It is interesting to note that any Bézier curve of degree n can be converted into a Bézier curve of degree n+1 with the same shape. The wiki article has a nice example but the main idea is based on the property that bn(t)=(1−t)bn(t)+tbn(t).
Jordanwyli
This slide specifically explains how changing one point can change the whole curve entirely. This raises important questions like do we always want our curves to respond so drastically to changes in control points. What if we had error or noise?
It is interesting to note that any Bézier curve of degree n can be converted into a Bézier curve of degree n+1 with the same shape. The wiki article has a nice example but the main idea is based on the property that bn(t)=(1−t)bn(t)+tbn(t).
This slide specifically explains how changing one point can change the whole curve entirely. This raises important questions like do we always want our curves to respond so drastically to changes in control points. What if we had error or noise?