So, what's the biggest difference between curves and surfaces when compared to meshes? *Math!* Okay, I'm sorry. That was mean of me; I know that math can be a four-letter word for many artists, but don't worry; you won't have to do any math here. What I mean to say is that you can describe curves and surfaces to the computer as a mathematical function. You describe meshes, on the other hand, using the positions of all the individual vertices that they're composed of. In terms of the computer, curves and surfaces have two advantages:

**Curves and surfaces are very precise.**When you get down to it, the best that a mesh can be is an approximation of a real object. A mesh can look really, really good, but it's not exact. Because curves are defined by math, they're exactly the correct shape, which is why designers and engineers like them.**Curves and surfaces take up less memory.**Because the shape is mathematically defined, the computer can save that shape by saving the math, rather than saving all the individual points. Complicated curves and surfaces usually take up quite a bit less hard drive space than the same shape made with meshes.

Of course, these advantages come with some caveats, too. For one, curves and surfaces can sometimes be more difficult to control. Because curves and surfaces don't really have vertices for you to directly manipulate, you have to use *control points*. Depending on the type of curve, control points can sit directly on the shape or ...

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