After writing yesterday's post I wondered how easy it would be to use the mathematics in a shader. This would be a natural way to extend my cross product shader, replacing the simple product in that with a more general geometric product.

## Thursday 12 April 2012

### Multiplying two vectors

In mathematics there are a number of ways to multiply two vectors. The most common is the dot product, which works for any two vectors of the same size. In three dimensions there's the cross product, while in two dimensions there's the perp dot product, sort of equivalent to the cross product.

But they all have the weakness that they are not invertible. Given the cross product

and knowing

**c**and another vector it isn't possible to calculate the third vector (**c**×**c**= 0, so given a solution all points on a line through this solution parallel to**c**are also solutions).## Sunday 8 April 2012

### Oops

I've been working on the front end, which also means I've been deciding how many levels, what distinguishes them etc. It's very different from Bug Tunnel Defense where every level was designed individually. Here the levels are mostly numbers. But at the same time I've been changing and adding things to make it easier to introduce elements progressively, and make for a more varied experience.

While testing some of these changes I generated the above screenshot, which is a really bad way to start a game (hence the title), but is also more aesthetically pleasing than the usual cluttered mess of the screenshots the game produces. It shows off some elements of the game much more clearly than usual, although they really need to be seen in motion to appreciate.

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