rotation matrix euler angles

The rotation matrix is calculated with: 5 0 obj There are multiple conventions as to what the euler angles are called (x,y,z,alpha,beta,gamma,yaw,pitch,roll,heading,elevation,bank,.) In this convention, the rotation given by Euler angles , where 1. the first rotation is by an angle about the z -axis using , 2. the second rotation is by an angle about the former x -axis (now ) using , and 3. the third rotation is by an angle about the former z -axis (now ) using . For example, one might want to factor a rotation as R= R x( x)R y( y)R z( z) for some angles x . Why can we add/substract/cross out chemical equations for Hess law? C ( 3 2 1) = R1()R2()R3() = [ cc cs s ssc cs sss + cc sc csc + ss css sc cc] 30 50 10 0. There are several methods to compute the axis and angle from a rotation matrix (see also axis-angle representation ). A rotation about any arbitrary axis can be written in terms of successive rotations about the Z, Y, and finally X axes using the matrix multiplication shown below. 3 Euler's angles We characterize a general orientation of the "body" system x1x2x3 with respect to the inertial system XYZ in terms of the following 3 rotations: 1. rotation by angle about the Zaxis; 2. rotation by angle about the new x The code below shows an example. Should we burninate the [variations] tag? Furthermore, there are 12 possible choices of the Euler angles. All of these forms are derived from the more general rotor form, which is provided by GA. about the z-axis, each rotation being applied about one of the world axes as opposed to one of the body axes. We have designed this FREE crash course in collaboration with OpenCV.org to help you take your first steps into the fascinating world of Artificial Intelligence and Computer Vision. xXrF+X"Iq*d!cTsowK8!>OLM!> j|2#lf9 }U48YYV\Lg,m-n+aPompy70IO#N%[b]0)y1\gw(*G*Hj mY-d&@^6GxKu~|U\w3}VS 7@\pa\oaOUXLV>/2 "0duUD?MTU-tkixc*k6oK1&1,[~!ftDct9 uX7h-E[zhSg=( Em[&M]a^u6{*whwAX>t So any rotation could be decomposed into the sequence of three elementary matrices. We hate SPAM and promise to keep your email address safe., Robotics Engineering, Warsaw University of Technology, PhD in HCI, Founder of Concepta.me and Aptum, Computer Science Student, University of Central Lancashire, Software Programmer, King Abdullah University of Science and Technology. 0. The default order for Euler angle rotations is "ZYX". So, I decided to be (almost) consistent with the MATLAB implementation of rotm2euler.m. Site design / logo 2022 Stack Exchange Inc; user contributions licensed under CC BY-SA. Let's say you want to rotate a point or a reference frame about the x axis by angle . The Euler angles are specified in the axis rotation sequence, sequence . Now suppose we are given a matrix and are required to extract Euler angles corresponding to the above rotation sequence, i.e. Let's further assume that we are talking about 3D rotations. Found footage movie where teens get superpowers after getting struck by lightning? Now you are thinking, the choice is easy. Their definitions are as shown in the following graph- The first Euler Angle is measured by a counterclockwise rotation about the z axis of the x axis. This example will show how the 3 successive rotations are carried out and that they indeed bring the laboratory frame (XYZ) }?E.X[N{`I+>N#)~ vZuTx4k'H/~6TI EvB^6EZq6R&RvZITQ_z_XZmhkdXKi~+"QGzaDJr.6W`ly )&.cwF7hbgeICx& cause the angles seem too interdependent ? If the second rotation is about the axis, this is called the " convention". The values in the rotation vector, will be the euler angles (roll, pitch, yaw --> angles about x,y,z axes respectively). The rotation matrix corresponding to this rotation is given by, Rotations by and about the y and z axes can be written as. The choice of rotation unit (radians or degrees) effects the interpretation of the theta in angle-axis form and all three Euler angles. Because there are three Euler angles, the parameterization of a rotation tensor by use of these angles is an example of a three-parameter representation of a rotation. This notebook demonstrates how to use clifford to implement rotations in three dimensions using euler angles, rotation matices and quaternions. There are six possibilities of choosing the rotation axes for proper Euler angles. However, when things get more complex, Euler angle will be hard to work with. How to draw a grid of grids-with-polygons? detail::tmat4x4<valType> glm::eulerAngleYX. However, no further explication and analysis are presented in the textbook for all the other matrices. What is the difference between the following two t-statistics? To subscribe to this RSS feed, copy and paste this URL into your RSS reader. Is it OK to check indirectly in