Biomedical Engineering Reference
In-Depth Information
intuitively. Transformations such as translation, scaling and rotation can be applied on
the curve by applying the respective transform on the control points. Bezier splines
are sets of low-order Bezier curves patched together to represent more complex
shapes. Another type of spline is Basis spline (B-spline) which is a generalization of
Bezier curves. They depend on the k-nearest control points at any point on the curve.
Combining B-splines allows creating B-spline surfaces. Another generalization of
Bezier splines is non-uniform rational basis spline (NURBS). The primary difference
of this type is the weighting of the control points which makes them rational.
Anothermethod tomodel deformation of bodies is using
implicit surfaces
. Implicit
surfaces are introduced as an extra layer coating any kind of structure that moves and
deforms over time. They can provide an efficient collision detection mechanism by
offering a compact definition of a smooth surface around an object [
67
]. An implicit
surface [
18
] generated by a set of skeletons
s
i
(
i
=
1
,
2
,...,
n
)
, with associated field
functions
f
i
, is defined at the isovalue
c
by:
P
c
3
ⓦₒ
|
f
(
P
)
=
where
n
(
)
=
f
i
(
)
f
P
P
i
=
1
The field function is generally a decreasing function of the distance from a given
point
P
to the associated skeleton. Based on the type of field function, various implicit
surfaces have been developed such as blobs, metaballs, soft objects, and convolution
surfaces [
18
].
Free Form Deformation
Free Form Deformation (FFD) consists in deforming the space embedding objects.
FFDs provide simple and fast control, but they do not permit direct manipulation.
Also, the regular lattice spacing used by FFDs prevents the detailed control needed to
produce more complex shapes [
18
]. As one of the early works, Chadwick et al. [
68
]
employed FFDs to represent muscle deformation. Articulated skeletons, located in-
side muscles, transform a surrounding lattice and cause changes in the shape of the
muscles. As another example, Moccozet and Thalmann [
69
] presented a generalized
method for FFDs that combines the traditional model with techniques of scattered
data interpolation based on Delaunay and Drichlet-Voronoi diagrams. They applied
the method to model deformations around a human hand model.
6.3.2.2 Physically Based Methods
While non-physical based methods are useful methods in many applications, phys-
ically based methods are a better choice for biomechanical human modeling with
