Adaptive Sonification of Mathematical Function Graphs

Graphical representations of mathematical functions remain difficult to access for blind and visually impaired users, particularly in educational contexts where understanding the overall shape and behavior of a function is essential. This paper proposes an adaptive sonification method for mathematical function graphs designed for touchscreen-based exploration supported by continuous auditory feedback and voice interaction. The study focuses on balancing perceptual accessibility and auditory saturation by analyzing the influence of key sonification parameters, including auditory plateau width, slope length, and slope curvature. Two user experiments involving participants with different levels of visual impairment were conducted to evaluate the perceived usability of the proposed approach. The results indicate that usability improves with increasing auditory coverage only up to a certain threshold, beyond which excessive auditory density reduces perceptual clarity. The experimental results suggest that the preferred auditory plateau width is approximately 52 dp (about 9.8 mm), while the optimal slope length is approximately 84 dp (about 15.8 mm). In contrast, slope curvature has relatively little influence on subjective usability. The paper also introduces the Sonification Index (SI) and Auditory Saturation (AS), two quantitative measures that support the analysis and adaptive selection of sonification parameters based on graph complexity and device characteristics.