MATRIX FOR REFLECTION OVER Y AXIS SERIES

If need to mirror a translated object, you may want to undo the translation, mirror and translate again, in doing so the object will keep its location while being flipped on the Z axis. The reflection matrix is intended to mirror across the XY plane ( Z = 0). Transformation Matrices : Reflection the line y-x : ExamSolutions Maths Tutorials ExamSolutions 241K subscribers Subscribe 379 83K views 10 years ago Matrix Algebra Tutorial on. So the effect of any set of mirrors can be reduced to a single 3x3.

which reduces to a single effective mirror matrix. If light bounces off mirror 1, then 2 then 3, the net effect of these three reflections is.

MATRIX FOR REFLECTION OVER Y AXIS SERIES

I have not taken translation into consideration. A series of reflections is modeled by successive mirror matrix multiplications. If that is not what you want, I hope you can build the matrix you need using this explanation.Īs you would expect, composing the reflection matrix twice should give you back the original. That means that you will flip the sign of the 1 for the Z axis.Īs said above, the shown matrix keeps X and Y values the same, and flips Z. In other words, both X and Y values stay the same but Z is mirrored. Use matrix multiplication to find the reflection of ( -1,2 ) about the a. (a) Counterclockwise rotation through 120 about the origin (b) Reflection over the y-axis, followed by clockwise rotation through 270 about the origin 2. Pads with the reflection of the vector mirrored on the first and last values of the vector along each axis. Translate the coordinates so that (a,b) becomes the origin. Let's say the point you want to reflect is (x,y). Let (a,b) and (c,d) be any two points on the reflection line.

You say you need to mirror the transformation on the Z axis, I understand this as reflecting against the XY plane. Find the standard matrix of the given linear transformation from R2 to R2. 2 Answers Sorted by: 2 No rotations are needed since there is a formula for reflecting about any line through the origin. To create the reflection matrix based on the major axis, you take the identity matrix and flip signs depending on the reflection you need.

That is, if you have your input matrix M and you multiply by a matrix N that has the reflection. The linear transformation matrix for a reflection across the line y m x is: 1 1 + m 2 ( 1 m 2 2 m 2 m m 2 1) So reflection across the x-axis would be: 1 1 + ( 0) 2 ( 1 ( 0) 2 2 ( 0) 2 ( 0) ( 0) 2 1) ( 1 0 0 1) But I’m having trouble thinking through what the matrix would be when we want to reflect every vector across the y-axis. To get a transformation matrix equivalent to the one you have, but reflected across a major axis you can compose it (multiply it by) a reflection matrix.

Matrix for reflection over y axis