Game Development Reference
In-Depth Information
Subdivision Surfaces
Subdivision surfaces, originally introduced by Catmull and Clark (1978) and Doo
and Sabin (1978), have recently emerged as a useful tool for modeling free-form
surfaces. A number of other subdivision schemes have been devised over the
years, including Loop's (1987), Dyn et al.'s (known as the “butterfly” scheme)
(1990) or Kobbelt's (2000). Subdivision is a recursive refinement process that
splits the facets or vertices of a polygonal mesh (the initial “control hull”) to yield
a smooth limit surface. The refined mesh obtained after each subdivision step is
used as the control hull for the next step, and so all successive (and hierarchically
nested) meshes can be regarded as control hulls. The refinement of a mesh is
performed both on its topology, as the vertex connectivity is made richer and
richer, and on its geometry, as the new vertices are positioned in such a way that
the angles formed by the new facets are smaller than those formed by the old
facets. The interest in considering subdivision surfaces for animation purposes
are related to the hierarchical structure: the animation parameters directly affect
only the base mesh vertex positions and, for higher resolutions, the vertices are
obtained through a subdivision process. Three subdivision surfaces schemes are
supported by the MPEG-4 standard: Catmull-Clark, Modified Loop and Wave-
let-based. For a detailed description of these methods and how they are
implemented in MPEG-4, the reader is referred to ISOIEC (2003).
M ESH G RID
M ESH G RID is a novel surface representation typical for describing surfaces
obtained by scanning the shape of “real” or “virtual” objects according to a
certain strategy. The scanning strategy should provide a description of the object
as a series of open or closed contours.
Virtual Character definition in M ESH G RID format
The particularity of the M ESH G RID representation lies in combining a wireframe,
i.e., the connectivity-wireframe (CW), describing the connectivity between the
vertices located on the surface of the object, with a regular 3-D grid of points,
i.e., the reference-grid (RG) that stores the spatial distribution of the vertices
from the connectivity-wireframe. The decomposition of a M ESH G RID object into
its components is illustrated in Figure 13 for a multi-resolution humanoid model.
Figure 13a shows the M ESH G RID representation of the model, which consists of
the hierarchical connectivity-wireframe (Figure 13b) and the hierarchical refer-
ence-grid (Figure 13c). The different resolutions of the mesh (Figure 13d), which
 
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