The availability of dummy-atom modelling programs to determine the shape of monodisperse globular particles from small-angle solution scattering data has led to outstanding scientific advances. However, there is no equivalent procedure that allows modelling of stacked, seemingly endless structures, such as helical systems. This work presents a bead-modelling algorithm that reconstructs the structural motif of helical and rod-like systems. The algorithm is based on a `projection scheme': by exploiting the recurrent nature of stacked systems, such as helices, the full structure is reduced to a single building-block motif. This building block is fitted by allowing random dummy-atom movements without an underlying grid. The proposed method is verified using a variety of analytical models, and examples are presented of successful shape reconstruction from experimental data sets. To make the algorithm available to the scientific community, it is implemented in a graphical computer program that encourages user interaction during the fitting process and also includes an option for shape reconstruction of globular particles.