a Bash if statement for exit codes if they are multiple? You'll get a detailed solution from a subject matter expert that helps you learn core concepts. Composing a rotation matrix Given 3 Euler angles , the rotation matrix is calculated as follows: Note on angle ranges These are (1) the rotation matrix, (2) a triple of Euler angles, and (3) the unit quaternion. How to constrain regression coefficients to be proportional, Horror story: only people who smoke could see some monsters, Correct handling of negative chapter numbers. Please read the Euler Angle Formulas document by David Eberly . Converting a rotation matrix to euler angles and back - special case? This produces an intersection line between the old x . http://www.staff.city.ac.uk/~sbbh653/publications/euler.pdf, I propose to use the PCL library to do that with this formulation, you need just to initialize the roll, pitch, yaw and a pre-calculated transformation matrix you can do it. A rotation matrix is a rotation matrix is a rotation matrix. And it quite looks like the formulas are wrong. The code below shows a method to find the Euler angles given the rotation matrix. If I use the rodrigues matrix I give as an example I get the following euler angles. I'm having trouble understanding the Euler angle decomposition order when defining a rotation matrix manually, via the python api, and then using matrix.to_euler() (from mathutils). `D% E SL mCak006R'R\IDgbE"Zp2Rj]-#VyT/9,c\MOF/kg?djcRP21 F{5]EzB)Ka|1T(%% CY(5 P A rotation matrix from Euler angles is formed by combining rotations around the x-, y-, and z-axes. The Euler angles are specified in the axis rotation sequence, sequence. In this formulation , and are the Euler angles. CiteSeerX - Document Details (Isaac Councill, Lee Giles, Pradeep Teregowda): This document discusses a simple technique to find all possible Euler angles from a rotation matrix. The form of the factorization depends on the needs of the application and what ordering is speci ed. ]MDHIx,#J^&C4s2z. Quaternion to Rotation Matrix, incorrect values using Eigen Library, Rotation matrix to euler angles with opencv. The six possible sequences are: z1 - x - z2 (intrinsic rotations) or z2 - x - z1 (extrinsic rotations) x1 - y - x2 (intrinsic rotations) or x2 - y - x1 (extrinsic rotations) The following command defines a rotation by its three Bunge Euler angles. Asking for help, clarification, or responding to other answers. 3 0 obj << 3D Math Primer - Aimed at complete beginners to vector and matrix algebra How to generate a horizontal histogram with words? I guess I am quite late but I'll answer it nonetheless. What is a good way to make an abstract board game truly alien? Euler Angles to Rotation Matrices The easiest way to think about 3D rotation is the axis-angle form. Asking for help, clarification, or responding to other answers. The easiest way to think about 3D rotation is the axis-angle form. The course will be delivered straight into your mailbox. z-y'-x'' (intrinsic) which means: First rotate around the z axis with an angle , then around the new y axis with and then around the new x axis with . Try to get the 3x3 matrix using the inverse conversion. If you use a row vector, you have to post-multiply the 33 rotation matrix and if you use the column vector representation you have to pre-multiply the rotation matrix to rotate the point. There are three distinct functions for computing elemental rotation . As far as I know, it is not convenient to use rotation matrices for angles like 90 or 180 degrees (no matters if they are positive or negative) because you are at risk of singularities. The Rodrigues function has the math harcoded into it ( and I think it can be checked by Taking the 2 rotation matrices and multiplying them as - R = Ry * Rz * Rx and then looking at the place in the code where there is a acos(R(2,0)) or asin(R(0,2) or something similar,since one of the elements of "R" will usually be a cos() or sine which will give you a solution as to which angle is being found. Given a rotation matrix R, we can compute the Euler angles, , , and by equating each element in Rwith the corresponding element in the matrix product R z()R y()R x(). Naively interpolating the X,Y and Z angles will be ugly. the set of Euler angles ZXZ is given by \varphi = A\tan 2\left (r_ {13}, - r_ {23} \right) = Atan2(r13,-r23) \vartheta = A\tan 2\left (\sqrt {r^ {2} _ {31} + r^ {2} _ {32} } , r_ {33} \right) = Atan2( r312 +r322,r33) \psi = A\tan 2 \left (r_ {31}, r_ {32} \right) = Atan2(r31,r32) when (0, ). The output of the following code should exactly match the output of MATLABs rotm2euler but the order of x and z are swapped. Euler Angles This means, that we can represent an orientation with 3 numbers Assuming we