The wave superposition method requires numerical integration of all discrete elements when solving the external radiation sound field of the sound source, resulting in low computational efficiency. However, the equivalent source method always has significant integration approximation errors due to excessively simplifying the elements. In response to the above shortcomings, a wave function that is equivalent to element integration and does not require integration was constructed using the Helmholtz equation in a spherical coordinate system. Inspired by the triangular stitching structure of biomimetic composite materials, taking the most widely applicable planar triangular element as an example, the general and internal forms of the wave function were constructed. Finally, the accuracy and efficiency of the two wave functions and the direct integration calculation of the sound field were compared through numerical simulation. The results show that the calculation error between the two wave functions and direct integration is less than 0.5%, and the calculation efficiency of the extrapolated wave function is about 6 times that of direct integration.