Make a funny face through the awesome power of mathematics! I was adding Bézier curves to my Tech Paint project when I decided that they were so much fun that they deserved their own project. You can drag the blue and red dots (the Bézier control points) around to make different noses. If you want to get really radical, you can drag the endpoints (triangles) around as well. If the pithy remarks get on your nerves, you can turn them on/off with the spacebar. Click on the Ear to get a randomly generated nose. This project reminds me a lot of a little plastic game you used to be able to get where the face had short pieces of fine chain making up part of the profile. By shaking the game, you could make some very odd people! For the interested: Bézier curves are polynomial functions that are often used to make smooth interpolation functions. They have many other uses as well, but that's what I use them for. The one used here is a cubic parametric polynomial. It has the following properties: It will pass through it's defining endpoints (marked with the triangles) and the slope at the endpoints will be tangent to the straight lines connecting the endpoints to the associated control points (marked with the dots). I've tried to show this by making the endpoints triangular and always pointing at their respective control points. The function is also continuous and has a continuous first derivative, although it can get some pretty sharp bends. There's a very good discussion of Bézier Curves at www.moshplant.com/direct-or/bezier Credit goes to LeBurt for his "Pink Jim in the Air" project. I borrowed his idea of annoying remarks to add interest!
