rotational-matrices

问题 Decomposing rotation matrix (x,y',z'') - Cartesian angles Im currently working with rotation matrices and I have the following problem: Given three coordinate systems ( O0,x0,y0,z0; O1,x1,y1,z1; O2,x2,y2,z2 ) which coincide. We rotate first the frame #1 with the respect to frame #0, then the frame #2 with respect to frame #1. The order of the rotations: R = Rx_alpha * Ry_beta * Rz_gamma , so first about x , then y' , then z'' , which are also known as the Cartesian angles . If R1 stands for

问题 This is a question from Cracking the Coding Interview. The solution says that the program rotates the exterior edges, then the interior edges. However, I'm having trouble following the logic of both the for loops. Could somebody explain the logic of the code (e.g. why they do "layer < n/2" and the four steps of "left -> top" and "bottom -> left" etc)? On a side note, how would one's thought process be when coming up with this during a coding interview? Given an image represented by an NxN

问题 This is a question from Cracking the Coding Interview. The solution says that the program rotates the exterior edges, then the interior edges. However, I'm having trouble following the logic of both the for loops. Could somebody explain the logic of the code (e.g. why they do "layer < n/2" and the four steps of "left -> top" and "bottom -> left" etc)? On a side note, how would one's thought process be when coming up with this during a coding interview? Given an image represented by an NxN

问题 Can anyone help me out with Eigen? I tried to convert quaternion to matrix and then back and got completely different matrices. I am not able to trust quaternion before understanding this issue. Here is the code: #include <Eigen/Geometry> #include <iostream> void Print_Quaternion(Eigen::Quaterniond &q){ std::cout<<"["<<q.w()<<" "<<q.x()<<" "<<q.y()<<" "<<q.z()<<"]"<<std::endl; } void Verify_Orthogonal_Matrix(Eigen::Matrix3d &m) { std::cout<<"|c0|="<<m.col(0).norm()<<",|c1|="<<m.col(1).norm()<

问题 I have two separate vectors of 3D data points that represent curves and I'm plotting these as scatter data in a 3D plot with matplotlib. Both the vectors start at the origin, and both are of unit length. The curves are similar to each other, however, there is typically a rotation between the two curves (for test purposes, I've actually being using one curve and applying a rotation matrix to it to create the second curve). I want to align the two curves so that they line up in 3D e.g. rotate

问题 I've been trying to work out how to solve the following problem using python: We have points a, b, c, d which form a rigid body Some unknown 3D translation and rotation is applied to the rigid body We now know the coordinates for a, b, c We want to calculate coordinates for d What I know so far: Trying to do this with "straightforward" Euler angle calculations seems like a bad idea due to gimbal lock etc. Step 4 will therefore involve a transformation matrix, and once you know the rotation

问题 I need to extract the roll pitch yaw angles from a rotation matrix and I want to be sure that what I do is correct. Eigen::Matrix< simFloat, 3, 1> rpy = orientation.toRotationMatrix().eulerAngles(0,1,2); const double r = ((double)rpy(0)); const double p = ((double)rpy(1)); const double y = ((double)rpy(2)); Is that correct? Because I was reading here: http://eigen.tuxfamily.org/dox/group__Geometry__Module.html#gad118fececd448d7485ffea4858775e5a And I was a bit confused when it says, at the

问题 I've recently began putting together an OpenGL ES 1.1/2.0 2D pipeline from the ground up (iPhone only). This pipeline is intended to be used by engineers with no 3D math experience. Commented out are the X and Y axis rotation matrices that produce the exact results they should . The Z rotation matrix seems to do nothing. VERTEX SHADER //THESE WORK /* highp mat4 rotationMatrix = mat4(1.0, 0.0, 0.0, 0.0, 0.0, cos(angle), -sin(angle), 0.0, 0.0, sin(angle), cos(angle), 0.0, 0.0, 0.0, 0.0, 1.0);

问题 I've recently began putting together an OpenGL ES 1.1/2.0 2D pipeline from the ground up (iPhone only). This pipeline is intended to be used by engineers with no 3D math experience. Commented out are the X and Y axis rotation matrices that produce the exact results they should . The Z rotation matrix seems to do nothing. VERTEX SHADER //THESE WORK /* highp mat4 rotationMatrix = mat4(1.0, 0.0, 0.0, 0.0, 0.0, cos(angle), -sin(angle), 0.0, 0.0, sin(angle), cos(angle), 0.0, 0.0, 0.0, 0.0, 1.0);

问题 I've spent a couple weeks on this issue and can't seem to find a proper solution and need some advice. I'm working on creating a Camera class using LWJGL/Java, and am using Quaternions to handle bearing (yaw), pitch and roll rotations. I'd like this camera to handle all 6 degrees of movement in 3D space, and roll. Bearing, Pitch and Roll are all quaternions. I multiply them into a 'change' quaternion, and create a translation matrix from that. I put that in a float buffer, and multiply the