Medial axis

The Medial Axis (MA) is the locus of the centre of the maximal sphere which shrinks and expands as it follows the object.

The Medial Axis Transform (MAT) is obtained by associating the MA with the readius function of the maximal sphere.

Local thickness of an object at a given point is the radius of the corresponding maximal sphere

There are many uses of the MA in CAGD, but the methods for its efficient construction are still subject of research.

The work to date has focussed on efficient and robust calculation of the object thickness and the construction of the MA for CAD models.

The main features of the approach are:

• Computation of the MA directly from the CAD model, without the need for Delaunay tetrahedrisation in the first step
• The CAD model may be defined as NURBS or as a triangular mesh
• The MA points are calculated incrementally, allowing refinement of the MA to arbitrary resolution
• 3D as well as 2D

The following illustration shows a CAD model of an extruded part with local thickness evaluated and coded in colour

Further examples below show the CAD model, the colour coded thicknes map and the Medial Axis (also colour coded according to thickness) for some complex engineering components.