It has been two weeks since I have done the slightest amount of work on the sword game. Kudos to Ben for keeping it moving along. Anyway, it’s time for some brainstorming.

Our current idea (as of last week) for a control scheme for the sword game is (1) to have it in slow motion for strategic, rather than strictly action, play, and (2) to control the sword based on gestures, of sorts. Not pre-programmed gestures like (ugh) Black and White; more like drawings of what you want the sword to do. Draw a Z and you’ll get a Zorro motion. I like this idea a lot, and I think it has a lot of potential. So, I have to tackle the problem of, given a gesture, how do you figure out what to do with the sword.

Well, we want it to be sort of vague and interpretive. We also want it to be natural, the way a human would interpret when given that gesture. These two things point me straight toward setting up descriptive equations, filling in known information, and solving for the rest of the details. But what kind of information does the gesture specify?

We know it starts about where the sword currently is when you draw the gesture, and it ends in the same direction as the end of the gesture. We can intuit velocities, but I think it’s better to let the equations figure those out. We also know a few points on the curve (as many as we need, really). We’re trying to solve for the force to exert at every step. Oh, and we know we have a maximum force we are allowed to exert, which should play a role in the solving process (so the solution doesn’t try to do anything impossible).

A Bezier-like spline might suffice. We are given a curve, i.e. a bunch of points, and we’re trying to find a smooth interpolant. Let’s look at what information we have at each point:

- A 2D position at each point.
- A 3D position and velocity at the first point.
- (perhaps) A time at the last point.

y much information. And the information we need:

- A 3D force for the handle at each point.
- A 3D force for the tip at each point.

I’m making the assumption that we linearly interpolate the forces between each point, so the force half-way between two points is the average of the forces at each of the two points. So we have 6 unknowns. We need 6 equations (for *each* point).

How do we interpret the 2D data? I’m going to say for simplicity’s sake that we put a plane in front of the fighter and require that the sword pass through the corresponding point. This may be the weakest assumption of the algorithm. And there’s another problem with this approach: in order to compute that, we need the position and orientation of the sword at each point, another five unknowns in exchange for only two equations!

Hmm, as I hash this approach out, it seems to be breaking down. Maybe I should scrap and come from a different angle.