I'm looking for information on how to move (and animate) 2D sprites across an isometric game world, but have their movement animated smoothly as the travel from tile to tile, as opposed to having them jump from the confines of one tile, to the confines of the next.
An example of this would be in the Transport Tycoon Game, where the trains and carriages are often half in one tile and half in the other.
Why are you thinking it'll jump from tile to tile? You can position your sprite at any x,y co-ordinate.
First create your background screen buffer and then place your sprites on top of it.
Look up how to do linear interpolation (it's a pretty simple formula). You can then use this to parameterise the transition on a single [0, 1] range. You then simply have a state in your sprites to store the facts:
and then each frame you can draw it in the correct position using an interpolation from the start point to the end point. Once you have exceeded the duration, the sprite then gets updated to be not-moving and positioned in the end point/tile.
Drawing the sprites in the right place isn't too difficult. The projection formula are:
screen_x = sprite_x - sprite_y
screen_y = (sprite_x + sprite_y) / 2 + sprite_z
sprite_x and sprite_y are fixed point values (or floating point if you want). Usually, the precision of the fixed point is the number of pixels on a tile - so if your tile graphic was 32x16 (a projected 32x32 square) you would have 5 bits of precision, i.e. 1/32th of a tile.
The really hard part is to sort the sprites into an order that renders correctly. If you use OpenGL for drawing, you can use a z-buffer to make this really easy. Using GDI, DirectX, etc, it is really hard. Transport Tycoon doesn't correctly render the sprites in all instances. The original Transport Tycoon had the most horrendous rendering engine you've ever seen. It implemented the three zoom levels are three instanciations of a massive masm macro. TT was written entirely in assembler. I know, because I ported it to the Mac many years ago (and did a cool version for the PS1 dev kit as well, it needed 6Mb though).
Skizz
P.S. One of the small bungalow graphics in the game was based on the house Chris Sawyer was living in at the time. We were tempted to add a Ferrari parked in the driveway for the Mac version as that was the car he bought with the royalties.