Smooth Joins

Chaining curves into shapes

An interactive lesson with 6 steps, about 5 minutes: you predict, drag and solve, with instant feedback on every answer. It runs in your browser and needs JavaScript.

What you’ll learn

• Shapes are chains of Bézier pieces (splines).
• A join is smooth when the handles on both sides are in a straight line through it.
• Mirrored handles (Q = 2J − P) match direction and speed.

Steps

1. Curves in a chain
2. Smooth the join
3. Mirror the handle
4. Same direction, different length
5. Letters made of curves
6. Counting points