Subdivision schemes for the fair discretization of the spherical motion group

Georg Nawratil; Helmut Pottmann

doi:10.1016/j.cam.2007.12.004

Subdivision schemes for the fair discretization of the spherical motion group

Georg Nawratil^*, Helmut Pottmann

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

7 Scopus citations

Abstract

We present two subdivision schemes for the fair discretization of the spherical motion group. The first one is based on the subdivision of the 600-cell according to the tetrahedral/octahedral subdivision scheme in [S. Schaefer, J. Hakenberg, J. Warren, Smooth subdivision of tetrahedral meshes, in: R. Scopigno, D. Zorin (Eds.), Eurographics Symposium on Geometry Processing, 2004, pp. 151-158]. The second presented subdivision scheme is based on the spherical kinematic mapping. In the first step we discretize an elliptic linear congruence by the icosahedral discretization of the unit sphere. Then the resulting lines of the elliptic three-space are discretized such that the difference in the maximal and minimal elliptic distance between neighboring grid points becomes minimal.

Original language	English (US)
Pages (from-to)	574-591
Number of pages	18
Journal	Journal of Computational and Applied Mathematics
Volume	222
Issue number	2
DOIs	https://doi.org/10.1016/j.cam.2007.12.004
State	Published - Dec 15 2008
Externally published	Yes

Keywords

600-cell
Discretization
Elliptic linear congruence
Spherical kinematic mapping
Spherical motion group

ASJC Scopus subject areas

Computational Mathematics
Applied Mathematics

Access to Document

10.1016/j.cam.2007.12.004

Cite this

@article{ea34ed7e831e42198d8279ece2cdd50d,

title = "Subdivision schemes for the fair discretization of the spherical motion group",

abstract = "We present two subdivision schemes for the fair discretization of the spherical motion group. The first one is based on the subdivision of the 600-cell according to the tetrahedral/octahedral subdivision scheme in [S. Schaefer, J. Hakenberg, J. Warren, Smooth subdivision of tetrahedral meshes, in: R. Scopigno, D. Zorin (Eds.), Eurographics Symposium on Geometry Processing, 2004, pp. 151-158]. The second presented subdivision scheme is based on the spherical kinematic mapping. In the first step we discretize an elliptic linear congruence by the icosahedral discretization of the unit sphere. Then the resulting lines of the elliptic three-space are discretized such that the difference in the maximal and minimal elliptic distance between neighboring grid points becomes minimal.",

keywords = "600-cell, Discretization, Elliptic linear congruence, Spherical kinematic mapping, Spherical motion group",

author = "Georg Nawratil and Helmut Pottmann",

note = "Funding Information: This research was carried out as part of the project S9206-N12 which was supported by the Austrian Science Fund (FWF).",

year = "2008",

month = dec,

day = "15",

doi = "10.1016/j.cam.2007.12.004",

language = "English (US)",

volume = "222",

pages = "574--591",

journal = "Journal of Computational and Applied Mathematics",

issn = "0377-0427",

publisher = "Elsevier B.V.",

number = "2",

}

TY - JOUR

T1 - Subdivision schemes for the fair discretization of the spherical motion group

AU - Nawratil, Georg

AU - Pottmann, Helmut

N1 - Funding Information: This research was carried out as part of the project S9206-N12 which was supported by the Austrian Science Fund (FWF).

PY - 2008/12/15

Y1 - 2008/12/15

N2 - We present two subdivision schemes for the fair discretization of the spherical motion group. The first one is based on the subdivision of the 600-cell according to the tetrahedral/octahedral subdivision scheme in [S. Schaefer, J. Hakenberg, J. Warren, Smooth subdivision of tetrahedral meshes, in: R. Scopigno, D. Zorin (Eds.), Eurographics Symposium on Geometry Processing, 2004, pp. 151-158]. The second presented subdivision scheme is based on the spherical kinematic mapping. In the first step we discretize an elliptic linear congruence by the icosahedral discretization of the unit sphere. Then the resulting lines of the elliptic three-space are discretized such that the difference in the maximal and minimal elliptic distance between neighboring grid points becomes minimal.

AB - We present two subdivision schemes for the fair discretization of the spherical motion group. The first one is based on the subdivision of the 600-cell according to the tetrahedral/octahedral subdivision scheme in [S. Schaefer, J. Hakenberg, J. Warren, Smooth subdivision of tetrahedral meshes, in: R. Scopigno, D. Zorin (Eds.), Eurographics Symposium on Geometry Processing, 2004, pp. 151-158]. The second presented subdivision scheme is based on the spherical kinematic mapping. In the first step we discretize an elliptic linear congruence by the icosahedral discretization of the unit sphere. Then the resulting lines of the elliptic three-space are discretized such that the difference in the maximal and minimal elliptic distance between neighboring grid points becomes minimal.

KW - 600-cell

KW - Discretization

KW - Elliptic linear congruence

KW - Spherical kinematic mapping

KW - Spherical motion group

UR - http://www.scopus.com/inward/record.url?scp=53349180531&partnerID=8YFLogxK

U2 - 10.1016/j.cam.2007.12.004

DO - 10.1016/j.cam.2007.12.004

M3 - Article

AN - SCOPUS:53349180531

SN - 0377-0427

VL - 222

SP - 574

EP - 591

JO - Journal of Computational and Applied Mathematics

JF - Journal of Computational and Applied Mathematics

IS - 2

ER -

Subdivision schemes for the fair discretization of the spherical motion group

Abstract

Keywords

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this