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. A number from the set (90, 180, ,270) by which we need to rotate the matrix.įor simplicity we will consider a matrix to be a 2 dimensional array of integers.We are trying to solve the problem of matrix rotations where the inputs are as follows: This is a very famous interview question and has been asked numerous times. Is there any particular reason you don't want to just write the matrix itself to the file? It would certainly be easier than decomposing it into Euler angles and then reconstructing it.Problem Definition – Matrix Rotation (by 90, 180, 270 degrees) Some of the conversions are easier than others. If you're worried about memory, Euler angles and (compressed) quaternions require only three entries, while matrices can be stored with six. There are methods for converting from any of these representations to any other. Commonly used are Euler angles, axis-angle pairs, matrices, and quaternions. When I come to save it, can I extract the _CURRENT_ x, y and z rotations so that when I reload the object I can apply the x, y and z and see the object in exactly the correct orientation - assuming I am multiplying Rotation x then y then z?There are several different ways to represent a rotation or orientation. Quote:Is there a way to extract the orientation from a Matrix once it needs to be saved? Let's say for example 3 rotations have taken place in 3 different views, each view's rotation looks correct and the object's maintained Matrix represents it's current orientation.
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