Photonic nanojet is a kind of highly focused subwavelength locally electromagnetic beam that is formed by the scattering of dielectric micro-particle on light field, when the symmetry of system that is composed of light field and micro-particle is broken, a kind of subwavelength locally curved beam is formed, photonic hook. It is featured by a sub-diffraction limit of half-height width and a much smaller radius of curvature than wavelength. Due to these excellent performance parameters, the photonic hook has broad application prospects in the field of optical imaging, optical manipulation and trapping. Since the concept of photonic hook was proposed, researchers have been exploring the factors influencing the effective length and bending angle of photonic hooks, such as the parameters related to the properties of the medium particles (e.g., size, structure, material) and the characteristics of the light field. Among them, most studies focus on the exploration of the structure of the micro-particle, and many different structures have been developed, but the material of the micro-particle is a dielectric or an artificial material. The state of water cylinder is changed at freezing, so frozen water cylinder can be a phase change material. Using frozen water droplet as phase change materials and the ice-water interface as plane, the generation of time-domain self-bending photonic hook has attracted much attention. However, the generated photonic hook has a relatively small effective length and a small curvature. During the freezing process of water cylinder, the shape at the state transition does not have a quantitative model for description. This paper sets the functions as boundaries for the state transition of materials and introduces the idea of functions from mathematics into the device design of photonic hooks. A twin photonic hook generator is designed using frozen water cylinder as phase change materials and function surfaces as the ice-water boundary interface. The software COMSOL is used for simulation, and effective control of the characteristic parameters of the photonic hooks was achieved by altering the structure of the frozen water cylinder and the coefficients of the functions. The variation patterns of characteristic parameters such as effective length, bending angle, and the bending number of the photonic hooks were analyzed. The results show that the coefficients A, B, and C are respectively related to the opening angle, rotation direction, and depth of concavity of the function. The opening of the ice-water boundary obtains a twin photonic hook when there is symmetry with respect to the direction of illumination. As the asymmetry increases, the twin photonic hook gradually transforms into a single photonic hook. When the ice-water boundary opening increases under symmetric incidence, the effective length shows an initial growth followed by a decrease trend. Meanwhile, the bending angle also shows an initial increase followed by a decrease trend. Moreover, during the gradual enlargement of the opening, the phenomenon of multiple bending of the photonic hook becomes more pronounced. When the concave depth continues to increase, the effective length initially decreases and then shows a lengthening trend, while the overall bending angle shows an initial increase followed by a decrease trend. Among them, the maximum bending angle of the photonic hook can reach up to 44° (A=14.79, B=0, C=-9, D=0), the maximum effective length can reach up to 17.43λ (A=177.51, B=0, C=-12, D=0), and the number of bending cycles can reach up to 4. Compared to traditional methods, this design introduces functions to achieve research on more complex structures of photonic hooks and further enables the modulation of characteristic parameters of photonic hooks. This provides new insights for the design and research of photonic hooks, while also offering references for their applications in areas such as optical manipulation and biomedicine.