Parts of a Bezier Curve – Control Points and Tangents

All 8 parts on the diagram

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The cubic curve 6

Start point The point where the curve begins. It is also the first control point.
End point The point where the curve stops. It is also the last control point.
First control point The curve sets off from the start point toward this point. The curve does not pass through it.
Second control point The curve arrives at the end point from its direction. The curve does not pass through it.
Tangent line The line from an end of the curve to its control point. The curve touches it at that end and then bends away.
Cubic curve A Bézier curve set by four points. Two are its ends and two are control points.

The quadratic curve 2

Quadratic curve A Bézier curve set by three points. Two are its ends and one is a control point.
Single control point The one control point of a quadratic curve. The lines from both ends meet at it.

How this list was compiled: Read 2026-10-01. (1) Wikipedia, Bézier curve, https://en.wikipedia.org/wiki/B%C3%A9zier_curve : a Bézier curve is set by a series of control points; the first and last are always the endpoints of the curve and the others generally do not lie on it; the start and end of the curve are tangent to the first and last sections of the polygon of control points; a quadratic curve has three points and the tangents at its two ends meet at its control point; a cubic curve has four. (2) MDN Web Docs, Paths (SVG from scratch), https://developer.mozilla.org/en-US/docs/Web/SVG/Tutorials/SVG_from_scratch/Paths : a cubic curve takes two control points, one for the start of the curve and one for the end; the curve sets off toward the first control point and bends to arrive in line with the second; a quadratic curve needs one control point, which sets the slope at the start and end points alike. (3) W3C, Scalable Vector Graphics 1.1, Paths, https://www.w3.org/TR/SVG11/paths.html : a cubic Bézier segment is set by its start and end points and two control points; a quadratic Bézier segment by its start and end points and one control point. (4) A Primer on Bézier Curves, https://pomax.github.io/bezierinfo/ : curves run from a start point to an end point, with their curvature influenced by control points; the tangent is the direction of travel at a point. Licence: own work

The drawing: Drawn for this site on 2026-10-01: both curves are computed from their control points; nothing traced. Licence: own work

How it works

The parts of a Bezier curve on two drawings. A cubic curve runs from its start point to its end point and is bent by two control points. A quadratic curve below it has one.

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Ends and control points

A Bézier curve always passes through its start point and end point. It is pulled toward its control points but does not usually pass through them.

What the straight lines show

The line from each end to its control point is tangent to the curve: the curve leaves the start point along one line and arrives at the end point along the other. On the quadratic curve both lines meet at the single control point.

A cubic curve can bend twice, into an S. A quadratic curve bends only once.

Questions and answers

What are the parts of a Bezier curve?

An end point, a start point and one or more control points between them. A quadratic curve has one control point; a cubic curve has two.

What does a control point do?

It sets the direction of the curve at the nearest end. The curve starts toward the first control point and arrives from the direction of the last one, so moving a control point bends the curve.

What is the difference between a quadratic and a cubic Bezier curve?

A quadratic curve is set by three points: two ends and one control point. A cubic curve is set by four: two ends and two control points.