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The formula for calculating a reflection vector is as follows: $$ R = V - 2N(V\cdot N) $$ Where V is the incident vector and N is the normal vector on the plane in question.

Why does this formula work? I haven't seen any good explanations of it. I don't understand the significance of doubling the normal vector, nor the relevance of taking the dot product.

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    Remember that the dot product is related to the cosine of the angle between two vectors.2011-05-01

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