I'll post some more as I do a bit more work on it. I have been away from it but I will get a photo of it - probably tomorrow now. As for a list of parts and instructions, the principle is very very easy but as always the devil is in the details and there's a lot of devilish detail to be overcome.

Basically you get a laser which fires a small dot. You put that through a line generator lens and it makes that into a line as shown in the piccy. Then if you project that at the object but view it on the side and turn the lights out then the line wibbles left and right based on how far away the object is from the center. See first pic and look at the line, where its right the object has large radius, where its to the left the object has little radius. So take a lot of photos, rotating the object a little each time and you have a series of radial measurements of the object. So get PC to look at photos and convert those lines back into 3D, stitch up all the points into a 3D mesh and there you have it.

The hard part is trying to minimize all the noise. Since the camera needs to be just a little off to one side of the laser line then the wibble is really not all that much in the pics. So to get a good resolution of model you need to be tightly in control of any noise on the images. So laser line needs to be quite clean and very straight, images need to be clean and you need to make sure you don't lose accuracy in the conversion stages. You need a platter that rotates smoothly and accurately. With the original LP platter, any heavy object off center used to tilt the platter so that it would precess and cause all sorts of warp on the final model.

So the principle is easy but the actual implementation does require a certain amount of diligence and precision. Its the sort of thing where you cant afford to be sloppy but otherwise its no more difficult than any other thing.