The problem of focusing light flux into an arbitrary curve in 3D space arises in the design of different laser or illumination systems. Using a diaphragm with a curved hole is not efficient and does not work for any 3D pattern. In this study, we propose a numerical analytical approach for designing reflective surfaces that efficiently produces the prescribed intensity distribution on the arbitrary curve in 3D space. The method consists of two steps: computation of the eikonal function on the curve and reconstruction of the reflective surface using the precomputed eikonal function. In the first step, we use the iterative technique for obtaining the eikonal function in the set of points on the curve. After that, we compute the continuous eikonal function by interpolation of the obtained values of the eikonal in points and reconstruct the reflective surface using continuous eikonal distribution. As examples, the reflectors generating spiral lines on the inclined plane and illumination system module are computed and simulated. Simulation data show the high quality of the produced illuminance distributions.