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Since November 2006 the World was introduced to the Playstation 3 and the Nintendo Wii. Both have motion sensing chips to detect motion. The Wii also has a motion detecting infrared camera. The question is how will a motion controller change game play. Is it simply just moving the controller or will it add to the game experience?

The X-box 360 has been out since November 2005. The controller was redesigned, but it did not include motion sensing. Admittedly the controller has improved and is a superior controller for shooter games. The controller is also compatible with the PC. However the Xbox 360 does have some technology that just might be better than a motion sensing chip. Instead the Xbox uses a camera with motion sensing software. It started with a racing game controlled by hand movements. But this is only the start. There have been game concepts proposed such as casting a spell with hand movements or a sword battle game. This is one technology Microsoft will have to develop if the new game play requires motion sensing technologies.

The camera is said to have limited technology, but that might just be wrong. This Hunch will present a way to describe unit using mostly elementary mathematics such as geometry and trigonometry. It will show how simple math can create a game with 3D sword play. This is not just swinging a controller in a circle to spin the character. Think of a green sword (colored like a movie effect’s blue screen.) The motion of this sword and the players arm are processed by the camera as the player fights a 3D sword’s man onscreen. This movement can be described simply by math so that it can be programmed into the Xbox.


Ok, how does recording 3D sword motion by the game system (Xbox 360) happen? Well motion captor has been established. Often actors or athletes were “ball shaped” markers at the joints that cause the movement of the body. So the web cam of the Xbox 360 has built in motion detection. (Note I do not know the limits of the motion sensor or its ability to recognize objects.) So it is assumed that if a player was to were “ball shaped” markers the camera would be able to sense the motions of the joints and measure the distance between joints. Also it would be helpful if the camera could measure the relative size of those objects on the screen. For example if a marker moved closer or further away from the screen.

If we have a sword and 4 markers on the joint of the arm: the 3D motion of a sword can be read by a motion sensing camera. Also this movement will be create the true 3D movement of the sword in the video game.

This theory is based mathematically on the relative velocity problems common in the study of dynamics. Also the sine curve from trigonometry will be used to simplify what would otherwise be very rigorous and complicated math. This problem will set each joint of position of sword as an individual sine curve. These curves will be compared to what is similarly done with alternating current in electricity. In other words, the angle which the sine curves are out of phase will help determine the position of the sword.


Key Ideas to Review First

1. The members, the arm’s joints and top and bottom of sword, are a set of 2D lines which when moved together create a unique and special curve.

2. The foreshortening of the arms and sword give the 3D position.

3. There is a sine curve for every member. This sine curve is compared to the other members as if it were “out of phase.”

4. If the phase angle of any member is changed: it is no longer the same curve. That is the position of the swing of the sword has changed it’s curve.

5. There is a need to account for a full swing. That is the swing of the sword from right to left. Note however, not only does this increase or decrease the flat 2D picture of the members in the camera it places them on the opposite side of the body. But it must also be noted the members are still revolving in a 2D circular path in the viewpoint of the camera.

6. A 2D sin curve could only happen with the given measurements (of the given members.) In other words if the 2D result of the members is less then their start measurements that length would have to be accounted for in the 3D plane (Z-axis.) — So each curve, even though seen by the camera in 2D, is unique and it simplifies calculations. It allows the entire technique to work.

7. This technique has many other applications. Combined with the parabola vs sine curve, it can be used to solve dynamics problems such as relative velocity problems. The key is a proportion between velocity and position of the members using sine curves and phase angle. Sounds complicated but it is not. It just needs explored further.


Arm + Sword = fixed length

So in theory measurements and position of the swing could be found using the sine curve and phase angle!

Hopefully it is clear what is being attempted to be solved here. I will post updates to better explain and hopefully solve this problem. This is a good group project. If you have read this and want to work on a problem email: . Also more math can be found in the math_hunches section of Constructor’s Corner.