# Linked Questions

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### How to find transformation matrix, specifically a rotation, between two given 3d vectors? [duplicate]

How to find transformation matrix, specifically a rotation, between two given 3d vectors? I've found something about it but with quaternions. I don't know anything about quaternions. So it would be ...
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If I know that a vector $\vec{y}$ resulted from shifting another vector by a vector $\vec{d}$, it is easy to get the original vector back as simple as $\vec{x}=\vec{y}-\vec{d}$. Now suppose that $\... 6answers 3k views ### How can I calculate a$4\times 4$rotation matrix to match a 4d direction vector? I have two 4d vectors, and need to calculate a$4\times 4$rotation matrix to point from one to the other. edit - I'm getting an idea of how to do it conceptually: find the plane in which the vectors ... 1answer 6k views ### How to find Euler's angles? I have read about Euler's angles and matrices, including$zxz,zyz$, etc . I am not obliged to use a specific rotation but rather I want to figure out what angles I need to use for alpha,theta, gamma ... 3answers 753 views ### Decomposing rotation into rotation around certain axis and remaining rotation Let R be a rotation matrix in three-dimensional euclidean space, R ∈ SO(3). Let v be a unit vector in said space. Is it possible to decompose R into matrices A and B so that following holds? AB = ... 2answers 993 views ### Rotation of a regular tetrahedron The tetrahedron can be written with its apex at the north pole of a sphere with the four vertices: \begin{eqnarray} a(0,0,\sqrt{6}/4) \; , \; a(\sqrt{3}/3, 0, -\sqrt{6}/12) \; , \; a(-\sqrt{3}/6, 1/... 2answers 2k views ### Calculate quaternions from two directional vectors. I am using RobotStudio to move an end-effector from one coordinate and direction to another coordinate and direction. I understand how to move the robot to all my points, but for the direction T need ... 2answers 302 views ### Is there a close form solution for parallel transport on 2 sphere along the great circles. I need to transport a tangent vector on 2-sphere from point$p$to$qalong the geodesic, which is defined using great circles in this case. I believe there are iterative solutions to achieve that ... 1answer 2k views ### Rotating a quaternion around its z-axis to point its x-axis towards a given point How can i rotate a quaternion around its z-axis in order to make the x-axis point towards a certain (x,y)-point? I have been able to calculate quaternions by rotating a unit vector [0,0,1] onto ... 1answer 1k views ### find 3 angles to rotate vector to align with second vector First I would like to say that I have seen posts such as that found here: Calculate Rotation Matrix to align Vector A to Vector B in 3d? As well as formulas such as: https://en.wikipedia.org/wiki/... 1answer 1k views ### Finding normal of arbitrarily oriented ellipsoid For an axis-aligned ellipsoid, the equation is $$\frac{x^2}{a^2} + \frac{y^2}{b^2} + \frac{z^2}{c^2} = 1.$$ Witha=b$this will give a spheroid with the$z$axis as its symmetry axis. A spheroid ... 2answers 488 views ### Find orthogonal matrix Q Find$3 \times 3orthogonal matrix Q such that: $$Q \left[\begin{array}{r} 3\\ 0 \\ 4\end{array}\right] = \left[\begin{array}{r} 5\\ 0 \\ 0\end{array}\right]$$ How can I find matrix Q if I only ... 2answers 327 views ### Generating uniformly distributed points within rotated ellipsoid I want to generate uniformly distributed points within an ellipsoid that has been rotated. I have the vectors for the major, minor and intermediate axes of the rotated ellipsoid. The ellipsoid is ... 0answers 514 views ### How can I use the Bullet-Physics's ray-cast normal to calculate angles for a object to lay on a surface? [Give the normal of a surface in XYZ format, how do I calculate rotations (also in XYZ format) needed to set an object parallel to the surface?] I have a collision library that uses the bullet ... 0answers 513 views ### Rotate basis to align with vector I have a coordinate system with the BasisB=(e_x, e_y, e_z)$and two vectors$r$and$a$. Now, I want to rotate the basis so that the$e_x$unit vector points in the direction of the vector$r(x,y,z)\$...

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