Solved

# Vector of Relfection

Posted on 2009-04-20

Hi again,

Right, I have come along way since my last post. I now fully understand why no answer was given before when I asked "How do I get the resultant angle of an object bouncing off a wall". Well first of all I asked the wrong question, what I really needed was the vector of reflection.

Second, oh boy, was I not prepared for the complexity of information that was involved lol! Anyway, I have read and re-read many papers on vectors and vector geometry. I am really really close to finally pulling off a proper vector reflection but im stuck!

I know how to add vectors together, I know how to use dot products, I know how to multiply a vector by another vectors magnitude (Just a scalar).

But I dont understand whats going on in this formala for the vector of reflection.

Given...

I = Normalised Vector of Incidence (IE, the vector velocity of the ball)

N = The Normalised version of the Perpendicular of the Line that has been collided with

R = The resulting vector of reflection

R = I - 2(I.N)N

Right, now the thing I dont understand the the bit on the end where we multiply (I.N) by N

(I.N)N

I can work out the dot product between I.N, but then I dont know how or WHAT method I should use to multiply that value by the N on the end.

Just as an example, I was doing some working on paper to produce a vector which I know what the answer should be.

I used

I = (1, -1)

Vector of the Line collided with = (2,2)

The perpendicular of the line collided with = (-2,2)

The magnitude of the perpendicular = 2.828427125

The normalised version of the perpendicular = (-0.7071067811, 0.7071067811) = N'

The normalised version of the vector of incidence = (0.7071067812, -0.7071067812) = I'

The Dot Product of I.N

(I.N) = (-0.5, 0.5)

Since R = I - 2 (I.N)N

I multiply the vector (I.N) by the two then I get

R = I - (-1,1)N

Ok, but at this point, -1,1 is already the answer!

So how do I finish this? How do I multiply (-1,1)N. If I used the magnitude, which is 1, I get the same answer but the completely wrong answer (I think) after I subtract it from I.

I read several tutorials on this and some seem to have slighty different equations than the one I should shown.

In one tutorial it told me to Normalise "I" before I do the equation R = I - 2(I.N)N

Any advice would be very much welcome.

Thanks again!