Reflection Matrix in 2D

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Here is a simple setup of a manipulation and reflection matrix in 2D space.

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By using a reflection matrix, we can determine the coordinates of the point , the reflected image of the point in the line defined by the vector from the origin.

The projection of onto the line is . The point is then determined by extending the segment by . As vectors, .

If is normalized (so that , the reflection matrix is . Then , that is, the reflection of a reflection is the identity. Also, .

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Contributed by: Jonathan Barthelet (March 2011)
Open content licensed under CC BY-NC-SA


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