## 1 Introduction
[29] proposed the best 2D mapping model when the number of calibration points is greater than or equal to 14, after comparing and analyzing the existing 2D mapping models, accuracy can be achieved within 0.5\({}^{\circ}\) and takes about 20 s. [PERSON] et al. [30] proposed a more accurate iris center detection method to obtain the iris center parameters, which are brought into the polynomial to obtain more accurate gaze point coordinates. [PERSON] et al. [31] conducted an in-depth research on the mapping equation and found a more appropriate high order odd polynomial fitting mapping equation, with an experimental accuracy of 0.87\({}^{\circ}\). [PERSON] et al. [33] proposed a compensation model for eye feature parameters in a single camera dual ring light source system to derive the head movements, thus correcting the corresponding parameters to obtain accurate information about the gaze point. [PERSON] et al. [34] verified that the quadratic polynomial is more suitable for solving the 2D sight direction through a variety of polynomial experiments. The Cross-ratio Invariance in projective geometry is applied in Cross-ratio [36; 37]. [PERSON] et al. [36] proposed the idea of using dynamic virtual tangent plane, describe the relationship between reflection point and virtual point of light source with dynamic matrix, the sight accuracy can reach 0.7\({}^{\circ}\). [PERSON] et al. [37] proposed a gaze estimation method based on Cross-ratio under two cameras and five LED infrared light sources, which can obtain clearer eye images and extract more accurate pupil features. Homography normalization [38; 39] is similar to the Cross-ratio method. [PERSON] et al. [38] proposed that in the four infrared light source system, no additional light source. Due to the characteristics of the normalized space, it is not necessary to know the screen rectangle size formed, which is convenient for system implementation, and has stronger robustness, they obtained average accuracy of 1.03\({}^{\circ}\)-1.17\({}^{\circ}\). Based on the above literature, it can be found that when the hardware system is simple, the accuracy is usually low, when the accuracy is high, the hardware system is usually more complex, there are limitations and inaccuracies in the actual experiment process. Therefore, in order to reduce the complexity of the algorithm, save the hardware cost and improve the stability and accuracy of the system, this paper proposes a mapping equation based on homography transformation, and calculates the gaze point through adjustment, calibration and experimental verification, this method can achieve higher experimental accuracy. This article will introduce the following aspects. Section 2 mainly compares our method with other methods. The derivation of the mapping equation will be introduced in the method section. Section 4 (Experiments) mainly introduces the experimental design and result analysis of the mapping equation. Section 5 (Discussion) is the discussion part, the practical significance of this equation is obtained by further polynomial surface fitting and analysis of characteristic parameters, and it is expected that it can be put into engineering applications. Finally, it introduces the conclusion of this paper and the significance of its existence.