I am planning to construct a CAD model from a point cloud.
The point cloud is a list of unique 3D point.
The CAD model is a list of triangles (2D triangles not tetrahedra) in a 3D space.
Lets say there is a triangle with vertices $(A,B,C)$ and there is a point $P$.
I would like to check if the $P$ is inside the inner region (sphere, ellipsoid or what ever based on Delaunay) belonging to the triangle.
Based on Delaunay method, how can I perform such a check?
I am looking for the mathematical details not just a English description.