9

Bulges 1093
In Cases where No E nv elopes Use Partial
Blending (the Default)
Ve r t e x v is assigned to links l1, l2, and l3,andthe
weights for these links are: w1 =0.2,w2 =0.3,and
w3 =0.4.
In a non-partial blended c ase, the sum of these
vertex weights is w1 + w2 + w3 = 0.9 (less than 1.0).
Withpartialblendingoff,Physiquewillnormalize
the weights so they sum to 1.0. For example:
w1’ = w1 / w1+w2+w3 = 0.2/0.9 = .2222222...
w2’ = w2 / w1+w2+w3 = 0.3/0.9 = .3333333...
w3’ = w3 / w1+w2+w3 = 0.4/0.9 = .4444444...
so
w1’+w2’+w3’ = 1.0
In Cases wher e A ll E nvelopes Us e Pa r t ial
Blending
The weight fill-in for vert ices with a weight less
than 1 will always fill with the weight of the root.
Whenever a vertex is assi gned to a g roup of
links, all of w hich are partially blended, then the
remaining weight will b e assig ned and blended
w ith the root link.
This works well for a case where you want partial
deformationfallingofftonodeformation. An
example would be a static head, where you are
deforming t he head for facial expressions, but the
head itself remains in place.
For example: vertex v is assigned to links l1, l2,
and l3. The weights for these links are: w1 =0.2,
w2 =0.3,andw3 =0.4.
The sum of these vertex weights is w1 + w2 + w3
= 0.9 (less than 1.0). We need an additional fill-in
weight (wf). The fill-in weig ht is determined by
1.0 - (w1+w2+w3) = 0.1, or 10%. Physique fills in
with weight wf from the root (leaving the vertex
partially u ndeformed).
The resulting deformation w ill be w1*l1 + w2*l2
+w3*l3+wf*root.Therootportionofthis
deformationisessentiallyanundeformedportion
that simply follows t he root of the skeleton.
InCaseswhereSomeEnvelopesUse
Par tial B lending and S ome Do Not
The vertex weight fill-in in overlap areas will be
based on the percentage of partial and non partial
weights.Forexample,Ifthetotalweightofnon
partial links is 80% of the total summed partial
and n on partia l weig ht, then 80% of the fill-in
will be more of the non partial deformation. The
remaining 20% fill-in will come from the root.
Example: If Vertex v is assigned to links l1, l2, and
l3, the weig hts for these links a re: w1 =0.2,w2 =
0.3, and w3 =0.4.
Let’s assume l1 and l2 are nonpartia l, and l3 is
part ial. The nonpartial weight is w1 + w2 =0.5;the
partial weight is w3 =0.4;thenonpartialweightis
0.5/(0.5+0.4) = .555555, or 56%; and the fill-in
weight is still (1.0 - .9) or wf =0.1.
The program fills in with 56% of wf with more
of the nonpartial blended links. The remaining
44% of wf is filled in with the root as in the partial
blended case. This provides a smooth transition
between the part ial and nonpartial links.
Bulges
For some animations, simply attaching the skin
and correcting its vertex assignments results in an
animated skin you c an use in final renderings. For
other animations, you might need to give the skin
more realistic movement, for example, muscles
that bulge.
Physique lets you simulate an underlying
musculature for the skin by adding tendons (page
2–1096) and bulges: