Complete SE(3) Invariants for a Comeagre Set of C3 Compact Orientable Surfaces in R3

Yair Hayut; David Lehavi

doi:10.1137/21m1445776

Complete SE(3) Invariants for a Comeagre Set of C³ Compact Orientable Surfaces in R³

Yair Hayut
, David Lehavi

Einstein Institute of Mathematics

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

Abstract

We introduce invariants for compact C¹-orientable surfaces (with boundary) in ℝ³ up to rigid transformations. Our invariants are certain degree four polynomials in the moments of the delta function of the surface. We give an effective algorithm for retrieving successive approximations of surface from successive prefixes of the invariants, which works on a comeagre subset of C³-surfaces. The reconstruction algorithm is continuous in numerical geometric properties of the surface in question.

Original language	English
Pages (from-to)	311-344
Number of pages	34
Journal	SIAM Journal on Applied Algebra and Geometry
Volume	7
Issue number	2
DOIs	https://doi.org/10.1137/21m1445776
State	Published - 2023

Bibliographical note

Publisher Copyright:
© 2023 Y. Hayut and D. Lehavi.

Keywords

Fourier
distribution
invariants
surfaces

Access to Document

10.1137/21m1445776

Cite this

@article{9b45a5f3f8744ecf92a89639ab0fea3e,

title = "Complete SE(3) Invariants for a Comeagre Set of C3 Compact Orientable Surfaces in R3",

abstract = "We introduce invariants for compact C1-orientable surfaces (with boundary) in ℝ3 up to rigid transformations. Our invariants are certain degree four polynomials in the moments of the delta function of the surface. We give an effective algorithm for retrieving successive approximations of surface from successive prefixes of the invariants, which works on a comeagre subset of C3-surfaces. The reconstruction algorithm is continuous in numerical geometric properties of the surface in question.",

keywords = "Fourier, distribution, invariants, surfaces",

author = "Yair Hayut and David Lehavi",

note = "Publisher Copyright: {\textcopyright} 2023 Y. Hayut and D. Lehavi.",

year = "2023",

doi = "10.1137/21m1445776",

language = "אנגלית",

volume = "7",

pages = "311--344",

journal = "SIAM Journal on Applied Algebra and Geometry",

issn = "2470-6566",

publisher = "Society for Industrial and Applied Mathematics Publications",

number = "2",

}

TY - JOUR

T1 - Complete SE(3) Invariants for a Comeagre Set of C3 Compact Orientable Surfaces in R3

AU - Hayut, Yair

AU - Lehavi, David

PY - 2023

Y1 - 2023

N2 - We introduce invariants for compact C1-orientable surfaces (with boundary) in ℝ3 up to rigid transformations. Our invariants are certain degree four polynomials in the moments of the delta function of the surface. We give an effective algorithm for retrieving successive approximations of surface from successive prefixes of the invariants, which works on a comeagre subset of C3-surfaces. The reconstruction algorithm is continuous in numerical geometric properties of the surface in question.

AB - We introduce invariants for compact C1-orientable surfaces (with boundary) in ℝ3 up to rigid transformations. Our invariants are certain degree four polynomials in the moments of the delta function of the surface. We give an effective algorithm for retrieving successive approximations of surface from successive prefixes of the invariants, which works on a comeagre subset of C3-surfaces. The reconstruction algorithm is continuous in numerical geometric properties of the surface in question.

KW - Fourier

KW - distribution

KW - invariants

KW - surfaces

UR - https://www.scopus.com/pages/publications/85167864477

U2 - 10.1137/21m1445776

DO - 10.1137/21m1445776

M3 - ???researchoutput.researchoutputtypes.contributiontojournal.article???

AN - SCOPUS:85167864477

SN - 2470-6566

VL - 7

SP - 311

EP - 344

JO - SIAM Journal on Applied Algebra and Geometry

JF - SIAM Journal on Applied Algebra and Geometry

IS - 2

ER -