In the context of mobile gaze tracking techniques, a 3D gaze point can be calculated as the middle point between two 3D visual axes. To infer gaze directions and eyeball positions, a nonlinear optimization problem is typically formulated to minimize the angular disparities between training gaze directions and prediction ones. Nonetheless, the experimental results reported by some previous works show that this kind of approaches is very likely to yield large prediction errors hence considered less useful for human-machine interactions. In this study, we aim to address this widespread issue in three aspects. At first, instead of using a global regression model, a simple local polynomial model is proposed to back-project a pupil center onto its corresponding visual axis. Based on the Leave-One-Out cross-validation criterion, the partition structure is automatically learned in the process of resolving a homographylike relationship. Secondly, a good starting point for nonlinear optimization is obtained by the image eyeball center, which can be estimated by systematic parallax errors. Meanwhile, it is necessary to add suitable constraints for 3D eye positions. Otherwise, the optimization may end up with trivial solutions, i.e., faraway eye positions. Thirdly, we explore a strategy for designing the spatial distribution of calibration points in a principled manner. The experiment results demonstrate that an encouraging gaze estimation accuracy can be achieved by our proposed framework for both the normal vision and eyewear users.