Cocone Software for surface reconstruction and medial axis

Tamal K Dey , Joachim Giesen, Samrat Goswami, James Hudson, Wulue Zhao


You are visitor number 

since Sep 05, 2001

Cocone software can reconstruct a surface from its sample points. The input is the co-ordinates of the point cloud  in 3D and output is a piecewise linear approximation of the surface  which  is made of Delaunay triangles with vertices in the input points only. The software is based on the cocone algorithm that uses a single Voronoi/Delaunay computation as described in the following papers. The program works on the assumption that the sample is dense and is obtained from a smooth surface.  We have four versions of the software catering different needs.

In addition to the  surface, Tight Cocone below can compute an approximate  medial axis or MAT of the object.

Codes are  available for Irix-6.4, Linux-2.4.-i386, Solaris-5.6-sparc and Windows. Please send an email to to get the password to access the download area. (Mention the code name(s)  from the list below for which download is requested)

1. Tight Cocone: This produces a  Water Tight  model no matter how the input is (implemented by Samrat Goswami).  It also computes the medial axis (implemented by Wulue Zhao). paper. Image gallery.   Download area.
Medial axis experiment paper, Theory paper, Image gallery.

2. Cocone: This detects Boundaries  in the surface. Thus, this version is suitable for reconstructing surfaces that have boundaries. Notice that it will also detect regions of undersampling. (implemented by Joachim Giesen.)  paper.  Image gallery. Download area.

3. SuperCocone: This handles very  Large data sets. For example,  it can handle data sets in the range of million points. (3.5 million points on a 733Mhz, 512MB memory machine takes 3hrs and 18 minutes).  (implemented by James Hudson).  paper.Image gallery.   Download area. 

4. RobustCocone: This handles noisy data sets.  If the input points are noisy, this reconstructs a surface interpolating through a subset of the points (implemented by Samrat Goswami).  paper,  Download area.

5. SingularCocone : This is our latest addition (2013). This handles sharp feature curves and corners and reconstructs the surface using a method called WeightCocone (which acts on weighted Delaunay triangulation). See the paper and web-page for details. Download area.

RobustCocone does not smooth data. It interpolates the data.
For smoothing noisy point clouds use
AMLS software


T. K. Dey and L. Wang. Voronoi-based Feature Curves Extraction for Sampled Singular Surfaces. Computers & Graphics, special issue of Shape Modeling International (SMI 2013). (This is for SingularCocone)

T. K. Dey and S. Goswami. Provable surface reconstruction from noisy samples. Computational Geometry: Theory & Applications, to appear.  (This is for RobustCocone)

T. K. Dey and S. Goswami.  Tight Cocone: A water tight surface reconstructor.  Proc. 8th ACM Sympos. Solid Modeling Appl., 2003,  127--134. (This is for TightCocone)

 T. K. Dey and W. Zhao. Approximate medial axis as a Voronoi subcomplex. Proc. 7th ACM Sympos. Solid Modeling Appl., 2002, 356--366. (This is for Medial axis)

T.  K. Dey, J. Giesen and J. Hudson.  Delaunay based shape reconstruction from large data. Proc.  IEEE Symposium in Parallel and Large Data Visualization and Graphics (PVG2001), (2001), 19--27.  (This is for SuperCocone)

T.  K. Dey and J. Giesen. Detecting undersampling in surface reconstructionProc. 17th ACM Sympos. Comput. Geom. (2001),  257--263. (This is for Cocone)

N. Amenta, S. Choi, T. K. Dey and N. Leekha. A simple algorithm for homeomorphic surface reconstruction. Intl. J. Comput. Geom. Appl.,  Vol. 12 (2002), 125--141. (This is a fundamental paper about Cocone preceeding all the above papers)

Other papers

Other Software:  AMLS, NormFet, QualMesh, SegMatch, LocPSC, ReebHanTun


The software was written using the CGAL libraries. 
The output of the cocone software can be viewed with GEOMVIEW

Disclaimer: We do not intend to be responsible for the maintenance of the software.

Copyright: Jyamiti group at the Ohio State University. No commercial use of the softwares is permitted.