
382 Chapter 7 Level of Detail
is really an edge contraction. Positive thresholds allow nonconnected vertices to be
paired.
The algorithm also requires taking the set of valid pairs and associating with each
pair a metric that is used to prior itize the pairs. The smaller the metric, the more
likely the pair should be contracted. This is accomplished by associating with each
vertex V = (X,1), treated as a homogeneous vector, a symmetric 4 ×4 matrix Q(V),
and choosing the metric to be the quadratic form
E(X) = V
T
QV =
.
X
T
1
/
A
B
B
T
c
X
1
= X
T
AX + 2B
T
X + c
where A isa3× 3 symmetric matr ix, B is a 3 × 1 vector, and c is a scalar. Note
that E(X) = d for a constant ...