Geometry/Time Measurement/Sundials Graphical Resolution via Algorithmic and Parametric Processes

Every people, in every historical period, developed methods to measure Time both at a daily scale and at a yearly scale. Some of them constructed sundials to represent the apparent trajectory of the Sun around the Earth, by using and developing tools from descriptive and projective Geometry, mainly. This subject acquired a great multidisciplinary interest since ancient times, also for Science of Representation applications. This study presents the first results of an ongoing research concerning some aspects related to Time Measurement. The geometric-spatial setting of the Sun-Earth system is described and is structured parametrically via algorithms, following the known conventions shared and endorsed by gnomonic treatises. A three-dimensional model built with a strictly geometrical approach was developed; this allowed to set parameters (e.g., the latitude of the site, the Sun declination angle, the hour angle, the altitude and collocation of the Sun relative to the sky) and relations dynamically, which define the variation of the length of day and night during the year. The 3D model allowed an in-depth study of the properties and peculiar characteristics of some sundials and a new variant of a known one is also proposed. The unreleased geometrical constructions in Monge’s orthogonal projections were elaborated using by GeoGebra and the 3D models and algorithmic definitions were developed using by Grasshopper and Ladybug plug-ins, eventually visualising the results in Rhinoceros.