Affine transformation can be decomposed to translation, rotation, and scale. As we know, the transformation can be represented by matrix. Related post: https://www.weiy.city/2021/11/the-releationship-between-local-transform-and-pose-transform/ It can be computed by translate matrix and rotate & scale matrix. Example: I try to do decomposition for a matrix. Read more…
We know the matrix shearing object along a particular axis looks like: The shear transform can help us to approve that when a normal vector is transformed using the same matrix that transforms the points on an object, the resulting vector may not be perpendicular to the surface Read more…
As with 2D transforms, any 3D transformation matrix can be decomposed using SVD into a rotation, scale, and another rotation. Any symmetric 3D matrix has an eigenvalue decomposition into rotation, scale, and inverse-rotation. Finally, a 3D rotation can be decomposed into a product of 3D shear matrices. Rotate about z-axis: Read more…
Here are three vectors (1, 0, 1), (-1, 0, 1) and (0, -1, 0) in the 3D world space. Define a position pos(1, 1, 0). These vector and position forms a new coordinate system A. The inverse result is status B. The original world coordinate system can be changed to Read more…
Here are four points in 3D space, we will take them and generate another four points to draw a cube. Construct triangles to form cells for the mesh, the normal of every cell is toward inside. Here are all details about the generation. Update on 2023.10.17: The cells’ normals generated Read more…
The post is based on https://www.weiy.city/2021/11/vtk-rotate-vector-to-special-direction/. We will rotate the three axes of the world coordinate system to particular directions. #include <iostream> #include <vtkSmartPointer.h> #include <vtkTransform.h> #include <vtkActor.h> #include <vtkConeSource.h> #include <vtkRenderer.h> #include <vtkRenderWindow.h> #include <vtkPolyDataMapper.h> #include <vtkRenderWindowInteractor.h> #include <vtkAxesActor.h> #include “../point.hpp” using namespace std; double AngleBeteewnTwoVector( Point vec0, Point Read more…
We have to create zip file from output folder. After that users can download the result. Install zipfile module for python. pip install zipfile36 Use it in our python script to generate zip file. import sys, fitz # import the bindings if sys.version_info >= (3, 6): import zipfile else: import Read more…
I take notes about how to rotate vector to a special direction.
We need to install PyMuPDF which is a Python binding with support for MuPDF (current version 1.19.*), a lightweight PDF toolkit before our work. pip3 install –upgrade pip pip3 install –upgrade pymupdf Write python script for saving PDF page to image. import sys, fitz # import the bindings if __name__ Read more…