Thanks. Ok, now I see the different resizing options, and I see that a cropped image has other parts in the name (e.g. filename_100_cw100_ch100_thumb.jpg. But the cw and ch 'options' don't work as a way to create the image on-the-fly - it doesn't 'call the file into existence' the way the _1024 suffix does.
I appreciate that it's not the intended use of the cache, but nevertheless it is a really useful feature. If I want to display a downsized image in a forum post I don't need to create it in advance, I simply paste the link to the full image, change '/albums/' for '/cache/' and then type the width suffix just before the .jpg extension. Clearly there are enough 'smarts' in the image processor to extract the width parameter from the filename, but not the cw and ch parameters. Is that right? And even if not, there is no parameter for 'longest side'. I guess I'll stick to resizing via the width.
Thanks for the pointers on editing the theme. I'm a PHP novice, but will take a look.