These are some thoughts on Trigonometry that I wanted to write down, and someone, somewhere may want to read. But probably not. If you're not into it, turn back immediately. In a top-down view on a two dimensional plane, you can face any direction and move in a forward direction by moving on the x-axis by the cosine of your rotation and moving on the y-axis by the sine of your rotation. This seems to require a physical orientation in the world, but this physical limitation is only on the surface. We can take one step back and use these abilities in more subtle ways. Imagine a side view on a plane in which you can move left and right, and jump up and fall back down to the ground. Let us first think of the left and right movement in terms of trigonometry. Facing right means 0 degrees and so we can move on x by the cosine of our rotation. Facing left is 180 degrees, and we move on x by the cosine of our rotation. Let's maintain a logical rotation factor called xf . When sta...
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