  We present a numerical technique to compute the gravitational lensing induced
by simulated haloes. It relies on a 2D-Tree domain decomposition in the lens
plane combined with a description of N-Body particles as extended clouds with a
non-singular density. This technique is made fully adaptive by the use of a
density-dependent smoothing which allows one to probe the lensing properties of
haloes from the densest regions in the center or in substructures to the
low-density regions in the outskirts. 'Smooth Particle Lensing' has some
promising features. First, the deflection potential, the deflection angles, the
convergence and the shear are direct and separate end-products of the SPL
calculation and can be computed at an arbitrary distribution of points on the
lens plane. Second, this flexibility avoids the use of interpolation or a
finite differentiation procedure on a grid, does not require padding the region
with zeros and focuses the computing power on relevant regions. The SPL
algorithm is tested by populating isothermal spheres and ellipsoids with
particles and then comparing the lensing calculations to the classical
FFT-based technique and analytic solutions. We assess issues related to the
resolution of the lensing code and the limitations set by the simulations
themselves. We conclude by discussing how SPL can be used to predict the impact
of substructures on strong lensing and how it can be generalized to weak
lensing and cosmic shear simulations.
