Finite Element Method (FEM) for Surface Creation
FEM is an approach generally
used for simulating very complex physical entities by approximating them
with much a smaller and more primitive finite number of "elements."
The behavior of these individual elements and their interactions with
one another is better understood and more feasible for computer-based
implementations. If enough of these simpler elements are used, the results
in most cases will closely approximate their more complex physical counterparts.
FEM for surface creation is based on energy
minimization where "energy" is defined as follows:
energy = A*(stretching energy)
+ B*(bending energy) + C*(spring
energy)
where:
A
= stretching resistance
B = bending resistance
C = spring constant
The value "A" is assigned automatically by VX. The values "B" and "C" are user defined using slider bars located under FEM Settings in the Optional Inputs section of the Options Forms for the supported commands. An example is shown to the right. Refer to the References section below for the complete list of commands.
As illustrated in the figure below, Spring Constant (SC) simulates the force that is exerted upon the surface by a sample point. With a minimum SC value of 1.0 (moving the slider to the left), the surface will not deform sufficiently as shown.
As the SC value increases (moving the slider to the right), the stronger the control points pull at the surface. This translates into a tighter fitting surface and thus better accuracy. However, if increased excessively, the surface can become "bumpy." This is because errant control points (if they exist) will pull on the surface just as hard.
The default value of 5.0 is chosen for optimal deformation and fit as shown. As you can see, as the SC value grows beyond this point, the effect is hard to distinguish. This means there is enough force already such that the surface is sufficiently deformed. So the primary use for this range of SC values is to compensate for high Bending Resistance (BR) values. In most cases the SC value will not need to be changed significantly.
As illustrated in the figure below, the lower Bending resistance (BR) value (moving the slider to the left), the "softer" the surface material it simulates. With BR = 1.0, the surface will "drape" over any sample points, just like a piece of soft cloth.
The default value of 4.3 is set such that there is no apparent drape in the surface and that it will also fit within tolerance. This is close to how a typical piece of flexible thin metal would behave if force is exerted upon it.
As the BR value further increases (moving the slider to the right), the surface becomes harder and harder to deform and is likely to ignore errand control points. This simulates relatively thick, inflexible surfaces. Eventually, when the BR value grows and the force exerted upon the surface is not large enough, there won't be any deformation at all. This is shown when BR is set to the maximum value of 10.0.
FEM-based
surface fitting requires that all data points can be projected to a common
base plane without any point being in the projection trajectory of another.
This makes point clouds with sharp angles more difficult to fit surfaces
through.
In some cases, even if the points can be projected, the surface may
contain "noise bumps," typically in the from of a series of
rapid undulations. This
can be controlled by adjusting the bending resistance and spring constant
values. By changing the surface's "stiffness" using these two
variables, bumpy surfaces can be smoothed with only moderately sacrificing
the overall fitting precision.
The maximum number of control points (not point cloud points) for a resulting FEM-based surface is approximately 100,000 (9 minimum). This number allows more complex surfaces to be fitted without overly sacrificing system performance.
