Bézier curve
A Bézier curve is a curve described by its two ends and two more points that pull it out of line.
In more detail
Take a straight line between two points, then place a handle near each end and drag: the line bends towards the handles without ever reaching them. Those handles are the two extra points, and four points is the whole description.
Any shape is built by laying several end to end. Because each is only four points, a complicated outline stays small, scales to any size and stays smooth at every one of them.
What it does on a real document
Every rounded shape on a page is written this way, and so is every letter of every typeface: a glyph is a set of these curves, which is why text stays crisp however far it is enlarged.
In a description, a curve gives the two handles and the point it ends at; where it starts is wherever the previous step left off.
Where it comes from, and why
The mathematics was worked out in the car industry, where a body panel had to be described precisely enough to be cut and smoothly enough to look right. Two engineers arrived at it separately, and the name of one of them stuck.
Drawing programs, typeface design and page description formats all took it up, which is why the same four points mean the same thing everywhere.
Glossary
- font
- The drawing of every letter, digit and mark a document writes, held in a file of its own. A PDF carries the fonts it is set in inside itself, which is why it opens looking the same on a machine that has never had them. Leave them out and a reader puts another font in their place, and the layout moves.
- glyph
- One drawn shape of a typeface. The letter A is a character; the particular drawing of it that lands on the page is a glyph. The same letter is drawn differently in every typeface.