20101207---recorded on site 20110127
I have a goal. I have a hunch that rectangles can be used to simplify physics in game development. In statics if you know the forces that make up a rectangle you can find the forces of the members easily. I don’t know if there is any benefit over the traditional vector method yet, but if you add or subtract the rectangles from each other you should have the resultant force. I also don’t know if it could be applied to dynamics. But the goal is to create fully active worlds in the game. For example, in The Legend of Zelda games the level is interactive. I want the same interaction in a shooter. How many times have you played a game and shot at the doors and nothing happens to the landscape? I realize that physics is very much a part of most games today. I just want to see if I can achieve an advanced effect in a simple way using only trigonometry.
I don’t have every detail worked out, but the following concept will demonstrate my idea:
Imagine a pool table where there is only x and y position changes. Move to a ping pong table where again it is 2D. But we want to play a game by ourselves so we lift up one side of the table. Now we can better see the 3 dimensional aspect of the ping pong table.
Straight line position changes are not hard to compute. Our pool table explains that. It is shapes like a parabola caused by gravity that makes our calculations tough. I do not have the dynamics of non-linear movements defined simply. That is simpler than any other known ways to compute this. However I do know the forces in statics.
Imagine the ping pong table again. Lift up one side so there is only one player. That folded up perpendicular side represents the 3D moment of force. And since the 3D moment is equal to the cross product, it also represents the cross product.
So just in 2D (x and y), the moment of x and y in the 2D is an orthogonal projection of the 3D moment of force. So as long as we know the 2D moment and the change in the Z direction we know the 3D moment and know what forces are holding the particle in equilibrium.
(The 2D line of action is also important as it relates to the orthogonal view, but needs to be explored further.)
I am not saying I have a definite way to compute the static equilibrium. I do not have the programming skills yet. I am not even familiar with the methods currently used. However, my goal is to write a class someone can take and incorporate in there program that uses simple calculations (even if it is not more efficient). I will be happy if the program, runs as is the way with my math problems.