Labs / Computer Science
Bezier Curves
Every letter in this sentence, every icon on your screen, is built from curves like this one. Drag the control points to reshape the curve, then scrub t from 0 to 1 and watch the De Casteljau construction repeatedly interpolate its way down to a single point riding along the curve.
points 4B(t) (0.00, 0.00)
What to try
- The curve never quite touches the middle control points — so what exactly are those points doing to its shape?
- At t = 0.5, where does the traced point sit relative to the control polygon? Is it ever the midpoint?
- Add a point to raise the degree. How many layers of scaffolding lines appear, and why that many?
- Can you drag the points so the curve crosses itself into a loop? What arrangement makes that happen?
- Turn off the scaffolding and just watch B(t) move. Where along the curve does the point travel fastest?