A Codification of the Cubic Projection to Generate Immersive Models

Lucas Fabián Olivero; Adriana Rossi; Salvatore Barba

doi:10.26375/disegno.4.2019.07

Authors

Lucas Fabián Olivero Dipartimento di Ingegneria. Università degli Studi della Campania “Luigi Vanvitelli”
Adriana Rossi Dipartimento di Ingegneria. Università degli Studi della Campania “Luigi Vanvitelli”
Salvatore Barba Dipartimento di Ingegneria Civile. Università degli Studi di Salerno

DOI:

https://doi.org/10.26375/disegno.4.2019.07

Keywords:

cubical projection, cubemap, equirectangular projection, dvanced representation techniques, VR panoramas

Abstract

The results of this research aim to describe the representation system made with immersive visualizations. The main goal is to transfer techniques that characterizes immersive models from raster images to models generated with vector images. This way is passed over the boundary that supposes the simple substitution of the elementary geometrical entity, point (or pixel), with the line. In order to do it, the transformations from bi-dimensional views to the immersive panoramic will be codified. It is proposed an advancement for the state of the art, connecting the studies with the descriptive geometry field, opening the cone of vision to the whole space that surrounds the observer. The work considers, as a departure point, previous studies about hybrid immersive models using both equirectangular and cubical projections. But, while for the equirectangular projection there is a complete bibliography for both intuitive (trail-error) and math- ematical methods, for cubical projection instead, the procedures are just approximated, without a necessary theoretical and complete framework. The used method previews, as a mandatory passage, the development of geometrical formulations that will constitute the base for the mathematical ones. Announcing future steps, the content here presented in graphical terms, will look to be synthesized in an algorithm with digital graphics output, written ad-hoc, looking to propose a new advanced technique of representation.

References

Araújo, A. (2017). Anamorphosis: optical games with perspective’s playful parent. In J.N. Silva (ed.) Recreational Mathematics Colloquium V. Proceedings of the Recreational Mathematics Colloquium V - Gathering for Gardner Europe, vol. 5, pp. 71-86. Lisboa, 28-31 January 2017. Lisboa: Associação Ludus. <https://repositorioaberto.uab.pt/handle/10400.2/6647> (accessed 2018, March 7).

Araújo, A. (2018a). Drawing Equirectangular VR Panoramas with Ruler, Compass, and Protractor. In Journal of Science and Technology of the Arts, vol. 10, n. 1, pp. 15-27. <https://doi.org/10.7559/citarj.v10i1.471> (accessed 2018, May 16).

Araújo, A. (2018b). Ruler, compass, and nail: constructing a total spherical perspective. In Journal of Mathematics and the Arts, vol. 12, n. 2-3, pp. 144-169. <https://doi.org/10.1080/17513472.2018.1469378> (accessed 2018, July 3).

Barazzetti, L., Previtali, M., Roncoroni, F. (2017). 3D modelling with the Samsung Gear 360. In International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, vol. XLII-2/W3, pp. 85-90. <https://doi.org/10.5194/isprs-archives-XLII-2-W3-85-2017> (accessed 2019, February 15).

Barba, S, Rossi, A., Olivero L.F. (2018). “CubeME”, a variation for an immaterial rebuilding. In R. Salerno (a cura di). Rappresentazione/Materiale/Immateriale. Drawing as (in)tangible representation. Atti del XV Congresso dell’Unione Italiana per il Disegno - 40° Convegno Internazionale dei Docenti della Rappresentazione. Milano, 13-15 settembre 2012, pp. 31-36. Roma: Gangemi Editore International.

Barre, A., Flocon, A., Bouligand, G. (1967). La Perspective curviligne: de l’espace visuel à l’image construite. Paris: Flammarion.

Bourke, P. (July 2016). Converting to/from cubemaps. <http://paulbourke.net/miscellaneous/cubemaps> (accessed 2018, May 21).