limit ourselves to 3 rotations without successive rotations about the same axis:. The only course I've ever bought online and it's totally worth it. Any arbitrary rotation can be defined by an axis of rotation and an angle the describes the amount of rotation. Moreover, rotation matrices are orthogonal matrices with a determinant equal to 1. The net transformation is given by the matrix equation. I was doing a self-study on AI, when I came across with Opencv summer course. This understanding is a crucial part to build a solid foundation in order to pursue a computer vision career. And I convert the received radians to degrees. For instance : Interpolating smoothly between 2 orientations is hard. When the rotation is specified as rotations about three distinct axes ( e.g. Thanks for contributing an answer to Stack Overflow! def isrotationmatrix (r) : rt = np.transpose (r) shouldbeidentity = np.dot (rt, r) i = np.identity ( 3, dtype = r.dtype) n = np.linalg.norm (i - shouldbeidentity) return n < 1 e- 6 # calculates rotation matrix to euler angles # the result is the same as matlab except the order # of the euler angles I can sure tell you that this course has opened my mind to a world of possibilities. To subscribe to this RSS feed, copy and paste this URL into your RSS reader. For example, rotation in 3D can be represented as three angles that specify three rotations applied successively to the X, Y and Z axes. Given these three angles you can easily find the rotation matrix by first finding , and and then multiply them to obtain . have a look at this paper - marcoresk Apr 24, 2017 at 8:40 Add a comment | 3 Answers I know it is a bad pun but truth can sometimes be very punny! Find centralized, trusted content and collaborate around the technologies you use most. %PDF-1.2 Now suppose we are given a matrix and are required to extract Euler angles corresponding to the above rotation sequence, i.e. )@_\+_DpL>5Ff@-9=U~I0;~3Th5QOjn w-f;N3AD!yEmCl^.H Sets of Euler Angles In this way, one can obtain 12 different rotations, depending on which axes one chooses: 1-2-1, 1-3-1, 2-1-2, 2-3-2, 3-1-3, 3-2-3; 1-2-3, 1-3-2, 2-1-3, 2-3-1, 3-1-2, 3-2-1. The problem is that Qapprox is no longer a rotation x y z all react to single pose change the rotation matrix is received from opencv cvPOSIT function so the points of interest might be wrong and giving this confusing effect but somehow i think im just doing the conversion wrong :). and in which order they need to be applied. So the problem is I get the correct values but in a wrong order. Computing Euler angles from a rotation matrix. The problem is how to approximate the rotation matrix. Every rotation in three dimensions is defined by its axis (a vector along this axis is unchanged by the rotation), and its angle the amount of rotation about that axis (Euler rotation theorem). I really enjoyed this course which exceeded my expectations. Sa3%2^]p'VIpNZ+r8wv] of the files ( {OPENCV_INSTALLATION_DIR}/apps/interactive-calibration/rotationConverters.cpp ) from the source code of openCV 3.3, It seems to me that openCV is giving you Y-Z-X ( similar to what is being shown in the code above ). Wrong. See Answer Show transcribed image text Expert Answer Transcribed image text: Q3. Suppose we have a square matrix P. Then P will be a rotation matrix if and only if P T = P -1 and |P| = 1. # checks if a matrix is a valid rotation matrix. This presentation is at a Undergraduate in Science (Math, Physics, Engineering) level. Find centralized, trusted content and collaborate around the technologies you use most. There are additional ambiguities while defining rotation matrices. Determination of Euler angles is sometimes a necessary step in computer graphics, vision, robotics, and kinematics. OpenCV Decompose Projection Matrix euler angle wrong direction? X-Y-Z ) they should be called TaitBryan angles, but the popular term is still Euler angles and so we are going to call them Euler angles as well. How to help a successful high schooler who is failing in college? Euler's angles Therefore a generic rotation is described in turn by a rotation matrix R. Any matrix of this type can be described as the product of successive rotations around the principal axes of the XYZ coordinates, taken in a precise order. Saving for retirement starting at 68 years old. My code returns x first. The keyword "engineering oriented" surprised me nicely. find angles , , which make the two matrices equal. So, with the function provided by the aruco library for pose estimation, rotation vector will be available. Otherwise, if (, 0) then the solution is Is it considered harrassment in the US to call a black man the N-word? Right ? Thanks for contributing an answer to Stack Overflow! Euler