Daylighting provided by horizontal openings using the illumination vector

Stemming from the expressions of the illumination vector provided by vertical openings at any point of the interior space, this article proposes and solves the equivalent expressions for openings in horizontal planes, thus completing the expressions of Navarro [Sobre iluminación natural en arquitectura. Ed. Secretariado de Publicaciones de la Universidad de Sevilla; 1983] and offering algorithms which give the value of the illumination vector for CIE skies [Natural daylight official recommendations. Paris: CIE COMMITE 3.2.; 1955] at any point of the interior space and for any size of window whether vertical or horizontal. This constitutes a highly potential tool of computerized calculation of the direct component of natural illumination which is eminently more flexible and precise than those systems which are based on finite elements.