Details
| Original language | English |
|---|---|
| Pages (from-to) | 574-592 |
| Number of pages | 19 |
| Journal | Graphical Models and Image Processing |
| Volume | 58 |
| Issue number | 6 |
| Publication status | Published - Nov 1996 |
Abstract
The medial axis transform is a representation of an object which has been shown to be useful in design, interrogation, animation, finite element mesh generation, performance analysis, manufacturing simulation, path planning, and tolerance specification. In this paper, the theory of the medial axis transform for 3-D objects is developed. For objects with piecewise C2 boundaries, relationships between the curvature of the boundary and the position of the medial axis are developed. For n-dimensional submanifolds of ℛn with boundaries which are piecewise C2 and completely G1, a deformation retract is set up between each object and its medial axis, which demonstrates that if the object is path connected, then so is its medial axis. Finally, it is proven that path connected polyhedral solids without cavities have path connected medial axes.
ASJC Scopus subject areas
- Mathematics(all)
- Modelling and Simulation
- Computer Science(all)
- Computer Vision and Pattern Recognition
- Mathematics(all)
- Geometry and Topology
- Computer Science(all)
- Computer Graphics and Computer-Aided Design
Cite this
- Standard
- Harvard
- Apa
- Vancouver
- BibTeX
- RIS
In: Graphical Models and Image Processing, Vol. 58, No. 6, 11.1996, p. 574-592.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - Differential and Topological Properties of Medial Axis Transforms
AU - Sherbrooke, Evan C.
AU - Patrikalakis, Nicholas M.
AU - Wolter, Franz Erich
PY - 1996/11
Y1 - 1996/11
N2 - The medial axis transform is a representation of an object which has been shown to be useful in design, interrogation, animation, finite element mesh generation, performance analysis, manufacturing simulation, path planning, and tolerance specification. In this paper, the theory of the medial axis transform for 3-D objects is developed. For objects with piecewise C2 boundaries, relationships between the curvature of the boundary and the position of the medial axis are developed. For n-dimensional submanifolds of ℛn with boundaries which are piecewise C2 and completely G1, a deformation retract is set up between each object and its medial axis, which demonstrates that if the object is path connected, then so is its medial axis. Finally, it is proven that path connected polyhedral solids without cavities have path connected medial axes.
AB - The medial axis transform is a representation of an object which has been shown to be useful in design, interrogation, animation, finite element mesh generation, performance analysis, manufacturing simulation, path planning, and tolerance specification. In this paper, the theory of the medial axis transform for 3-D objects is developed. For objects with piecewise C2 boundaries, relationships between the curvature of the boundary and the position of the medial axis are developed. For n-dimensional submanifolds of ℛn with boundaries which are piecewise C2 and completely G1, a deformation retract is set up between each object and its medial axis, which demonstrates that if the object is path connected, then so is its medial axis. Finally, it is proven that path connected polyhedral solids without cavities have path connected medial axes.
UR - http://www.scopus.com/inward/record.url?scp=0030287943&partnerID=8YFLogxK
U2 - 10.1006/gmip.1996.0047
DO - 10.1006/gmip.1996.0047
M3 - Article
AN - SCOPUS:0030287943
VL - 58
SP - 574
EP - 592
JO - Graphical Models and Image Processing
JF - Graphical Models and Image Processing
SN - 1077-3169
IS - 6
ER -