Surface reconstruction from unorganized data points is a challenging
problem in Computer Aided Design and Geometric Modeling. In this
paper, we extend the mathematical model proposed by Jüttler and
Felis (Adv. Comput. Math., 17 (2002), pp. 135-152) based on tensor
product algebraic spline surfaces from fixed meshes to adaptive
meshes. We start with a tensor product algebraic B-spline surface
defined on an initial mesh to fit the given data based on an
optimization approach. By measuring the fitting errors over each
cell of the mesh, we recursively insert new knots in cells over
which the errors are larger than some given threshold, and construct
a new algebraic spline surface to better fit the given data locally.
The algorithm terminates when the error over each cell is less than
the threshold. We provide some examples to demonstrate our algorithm
and compare it with Jüttler's method. Examples suggest that our
method is effective and is able to produce reconstruction surfaces
of high quality.