OOF2: The Manual
| Relax (Relax) | ||
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6.5.2. Subclasses |  |
Name
Relax (Relax) — Improve a skeleton by solving a finite element system where the properties are functions of the underlying homogeneity and shape
Synopsis
Relax(alpha,gamma,iterations)
Details
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Base class:
SkeletonModifier -
Parameters:
alpha- alpha controls the relative importance of element shape and homogeneity. alpha=0 emphasizes shape and ignores homogeneity. alpha=1 emphasizes homogeneity and ignores shape. Type: A real number in the range [0, 1].
gamma- Node mobility Type: A real number.
iterations- number of steps Type: Integer.
Description
Relax is a Skeleton modifier that
moves Nodes to improve Element homogeneity and shape. In spirit
it's like a deterministic version of Anneal.
Relax works by giving each Element an isotropic
elastic modulus and an elastic driving force with two components.
The first component is isotropic and proportional to the Element's
homogeneity
energy.[33]
This causes inhomogeneous elements to shrink. The
second part is anisotropic and proportional to the traceless part
of the Element's moment of inertia tensor. This drives the Elements
shapes toward squares and equilateral triangles. The relative
weight of the two terms is given by alpha.
One iteration of the Relax algorithm is
equivalent to taking one Euler time step of the equation
![\[
\frac{du}{dt} = \gamma\nabla\cdot\sigma
\]](equations/6.5.2-eq-37.gif)
where 
is the stress and
is the displacement of a
Node. After each step, the driving force is recomputed. The
parameter gamma plays the role of a Node
mobility. Using a large gamma will make the
Skeleton change faster but will risk moving Nodes too far and
overstepping their optimal positions.
Figure 6.95. Skeleton Relaxation
A Skeleton in a Microstructure with three types of pixels.
The Skeleton after applying Relax with
alpha=0.3, gamma=0.3,
and iterations=5.
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| Relative (RelativeOutputSchedule) |  |
Remove Bad Triangles (RemoveBadTriangle) |