In Non-Sequential Mode, all the objects’ orientation are specified by the parameters Tilt About X/Y/Z. In Sequential Mode, Coordinate Break surfaces use Tilt About X/Y/Z to define the orientation of the next surface. In OpticStudio, we commonly use Tilt About X/Y/Z to rotate Sequential surfaces or Non-sequential objects to a desired orientation. Global_tilt_xyz_from_glcr_zplm.zip Introduction It will explain what the rotation matrix and the Tilt About X, Y, Z are, as well as it will answer some related frequently asked questions.Īuthored By Michael Cheng, Yuan Chen, and Michael Humphreys Downloads * Method to get the horizontal reflection of the matrix.This article will give a better insight on how surfaces are positioned in OpticStudio in Sequential and Non-Sequential Mode. * part of the transpose operation in case its not a square matrix. * elements because the physical structure of the matrix may change as a Take reflection of the transpose against the vertical axis.Take reflection of the resultant matrix against the vertical axis. Take reflection of the matrix against the horizontal axis.Take reflection of the transpose against the horizontal axis.Here is an example of vertical reflection. If the value of N is odd then the position of Column 1 + N/2 remains intact and it is not changed, that is why it is also called vertical reflection through the middle column. This precisely means exchanging one column with the other such that the first column becomes the last, the second column becomes the second last and so on.įor a matrix of dimension M * N there are M rows and N columns and vertical reflection means Column N is exchanged with Column 1, Column N-1 is exchange with Column 2 so on. Here is an example of horizontal reflection. If the value of M is odd then the position of row 1 + M/2 remains intact and it is not changed, that is why it is also called horizontal reflection through middle row. This precisely means exchanging one row with the other such that the first row becomes the last, the second row becomes the second last and so on.įor a matrix of dimension M * N there are M rows and N columns and horizontal reflection means Row M is exchanged with Row 1, Row M-1 is exchange with Row 2 so on. In simple words, if we can exchange each column with each of the rows in order (1st column with first row, second column with second row and so on.) then at the end of the iteration we will get the transpose of the matrix. The red boundaries (rows) in the matrix A becomes the column in A T and the blue boundaries (columns) in matrix B becomes the row in B T. Here is an image to demonstrate the transpose of a given matrix. So, let us first talk about transpose.Ī transpose of a matrix A(M * N) is represented by A T and the dimensions of A T is N * M. Prerequisites – Matrix RotationsĪ necessary prerequisite for the matrix rotations is to have knowledge about matrix transpose. Depending on the degrees by which we want to rotate, the permutations of the operations may vary. Just for a formal definition, I would say that matrix rotation is a structural re-arrangement of the rows and columns of the matrix and it is achieved by a sequence of operations on the matrix as a whole. This can only be explained by nice diagrams.
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