Abstract
Focusing on the links between space and image, this paper aims at investigatingsome visual aspects of the so called ‘impossible spaces’, taking advantage of virtual reality. Starting from a series of worksof Maurits Cornelis Escher, a three dimensional version ofa selected example will be presented, visualized, and explored with the help of VR, in order to detect the relevant projective characters making the illusion possible.
1. Introduction
This paper, related to a PhD thesis focusing on the immersive experience in relation to architectural spaces, proposes a research on “Impossible Spaces” through virtual reality, aiming to explore spatial navigable configurations that are visually sensible and perceptible however impossible to construct in the physical world. Virtual Reality will be used as a digital representational tool useful not only to show architectural materiality, but also to study the mathematical and geometric logic compositional principles and to appreciate aesthetic issues of the work. Maurits Cornelis Escher, as a versatile graphic artist has created many related works of graphic art throughout his life, including the representations of “Impossible Spaces”. These graphic art works, are often strongly based on mathematical relationships among shapes, figures and space. Additionally, interlocking figures based on the use of black and white to enhance different dimensions are explored. With the help of VR technology and equipment, these potentially multi-dimensional graphic works of art can be digitally reconstructed and expressed in the form of three-dimensional spatial simulations. The relationship between space, geometry and art would be then studied by simulating the digital experience of three-dimensional environments.
In this paper, we will focus on the graphic work Reliativity to which we refer as to an impossible space.
2. M.C. Escher and His Impossible Spaces
Maurits Cornelis Escher (1898-1972) was a Dutch graphic artist who made mathematically-inspired woodcuts, lithographs, and mezzotints. Despite wide popular interest, Escher was for long somewhat neglected in the art world, even in his native Netherlands, he was 70 before a retrospective exhibition on his work was held. In the late twenty-first century, he finally became more widely appreciated, with exhibitions across the world. He is also famous for his so-called impossible constructions, such as Ascending and Descending, Relativity, his Transformation Prints, such as Metamorphosis I, Metamorphosis II and Metamorphosis III, Sky & Water I or Reptiles.
Fig.1. M.C. Escher, Other World, 1947, MoMA
He tried a variety of illusionary graphic ways, all based on the background of geometric logic in the creation of artistic works representing impossible spaces. Some works take advantage of the function of light and shadow on objects through the expression of black and white, and shadows, and use this as an opportunity to complete the deception of the brain by visual illusion. Other works force the elements in the surface to obey certain visual standards despite the impossible geometric configurations shown, through the graphic change of some perspective effects and distinctive vanishing points in the painting. He also focused on the division of the plane in order to represent impossible spaces. He produced polytypes, sometimes in drawings, which cannot be constructed in the real world, but can be anyway described using mathematics. Many of his drawings caught the eyes and looked possible by perception, but actually corresponding to mathematically impossible spaces. Some drawings also seem very realistic as the following image (Fig.2) “Reliativity”.
Fig.2. M.C. Escher, Reliativity, 1953, MoMA
3. Virtual Reality for Spatial Simulation: a testing room
Virtual reality (VR) is a computer technology that uses glasses, headsets, or helmets, sometimes in combination with physical spaces or multi-projected environments, to generate realistic 3D stereoscopic images, sounds and other sensations that simulate a user's physical presence in a virtual or imaginary environment. A person using virtual reality equipment is able to "look around" the artificial world, and with high quality VR to move about in it and with virtual features or items.
The spatial simulation brought by VR technology can restore the original appearance of three-dimensional space to the greatest extent, and can even accurately express the change of material and light and shadow based on realistic rendering technology. At the same time, this immersive experience based on VR technology is a panoramic experience in which the user does not only see the graphic information inside the frame, but is immersed in a complete, 360-degree digital panoramic model.
Fig.3. 360-degree panoramic model of our testing room (images by authors)
Figure 3 shows on the left the well-known graphic pattern generated for the panoramic construction of a cubic room, and the final effect on the right, where also a sphere, a cube, and a cylinder appear in the testing space prepared. In this study, we used V-Ray as a renderer to process the resulting image results. In the renderer settings, we select the “VR Spherical Panorama” as the camera used for rendering and keep it in line with human body's view height (1.5m above ground) to achieve the ultimate experience that matches the real world. As the result, the aspect ratio of the picture should be 2:1.
