## Three Styles for LaTeX Vector Notation

LaTeX is a very flexible program for typesetting math, but sometimes figuring out how to get the effect you want can be tricky. Most of the stock math commands are written for typesetting math or computer science papers for academic journals, so you might need to dig deeper into LaTeX commands to get the vector notation styles that are common in physics textbooks and articles.

This post shows how to typeset a LaTeX vector with an arrow, a hat, or bold. Read the rest…

## Better billboarding in Papervision3D

The Papervision3D wiki has an example for making billboarded sprites with just three extra lines of code. Trouble is, it doesn’t really work. Anyone who’s tried it may have noticed that when the planes get too close to the camera, or if the camera rotates around it’s z-axis at all, the planes start rolling instead of staying vertical.

The problem is that the lookAt method defaults to using the world y-axis as “up” for the billboards, which isn’t usually correct. Of course we don’t really care about the world y-axis with billboards. We just want them to be vertical in the camera. Here’s some code that does it.

// calculate the camera vertical in world coordinates
var up : Number3D = new Number3D(0, 1, 0);
Matrix3D.rotateAxis(camera.transform, up);

// billboard is the plane you want to billboard.
billboard.lookAt(viewpoint, up);
billboard.roll(180);
billboard.pitch(180);

## Easy Scientific Notation In LaTeX

I use LaTeX for all my physics homework and lab reports, and I’ll be using it for a master’s thesis in the next few years, so I’m constantly adding to my library of LaTeX commands to save some typing. Here’s a good one when you need to use scientific or engineering notation. Put the following in the document preamble (before \begin{document}):

\providecommand{\e}[1]{\ensuremath{\times 10^{#1}}}

Then, typing

The [111] crystal planes are 3.2\e{-10} m apart.

gives you: The [111] crystal planes are 3.2×10-10 m apart. whether or not you’re already in a math environment. If the exponent is just one number, you can omit the braces, like this: 3\e8 m/s. Cool, huh?

(Of course, for 10-10 m you can just use Angstroms, \AA. If you’re in a math environment, use \text{\AA}, or else the circle won’t line up with the A. That is, if you’re okay with non-SI units.)