ISOTOPIC CONVERGENCE THEOREM

被引：1

作者：

Li, J. ^{[1
]}

Peters, T. J. ^{[2
]}

机构：

[1] Univ Connecticut, Dept Math, Storrs, CT 06269 USA

[2] Univ Connecticut, Dept Comp Sci & Engn, Storrs, CT 06269 USA

来源：

JOURNAL OF KNOT THEORY AND ITS RAMIFICATIONS | 2013年 / 22卷 / 03期

基金：

美国国家科学基金会;

关键词：

Knot; ambient isotopy; convergence; total curvature; visualization; COMPUTATIONAL TOPOLOGY; OFFSET CURVES; SUBDIVISION;

D O I：

10.1142/S0218216513500120

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

When approximating a space curve, it is natural to consider whether the knot type of the original curve is preserved in the approximant. This preservation is of strong contemporary interest in computer graphics and visualization. We establish a criterion to preserve knot type under approximation that relies upon pointwise convergence and convergence in total curvature.

引用

页数：18

共 50 条

[1] ISOTOPIC CONVERGENCE THEOREM (vol 22, 1350012, 2013)
Li, J.
Peters, T. J.
JOURNAL OF KNOT THEORY AND ITS RAMIFICATIONS, 2013, 22 (05)
[2] CONVERGENCE THEOREM
APPLING, WDL
NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY, 1973, 20 (06): : A570 - A570
[3] RATE OF CONVERGENCE IN MARTINGALE CONVERGENCE THEOREM
HEYDE, CC
ADVANCES IN APPLIED PROBABILITY, 1977, 9 (02) : 196 - 196
[4] A Unified Convergence Theorem
Jun De Wu
Jian Wen Luo
Shi Jie Lu
Acta Mathematica Sinica, 2005, 21 : 315 - 322
[5] A MOMENT CONVERGENCE THEOREM
TAKACS, L
AMERICAN MATHEMATICAL MONTHLY, 1991, 98 (08): : 742 - 746
[6] BOUNDED CONVERGENCE THEOREM
WADE, WR
AMERICAN MATHEMATICAL MONTHLY, 1974, 81 (04): : 387 - 389
[7] ON SEMIMARTINGALE CONVERGENCE THEOREM
JOHANSEN, S
KARUSH, J
ANNALS OF MATHEMATICAL STATISTICS, 1966, 37 (03): : 690 - &
[8] CONVERGENCE THEOREM WITH BOUNDARY
SIMONS, S
BULLETIN DE LA SOCIETE MATHEMATIQUE DE FRANCE, 1972, (31-3): : 359 - 363
[9] CONVERGENCE THEOREM WITH BOUNDARY
SIMONS, S
PACIFIC JOURNAL OF MATHEMATICS, 1972, 40 (03) : 703 - &
[10] A DOMINATED CONVERGENCE THEOREM
WAYMENT, SG
NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY, 1969, 16 (01): : 118 - &

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