Find a closest point in an element given a free point

[YaqiWang]

This can be a useful functionality. In my use case, I have a lot of source points generated separately from the mesh generation. These points are located on a surface, which may not exactly located on element sides when the surface is curved. For each source point, I need to put its contribution on a variable defined on the surface, which requires me to find a point on an element side that is closest to the source point. Currently, I am using a point locator to find an element side closes to the point and then call

const Point mapped_point = FEInterface::inverse_map(dim, elem_side, source_point);

to get the point on the reference element. The reference coordinates are probably outside of the reference element. But because the point is fairly close to the element, this inverse_map call is expected to be successful. I am thinking a quick sub-optimal way to fix mapped_point up so that it is inside the element. Tag @roystgnr because he mentioned he already had some code like this.

I made this a broader issue. For some special types of elements, like an edge, or a triangle, there exists algorithms to do this. But hopefully we can make this support general types of elements including high-order isoparametric elements.