  We present a simple direct discretization for functionals used in the
variational mesh generation and adaptation. Meshing functionals are discretized
on simplicial meshes and the Jacobian matrix of the continuous coordinate
transformation is approximated by the Jacobian matrices of affine mappings
between elements. The advantage of this direct geometric discretization is that
it preserves the basic geometric structure of the continuous functional, which
is useful in preventing strong decoupling or loss of integral constraints
satisfied by the functional. Moreover, the discretized functional is a function
of the coordinates of mesh vertices and its derivatives have a simple
analytical form, which allows a simple implementation of variational mesh
generation and adaptation on computer. Since the variational mesh adaptation is
the base for a number of adaptive moving mesh and mesh smoothing methods, the
result in this work can be used to develop simple implementations of those
methods. Numerical examples are given.
