In blender, If you subdivide any shape, (this works best with a simple cube, however.) take one of the points and move it into or out from the face it belongs to, you will find something strange. Oddly, the engine seems to randomly select the vertices that make 2 of the faces, and run the newly created face through those. However, this does not happen with 2 of the faces. To see what I mean, just open a new project with a cube, go into edit mode, hit W to subdivide the top face (or all faces if you wish) and move the point on the top-middle downward, protruding into the cube. Move the camera a bit, and you will see that 2 of the faces strangely split into 2 triangles, while the other two behave as normal. I am looking into this, and a way to avoid it (as it has been the bane of my existence for the past 5 hours, most likely something in sculpt mode) but until then, try it yourself and post any new discoveries here!
thats the surface normal direction.
At the end of the day, it’s still rendering triangles. and it has to pick a way to turn a quad into a tri. It either splits it between the point you are moving and the opposite one, or it crosses between them.
Warping quads is a great way to find artifacts like this and that is why it isn’t really good practice to warp quads like that.
if the purpose is realtime, then manually triangulate* the surfaces (modifier or edit) to achieve the preferred smooth effect. if the purpose is rendering with a sudsurf, then leave it a quad for best subsurf interpolation.
*CTRL-T, or Mesh -> Faces
CTRL-E -> Rotate Edge, or Mesh -> Edges, to flip triangle