How to Rotate and Scale a Vector in Python

Vector in Python
Vector in Python

Whether you are doing a 3D render or a complex numerical calculations, there are times when you need to rotate and scale a vector. There are many tools available to accomplish this, but which one is right for you? When deciding on a scaling strategy, it is important to keep in mind the magnitude of the operation, as well as the order in which it is performed. This will ensure that the results are both accurate and useful.

The most obvious choice is to do the rotation first, but this can have negative repercussions on the subsequent scaling operation. For instance, if you are attempting to multiply matrices, you will need to translate a matrix of length L into a smaller matrix of width T. The best way to accomplish this is to do it in the order of L to T. This will also ensure that you are able to read the results from left to right.

Similarly, the most obvious operation is to rotate the vector, but this can be done in the opposite direction. This is especially true if the axis of rotation is the z axis. In other words, rotate and scale a vector in python. You can do so by setting the axes of rotation to the appropriate axis. The pygame function above is an excellent example of this, as it rotates a vector counterclockwise around the z axis. In pygame, this makes the rotation look clockwise when displayed.

While there are a number of tools available for rotating and scaling a vector, none of them are quite as efficient as the Python arithmetic functions, which offer a high level of abstraction and robustness. For example, you can use the matrix subclass in NumPy, whereas this is still available in version 1.17 of Python. Likewise, if you want to create an object with multiple axes, you can use the corresponding subclass in the same package. The latter is of particular interest for the mathematically inclined.

The Python maketransform function above builds a 3×3 transform matrix. It is built using the same dtype as the input. You can then use the reshape function to adapt the output shape to the input array. As with other Python transformations, the reshape function is a bit more complicated than it sounds. You can also scale and reverse the axes of rotation, but this is usually not required.

The most important lesson to learn from this lesson is that in order to do the rotation and scale a vector correctly, you will need to take into account the order in which you perform the aforementioned operations. For instance, if you want to translate a vector of length L into a matrix of size T, you should first translate L into T, then apply a scale transformation to T. After that, the transformation can be repeated. This is an effective and time efficient method, but it should be used in conjunction with the aforementioned operations.