An example of the result of this decomposition are given in Figure 6. Since the heart fiber model consists of several overlapping regions, a surface representation of just the points forming the bounding surface seemed possible. However, with the movement of the fiber points as a function of time it became problematic to be able to define a surface that approximated the exterior of the heart structure that could be generated from the collection of fiber points at any given timestep. If the parameter is zero the resultant shape is merely the collection of original points. If the parameter has the value of infinity, the resultant shape is the convex hull encompassing all of the points.
Some geometries have an optimum alpha-shape.
An example of such an optimum shape can be found in the collection of points that describe an annulus. For an alpha value of infinity the shape is a lozenge, for the optimum shape the surface described is the doughnut-shaped structure. Annulus and heart fibers alpha-shapes. Heart fiber structure surface. Surface and fluid pressure data.