The eigenvector of a linear transformation doesn’t change in the transformation, and the scale of this vector under the transformation is called the eigenvalue. Practice We use 3D Model Editor to perform the following linear transformation: For more information on how to use the web app 3D Model Editor to Read more…
There are many magical properties in matrix computation, such as: AB != BA A != 0, B != 0, but maybe AB = 0. AB = AC, A != 0, but we can’t get that B = C. People couldn’t understand why it was so different from ordinary numerical calculations Read more…
I found a bug when we do matrix inverse calculation by vtkTransform object. The version 8.2.0 and 9.1.0 of VTK has the same potential risk in vtkMatrix4x4::Invert(const double inElements[16], double outElements[16]).Let’s see the source code, it judges whether the determinant value is zero by ==. The equal comparison operation for Read more…
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…
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…
I take notes about how to rotate vector to a special direction.