math - Reflection? How do I do it? -


It's on my head, can someone tell me better?

I am making a game of 2D Breakout Fighting, so I need the ball when it will be able to display the wall, paddle or enemy (or kills any enemy).

All their formulas are like this: x_1 ^ '- x_0 = v-2 (vĂ‚ · n ^ ^) n ^ ^

And I can not fall it (What does it mean or x_0? Or ^^?)

It is easy to understand the formula for reflection if you Think about the geometrical meaning of the "dot product" operation.

Dot product is defined mathematically between two 3D vectors

    

But there is a good geometric interpretation in it

a and < Strong> B If two vectors are pointing in the opposite direction, the length of the launch of a is b with a negative signal, b is multiplied by the length.

dot product geometric interpretation

something like The thing which is clearly explained by using this definition and it is not clear that you are only looking at the formula, for example, that the dot product of two vectors does not change if the coordination system is rotated, That the dot product of two straight vectors is 0 (the length of the projection is clearly shu in this case Somewhere) or a vector dot product is the square of its length.

Instead of using a geometric interpretation there is something less obvious, that is the e-dot product commute, i.e. the (The fact that is considering the formula).

There is also an important point to consider that if b 1 is then the length of the dot product & lt; A, b & gt; Only a is the length of the launch of B (taken with the proper signal).

Given this explanation, the formula for calculating reflection on the plane is quite simple:

Comments