Algorithm to find the coordinates of a point which is the reflection of a point about a line in 3D

Question

I am currently working on a project on Matlab and I need to find the coordinates of a point which is reflected about a line. I know how to do it in 2D but in 3D things are getting ugly.

So, we have a line which goes through two points A(x1,y1,z1) and B(x2,y2,z2). P1(x0,y0,z0) is reflected about that line and i need an algorithm to find the coordinates of reflection of P1.

This question appears to be off-topic because it is about maths/geometry (try http://math.stackexchange.com). — Oliver Charlesworth, Mar 30 '14 at 16:26
I need the algorithm for this question. So, I better edit the content. — user3478485, Mar 30 '14 at 17:15
It sounds like you need the equation(s), which makes it a pure geometry issue. — Oliver Charlesworth, Mar 30 '14 at 17:17
Can you look at this question: [link](http://stackoverflow.com/questions/3306838/algorithm-for-reflecting-a-point-across-a-line) — user3478485, Mar 30 '14 at 17:20

score 0 · Accepted Answer · answered Mar 30 '14 at 17:33

0

At first, find projection L of point P to line AB.

L = A + AB * ScalarProduct(AB, AP) / ScalarProduct(AB, AB)

Then calculate reflection

P' = P + 2*(L-P) = 2*L-P

answered Mar 30 '14 at 17:33

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Algorithm to find the coordinates of a point which is the reflection of a point about a line in 3D

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