Many procedures have been developed to design and optimize a heliostat field, however it is a rather challenging work partly because many influencing factors of a heliostat optical efficiency, especially the shading and blocking efficiency, are computationally intensive. And it's difficult to judge whether a heliostat field layout is an ideal design intuitively and reliable. In this paper, two concise and accurate analytic geometry methods (AGM-I and AGM-II) are developed to identify the heliostats with the possibilities of shadowing or blocking a given heliostat firstly. The results compared with the Sassi method and bounding sphere & Sassi method show that the same accurate results are obtained while the computational time is significantly reduced by 32% and 23%, respectively. Then an intuitive approach is proposed to optimize and evaluate the rationality of a heliostat field layout by applying the maximum optical efficiency map (MOEM). Finally, a heliostat field based on the Gemasolar plant is studied, whose optical efficiency is optimized and evaluated by the proposed methods. Compared with the un-optimized result and the result optimized by using the reference method, the MOEM optimization result of the heliostat field with higher instantaneous optical efficiency and annual optical efficiency is more reasonable.