3-D Shadows of 4-D Algebraic Hypersurfaces in a 4-D Perspective
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11410%2F25%3A10509352" target="_blank" >RIV/00216208:11410/25:10509352 - isvavai.cz</a>
Alternative codes found
RIV/68407700:21450/25:00389578
Result on the web
<a href="https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=dILJ.s6x0Q" target="_blank" >https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=dILJ.s6x0Q</a>
DOI - Digital Object Identifier
—
Alternative languages
Result language
angličtina
Original language name
3-D Shadows of 4-D Algebraic Hypersurfaces in a 4-D Perspective
Original language description
Visualizing a scene of objects in 4-D space faces several challenges. Mere projections into 3- or less-dimensional spaces usually contain overlapping parts, making them difficult to comprehend or study. Illuminating the scene can enhance intuition about its "dimensionality." Our contribution describes a geometric approach to creating visualizations of 4-D hypersurfaces represented by implicit algebraic equations without their parametrization. By geometric, we mean methods using constructions of geometric objects without their approximation, for example, by polyhedral meshes. Therefore, instead of sets of many points and operating with meshes, we work with implicitly represented hypersurfaces, their projections, contours, intersections, etc. We provide a general algorithm to find shadow boundaries in an arbitrary dimension and apply it in a 4-D space. Furthermore, we design a system of polynomial equations to construct occluding contours of algebraic surfaces in a 4-D perspective. The results of our algorithm are components of the 3-D model of a scene image represented by polynomial equations and inequalities prepared for plotting by standard computer algebra systems with visualization tools. The method is presented on three 4-D scenes with gradual many properties of the visualized shapes, they are suitable for precise mathematical or scientific visualization. On the other hand, processing higher-degree time.
Czech name
—
Czech description
—
Classification
Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
—
OECD FORD branch
10102 - Applied mathematics
Result continuities
Project
—
Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace
Others
Publication year
2025
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Journal for Geometry and Graphics
ISSN
1433-8157
e-ISSN
—
Volume of the periodical
29
Issue of the periodical within the volume
2
Country of publishing house
DE - GERMANY
Number of pages
23
Pages from-to
199-221
UT code for WoS article
001664223400007
EID of the result in the Scopus database
2-s2.0-105028979464