Abstract
The human being has the need to represent the objects that surround him. But the world around us constitutes a three-dimensional reality and the formats in which it is represented are two-dimensional. Then the problem arises of representing on paper, which has two dimensions, any object immersed in a space that has three dimensions. In response to the problem, the Descriptive Geometry and the Representation Systems are born. The representation systems are a set of operations that allow make projections of objects immersed in three-dimensional space on a plane that is usually the role of drawing. A class of these systems are those obtained from axonometric projections of \(\mathbb {R}^{3}\) to \(\mathbb {R}^{2}\) based on Pohlke’s theorem and widely used in the vast majority of scientific texts. In this paper it is proposed to build axonometric projections from \(\mathbb {R}^{4}\) to \(\mathbb {R}^{3}\) to obtain projections of objects immersed in the four-dimensional space on a 3D hyperplane. To visualize the results, a new package encoded in the Maxima open source software will be used.
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Notes
- 1.
This paper will work only with linear projections, specifically with axonometric projections.
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Sobrino, E.E., Ipanaqué, R., Velezmoro, R., Mechato, J.A. (2020). New Package in Maxima to Build Axonometric Projections from \(\mathbb {R}^{4}\) to \(\mathbb {R}^{3}\) and Visualize Objects Immersed in \(\mathbb {R}^{4}\). In: Gervasi, O., et al. Computational Science and Its Applications – ICCSA 2020. ICCSA 2020. Lecture Notes in Computer Science(), vol 12255. Springer, Cham. https://doi.org/10.1007/978-3-030-58820-5_60
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