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.
how to find the closest plane closest to a few random points in the 3D environment. We know that the sum of square distances from point to plane can be calculated.
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.
I want to fill the clipped model in a simple way.
For every single list, sort the points on the list and connect the last point and the first one if it’s opened. Take the first point on the list and find its two neighboring points, construct a triangle by them.
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.
I want to find the boundary of all projected points which are computed from the points on the 3D model. The red arrow in the following image represents the projected vector. I will project the original points on the 3D model to a plane.
cut a volume by a plane and display the cut section. The left renderer contains the original volume object, and the right renderer shows the cross section in the window.
I create two renderers that show the same 3D model. Make the camera in the right renderer linkage with the left one’s, that means we can get the same view in the right renderer when we modify the status of the camera of the left renderer.
Here is all information of implementations.