The algorithm based on the physical-geometric optics method is developed to compute the linearization of single-scattering properties, such as extinction, absorption and scattering cross-sections, and the scattering phase matrix. The algorithm can be applied to any convex facet particles, where a new beam-splitting technique is employed. With the introduction of the winding number method, beams incident on multiple facets can be precisely divided into independent parts that are incident on single facets. The linearization algorithm is verified by the finite-difference method using the regular hexagonal prism. The sensitivities of single-scattering properties with respect to size, aspect ratio, and refractive index are discussed.