I originally wrote about how I had a shadow that houdini was rendering in a really bonkers way, see: http://www.s0hungry.com/2016/10/24/incorrect-shadows-in-houdini-with-the-mantra-renderer/
I have figured out what is going on, thanks to the help of a side fx engineer who commented on a post I made on the forums.
It seems like when you place down a box in houdini, by default there is a single vertex normal on each corner of the box. This is a shared vertex normal (notice that it is pointing in a direction that isn’t really normal to the flat surface).
This means that if a shadow is going to fall on this box, the renderer will try to figure out what the surface geometry is shaped like by interpolating between these shared vertex normals. This means that the surface appears to be curved to the renderer, like a sphere.
The fix was to check off the ‘Add vertex normals’ option on the box geometry.
This gives us a result like this, where we have 1 vertex normal per vertex (All 3 at each corner).
With this, when the surface is approximated by interpolating these vertex normals we end up with a correct result since the vertex normals are pointing in a reasonable direction (opposed to the what we have in the previous image where the vertex normal appears to be the average (?) of what these 3 vertex normals are). By doing this, we get an expected result: