Game Development Reference
220.127.116.11 Error metrics
In this section, we will have a quick look at the concept of error or precision of
decimation. Error metrics are classified on the basis of three criteria:
Measured properties: topology, geometry and attributes;
Scope of the metric: Is the error assessed step-by-step, or is the newmesh compared
with the original mesh?
Interpretation: Can the metric be interpreted intuitively?
The first idea involves measuring the distance between a mesh and a mesh of the previ-
ous step (Schröder et al., 1992). Unfortunately, this step is purely local, which makes it
difficult to estimate a global error. This does not give a precise and reliable upper error
limit, as required in CAD for example. Most of the metrics try to estimate a guaranteed
upper limit of error. For this purpose, we can use the Hausdorff distance . The Haus-
dorff distance between two shapes A and B is defined as the maximumdistance between
a point of A from its closest point in B . The disadvantage of the Hausdorff distance
(which is not a distance in the mathematical sense), other than that it is not symmetric,
is that it is particularly difficult to calculate. An alternative is calculating only the dis-
tance between the points of the initial vertex and the triangles of the decimated mesh.
We can also use a completely new metric, while trying to maintain the volume.
The modern approaches try to define quality metrics that incorporate the concepts
of geometric precision of error metrics as well as concepts like visual quality, absence
of surface roughness, curvature limits, conservation of the topology, etc. In general,
the criteria are related to the application in question.
14.5 OPTIMISATION OF MODELS FOR VIRTUAL REALITY
As explained in the previous paragraphs, we have a variety of models that are more
or less adapted to the constraints of a virtual reality application. Conversion between
these models is of course possible, but this is not always enough: a surface model based
on triangles or polygons can be too complex for the machine which will have to run it.
Hence today we have some techniques which aim at reducing the number of triangles
displayed on the screen. Some of these techniques can be used off-line before the
simulation, while others can be integrated in the same application. Other techniques,
like the levels of detail, offer mixed solutions where a part of the calculations is done
off-line and the rest is done during the simulation.
All the techniques mentioned in the next part aim at reducing the number of
triangles of the model or the part of the model displayed on the screen. The algorithms
described in section 14.4.3 are of course included in the model optimisation techniques.
Intuitively, the texture of an object represents its surface condition. In computer graph-
ics, it is a plane image which will be mapped on a three-dimensional surface, which will