  We present a new numerical method for the isometric embedding of 2-geometries
specified by their 2-metrics in three dimensional Euclidean space. Our approach
is to directly solve the fundamental embedding equation supplemented by six
conditions that fix translations and rotations of the embedded surface. This
set of equations is discretized by means of a pseudospectral collocation point
method. The resulting nonlinear system of equations are then solved by a
Newton-Raphson scheme. We explain our numerical algorithm in detail. By
studying several examples we show that our method converges provided we start
the Newton-Raphson scheme from a suitable initial guess. Our novel method is
very efficient for smooth 2-metrics.