Angles; Matrix; Rotations . We have designed this Python course in collaboration with OpenCV.org for you to build a strong foundation in the essential elements of Python, Jupyter, NumPy and Matplotlib. However, the solution may or may not be obvious. This can be written with , , etc. 3D rotations matrices can make your head spin. example rotm = eul2rotm (eul,sequence) converts Euler angles to a rotation matrix, rotm. too bad i suck at maths, even though im using my own formula since it also works (imho even better) i accept this cause this pdf is a great resource for anyone looking for the answer ;), soi.city.ac.uk/~sbbh653/publications/euler.pdf, Making location easier for developers with new data primitives, Stop requiring only one assertion per unit test: Multiple assertions are fine, Mobile app infrastructure being decommissioned. But you could also represent the same rotation as three angles applied successively to Z, Y and X axes. To these we add a fourth, the rotation vector, which has many of the benets of both Euler angles and quaternions, but neither the singularities of the former, nor the quadratic constraint of the latter. To learn more, see our tips on writing great answers. How do I compose a rotation matrix with human readable angles from scratch? Applying the small angle approximation to Q in (5.5) Qapprox = 1 1 1 = I+b , = . The angles are commonly called yaw pitch roll or heading, elevation and bank. To transform from a coordinate frame XYZ to another frame xyz via Euler angles ( , , ) in the order (X-Y-X) rotation, we can write the overall rotation matrix as the triple product of the individual rotations in reverse order: R = R x ( ) R y ( )R x ( ) Can I spend multiple charges of my Blood Fury Tattoo at once? From the code, it's clear that pytorch3d first compute 3 rotation matrices Rx, Ry and Rz with _axis_angle_rotation, and simply multiply with RxRyRz.You can confirm that from the output that the Rotation Matrix from pytorch3d is exactly the same with the one from RxRyRz.Geometrically, this means first apply the rotation around z axis, then apply rotation around y axis, and then apply . See also: GLM_GTX_euler_angles: Matrix from euler angles. Not the answer you're looking for? And it quite looks like the formulas are wrong Did you find out if openCV is using Y-Z-X? Note that the equation will be different based on which set of Euler angles are desired (i.e., the order in which the Euler angle elemental rotations are intended to be executed). find anglesmatrix and are required to extract Euler angles corresponding to the above Browse other questions tagged, Where developers & technologists share private knowledge with coworkers, Reach developers & technologists worldwide, There are many conventions for euler angles; if you don't tell us which one you are using, it's hard to even check if your formula is right. Where I can, I have put links to Amazon for books that are relevant to the subject, click on the appropriate country flag to get more details of the book or to buy it from them. rotations about 3 dierent axes, to nd the form of a general rotation matrix. There are multiple conventions as to what the euler angles are called (x,y,z,alpha,beta,gamma,yaw,pitch,roll,heading,elevation,bank,) and in which order they need to be applied. We hate SPAM and promise to keep your email address safe. Euler angles are a common way of defining a rotation by combining 3 successive rotations around different axes. The code to be considered takes into account 3 input parameters: the rotation matrix, expressed as a multidimensional array of doubles; the rotation sequence of the axes with which we wish to carry out the transformation; the units of the Euler angles we wish to calculate. What is the deepest Stockfish evaluation of the standard initial position that has ever been done? This implies that it will always have an equal number of rows and columns. Rotations in 3-D can be represented by a sequence of 3 rotations around a sequence of axes. This is a example of a rodrigues matrix I get: I use the predefined rot2euler to convert from rodrigues matrix to euler angles. . I want to do an 'XYZ' euler decomposition, which in common convention assumes a rotation matrix composed of Rx * Ry * Rz (eg. What is the deepest Stockfish evaluation of the standard initial position that has ever been done? By clicking Post Your Answer, you agree to our terms of service, privacy policy and cookie policy. Any arbitrary rotation can be defined by an axis of rotation and an angle the describes the amount of rotation. k:hxaDEGwuo#"I xYtSn'm70T1-OhV@7P Ii$sZ?