Bezier Curve Editor

This simulation shows how the smooth curves in fonts, logos and drawing tools are made. Students drag four control points anywhere in 3D, and the curve starts at the first point, ends at the last and is only pulled toward the two in between. A slider, animation or the left and right arrow keys move the parameter t from 0 to 1. Colored lines show the construction: the control polygon in blue, the first level of points in amber, the second in green and the curve point in red. Readouts give t, the curve point B of t, its speed and the curve length. A button flattens the curve to a plane. It teaches interpolation and parametric curves.

• Drag the second control point far away and see how the curve bends toward it without touching it.
• Pause Animate t and move the t slider, watching the blue, amber and green lines.
• Press the left and right arrow keys to move t in small steps.
• Press Flatten to a plane and compare the curve with a flat drawing program curve.
• Move the points to make an S shape, then read the Curve length readout.

1. 1Describe how four control points define a cubic Bezier curve.
2. 2Explain how repeated interpolation builds a point on the curve.
3. 3Relate the parameter t to the position along the curve.
4. 4Predict how moving a control point changes the shape of the curve.

Questions teachers ask