## 1 Introduction  
Concentrating solar power (CSP) technologies are promising renewable energy systems with high exergy efficiency [1, 2] and a comparatively low environmental footprint. Modern solar thermal power plants consist of a solar tower or a central receiver system equipped with a field of heliostats that reflect (re-direct) the so-called DNI (direct normal irradiance) onto a central receiver mounted at the top of a tower [3]. Each heliostat is a two-axis tracking system with an almost flat mirrored surface. However, historically, the first heliostats were used in another type of point-focusing concentrating solar technology: the solar furnace. In fact, in an article published in 1958, [PERSON] [4] described a two-component solar furnace, a condenser-heliostat combination, in which the condenser faces downward at 30\({}^{\circ}\) towards a heliostat comprised of numerous rows of plane mirrors mounted on a horizontal turntable. The world's first solar tower plant was equipped with a field of point-focus Fresnel mirrors, and it was built and tested at Sant'Ilario, near Genoa (Italy), in 1965 [5]. Using almost flat mirrors and following four decades of prototype test facilities built around the world, solar tower or central receiver plants only started gaining large commercial momentum with Abengoa's PS10 in 2007 [6], followed by other plants, like Gemasolar (also located in the Spanish province of Andalucia), which was commissioned in 2011 [7]. Computer modeling of CSP facilities, namely those with a heliostat field, can be an invaluable tool for improving their efficiency, allowing us to better understand and simplify their inner mechanisms. In the literature, there are several examples of studies that present interesting findings, not only concerning blocking and shading effects, e.g., [8; 9; 10], but also analyzing the mechanical rotations of the heliostats, e.g., [11; 12; 13; 14]. More recently, generative deep learning models have been used to predict heliostat surfaces from target images [15], and novel pointing correction techniques based on nonlinear Limit Cycle Oscillators (LCOs) have been applied to the digital twin [16] of a heliostat field. In this manuscript, computer simulations of heliostat fields are reported, specifically those looking into the mechanical rotations needed to properly orient the heliostat mirrors. These studies allow for the assessment of the overall efficiency of the various models (equivalent studies covering optical aspects were reported in a previous publication [17]). Simple mathematical models are introduced to simulate the most common mirror orientation models, which involve two rotation axes: azimuth-elevation, tilt-roll, and target-aligned. Simple layouts to represent realistic heliostat fields are then suggested and simulated. The number of ray-tracing computer packages currently available to model optical systems is vast, ranging from software commonly used to model CSP systems (Tonathium [18], SolTrace [19]) to general-purpose optical software designed to project complex optical devices, including lenses (FRED [20], Zemax [21], Code V [22], LightTools [23], TracePro [24]). Tonathium and SolTrace are distributed as open-source software (available from the GitHub repository). All other packages are commercially available from the cited companies. However, the software used in this work was specifically written for these studies, providing maximum control, flexibility, efficiency, and accuracy, thus increasing our knowledge and error detection capacity. This software includes the algorithms recently reported [25] to calculate the sun's position (as a function of time, date, latitude, and longitude), which are essential for the work reported here. Code to detect shading and blocking effects, as well as mechanical collisions and to implement attenuation effects, has also been applied throughout this work.