Buzz’s Blog: On Web 3.0 and the Semantic Web

Mar 26 2011   3:32AM GMT

Perfect curves: Bezier, part 1

Roger King Roger King Profile: Roger King

Vector versus raster graphics.

There are two very different ways that computer programs can internally represent 2D images.  The first is the way a computer display presents images – as a 2D grid of pixels, each with properties that control its physical appearance.  We call this “raster” graphics.

The second is by using geometry.  An image is represented with lines, some of which might be straight and some of which might be curved.  We call this “vector” graphics.

But  here’s something very important and very intriguing…

Note that a straight line can be represented unambiguously with two points, a start and an end point.

But a curved line is far more complicated to represent.  It cannot be represented by a beginning and an end point – or at least we need more than this.  Three points won’t do it, either.  Or four.  You can lay down a large number of points, and there will be many, many curves that can go through them all.

This is a core problem underlying graphics and animation.

If we design a house using only straight lines, we know precisely how to specify the location of every line in 3-space.

But if we want to design, say, a car, there will be a lot of lines that are not straight.  Our car might have a lot of curves on it.  For that matter, our house probably has curves, too, maybe in a half moon window or the water heater or the bottom of a pool or the air conditioning ducts.

How do we tell the folks who build the car or the house precisely how to make those curved surfaces?

Bezier was an engineer who designed cars in France and he confronted this problem – and came up with an elegant, simple answer, one that requires a minimal amount of information that must be passed from designer to builder.

More next time…

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