View-Dependent Refinement adresses the problems described in section 2.1. Although it was already considered in [5], it turned out that some modifications of the original approach are required ([6]). View-dependence is integrated into the PM framework by only performing those vertex split operations required for a certain screen-space error. Because the mesh operations can't be performed independently, a PM hierarchy tree is to be considered instead of a simple list. It proved useful to redefine the ecol/vsplit operations as shown in figure 3(b). The vertex split is legal if the faces fn0 to fn3 are already present in the mesh.
Some conditions have to be tested for each vertex to decide if it should be split or not. In [6], viewing volume, backfacing, and screen-space error tests are used. A vertex obviously doesn't need to be split if it lies outside the viewing volume or belongs to a backfacing region. If the vertex is visible from the current viewpoint, an estimation of the screen-space error introduced by the corresponding edge collapse is needed. HOPPE extends the metric used in [12] and defines an error volume called deviation space (figure 4(a)), whose projection to screen is used for the screen-space error test. All these conditions are packed into a single function qrefine which returns true if a vertex should be split and false otherwise.