## 1 Introduction  
In the acoustic design of performance buildings, walls and ceilings are usually fitted with diffusion devices to diffuse indoor sound fields. The acoustic reflection, which results from the tilt or concave/convex shape of surfaces, changes the transmission direction of sound energy and the distribution of resonance frequency in indoor spaces. The diffusion of indoor sound fields is considered a very important method of improving acoustic quality [1]. Two parameters describe the reflection state of sound on surfaces, the diffusion coefficients and scattering coefficients. The scattering coefficient refers to the ratio of the non-specular reflection energy to the total reflection energy, while the diffusion coefficient is used to describe the spatial polar distribution of non-specular reflection sound energy [2, 3]. The difference between diffusion coefficient and scattering coefficient is that diffusion coefficient describes the spatial distribution of non-specular sound energy, while scattering coefficient describes the energy proportion of non-specular sound energy. [PERSON] et al. [4] found that using the diffusion coefficients in geometric room acoustic models is likely to produce incorrect results. In this paper, the scattering coefficient was used. To evaluate the effect of diffusion and scattering, a key room acoustics parameter is reverberation time (_RT_), determined by 20 dB decay or 30 dB decay, specifically referred to as \(T_{20}\) and \(T_{30}\), respectively in this paper, whereas _RT_ refers to general concept of reverberation time. Previous studies have investigated the impact of surface scattering on the acoustic quality of performance buildings using three methods: subjective surveys, computer simulations, and scale-model tests. By assigning values to the concavity or convexity of the walls and ceilings of concert halls, [PERSON] [5] conducted a subjective survey, concluding that the scattering state of walls and ceilings was highly correlated (or to be more specific, positively correlated) with concert-hall evaluation scores. However, high acoustic quality was not analyzed in detail in these evaluations. In terms of the overall diffusion sound field of each space, the inherent diffusivity of the space and the scattering coefficient of the indoor surface work jointly to diffuse sound energy. In the acoustic design of concert halls, numerous decorative \"shoeboxes\" and irregularly shaped \"vineyards\" in the walls and ceilings are thought to play an important role in diffusing sound fields [6]. The recognition of sound scattering by human ears is a very important index for acoustic design; during the process of constructing performance buildings, the design pattern of surface scattering affects the architectural design, decoration design, and construction cost. [PERSON] [7] and [PERSON] et al. [8] studied surface diffusion through computer simulations and scale-model tests. Using a computer simulation of Dortmund Concert Hall, [PERSON] [7] found that the average scattering coefficient variation perceived by listeners was 0.6. However, [PERSON] did not further investigate the relationship between scattering and acoustic parameters. In terms of the study of objective parameters, [PERSON] et al. [8] found that \(RT\) decreased by 0.1 s when diffusers were added to the side walls of Miral Concert Hall. Using the scale-model method, [PERSON] and [PERSON] studied the impact of side wall scattering. Based on a 1/10 scale model and also a real performance hall, [PERSON] et al. [9] compared two states (diffusion and reflection) of wall surfaces; they found that adding diffusers reduced the standard error of early decay time, and increased the quantity of high-frequency reflected sound peaks. Using a 1/10 scale model, [PERSON] [10] compared acoustic parameters before and after adding cylindrical diffusers in a leaf-shaped concert hall, finding that the difference in sound pressure level of the 1/3 octave (1000 Hz) between seats increased from 5 to 7 dB after diffusers were added to the walls.