$DB~Zk&WC0kWa]#O`l Euler angles describe any arbitrary rotation using a set of 3 angles, each angle representing a single axis rotation that is applied in an intrinsic sequence. Why I said I wasn't sure because I just looked at the source code of cv::Rodrigues and it doesnt seem to call this piece of code that I have shown above. Gimbal Lock Gimbal Lock Animation. Is there something like Retr0bright but already made and trustworthy? How do I simplify/combine these two methods for finding the smallest and largest int in an array? Let \mathbf {\Phi} be a set of Euler Angles consisting of the angles \ {\phi, \theta, \psi \}. LO Writer: Easiest way to put line of words into table as rows (list). These angles are called Euler angles or TaitBryan angles. 2 Factor as a Product of Three Rotation Matrices A common problem is to factor a rotation matrix as a product of rotations about the coordinate axes. Quaternions Quaternions are a number system that extends the complex numbers They were first described by Irish mathematician William . By clicking Accept all cookies, you agree Stack Exchange can store cookies on your device and disclose information in accordance with our Cookie Policy. . LO Writer: Easiest way to put line of words into table as rows (list), Short story about skydiving while on a time dilation drug. Comment. Please read the Euler Angle Formulas document by David Eberly. And in my mind, the second matrix represents physically the rotational motion of small rotations. All views expressed on this site are my own and do not represent the opinions of OpenCV.org or any entity whatsoever with which I have been, am now, or will be affiliated. And there are a ton of different ways of representing a rotation as three numbers and a few ways to represent it as 4 numbers. The three independent parameters of the tensor are the angle of rotation and the two independent components of the unit vector . AprilTag - Obtaining rotation information as Euler angles, Euler angles -> 3D rotation matrix-> Euler angles with tensorflow-graphics. As we have already mentioned, any orientation in space can be represented with a 33 rotation matrix. A rotation matrix has three degrees of freedom, and mathematicians have exercised their creative freedom to represent a 3D rotation in every imaginable way using three numbers, using four numbers, using a 33 matrix. Its very useful and includes a lot of formulas for various conventions and you probably should base your code on them if you want to have stable formulas even in the corner cases. %PDF-1.4 The rotation matrix lies on a manifold so standard linearization will result in a matrix which is no longer a rotation. Not specific to OpenCV, but you could write something like this: https://www.learnopencv.com/rotation-matrix-to-euler-angles/ Rotation.from_euler() # Initialize from Euler angles. Is MATLAB command "fourier" only applicable for continous-time signals or is it also applicable for discrete-time signals? For instance, rotating degrees around Z can be done with the matrix cos -sin 0 Rz = sin cos 0 0 0 1 Similar matrices exist for rotating about the X and Y axes: There are several other subsidiary Euler angles can represent any rotation from SO(3) by means of three successive elemental rotations around three independent axes. Lets say you want to rotate a point or a reference frame about the x axis by angle . Euler Summary Video. I prefer women who cook good food, who speak three languages, and who go mountain hiking - what if it is a woman who only has one of the attributes? This can be written with , , etc. Note that the angles needs to be multiplied with degree since all commands in MTEX expect the input in radiant. (I am aware of the fact that the tool works with ZYX coordinates). Correspondence about this page: Book Shop - Further reading. There are six possible ways you can describe rotation using TaitBryan angles X-Y-Z, X-Z-Y, Y-Z-X, Y-X-Z, Z-X-Y, Z-Y-X. OSG CameraViewMatrix). stream I use the following code to convert a 3X3 rotation matrix to angles : does this make any sense ? Is it OK to check indirectly in a Bash if statement for exit codes if they are multiple? A rotation matrix is always a square matrix with real entities. Euler angles are three angles used to describe the orientation of a rigid body, they are typically denoted , , , these angles represent a sequence of three elemental rotations about the axes of some coordinate system Intrinsic and extrinsic rotations Intrinsic rotations For example rodrigues matrix: If someone knows a solution to the problem or can provide me with a explanation how the rot2euler function works exactly. This course is available for FREE only till 22. Water leaving the house when water cut off. Converting a Rotation Matrix to Euler Angles Given a rotation matrix, it is possible to convert back to Euler angles. wXS0k, nva&`^WRm|g4,mwE0nc8)~)26hrO+YKNBG:NY*o|7V53p]?]t3w400#FQ_cuX#O+VAbA aN8\5\Ejb4r5F)bJDHOLWA^;"vf  &*9[H[s9#uJhrc8;D$/PfB/ex*zA5Du6SN9zKx_WK-\kAQM{rUx6]au.