rotational-matrices

问题 How can I calculate in MatLab similarity transformation between 4 points in 3D? I can calculate transform matrix from T*X = Xp , but it will give me affine matrix due to small errors in points coordinates. How can I fit that matrix to similarity one? I need something like fitgeotrans , but in 3D Thanks 回答1: The answer by @rayryeng is correct, given that you have a set of up to 3 points in a 3-dimensional space. If you need to transform m points in n-dimensional space ( m>n ), then you first

问题 I want to compute rate of change of orientation of the iPhone along y axis. 1. Initially i need to define the reference as y axis, 2. Then measure the rate of change of orientation(angular measurement) from the defined reference. Does CMAttitude provides a reliable angular measurements to implement this? Or Can i use rotational matrix or integrate gyroscope data(I implement this method, but it's not going to work due to the drift of the gyroscope). So please suggest me a reliable method to

问题 So I nearly implemented a free-flight camera using vectors and something like gluLookAt. The movement in all 4 directions and rotation around the Y-axis work fine. For the rotation around the Y-axis I calculate the vector between the eye and center vector and then rotate it with the rotation matrix like this: Vector temp = vecmath.vector(center.x() - eye.x(), center.y() - eye.y(), center.z() - eye.z()); float vecX = (temp.x()*(float) Math.cos(-turnSpeed)) + (temp.z()* (float)Math.sin(

问题 I have seen many questions and articles mentioning that Quaternions can be used to derive better,accurate and stable yaw, pitch and roll readings from the iPhone rather than reading it's direct yaw, pitch and roll readings. But at the same time, I haven't seen any proper methods of implementing Quaternions in iPhone platform. As a beginner, It's really hard to know, How these Quaternions works and implementing them in a piece of code? (Sorry for not providing any code as i have no idea of how

问题 After multiplying a lot of rotation matrices, the end result might not be a valid rotation matrix any more, due to rounding issues (de-orthogonalized) One way to re-orthogonalize is to follow these steps: Convert the rotation matrix to an axis-angle representation (link) Convert back the axis-angle to a rotation matrix (link) Is there something in Eigen library that does the same thing by hiding all the details? Or is there any better recipe? This procedure has to be handled with care due to

问题 I am trying to quickly solve the following problem: f[r_] := Sum[(((-1)^n (2 r - 2 n - 7)!!)/(2^n n! (r - 2 n - 1)!)) * x^(r - 2*n - 1), {n, 0, r/2}]; Nw := Transpose[Table[f[j], {i, 1}, {j, 5, 200, 1}]]; X1 = Integrate[Nw . Transpose[Nw], {x, -1, 1}] I can get the answer quickly with this code: $starttime = AbsoluteTime[]; Quiet[LaunchKernels[]]; DIM = 50; Print["$Version = ", $Version, " ||| ", "Number of Kernels : ", Length[Kernels[]]]; Nw = Transpose[Table[f[j], {i, 1}, {j, 5, DIM, 1}]];

问题 I am trying to rotate a pinhole camera in 3D space. I have previously raytraced a room. As good practice I have first done the maths and the tried to program the maths in c++. // Camera position vec3 cameraPos(0, 0, -19); // Rotate camera float& yaw; vec3 c1(cos(yaw), 0, sin(yaw)); vec3 c2(0, 1, 0); vec3 c3(-sin(yaw), 0, cos(yaw)); glm::mat3 R(c1, c2, c3); What I have done to rotate the camera is this: if (keystate[SDLK_LEFT]) { //cameraPos.x -= translation; if (yaw > 0) { yaw = 0.01; } cout

问题 I am having following problem, I have developed code for converting the large array of euler angles to rotation matrices, my data is phi1,phi and phi2 values like as follows phi1 phi phi2 2 3 5 1 2.2 4.3 3 4 5 .....there are other 2 million array of data. but I want to carry out inverse of the rotation matrix formed from first row of euler angles and multiply it to matrix developed from the second row. Then I have to use one of the elements of the resultant matrix. Is there any way to do that

问题 Suppose I have two matrices of PCA loadings loa.orig , and loa.rot , and I know that loa.rot is a rotation (by-hand or otherwise) of loa.orig . ( loa.orig might also have been already orthogonally rotated by varimax or something, but I don't think that matters). I know want to know the angles by which loa.orig has been rotated to arrive at loa.rot . I understand from this comment on another question that "rotations don't commute", and therefore, the order of pair-wise (plane-wise) rotations

问题 Creating a Virtual Trackball Using JavaFX I want to create a virtual trackball device where X and Y mouse drag events rotate my virtual trackball in an intuitive way. Intuitive (at least to me) means, with my scene axes being: X increasing left to right Y increasing top to bottom Z increasing perpendicular to the screen towards the viewer I want vertical mouse drag events to cause the trackball to roll around the scene X axis, and mouse horizontal drag events to cause the trackball to rotate