What information entered the process?
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.
Labs / Computer Science / Bezier Curves
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.
Why it matters
Why explore this?
Computer science turns clear rules into reliable processes. This model lets you step through those rules and see how each decision changes the result.
Explore
Try the model
points 4B(t) (0.00, 0.00)
Investigate
Questions to test
Predict first, try it in the model, then use what you observe to answer.
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?
Explain
Make sense of what happened
Trace the process one step at a time. Name the rule used at each important step, then explain why the final result follows from those rules.
Check
Before you leave
Which rule changed it?
Why did the process produce this result?
If you can answer all three using evidence from the model, you understand the main idea. If not, return to Explore and change one setting at a time.