We can get the third vector by cross product of two vectors, the new vector is perpendicular to the first vectors. We also know the geometry meaning of the determinant, it’s sign volumn value for three vectors.
Let’s create a few random points and use algorithm library CGAL and the visualization toolkit (VTK) to find and draw the closest line by a demo.
We defined three different matrix A(m x n), B(n x r), and C(n x r), they satisfy distributivity of multiplication over addtion: A(B+C) = AB + AC.
Building CGAL libraries (non header-only mode)
Then we can build the project and install libraries.
Create a matrix and do transpose operation.
Here are simple demos show how to use CGAL, the Computational Geometry Algorithms Library. I use cmake to manage these small projects.
Use vtkSurfaceReconstructionFilter to get mesh from the point coordinates.
I use the advancing front surface reconstruction way to get the mesh from point cloud information.