The Bezier Curve -- String Art (1-19 thur 1-25)


We worked with straight lines that worked together to form curves.  I created templates for the Mathletes with right angles, coordinate grids, squares, rectangles, pentagons, hexagons, circles, acute angles and many others.  Use the attached pdf file to create beautiful curves and apply as much color as possible.

The history of string art became famous with Pierre Bezier (1910-1999).  Bezier worked as an engineer for a french automaker. To satisfy the needs of manufacturing, they needed a way of describing a curve exactly at every point. In those days, engineers sitting at drafting tables would mark a starting point and an ending point of the curve they wanted, then pulled out a french curve and drew an approximate best-fit curve.

At the machine shop level, these best fit approximations were not good enough. In order for pieces to fit together the parts could only vary within certain tolerances, many of these approximate curves were outside the tolerances. By 1960, hardware became available that allowed the machining of 3D shapes out of blocks of wood or steel, known today as CAM or Computer Aided Manufacturing. Computer graphics was still in its infancy at the time, so designing a method of describing any curve you wanted was of utmost importance.

Bezier had to come up with a method of describing a best fit curve that would be easy to use and exact enough to meet the demands of manufacturing. Unfortunately, no mathematics existed at the time to do the job adequately(1). After numerous schemes, he came up with a method of describing any 2nd degree curve using only four points.

In today's computer aided world, the applications are numerous. Not just in obvious applications like computer graphics and animation (animation often uses Bezier curves applied to the fourth dimension to describe smooth motion), but also in robot controlled manufacturing. The Bezier Curve changed the world.


String_Art_Bezier_Curve.pdf827.8 KB