## 1 Introduction  
In the last 50 years, a wide range of new technologies have emerged to concentrate and harness the radiation energy of the sun, such as solar furnaces (e.g., [1, 2]), dish-Stirling systems (e.g., [3]), Fresnel-linear (e.g., [4]), and cylinder-parabolic concentrators (e.g., [5]), plus large heliostat fields, in some cases with many hundreds of mirrors (e.g., [6]). These technologies have always been overshadowed by non-concentrated photovoltaic (PV) solar cells, which are much easier to install and maintain. Heliostat fields still have some economic relevance in the energy sector, but all other technologies rarely make it outside research institutes. These concentrated solar power (CSP) technologies are marred by their non-trivial installation and daily operation, but also by the need to transport the thermal energy using oils or molten salts, which is always a cumbersome process. However, CSP technologies are usually regarded as cleaner for the environment than PV, when the whole life process of its components is considered, from manufacturing to decommissioning, allowing high-energy applications that are unsuitable for PV. Computermodelling of CSP facilities can be an invaluable tool to improve the attractiveness of these technologies, allowing us to better understand and simplify its inner workings. Ray-tracing techniques in particular are ideally suited to simulate shading, blocking, and other important inefficiencies, which are easy to understand but difficult to quantify by standard methods. The more is known about these CSP facilities, the easier and cheaper it will be to use them in economic activities. Geometric studies of shading and blocking effects in heliostat fields have recently (2019, 2022) been reported [7, 8], including other attenuation contributions (such as the atmospheric attenuation used in our software). As these works show, there is no simple analytical way to solve the purely geometric problem of shading and blocking, because it depends on the many geometric parameters of the heliostats involved, plus the varying coordinates of the solar rays. Computer optimization of heliostat fields, such as the heliostat size and the aspect ratio, has also been reported (2017, 2022) using several different optimizing software approaches [9, 10]. Up to now, the literature describing computer modelling of heliostat fields by ray-tracing techniques has been relatively limited. In 2009, ray-tracing software was reported by [PERSON] et al. [11] at the German Aerospace Center to accurately and efficiently simulate the flux density of heliostat fields. The software was primarily designed to process real sun shape distributions and real highly resolved heliostat geometry data [11]. Later (2012), [PERSON] et al. [12] introduced a biomimetic pattern for heliostat field layout optimization and concluded that it is possible to both reduce the land area of the plant and the number of heliostats for fixed energy collected [12]. Also in 2012, [PERSON] [13] numerically examined the error sources introduced into mirror tracking systems, arising from component limitations, the construction and placement of the reflectors, and the discrete motion of the tracking system itself. He used the SolTrace software developed at the National Renewable Energy Laboratory to model CSP systems and analyze their optical performance. Commercially available ray-tracing software (like TracePro and ray-tracing Matlab code) was used by other authors [14, 15] to analyze the drift of heliostats and the influence of the geometrical parameters associated with the heliostat mechanical structure and the local time.