A new algorithm for isosurface extraction is proposed and implemented.
The algorithm is based on the new mathematical understanding of the
theory of the quasi-Monte Carlo methods. Different from the general
isosurface extracting methods, which work on the whole data set, this
algorithm works on a subset of the original large three-dimensional data
set, which is generated by the quasi-Monte Carlo method.  The isosurface
is generated on this subset data as an approximation to the isosurface
generated from the whole data set.  Hammersley, Halton and Hyperbolic
Cross points are used as the quasi-Monte Carlo points in the
implementation.  The results show that the QMC techniques enjoy a linear
speedup with the number of QMC points.  For large data sets, we usually
can reduce the data size remarkably and still get a good representation
of the original isosurface.  The advantage of the techniques becomes
more prominent when the data size gets larger.  The QMC points generally
generate visually better and smoother isosurfaces and these isosurfaces
represent the overall shape of the original isosurfaces better than
a regular subset of the original data.  The preprocessing of the QMC
isosurface extraction might be time consuming.  But this is a one-time
process.  After it is done, the postisosurface extraction is very fast.