NDLI: Visibility of the higher-dimensional central projection into the projective sphere

Content Provider	Springer Nature Link
Author	Katona, J. Molnár, E.
Copyright Year	2009
Abstract	We can describe higher-dimensional classical spaces by analytical projective geometry, if we embed the d-dimensional real space onto a d + 1-dimensional real projective metric vector space. This method allows an approach to Euclidean, hyperbolic, spherical and other geometries uniformly [8].To visualize d-dimensional solids, it is customary to make axonometric projection of them. In our opinion the central projection gives more information about these objects, and it contains the axonometric projection as well, if the central figure is an ideal point or an s-dimensional subspace at infinity. We suggest a general method which can project solids into any picture plane (space) from any central figure, complementary to the projection plane (space). Opposite to most of the other algorithms in the literature, our algorithm projects higher-dimensional solids directly into the two-dimensional picture plane (especially into the computer screen), it does not use the three-dimensional space for intermediate step.Our algorithm provides a general, so-called lexicographic visibility criterion in Definition and Theorem 3.4, so it determines an extended visibility of the d-dimensional solids by describing the edge framework of the two-dimensional surface in front of us. In addition we can move the central figure and the image plane of the projection, so we can simulate the moving position of the observer at fixed objects on the computer screen (see first our figures in reverse order).
Ending Page	309
Page Count	19
Starting Page	291
File Format	PDF
ISSN	02365294
e-ISSN	15882632
Journal	Acta Mathematica Hungarica
Issue Number	3
Volume Number	123
Language	English
Publisher	Springer Netherlands
Publisher Date	2009-01-26
Publisher Place	Dordrecht
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Computer graphics, image analysis, and computational geometry Image processing Exterior algebra, Grassmann algebras Computer graphics; computational geometry projective spherical space Mathematics visibility algorithm central projection in higher dimensions Projective analytic geometry
Content Type	Text
Resource Type	Article
Subject	Mathematics

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4	Project PI / Joint PI	Principal Investigator and Joint Principal Investigators of the project	Dr. B. Sutradhar bsutra@ndl.gov.in Prof. Saswat Chakrabarti will be added soon
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