I kind of understand that the correct way to do the projection is that we first calculate the angle and project to 2D, which gives us the right image. But I don't quite understand how we get the middle image. Why do we usually split the square into two triangles? Why does the two triangles look consistent inside themselves but look wrong when they are put put together?

I kind of understand that the correct way to do the projection is that we first calculate the angle and project to 2D, which gives us the right image. But I don't quite understand how we get the middle image. Why do we usually split the square into two triangles? Why does the two triangles look consistent inside themselves but look wrong when they are put put together?