Geomorphing

HOPPE suggests that geomorphing sequences should cover a constant time, typically one second. This causes two problems. After an immediate stop in the viewer's movement the mesh needs this constant time for stabilization. Moreover, it is hard to deal with the PM dependencies when geomorphing is used to smoothly coarsen the mesh.

An alternative approach not explicitly dealing with time redefines the function qrefine (see section 3.3) to have continuous range. Figure

Figure 5: Modifying the function qrefine to support geomorphing

[boolean] [linear] [smooth]

5 shows the output of different types of this function for a visible vertex (inside the viewing-volume, not backfacing). The x-axis is the screen-space geometric error (the projected size of the deviation space), using an arbitrary scaling for demonstration purposes. With qrefine defined as in figure 5(b) or 5(c) flexible geomorphing sequences are generated depending on the current viewing parameters instead of time. Such a sequence can even be reverted before it is finished.

For reasons not explained here a more sophisticated algorithm is required for the traversal of vertices to be evaluated with qrefine. However, this procedure can be optimized, so only little computational overhead is added.