This Article 
 Bibliographic References 
 Add to: 
Shape Description By Medial Surface Construction
March 1996 (vol. 2 no. 1)
pp. 62-72

Abstract—The medial surface is a skeletal abstraction of a solid that provides useful shape information, which compliments existing model representation schemes. The medial surface and its associated topological entities are defined, and an algorithm for computing the medial surface of a large class of B-rep solids is then presented. The algorithm is based on the domain Delaunay triangulation of a relatively sparse distribution of points, which are generated on the boundary of the object. This strategy is adaptive in that the boundary point set is refined to guarantee a correct topological representation of the medial surface.

[1] D. Levender, A. Bowyer, J. Davenport, A. Wallis, and J. Woodwark, “Voronoi Diagrams of Set-Theoretic Solid Models,” IEEE Computer Graphics and Applications, vol. 12, no. 5, pp. 69-77, 1992.
[2] C.S. Chiang, The Euclidean Distance Transform, doctoral dissertation, Purdue Univ., West Lafayette, Ind., 1992.
[3] C.M. Hoffmann,"How to Construct the Skeleton of CSG Objects," The Mathematics of Surfaces IV, Oxford Univ. Press, 1994.
[4] A. Sudhalkar,L. Gursoz, and F. Prinz,"Continuous Skeletons of Discrete Objects," Proc. ACM Solid Modelling Conf., pp. 85-94, May 1993.
[5] T.K.H. Tam and C.G. Armstrong,"2D Finite Element Mesh Generation by Medial Axis Subdivision," AES, vol. 13, pp. 313-324, Sept./Nov. 1991.
[6] X. Yu,J.A. Goldak, and L. Dong,"Constructing 3D Discrete Medial Axis," Proc. ACM Symp. Solid Modelling Foundations and CAD/CAM Applications, pp. 481-485, June 91.
[7] J.M. Reddy and G. Turkiyyah,"Computation of 3D Skeletons Using a Generalized Delaunay Triangulation Technique," Computer Aided Design, vol. 27, no. 9, pp. 677-694, 1995.
[8] E.C. Sherbrooke,N.M. Patrikalakis, and E. Brisson,"Computation of the Medial Axis Transform of 3D Polyhedra," Proc. ACM Symp. Solid Modeling and Applications, pp. 187-199, ACM Press, 1995.
[9] D. Dutta and C.M. Hoffmann,"On the Skeleton of Simple CSG Objects," ASME Trans. J. Mechanical Design, pp. 87-94, 1993.
[10] F.P. Preparata and M.I. Shamos, Computational Geometry. Springer-Verlag, 1985.
[11] N.S. Sapidis and R Perucchio,"Domain Delaunay Tetrahedralization of Arbitrarily Shaped Curved Polyhedra Defined in a Solid Modeling System," Proc. ACM Solid Modelling Conf., pp. 465-480, 1991.
[12] D.J. Sheehy,C.G. Armstrong, and D.J. Robinson,"Computing the Medial Surface of a Solid from a Domain Delaunay Triangulation," Proc. ACM Symp. Solid Modeling and Applications, pp. 201-212, ACM Press, 1995.
[13] G.H. Golub and C.F. Van Loan, Matrix Computations. Baltimore: John Hopkins Univ. Press, 1989.
[14] D.J. Sheehy,C.G. Armstrong, and D.J. Robinson,"Numerical Computation of Medial Surface Vertices," Proc. IMA Conf. Mathematics of Surfaces VI, Brunel Univ., U.K., Sept. 94.
[15] D.J. Sheehy,"Medial Surface Computation Using a Domain Delaunay Triangulation," PhD thesis, Dept. of Mechanical Manufacturing Engineering, Queen's Univ. of Belfast, 1994.
[16] M.A. Price,C.G. Armstrong, and M.A. Sabin,"Hexahedral Mesh Generation by Medial Surface Subdivision: Part 1. Solids with Convex Edges." IJNME, vol. 38, pp. 3,335-3,359, 1995.

Index Terms:
Voronoi diagram, medial axis, skeleton, collision detection, mesh generation, feature recognition, solid modeling.
Damian J. Sheehy, Cecil G. Armstrong, Desmond J. Robinson, "Shape Description By Medial Surface Construction," IEEE Transactions on Visualization and Computer Graphics, vol. 2, no. 1, pp. 62-72, March 1996, doi:10.1109/2945.489387
Usage of this product signifies your acceptance of the Terms of Use.