Graphics Reference
In-Depth Information
the computation. The key feature of the model reduction described in the “de-
formable scenes” paper is that the same approach is applied for both deformation
and appearance.
10.3.1 Basics of Deformation Simulation
Deformation is normally computed using the finite element method (see Chap-
ter 2). A mesh of points is constructed that represents the shape of the deformable
object, along with adjacency information and constraints that represent the in-
terdependence of the points in deformation. There may be other other physical
constraints to prevent such things as self intersection. The points along with the
interdependencies and the constraints are known as a
deformation model
.Ifthere
are several objects, they collectively form a
deformable system
.The
state
of the
object or system of objects at time
t
is represented by the position and velocity
of the model points in the object or system. All the positions and velocities (each
of which is a 3D vector) are collected into a single large vector
x
t
, known as the
system state vector
.
The cloth hanging on the door shown in Figure 10.21 is a representative ex-
ample of a deformable dynamic system. The cloth is a deformable object, in the
sense that outside forces change its shape. The door is rigid, but its movement af-
fects the shape and position of the cloth through direct contact also by imparting
other forces, such as air resistance. A regular grid of points on the cloth represents
its shape; the state vector of the cloth contains the positions and velocities of all
these points combined into a single large vector. Each position and velocity vector
has three components, so if there are
N
points, the state vector has 6
N
elements.
Figure 10.21
Cloth on a moving door. (From [James and Fatahalian 03] c
2003 ACM, Inc. Included
here by permission.)
