Mathematical elements for computer graphics (2nd ed.)
Mathematical elements for computer graphics (2nd ed.)
Ball-end cutter interference avoidance in NC machining of sculptured surfaces
Computer-Aided Design
Computational geometry in C
Boundary surface recovery from skeleton curves and surfaces
Computer Aided Geometric Design
Computation of the Medial Axis Transform of 3-D polyhedra
SMA '95 Proceedings of the third ACM symposium on Solid modeling and applications
The bisector surface of rational space curves
ACM Transactions on Graphics (TOG)
Computing the medial surface of a 3-D boundary representation model
Advances in Engineering Software
Rational bisectors of CSG primitives
Proceedings of the fifth ACM symposium on Solid modeling and applications
Accurate computation of the medial axis of a polyhedron
Proceedings of the fifth ACM symposium on Solid modeling and applications
Continuous Skeletons from Digitized Images
Journal of the ACM (JACM)
Computing Voronoi skeletons of a 3-D polyhedron by space subdivision
Computational Geometry: Theory and Applications
An Algorithm for the Medial Axis Transform of 3D Polyhedral Solids
IEEE Transactions on Visualization and Computer Graphics
Shape Description By Medial Surface Construction
IEEE Transactions on Visualization and Computer Graphics
Voronoi Diagrams of Set-Theoretic solid Models
IEEE Computer Graphics and Applications
Voronoi Diagrams for Planar Shapes
IEEE Computer Graphics and Applications
IEEE Computer Graphics and Applications
Computing the Voronoi cells of planes, spheres and cylinders in R3
Proceedings of the 2008 ACM symposium on Solid and physical modeling
3D Block-Based Medial Axis Transform and Chessboard Distance Transform on the CREW PRAM
ICA3PP '08 Proceedings of the 8th international conference on Algorithms and Architectures for Parallel Processing
Computing the Voronoi cells of planes, spheres and cylinders in R3
Computer Aided Geometric Design
MOS surfaces: medial surface transforms with rational domain boundaries
Proceedings of the 12th IMA international conference on Mathematics of surfaces XII
Interior Medial Axis Transform computation of 3D objects bound by free-form surfaces
Computer-Aided Design
3D block-based medial axis transform and chessboard distance transform based on dominance
Image and Vision Computing
Computing medial axes of generic 3D regions bounded by B-spline surfaces
Computer-Aided Design
Research on 3D medial axis transform via the saddle point programming method
Computer-Aided Design
Minimum area enclosure and alpha hull of a set of freeform planar closed curves
Computer-Aided Design
| Hi-index | 0.00 |
This paper presents an algorithm for generating the Medial Axis Transform (MAT) of 3D objects with free form boundaries that are obtained by extrusion along a line or revolution about an axis. The algorithm proposed uses the exact representation of the part and generates an approximate rational spline description (to within a defined tolerance) of the MAT. The algorithm uses the 2D MAT of the profile being extruded or revolved to identify the limiting entities (junction points, seams and points of extremal maximum curvature) of the 3D MAT. It is shown that the MAT points of the profile face are sufficient to determine the topology and geometry of the MAT of this class of solids. The algorithm works for multiply-connected objects as well. Results of implementation are presented and use of the algorithm to handle general solids is discussed.