4. Workflow for the VR Experience
In order to achieve this kind of spatial simulation, it is necessary to model and prepare the three-dimensional whole model in advance, supplemented by certain rendering techniques to enhance its realism. In this research, we choose to use static VR, that is, the user is not free to move within this space. We will choose some best viewing points in this model and will render 360-degree panoramic images based on these camera points. Once we get these images, we can import them into a VR equipment (VR glasses through phone in this case). With VR equipment, users can enter into the spaces we simulated.
Fig.4. Scheme of a VR workflow
As shown in Figure 4, as long as the designer completes a complete model and sets the position of the camera, he can complete a VR picture with the help of a renderer. If further development is required, interactive designs can also be carried out through other software to complete the movement, transform the scene, and even simply interact with the objects in the scene.
5. Rebuilding Relativity
As already said, we choose to reconstruct the spatial configuration of the Escher’s art work Relativity. In spite of its apparently hypnotic feature, and apart from the absence –or the multiple action- of the gravity force, Relativity is a perfect regular space in the Euclidean world, therefore it seemed to work well for a simple ‘entry level’ test case for our purposes. The three directions characterizing the real space are here respected, so that the construction of the 3D model has been easily carried out, also with the help of the light, appearing as generated by a light source located over the top of the image.
Fig.5. Analysis of Reliativity
Based on the analysis of the painting itself, the work is connected by stairs in different planes. For example, as shown in Figure 5, surface A is both the side wall of No.1 staircase and the lower ground of No.2 staircase. Following its space and geometric logic, we first create a 3D model through images, in which only show 3 main faces, (as shown in Figure 6). In order to make a more convenient study of Eschel's works of art, we speak of a material division between the visible part of the work and the invisible part (that is, the wall that does not appear in the painting).
Fig.6. axonometrics view and art work view of 3D model Reliativity
In order to further complete the immersive experience process, we selected some of the characters in the painting and established these character viewpoints in the model. In order to further complete the immersive experience process, we selected some of the characters in the painting and established these character viewpoints in the model (as shown in Figure 7).
Fig.7. Works of art and digital reconstruction and selected points
Since we have selected five people in the original painting based on different coordinate systems, we use VR technology to simulate the space observed by these five people at different water planes. The space here will rotate as a whole as the coordinate system changes. Through the perspective of different people in the painting and the images observed, as well as the position of different characters, we can further understand Eschel's shaping of the impossible space through panorama view. We combine the 5 images generated by VR to get the following results. Based on the above results, we have designed a set of small programs that can complete simple interaction. In this design, you can quickly switch between different perspectives by clicking on the color ball in the interactive image.
6. Conclusion and Future Work
Through VR, a new technology, we can rebuild and interpret works of art by artists such as M.C. Escher, especially when these works of art are filled with a great deal of geometric and mathematical logic. With the help of VR technology, we can not only truly three-dimensional works of art, but also from the artist or the visual of the specific characters in the works of art, to re-understand the works of art, and even find more interesting artistic details and its rich geometric and mathematical logic. VR can be more efficient in helping users understand the relationship between geometry and art, geometry and space, and this experience is immersive.
In order to get a better experience, we can create a strong interactive virtual environment in the future. Devices such as HTC Vive can detect user displacement, which in turn allows users to move, run, jump, and so on in a virtual environment as if they were immersive. Through this rich interaction, users can be made more realistic to observe changes in space.
References
[1] URL, https://www.mcescher.com/
[2] Escher M C, Bussagli M, Giudiceandrea F. Escher[M]. Skira, 2014.
[3] Dünser, Andreas, Kaufmann, H, et al. "Virtual and augmented reality as spatial ability training tools." Proceedings of the 7th ACM SIGCHI New Zealand chapter's international conference on Computer-human interaction: design centered HCI. ACM, 2006.
[4] G. Bruder, F. Steinicke, and P. Wieland. Self-Motion Illusions in Immersive Virtual Reality Environments. In IEEE Virtual Reality, pages 39–46, 2011.
[5] Savransky, Guillermo, Dan Dimerman, and Craig Gotsman. "Modeling and Rendering Escher‐Like Impossible Scenes." Computer Graphics Forum. Vol. 18. No. 2. Oxford, UK and Boston, USA: Blackwell Publishers Ltd, 1999.
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