Details
| Original language | English |
|---|---|
| Title of host publication | Proceedings Computer Graphics International 2000 |
| Publisher | Institute of Electrical and Electronics Engineers Inc. |
| Pages | 137-151 |
| Number of pages | 15 |
| ISBN (print) | 0-7695-0643-7 |
| Publication status | Published - 2000 |
| Event | CGI 2000: The 18th Computer Graphics Internationa 'Humans and Nature' - Geneva, Switz Duration: 19 Jun 2000 → 24 Jun 2000 |
Abstract
This paper gives an overview of some recent methods useful for local and global shape analysis and for the design of solids. These methods include as new tools for global and local shape analysis the Spectra of the Laplace and the Laplace-Beltrami Operator and the Concept of stable Umbilical Points i.e. stable singularities of the principal curvature line wire frame model of the solid's boundary surface. Most material in this paper deals with the Medial Axis Transform as a tool for shape interrogation, reconstruction, modification and design. We show that it appears to be possible to construct an intuitive user interface that allows to mould shape employing the Medial Axis Transform. We also explain that the Medial Axis and Voronoi Diagrams can be defined and computed as well on free form surfaces in a setting where the geodesic distance between two points p, q on a surface S is defined by the shortest surface path on S joining the two points p, q. This leads to the natural and computable generalized concepts of geodesic Medial Axis and geodesic Voronoi Diagram on free form surfaces. Both can be computed with a reasonable speed and with a high accuracy (of about 12 digits when double floating point arithmetic is used for the computations).
ASJC Scopus subject areas
- Computer Science(all)
- Software
- Computer Science(all)
- Computer Graphics and Computer-Aided Design
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Proceedings Computer Graphics International 2000. Institute of Electrical and Electronics Engineers Inc., 2000. p. 137-151.
Research output: Chapter in book/report/conference proceeding › Conference contribution › Research › peer review
}
TY - GEN
T1 - Local and Global Geometric Methods for Analysis Interrogation, Reconstruction, Modification and Design of Shape
AU - Wolter, F. E.
AU - Friese, K. I.
PY - 2000
Y1 - 2000
N2 - This paper gives an overview of some recent methods useful for local and global shape analysis and for the design of solids. These methods include as new tools for global and local shape analysis the Spectra of the Laplace and the Laplace-Beltrami Operator and the Concept of stable Umbilical Points i.e. stable singularities of the principal curvature line wire frame model of the solid's boundary surface. Most material in this paper deals with the Medial Axis Transform as a tool for shape interrogation, reconstruction, modification and design. We show that it appears to be possible to construct an intuitive user interface that allows to mould shape employing the Medial Axis Transform. We also explain that the Medial Axis and Voronoi Diagrams can be defined and computed as well on free form surfaces in a setting where the geodesic distance between two points p, q on a surface S is defined by the shortest surface path on S joining the two points p, q. This leads to the natural and computable generalized concepts of geodesic Medial Axis and geodesic Voronoi Diagram on free form surfaces. Both can be computed with a reasonable speed and with a high accuracy (of about 12 digits when double floating point arithmetic is used for the computations).
AB - This paper gives an overview of some recent methods useful for local and global shape analysis and for the design of solids. These methods include as new tools for global and local shape analysis the Spectra of the Laplace and the Laplace-Beltrami Operator and the Concept of stable Umbilical Points i.e. stable singularities of the principal curvature line wire frame model of the solid's boundary surface. Most material in this paper deals with the Medial Axis Transform as a tool for shape interrogation, reconstruction, modification and design. We show that it appears to be possible to construct an intuitive user interface that allows to mould shape employing the Medial Axis Transform. We also explain that the Medial Axis and Voronoi Diagrams can be defined and computed as well on free form surfaces in a setting where the geodesic distance between two points p, q on a surface S is defined by the shortest surface path on S joining the two points p, q. This leads to the natural and computable generalized concepts of geodesic Medial Axis and geodesic Voronoi Diagram on free form surfaces. Both can be computed with a reasonable speed and with a high accuracy (of about 12 digits when double floating point arithmetic is used for the computations).
UR - http://www.scopus.com/inward/record.url?scp=0033717159&partnerID=8YFLogxK
U2 - 10.1109/CGI.2000.852329
DO - 10.1109/CGI.2000.852329
M3 - Conference contribution
AN - SCOPUS:0033717159
SN - 0-7695-0643-7
SP - 137
EP - 151
BT - Proceedings Computer Graphics International 2000
PB - Institute of Electrical and Electronics Engineers Inc.
T2 - CGI 2000: The 18th Computer Graphics Internationa 'Humans and Nature'
Y2 - 19 June 2000 through 24 June 2000
ER -