Adjusting degree of visual complexity: an interactive approach for exploring four-dimensional polytopes

被引：4
|
作者：
Morey, J [1 ]
Sedig, K
机构：
[1] Univ Western Ontario, Dept Comp Sci, Cognit Engn Lab, London, ON N6A 3K7, Canada
[2] Univ Western Ontario, Fac Informat & Media Studies, Cognit Engn Lab, London, ON N6A 3K7, Canada
来源：
VISUAL COMPUTER | 2004年 / 20卷 / 8-9期
关键词：
mathematical visualization; high-dimensional geometry; interactive techniques; computer-aided visual reasoning; dynamic exploration;
D O I：
10.1007/s00371-004-0259-x
中图分类号：
TP31 [计算机软件];
学科分类号：
081202 ; 0835 ;
摘要：
Few mathematical visualization tools support integrated, flexible interaction with complex, 4D mathematical concepts. This paper presents a solution to exploring uniform 4D polytopes through a mathematical visualization tool by introducing an approach for adjusting the degree of visual complexity of these complicated geometric structures. This approach introduces a number of interactive techniques: contextualizing, filtering, focus+scoping, and stacking-unstacking. Although these techniques can be effectively used in isolation, their integrated application provides highly specified and sophisticated interaction with polytopes, helping users make sense of these challenging mathematical structures. Exploring complicated structures from other domains such as chemistry and biology may benefit from this approach.
引用
收藏
页码：565 / 585
页数：21
相关论文
共 50 条
  • [1] Adjusting degree of visual complexity: an interactive approach for exploring four-dimensional polytopes
    Jim Morey
    Kamran Sedig
    [J]. The Visual Computer, 2004, 20 : 565 - 585
  • [2] A classical approach to the study of Archimedean four-dimensional polytopes
    Polo-Blanco I.
    [J]. Mathematische Semesterberichte, 2008, 55 (2) : 107 - 111
  • [3] Visual perception of objects and boundaries: A four-dimensional approach
    Kellman, PJ
    [J]. PERCEPTUAL ORGANIZATION IN VISION: BEHAVIORAL AND NEURAL PERSPECTIVES, 2003, : 155 - 201
  • [4] COMPUTING REEB DYNAMICS ON FOUR-DIMENSIONAL CONVEX POLYTOPES
    Chaidez, Julian
    Hutchings, Michael
    [J]. JOURNAL OF COMPUTATIONAL DYNAMICS, 2021, 8 (04): : 403 - 445
  • [5] On the angles of the regular polytopes of four-dimensional space.
    Schoute, PH
    [J]. AMERICAN JOURNAL OF MATHEMATICS, 1909, 31 : 303 - 310
  • [6] Four-dimensional polytopes of minimum positive semidefinite rank
    Gouveia, Joao
    Pashkovich, Kanstanstin
    Robinson, Richard Z.
    Thomas, Rekha R.
    [J]. JOURNAL OF COMBINATORIAL THEORY SERIES A, 2017, 145 : 184 - 226
  • [7] Four-Dimensional Polytopes: Alicia Boole Stott's Algorithm
    Polo-Blanco, Irene
    Gonzalez-Sanchez, Jon
    [J]. MATHEMATICAL INTELLIGENCER, 2010, 32 (03): : 1 - 6
  • [8] On the four-dimensional angles of the semiregular polytopes of S-4
    Schoute, PH
    [J]. AMERICAN JOURNAL OF MATHEMATICS, 1913, 35 : 357 - 368
  • [9] Four-dimensional imaging: Exploring time
    Thomas, CF
    White, JG
    [J]. BIOFUTUR, 1999, (186) : A1 - A10
  • [10] Compact hyperbolic Coxeter four-dimensional polytopes with eight facets
    Jiming Ma
    Fangting Zheng
    [J]. Journal of Algebraic Combinatorics, 2024, 59 : 225 - 290
12345