Topic
Perspective (geometry)
About: Perspective (geometry) is a research topic. Over the lifetime, 277 publications have been published within this topic receiving 5795 citations. The topic is also known as: perspective (geometry).
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29 Jun 2003
TL;DR: In this paper, an extended P3P (Perspective Three Points) problem is investigated, formulated as fitting three moving vertices along their associated optical rays to a known triangle structure that allows the three Optical rays to come from one, two or three cameras respectively.
Abstract: In this paper, an extended P3P (Perspective Three Points) problem is investigated. It is formulated as fitting three moving vertices along their associated optical rays to a known triangle structure. This allows the three optical rays to come from one, two or three cameras respectively. The classical P3P problem for only single camera is considered as a special case of the extended P3P problem. An analysis on these different cases is given in a uniform way. Experiments with simulated data show the effectiveness of the approach.
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TL;DR: The article shows that usual, naive, lines are not all lines, and a formalization of Pappus geometry should enable to automatize these generalizations of lines.
Abstract: The playground is the projective complex plane. The article shows that usual, naive, lines are not all lines. From naive lines (level 0), Pappus geometry creates new geometric objects (circles or conics) which can also be considered as (level 1) lines, in the sense that they fulfil Pappus axioms for lines. But Pappus theory also applies to these new lines. A formalization of Pappus geometry should enable to automatize these generalizations of lines.
Posted Content•
TL;DR: In this article, an upper bound for the digital LS-category of the digital projective product spaces is derived for the first digital sphere and the digital topological complexity of remaining digital spheres through an explicit motion planning construction.
Abstract: We introduce the digital projective product spaces based on Davis' projective product spaces. We determine an upper bound for the digital LS-category of the digital projective product spaces. In addition, we obtain an upper bound for the digital topological complexity of these spaces. We prove the relation between the digital topological complexity of the digital projective product spaces and sum of the digital topological complexity of the digital projective space by associating with the first digital sphere and the digital topological complexity of the remaining digital spheres through an explicit motion planning construction, which shows digital perspective validity of the results given by S. Fisekci and L. Vandembroucq. We apply our outcomes on specific spaces in order to be more clear.
Patent•
02 Mar 2021TL;DR: In this article, the authors proposed a method to determine the locations of electro-optical pens based on the tilt orientation of the scribing plane relative to the pen based on a plurality of distance measurements.
Abstract: Determining locations of electro-optical pens. A disclosed example includes, a distance determiner to determine a distance from a pen to a scribing plane at a plurality of points to produce a plurality of distance measurements, a tilt orientation determiner to determine a tilt orientation of the scribing plane relative to the pen based on the plurality of distance measurements, a plane of view corrector to, based on the tilt orientation of the scribing plane, correct a plane of view associated with at least one of the first perspective and the second perspective, and a coordinate determiner to determine coordinates of the pen based on the corrected plane of view. A location determiner determines the location of the pen on a display based on the coordinates.
TL;DR: In this paper, a geometric theory of images based on the general principles of light ray behaviour is shown, and a new theoretical and experimental study on hologravures, as holographic computer-generated laser-engravings.