Restricted mesh simplification using edge contractions
Andersson, Mattias LU ; Gudmundsson, Joachim and Levcopoulos, Christos LU
(2009)
In International Journal of Computational Geometry and Applications
19(3).
p.247-265
- Abstract
- We consider the problem of simplifying a planar triangle mesh using edge contractions, under the restriction that the resulting vertices must be a subset of the input set. That is, contraction of an edge must be made on to one of its adjacent vertices, which results in removing the other adjacent vertex. We show that if the perimeter of the mesh consists of at most five vertices, then we can always find a vertex not on the perimeter which can be removed in this way. If the perimeter consists of more than five vertices such a vertex may not exist. In order to maintain a higher number of removable vertices under the above restriction, we study edge flips which can be performed in a visually smooth way. A removal of a vertex which is preceded... (More)
- We consider the problem of simplifying a planar triangle mesh using edge contractions, under the restriction that the resulting vertices must be a subset of the input set. That is, contraction of an edge must be made on to one of its adjacent vertices, which results in removing the other adjacent vertex. We show that if the perimeter of the mesh consists of at most five vertices, then we can always find a vertex not on the perimeter which can be removed in this way. If the perimeter consists of more than five vertices such a vertex may not exist. In order to maintain a higher number of removable vertices under the above restriction, we study edge flips which can be performed in a visually smooth way. A removal of a vertex which is preceded by one such smooth operation is called a 2-step removal. Moreover, we introduce the possibility that the user defines "important" vertices (or edges) which have to remain intact. Given m such important vertices, or edges, we show that a simplification hierarchy of size O(n) and depth O(log(n/m))can be constructed by 2-step removals in O(n) time, such that the simplified graph contains the m important vertices and edges, and at most O(m) other vertices from the input graph. In some triangulations, many vertices may not even be 2-step removable. In order to provide the option to remove such vertices, we also define and examine k-step removals. This increases the lower bound on the number of removable vertices. (Less)
Please use this url to cite or link to this publication:
https://lup.lub.lu.se/record/1463174
- author
- Andersson, Mattias
LU
; Gudmundsson, Joachim
and Levcopoulos, Christos
LU
- organization
- publishing date
- 2009
- type
- Contribution to journal
- publication status
- published
- subject
- keywords
- edge contractions, Computational geometry, computer graphics
- in
- International Journal of Computational Geometry and Applications
- volume
- 19
- issue
- 3
- pages
- 247 - 265
- publisher
- World Scientific Publishing
- external identifiers
-
- wos:000267510600004
- scopus:68049144811
- ISSN
- 0218-1959
- DOI
- 10.1142/S0218195909002940
- project
- VR 2008-4649
- language
- English
- LU publication?
- yes
- id
- f6883800-e775-4f11-991b-15d18d04aea7 (old id 1463174)
- date added to LUP
- 2016-04-01 12:53:57
- date last changed
- 2022-04-06 01:21:55
@article{f6883800-e775-4f11-991b-15d18d04aea7,
abstract = {{We consider the problem of simplifying a planar triangle mesh using edge contractions, under the restriction that the resulting vertices must be a subset of the input set. That is, contraction of an edge must be made on to one of its adjacent vertices, which results in removing the other adjacent vertex. We show that if the perimeter of the mesh consists of at most five vertices, then we can always find a vertex not on the perimeter which can be removed in this way. If the perimeter consists of more than five vertices such a vertex may not exist. In order to maintain a higher number of removable vertices under the above restriction, we study edge flips which can be performed in a visually smooth way. A removal of a vertex which is preceded by one such smooth operation is called a 2-step removal. Moreover, we introduce the possibility that the user defines "important" vertices (or edges) which have to remain intact. Given m such important vertices, or edges, we show that a simplification hierarchy of size O(n) and depth O(log(n/m))can be constructed by 2-step removals in O(n) time, such that the simplified graph contains the m important vertices and edges, and at most O(m) other vertices from the input graph. In some triangulations, many vertices may not even be 2-step removable. In order to provide the option to remove such vertices, we also define and examine k-step removals. This increases the lower bound on the number of removable vertices.}},
author = {{Andersson, Mattias and Gudmundsson, Joachim and Levcopoulos, Christos}},
issn = {{0218-1959}},
keywords = {{edge contractions; Computational geometry; computer graphics}},
language = {{eng}},
number = {{3}},
pages = {{247--265}},
publisher = {{World Scientific Publishing}},
series = {{International Journal of Computational Geometry and Applications}},
title = {{Restricted mesh simplification using edge contractions}},
url = {{http://dx.doi.org/10.1142/S0218195909002940}},
doi = {{10.1142/S0218195909002940}},
volume = {{19}},
year = {{2009}},
}