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Mesecina – computational geometry you can see

The Scale Axis Transform

A new skeletal structure has been designed with the support of Mesecina. You can find the formal definition and discussion about its behaviour including topological proofs in the paper on "The Scale Axis Transform" page.

The scale axis transform

Additionally you can check out a video about the scale axis -- results are generated with an extended (yet unreleased) version of Mesecina. All these results has been presented at Symposium on Computational Geometry 2009.

Web application

Mesecina inspired Yang Chenglin to implement a cool web gadget which is great to get to know computational geometry constructs. There is no download, you can simply try this JavaScript Google gadget here!


The manuscript containing the proofs for the structural results visualized in the SoCG 2007 video is available for download: Joachim Giesen, Balint Miklos, Mark Pauly: The Medial Axis of the Union of Inner Voronoi Balls in the Plane.


The Windows binaries of Mesecina are available for download. The download includes user manual and some sample datasets, as well. For more info see the download page. If you just want to see how Mesecina looks like in action click here.

SoCG Video

The Medial Axis Approximation from Inner Voronoi Balls: A Demo of the Mesecina Tool will appear in the Multimedia Session of the Symposium on Computational Geometry 2007. See the video and the extended abstract here.

Visit the Images page to see dozens of interesting, colorful figures created with Mesecina.

About Mesecina

This software allows you to visualize and study the medial axis and related computational geometry structures in the plane. It is ideal to visualize and show computational geometry structures for educational purposes, and it is a very useful tool supporting computational geometry research.

Mesecina is built on the top of CGAL and CORE, and uses Qt and OpenGL for user interface. Big thanks to these projects!

Mesecina has a powerful high quality rendering with transparency, hardware accellerated anti-aliazing. Color, line width, point size, opacity and display order of any object is configurable using simple sliders and color pickers. Mesecina's flexible user interface allows nice navigation functions including paning, smooth zoom in/out, exporting images in png or ps, pdf vector formats.

The input is a point sample of a shape boundary, which can be interactively edited while the computational geometry structures are updated on-the-fly. Mesecina can compute and visualize the following structures:

  • Delaunay triangulation of the samples
  • Vornoi diagram of the samples
  • Regular triangulation of the voronoi vertices
  • Regular triangulation of the polar vertices
  • Power crust
  • Voronoi vertices in the interior of the shape
  • Approximation of the shape using polar or all inner voronoi balls
  • Dual of union of balls approximating the shape
  • Exact medial axis of union of balls approximating the shape
  • Other sturctures related to the algorithms and structures mentioned above

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