![]() This file can be saved to the folder "\Macros\" A ZPLM User Defined Operand called "ZPL19.zpl".The attachments of this article contains: A User-Defined Operand can be written using ZPL to retrieve the Tilts About X/Y/Z. However, right now, there is no single operand to give Tilt About X/Y/Z for arbitrary surfaces. The Rotation Matrix can be displayed in the Merit Function using the GLCR operands. LanguageĬalculating Tilt About X/Y/Z in merit function with ZPL macro Here is a list of the ATAN2 definition for some common programming languages. The arguments definition for ATAN2 may be different for a programming language to another. The function ATAN2 used in the above picture takes two arguments: the first argument is x and the second argument is y. The 3 angles are for Intrinsic Rotations (see below). Converting From Rotation Matrix to Tilt About X/Y/Zįrom Rotation Matrix to Tilt X/Y/Z, the 3 angles can be calculated as below. More details are included in the section Intrinsic and Extrinsic Rotations. This is equivalent to rotate the system intrinsically first about X, then about Y, lastly about Z. The above formula could describe the rotation matrix created by an extrinsic rotation, first tilt about Z, then tilt about Y, lastly tilt about X. To get the Rotation Matrix from the three Tilt About X/Y/Z values, the Rotation Matrix can be decomposed as a product of three elemental rotation matrices: a Rotation Matrix around X, a Rotation Matrix around Y and a Rotation Matrix around Z. In Non-Sequential Mode, open Analyze > Prescription Data to see the Rotation Matrix for each object: Converting From Tilt About X/Y/Z to Rotation Matrix ![]() The Global Vertex section shows the rotation matrix, R11 to R33, and Tilt About X/Y/Z together. The Prescription Data in OpticStudio under Analyze.Reports gives the orientation of a surface or object with a Rotation Matrix. The rotation matrix in OpticStudio describes how the local coordinate can be converted to the global coordinate. Here is the relation between the object local coordinates, global coordinates, and the rotation matrix. OpticStudio calculates the rotation matrix to convert between the local coordinate and the global coordinate. In other words, a surface or an object can be rotated to any orientation by first rotating about the X-axis and then the Y-axis and finally the Z-axis. Theoretically, all the possible orientations can be defined by these three values: Tilt About X/Y/Z. ![]() ![]() 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 Since rotations are linear transformations, the effect of rotating a vector from the origin to some arbitrary point, $P = (x, y)$, can be established by considering the rotation of the basis vectors $\hat\right).This article will give a better insight on how surfaces are positioned in OpticStudio in Sequential and Non-Sequential Mode. array ((( c, - s ), ( s, c ))) Out : print ( R ) ]Īs of NumPy version 1.17 there is still a matrix subclass, which offers a Matlab-like syntax for manipulating matrices, but its use is no longer encouraged and (with luck) it will be removed in future. ![]()
0 Comments
Leave a Reply. |
AuthorWrite something about yourself. No need to be fancy, just an overview. ArchivesCategories |