Details
| Originalsprache | Englisch |
|---|---|
| Titel des Sammelwerks | 2007 International Conference on Cyberworlds |
| Untertitel | (CW'07) |
| Herausgeber (Verlag) | IEEE Computer Society |
| Seiten | 386-395 |
| Seitenumfang | 10 |
| ISBN (Print) | 0769530052, 9780769530055 |
| Publikationsstatus | Veröffentlicht - 2007 |
| Veranstaltung | 2007 International Conference on Cyberworlds, CW'07 - Hannover, Deutschland Dauer: 24 Okt. 2007 → 27 Okt. 2007 |
Abstract
The main contribution of this work is the generalisation of the Medial Axis Transform (MAT) and the Medial Axis Inverse Transform MAIT) on complete Riemannian manifolds. It is known that almost every solid can be reconstructed from its medial axis and the corresponding radius function. In the past this reconstruction scheme has only been implemented in Euclidean spaces. We will use the concepts of Fermi coordinates that represent a natural generalisation of normal coordinates. However, this concept only works out properly if some substantial conditions for the radius function are established. Several approaches for the computation of the medial axis have been implemented so far but almost all of them lack good numerical results. Usually numerical errors occur because the approaches operate on a discretised model of the corresponding objects. In this work we will assume that both the 3D Riemannian space and the modelled object can be represented by smooth mappings and coordinate charts respectively. Therefore, we can introduce the so called medial equations that will allow us to compute medial surface patches using the implicit function theorem. Finally we will give examples for the MAT and the MAIT and show to what extent the inverse transform is applicable in the context of Computer Aided Geometric Design. The Geodesic Medial Modeller is one of those applications.
ASJC Scopus Sachgebiete
- Energie (insg.)
- Erneuerbare Energien, Nachhaltigkeit und Umwelt
- Umweltwissenschaften (insg.)
- Management, Monitoring, Politik und Recht
- Energie (insg.)
- Feuerungstechnik
- Informatik (insg.)
- Computernetzwerke und -kommunikation
- Informatik (insg.)
- Mensch-Maschine-Interaktion
- Sozialwissenschaften (insg.)
- Kommunikation
- Energie (insg.)
- Energie (insg.)
- Energieanlagenbau und Kraftwerkstechnik
- Mathematik (insg.)
- Modellierung und Simulation
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2007 International Conference on Cyberworlds : (CW'07). IEEE Computer Society, 2007. S. 386-395 4390943.
Publikation: Beitrag in Buch/Bericht/Sammelwerk/Konferenzband › Aufsatz in Konferenzband › Forschung › Peer-Review
}
TY - GEN
T1 - Medial Axis (Inverse) Transform in Complete 3-Dimensional Riemannian Manifolds
AU - Naß, Henning
AU - Wolter, F. E.
AU - Doǧan, Cem
AU - Thielhelm, Hannes
PY - 2007
Y1 - 2007
N2 - The main contribution of this work is the generalisation of the Medial Axis Transform (MAT) and the Medial Axis Inverse Transform MAIT) on complete Riemannian manifolds. It is known that almost every solid can be reconstructed from its medial axis and the corresponding radius function. In the past this reconstruction scheme has only been implemented in Euclidean spaces. We will use the concepts of Fermi coordinates that represent a natural generalisation of normal coordinates. However, this concept only works out properly if some substantial conditions for the radius function are established. Several approaches for the computation of the medial axis have been implemented so far but almost all of them lack good numerical results. Usually numerical errors occur because the approaches operate on a discretised model of the corresponding objects. In this work we will assume that both the 3D Riemannian space and the modelled object can be represented by smooth mappings and coordinate charts respectively. Therefore, we can introduce the so called medial equations that will allow us to compute medial surface patches using the implicit function theorem. Finally we will give examples for the MAT and the MAIT and show to what extent the inverse transform is applicable in the context of Computer Aided Geometric Design. The Geodesic Medial Modeller is one of those applications.
AB - The main contribution of this work is the generalisation of the Medial Axis Transform (MAT) and the Medial Axis Inverse Transform MAIT) on complete Riemannian manifolds. It is known that almost every solid can be reconstructed from its medial axis and the corresponding radius function. In the past this reconstruction scheme has only been implemented in Euclidean spaces. We will use the concepts of Fermi coordinates that represent a natural generalisation of normal coordinates. However, this concept only works out properly if some substantial conditions for the radius function are established. Several approaches for the computation of the medial axis have been implemented so far but almost all of them lack good numerical results. Usually numerical errors occur because the approaches operate on a discretised model of the corresponding objects. In this work we will assume that both the 3D Riemannian space and the modelled object can be represented by smooth mappings and coordinate charts respectively. Therefore, we can introduce the so called medial equations that will allow us to compute medial surface patches using the implicit function theorem. Finally we will give examples for the MAT and the MAIT and show to what extent the inverse transform is applicable in the context of Computer Aided Geometric Design. The Geodesic Medial Modeller is one of those applications.
UR - http://www.scopus.com/inward/record.url?scp=46449129705&partnerID=8YFLogxK
U2 - 10.1109/CW.2007.55
DO - 10.1109/CW.2007.55
M3 - Conference contribution
AN - SCOPUS:46449129705
SN - 0769530052
SN - 9780769530055
SP - 386
EP - 395
BT - 2007 International Conference on Cyberworlds
PB - IEEE Computer Society
T2 - 2007 International Conference on Cyberworlds, CW'07
Y2 - 24 October 2007 through 27 October 2007
ER -