virtual-template | Combining Template Engine and Virtual-DOM

I have been using ceres-solver for a long time now and it is an amazing tool. My usage up until now was not based on reusable code and I am trying to improve this. Ceres uses a specific structure with a specific templated method as an interface to its automatic differentiation. In the problem that I am trying to solve, inheritance makes sense because the different cost functions that I need to have are very similar to each other. I have created an example that is similar (but it makes no sense, sorry). Imagine we want to be able to find the polygon that has a given area. In my example, polygons can be either triangles or rectangles. With this in mind, it makes sense to have a base class that implements everything and specific classes that implement, in this case, the area computation for each specific polygon:

ShapeCostFunction