**The Problem of Lighting in Underground Domes, Vaults, and Tunnel-Like Structures of Antiquity; An Application to the Sustainability of Prominent Asian Heritage (India, Korea, China)**

### **Francisco Salguero Andujar 1, Inmaculada Rodriguez-Cunill 2 and Jose M. Cabeza-Lainez 2,\***


Received: 30 September 2019; Accepted: 20 October 2019; Published: 22 October 2019

**Abstract:** Lighting in heritage is complex because of the forms intervening in it. The historical evolution of cultures has not been analytical and therefore, the shapes involved differ greatly from the cuboids typically found in 21st century architecture. As a vector, light inevitably attaches to surface sources. In this research, we focused on 3D curved geometries. Following a different trail to radiative transfer by virtue of detailed knowledge of the spatiality of volumes, we present new expressions, previously undefined in the literature, that are derived from a combination of surfaces that we have found in many archaeological sites around Asia. In the discussion, we start from the particularities of spherical surfaces where a normal vector has to pass through the center. By means of easy calculations, we deducted innovative laws. These in turn, allowed us to formulate several new expressions for configuration factors based on the adroit use of spherical fragments. The method easily extends to organic shapes that are often contained in the sustainable architecture of the past. The method finishes with suitable algorithms to assess the reflections in such curved forms. Finally, we implemented the results in our creative software. In this way, we enhanced the sustainable paradigms for heritage structures in Asia that we present as a conclusion of the article.

**Keywords:** lighting of tunnels and domes; Asian architecture; lighting of heritage; curvilinear radiative transfer; new solutions for equations of geometric optics