Cabezos Bernal, P., Cisneros Vivó, J., Soler Sanz, F. (2014). Anamorfosis, su historia y evolución. In EGA Expresión Gráfica Arquitectónica, n. 23, pp. 148-161. <https://doi.org/10.4995/ega.2014.2184> (accessed 2019, January 29).

Cardone, V. (2015). Modelli grafici dell’architettura e del territorio. Santarcangelo di Romagna: Maggioli Editore.

Fernández Rodríguez, M. (2002). Homología entre figuras de tercera categoría. In Geometría y Cartografía: las más viejas ciencias, las más nuevas tecnologías. Actas del XIV Congreso Internacional de Ingeniería Gráfica de INGEGRAF. Santander, 5-7 junio 2002, s.e.

Grau, O. (2003). Virtual Art: From Illusion to Immersion. Cambridge, Mass.-London: The MIT Press.

Greene, N. (1986). Environment Mapping and Other Applications of World Projections. En IEEE Computer Graphics and Applications, vol. 6, n.11, pp. 21-29. <https://doi.org/10.1109/MCG.1986.276658> (consultado el 21 de enero de 2019).

Habakuk, I.J., Zöllner, C., Müller, A. (2010). Sketching in space. <http://theconstitute.org/sketching_in_space/> (accessed 2018, April 25).

Hernández Falagán, D., Signes Orovay, F., Berdié Soriano, A. (3 March 2015). Sistema cónico-diédrico, pp. 10-12. <https://sistemesderepresentacio.files.wordpress.com/2015/03/03.pdf> (accessed 2019, March 10).

Kurbatov, V. (18 January 2017). Draw Sketches for Virtual Reality Like a Pro. <https://medium.com/inborn-experience/vr-sketches56599f99b357> (accessed 2018, May 21).

Leopold, C. (2016). Points of view and their interrelations with space and image. In V. Viana et al. (eds.). Geometrias & graphica 2015. Proceeding of III Conferência Internacional de APROGED - Associação dos Professores de Desenho e Geometria Descritiva – XI International Conference onGraphics Engineering for Arts and Design. Lisboa, 1-3 Outubro 2015, vol I, pp. 365-373. Porto: APROGED.

Lolas, C. (2014). Inmersividad, orígenes y nuevos medios. Escáner Cultural. Revista Virtual de Arte Contemporáneo y Nuevas Tendencias. <http://escaner.cl/revista/node/7473> (accessed 2019, June 3).

Masetti, M. (2014). La prospettiva e la costruzione dello spazio figurativo. Tricase (LE): Youcanprint.

Michel, G. (2013). L’oeil, au centre de la sphere visuelle. En Boletim da Aproged, n. 30, pp. 3-14.

Migliari, R. (2012). La Geometria descrittiva: evoluzione di una teoria. In M. Filippa, L. Carlevaris (a cura di). Elogio della teoria. Identità delle discipline del disegno e del rilievo. Atti del IX Congresso dell’Unione Italiana per il Disegno - 34° Convegno Internazionale dei Docenti della Rappresentazione. Roma, 13-15 dicembre 2012, pp. 23-29. Roma: Gangemi Editore.

Rossi, D. (2018). Brand new: panorama. L’immagine continua per il disegno della realtà virtuale. En R. Salerno (a cura di). Rappresentazione/Materiale/Immateriale. Drawing as (in)tangible representation. Atti del XV Congresso dell’Unione Italiana per il Disegno - 40° Convegno Internazionale dei Docenti della Rappresentazione. Milano, 13-15 settembre 2012, pp. 1389-1396. Roma, Italy: Gangemi Editore International.

Shannon, S. (2016). Panoramas: 19th-Century Virtual Reality. <https://shannonselin.com/2016/11/panoramas-19th-century> (accessed 2019, February 13).

Wong, T., Wan, L., Leung, C. (2007). Isocube: Exploiting the Cubemap Hardware. In IEEE Transactions on Visualization & Computer Graphics, vol. 13, n.4, pp. 720-731. <https://doi.org/10.1109/TVCG.2007.1020> (accessed 2019, February 17).