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Tag Archives: math
3D Rotations using Rodrigues Rotation Formula
The problem we are addressing here is the rotation of a general 3D vector about a given axis of rotation denoted by by radians. The Rodrigues Rotation Formula is as follows: Example: for a sanity check we can consider that … Continue reading
Posted in Machine Learning, Robotics
Tagged 2D, 2D rotation, 3d, 3D rotation, axis, axis of rotation, cross product, dot product, easy, example, general rotation, math, mathematics, programming, py, python, Robotics, rodrigues, rodrigues formula, rotation, simple, source, source code, spatial, spatial rotation, tutorial, vector
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Extension of 2D Complex Exponential Formula to 3D Rotation
In our previous post, we used , where and are 2D vectors and the formula rotates vector by . This idea can be extended to 3D by converting the vectors to quaternions. Assume and . Also, we consider to be … Continue reading
Posted in Linux, Machine Learning, programming, Python, Robotics, Software, Ubuntu
Tagged 2D rotation, 3D rotation, code, easy, euler formula, euler rotation, exponential complex, math, mathematics, multiply, normal, numpy, pi, plane, programming, pyquaternion, python, quaternion, simple, source code, sourcecode, spatial, vector
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2D Vector Rotation using Complex Exponential
Complex exponential formula represents the relationship between a vector and the rotated version of that vector by as where . Example: Rotate vector by . Answer: which is a vector towards Y-axis (Im axis). In python, we can compute this … Continue reading
Posted in Machine Learning, programming, Python, Robotics, Software
Tagged 2D rotation, code, complex, complex exponential, e, easy, exp, exponential, i, imaginary, j, linux, math, mathematics, numpy, pi, python, python programming, quaternion, real, rotation matrix, rotation vector, sample, simple, source code, sourcecode, transformation, vector, vector rotation, windows
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What is Kronecker Product?
Kronecker Product is a generalization of the outer product of two arbitrary size matrices and results in a block matrix. and then Example: Python example using numpy
Posted in Linux, Machine Learning, Optimization, programming, Python, Software, Ubuntu
Tagged algebra, array, code, easy, explained, inner product, kronecker, kronecker product, math, mathematics, matrix, numpy, outer product, product, programming, python, sample, simple, source code, sourcecode, step-by-step, tutorial, windows
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Quaternions – Use them for Rotation and Transformation
This is the second tutorial on Quaternions. In the previous post, I explained how to use basics of quaternions from the pyquaternion python library. Check the previous post here. In this post, I will show you how to perform spatial … Continue reading
Posted in Linux, Machine Learning, programming, Python, Robotics, ROS, Software, Ubuntu
Tagged beginner, code, computer, easy, example, function, math, mathematics, matplotlib, matrix, numpy, programming, pyplot, pyquaternion, quaternion, rotation, sample, simple, software, source, source code, spatial rotation, spatial transformation, step by step, transformation, tutorial, vector, windows
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Quaternions – How to generate and operate them in Python?
Python Package There are several python libraries (modules) that you can install. Here, I am going to use pyquaternion Installation This package can be installed as follows pip install pyquaternion Usage After installing the package, use it as follows: Â Forming … Continue reading
Posted in Linux, Machine Learning, programming, Python, Robotics, ROS, Software, Ubuntu
Tagged 3d, 3D rotation, beginner, code, conjugate, conjugation, easy, example, inverse, inversion, magnitude, math, mathematics, matrix, norm, normalization, normalized, numpy, package, pyquaternion, python, quaternion, Robotics, rotation, sample, script, simple, spatial, spatial rotation, spatial transformation, step by step, transformation, tutorial, vector
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Linear Transformation of Random Variables
Linear Transformation of Random Variables is a very basic yet important operation in Statistics results of which are extensively used in different methods and algorithms in Machine Learning. Assume is a linear function, , where, is a random variable, and … Continue reading
Generating a trajectory of quaternions between two given quaternions
First, check my previous post on slerp to learn how to interpolate between two quaternions. In this post, we make a function that uses the previously developed interpolation to generate points (quaternions) between and initial and a final quaternion namely, … Continue reading
Posted in control, Linux, Machine Learning, MATLAB, programming, Robotics, ROS, Software, Ubuntu, Uncategorized
Tagged code, end-effector, example, geometry, interpolate, lerp, linear interpolate, math, mathematics, Matlab, quaternion, robot, rotation, simple, slerp, source code, step by step, trajectory, tutorial
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Slerp: Spherical linear interpolation in quaternion space
in my previous post, I explained the simple Lerp method for calculating linear interpolation in the quaternion space. I also mentioned that while normalizing the output could help to get an optimized result, the velocity curve is not constant. To … Continue reading
Posted in Linux, Machine Learning, MATLAB, Optimization, programming, Robotics, ROS, Software, Ubuntu, Uncategorized
Tagged 3d, 4D, code, easy, example, geometry, interpolation, lerp, lie group, linear, math, mathematics, Matlab, orientation, quaternion, robot, Robotics, ROS, rotation, simple, slerp, source code, step by step, tutorial
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