle attached at the side.  These triangles, when they were sewn in, gave the skirt an effect not of a smooth flowing silk dress, but rather appeared to be “the fins of a rocket ship preparing for launch.”  Upon seeing a mockup of this design, one of the other pattern makers refused to cut out the mockup,  as it “would not look good on a human body.”

Image: Kristy Draper.

My sister began to explain to me how these concepts work on the human body.  To explain these, since costuming is a visual art, I will need to present some pictures of what I am describing.

When we make a skirt flow, we create a type of parabola or hyperbola in 3D that surrounds the lower half of the body, and so any increase in the diameter of the parabola needs to be taken into account with respect to the whole shape.  Skirts can have greater hem circumferences than a circle with the same radius as the skirt length, this means that sometimes a simple parabola doesn’t adequately describe the situation at hand.

In this particular project the goal was to give the skirt a hem circumference greater than that given by a full circle. This is basically intended to make it more flowy and elegant.  In order to accomplish this, while still yielding an even curve to the skirt, the pattern maker needs to perform an action known as “slash and spread.” (See figure 1b.)

The “slash and spread” technique is used to create a fuller skirt based off of another basic skirt pattern.  It is done by taking a pattern piece, and drawing a certain number of lines down it parallel to the front center seam, or back center, depending on what part of the skirt we are working on. The pattern piece is then cut along those lines, the top point of each cut is still connected at a point on the waistline, or in this case a design line, and the bottom edges are separated, each by an equivalent amount.  After completing this step, the pattern is traced onto a new sheet of pattern paper, and all of the connecting lines are smoothed out using a tool called a french curve, which is a drawing tool based off of sections of the “euler curve”.  The smoothing is done in such a way that all four corners are locally right angles, even if they curve afterwards, they must be right angles to be able to fit on the shape of the human body. (This rule does not include design lines, only structural ones.)  (See fig 1b.)

After applying this technique to the skirt, it was able to hang well, no rocket fins, and it actually had a fuller skirt as can be seen in the drawing (compare length l to length k). Each section was made to fill much more space than just adding triangles to the edge could.

The finished dress. Image: Kristy Draper.

I found it interesting that this discipline, which sometimes is considered to be limited in its use of mathematics, actually uses many complicated methods that are reminiscent of non-euclidean geometry, such as its use of parallel lines that appear curved on paper, but on the complex shape of the human body appear straight.  It is also striking that an innate understanding of these concepts are required to create something that looks good.  It was interesting that even though I am not a trained pattern maker, I was able to understand these concepts as well as I did.  In our discussions my sister and I learned that our disciplines have a lot more similarities than is often thought: this is great for all those kids who say that they will never need geometry after they leave school, they don’t realize that they are wearing it.

Sources:

Personal Interview with Kristy Draper, Costume Shop Manager, Hale Centre Theatre.

Armstrong, Helen Joseph. Patternmaking for Fashion Design. 4th ed. Upper Saddle River, N.J.: Pearson Prentice Hall, 2006. Print.

Image credits Kristy Draper: Technical Drawings, Finished Dress

“Inspiration Pic”    http://www.pinterest.com/pin/339529259379580951/