Bezier Curves — How computers create curves with straight lines

Last week, we learned about Benford’s Law which creates a logarithmic curve. We looked at how easy it is to create a curve long hand using your arm as a natural compass. So when we looked at a curve on a computer or the graphing calculator, they look like beautiful curves, but when you look more closely, they are just straight lines. 


In 1962 Bezier was a designer working for the French car company, Renault, and wanted to use computers to create designs of his cars. Computers can only create equations for straight lines and Bezier figured out a way to overlap those lines to create curves. 


All 3D animation on computers are created with triangles. The more triangles used, the more detailed the picture. The children were able to create curves with right angles (90 degrees), acute angles (between 0 and 90 degrees) and obtuse angles (between 90 and 180 degrees), with squares, circles, pentagons, hexagons, a fish, and many other designs.


The more segments you create on a line, the greater the detail of the curve. 


The key was teaching the children how to use a ruler. The best practice is to always draw lines top down; place your pencil on the vertex and push the rule up against the pencil and then rotate the ruler to meet the corresponding point. The pressure on the ruler should be forefinger and middle finger together and thumb straddling the space for the line. The pencil should be held lightly and angled towards the student to relieve pressure.


Once they got the motion of using  ruler, it was easy to create the line drawings and beautiful curves.


The document has dozens of drawings but also instructions for making your own line drawing.


The best comment from a 2nd grade student this week was that her sister that is in 7th grade has been creating line drawings for the last four years after a similar lesson I taught in 2013.


Line drawings are addictive and so much fun. 

Bezier_Curves_and_Line_Drawings.pdf331.71 KB