The International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences
https://doi.org/10.5194/isprs-archives-XLII-2-W15-231-2019
https://doi.org/10.5194/isprs-archives-XLII-2-W15-231-2019
| 21 Aug 2019

# 3D DATA INTERPRETATION USING TREATISES GEOMETRIC RULES TO BUILT COFFERED DOMES

M. Capone and E. Lanzara

Keywords: Generative modeling, Coffered Domes, Parametric modeling, S. Giovanni Maggiore, Vannini, Apollonio theorem, Archimedes theorem, HBIM

Abstract. The contribution is part of a research that aims to address the problems of knowledge, interpretation and documentation of coffered domes geometry. The main question is to define the relationships between the coffer shape, the layout used for coffers distribution on dome surface and different kind of surfaces. With regard to coffered domes we have analyzed the methods illustrated by Francesco Milizia, Giuseppe Vannini and some historical surveys. We have grouped coffered domes in relation to grid geometry and to coffer shape. We have defined three different ways to distribute the coffers in relation to different grid layout: grid composed by 2D lines (meridians and parallels), grid composed by 3D lines on surface (lattice of rhumb lines) or coffers distribution between ribs. We have analyzed each of them and we have defined algorithmic models in relation to spherical domes. The main goal of our research is to study what's different in not spherical domes, such as policentrical domes, ellipsoidal domes or ovoidal domes, generated using curves network. We have compared computational models based on treatises rules with particular case studies. This comparison allows us to do a critical analysis based on geometric rules. From a methodological point of view we have built a parametric model able to connect the different processes, using the same parameters. By comparing this model with point clouds, it is possible to evaluate analogies or identify new rules that will be used to develop a more complex parametric model based on surveys.