~PJ\19B{Xo7SPF Q,Kn$q1&bCsOA[6>?h 1PB'Kiy|2sG Examples collapse all Convert Rotation Matrix to Euler Angles rotm = [0 0 1; 0 1 0; -1 0 0]; eulZYX = rotm2eul (rotm) eulZYX = 13 0 1.5708 0 The rotation matrix ( ) is used to transform the stresses from the machine coordinate system (global) to the slip plane (local) coordinate system based on euler angles. is calculated as. about the z-axis, each rotation being applied about one of the world axes as opposed to one of the body axes. relate the two coordinate systems is by the use of Euler Angles which are denoted in the literature by either[ , ,] or [, , ]. Connect and share knowledge within a single location that is structured and easy to search. How can we build a space probe's computer to survive centuries of interstellar travel? In 2007, right after finishing my Ph.D., I co-founded TAAZ Inc. with my advisor Dr. David Kriegman and Kevin Barnes. Not the answer you're looking for? Creates a 3D 4 * 4 homogeneous rotation matrix from an euler angle Y. I am really impressed with the mix of rich content offered in the course (video + text + code), the reliable infrastructure provided (cloud based execution of programs), assignment grading and fast response to questions. However, the solution may or may not be obvious.. Rotation matrices We start off with the standard . By clicking Accept all cookies, you agree Stack Exchange can store cookies on your device and disclose information in accordance with our Cookie Policy. >> How can we build a space probe's computer to survive centuries of interstellar travel? One of the reasons to avoid them altogether; see, I am trying to use it in opengl glRotatef - updated answer, this one has pseudo code but i feel like i already tried that.. but 1+ and ill try again. Opencv, Rotation matrix to euler angles with opencv Author: Kay Perez Date: 2022-07-13 Solution: rvecs is axis angle representation of rotation, which usually require 4 numbers, [v,theta], but v is required to be unit vector, and thus it's length is encoded as theta, reducing the required numbers to 3. for the code, it should be something like . If you continue to use this site we will assume that you are happy with it. Earliest sci-fi film or program where an actor plays themself. Stack Overflow for Teams is moving to its own domain! x]q?OhG#@l6" (x(\]7W3==3{vC0twWWU|_Oowo$W{6t8yUzKn2~7Wo\D\AnU:n_^O#GXz! A rotation can be represented by several different conventions of euler angles, ex, the Z-X-Y, ect. Determination of Euler angles is sometimes a necessary step in computer graphics, vision, robotics, and kinematics. rev2022.11.3.43005. The authors of the lessons and source code are experts in this field. It seems that you are in the case of singularities. My point is that there is no standard way to convert a rotation matrix to Euler angles. /Filter /FlateDecode 2022 Moderator Election Q&A Question Collection, How to calculate the angle from rotation matrix, Quaternions -> Euler Angles -> Rotation Matrix trouble (GLM), Offset Euler Angles using rotation matrix, Computing Euler angles from rotation matrix: boundary cases, Euler angles to rotation matrix manual transformation for iOS devices, Euler Angles and Rotation Matrix from two 3D points. In general, Euler angles (or specifically roll-pitch-yaw angles) can be extracted from any rotation matrix, regardless of how many rotations were used to generate it.For a typical x-y-z rotation sequence, you end up with this rotation matrix where is roll, is pitch, and is yaw:. Is there a way to make trades similar/identical to a university endowment manager to copy them? When using the rotation matrix, premultiply it with the coordinates to be rotated (as opposed to postmultiplying). I am quite far in the project progress. The course exceeded my expectations in many regards especially in the depth of information supplied. This results in nine equations that can be used to nd the Euler angles. Making statements based on opinion; back them up with references or personal experience. The industry standard is Z-Y-X because that corresponds to yaw, pitch and roll. As far as I know, it is not convenient to use rotation matrices for angles like 90 or 180 degrees (no matters if they are positive or negative) because you are at risk of singularities. Dont quote me on this, ie I'm not 100 % certain but this is one When is use this tool http://danceswithcode.net/engineeringnotes/rotations_in_3d/demo3D/rotations_in_3d_tool.html, You can see that [0; 90; -180] doesn't match the rodrigues matrix but [-180; 0; 90] does.

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