Performance Boost

I recently learned about the foreach_get and foreach_set functions that makes access to Blender arrays much faster. The latest versions of the Daz Importer (5.1.0) use these functions to loop over vertices, shapekeys, polygons etc. This had led to a quite nice performance boost.

A a test case I import a Genesis 9 Female character with eyebrows card style 06 and dForce Pixie cut hair. All global settings were set to the factory values (except the DAZ root paths), and the Genesis 9 preset was used for Easy import. I imported the character twice and hit ctrl-Z inbetween. Here are the results.

Blender 4.4:
addon 5.1:    39.398 seconds    37.200 seconds
addon 5.0:    75.642 seconds    75.424 seconds
addon 4.4:    70.669 seconds    70.991 seconds

Blender 5.0:
addon 5.1:    34.721 seconds    35.120 seconds
addon 5.0:    85.280 seconds    77.256 seconds

Blender 5.1 beta:
addon 5.1:    60.276 seconds    60.069 seconds

Notes:

1. The addon is backward but not forward compatible. Newer versions of the addon can be used in old blender versions, but not vice versa.

2. Version 5.1 (development version) of the addon is significantly faster than version 5.0.

3. Blender 5.1 beta is slower than previous Blender versions. This probably only reflects that a beta is not as optimized as a proper release.

The old method of loading shapekeys used to loop over the nonzero shapekeys in Blender, whereas the new method uses foreach_set to copy a numpy array in one sweep. However, for small morphs like the FACS, i.e. morphs that a localized to a small part of the full mesh, the old method may actually be faster. A python loop is much slower than the builtin method, but it only needs to access the nonzero shapekeys. For example, for the first Genesis 9 FACS morph, facs_bs_BrowDownLeft:
Mesh size:       25182
Morph size:     661
In that case the slow python loop is actually faster than using numpy.

For this reason, there is a new global setting, "Numpy Morph Fraction". The old method is used if the shapekey size (i.e. the number of nonzero deltas) is smaller than this fraction, otherwise the new method is used.

Active Morphs Panel

In the previous post I described how the Head and FACS morphs can be organized in subpanels; this is now the default behaviour. Another change is that the currently active morphs are collected in a separate panel, in the same way as in DAZ Studio. 

Here we have several active morphs, both head morphs (brows, mouth, tongue, visemes), an expression, and even some custom morphs like elf ears. All active morphs are present in a single place. 

The data structures needed to display the active morphs are built when the morphs are imported. If you have an old character, or if the active morphs have been corrupted for some reason, you can rebuild this data structure with the "Update Active Morphs" button at the top of the Morphs panel.

The existence of the "Active Morphs" panel is also governed by the global setting "Face Morphs Subpanels". If that option is disabled, the "Update Active Morphs" button is replaced by the old "Show Used Morphs Only" checkbox. The Morphs panel now looks like it did before, where the active morphs are spread out over the various panels.

One thing that I found annoying with the legacy behaviour was that a morphs disappeared when you drag the slider to zero, and "Show Active Morphs Only" had to be disabled to turn the morph back on. With the new setup a zero morph disappears from the "Active Morphs" panel, but the slider is still available in its native location.

Face Morph Subpanels

Standard morphs are grouped into various panels, but all morphs in a group are simply listed in alphabetical order. Mickey Ho pointed out that this is not practical for animating sliders, in particular for the hundreds of Genesis 9 FACS morphs. In DAZ Studio the various FACS morphs are grouped into subpanels, which makes access more convenient.

In the last commit the FACS panel has the same subpanels in Blender. To enable this feature, enable the global setting "Face Morph Subpanels".

The FACS panel now has the same subpanels as in DAZ Studio. The morphs are assigned to subpanels which makes them better organized.

The button on the top of a subpanel only apply to the morphs in this panel. The buttons at the top of the FACS panel affect the sliders in all subpanels.

Subpanels are also generated for the head pose morphs for previous generations, Genesis - Genesis 8. Before we had two types of face morphs, Face units and Visemes. That was a completely ad hoc separation that I did long ago, and may have made sense for the first Genesis generations. In the last commit those types are replaced by a single Head type. 

There used to be another type of standard morphs called Head which were taken from another directory. That included morphs like elf ears which are normally baked into the character, so those are not considered to be standard morphs anymore. If you need such morphs you can always import them as custom morphs.

Import standard morphs with the Head option enabled.

The panel with Head morphs is now split into subpanels, which work like the FACS subpanels.

If we import morphs with "Face Morphs Subpanels" disabled, or if we load an old character into the  scene, the old style morphs appear and work as before. The new option does not change how the morphs themselves work, but only how they are displayed in the user interface.

Diffeomorphic Add-ons Version 5.0.0 Released

Version 5.0.0 of the DAZ Importer, MHX Runtime System and BVH and FBX Retargeter have been released. They can be downloaded from

DAZ Importer: 
https://www.dropbox.com/scl/fi/8b5z3cy6kd9pcxeo17bh1/import_daz-5.0.0.zip?rlkey=udvj5mbw4f1psmvrnt8949ed5

MHX Runtime System: 
https://www.dropbox.com/scl/fi/0nf018loxjpy0nbe26zpr/mhx_rts-5.0.0.zip?rlkey=dd33350oazwagkund3puqt7up

BVH and FBX Retargeter: 
https://www.dropbox.com/scl/fi/0ftrenp005ub78ov5fek0/retarget_bvh-5.0.0.zip?rlkey=c27jhf4pxc3scpu0ffmil197d

The add-ons have been tested on Blender 3.6, 4.5 and 5.0. They should run on Blender versions from 3.0 onwards.

The main reason for this release is compatibility with Blender 5.0. Several other bugs have also been fixed.

Conclusion

The time has come to wrap up this series of posts. I went to grad school in the early 1980s, and specialized in phase transitions and critical phenomena, often working on 2D models. A few years later conformal field theory (CFT) came along, and essentially finished my field of research. I was too young and isolated to notice at the time, but when I did notice a few years later I felt that I had missed the bandwagon. CFT explains everything worth knowing about 2D critical phenomena, but it says nothing about the much harder and physically more relevant case of critical phenomena in 3D. So I started to think that something similar might work in higher dimensions as well. It can not be conformal symmetry, because the conformal group is infinite-dimensional only in 2D. But the same group also described diffeomorphisms in 1D, and that has a natural generalization to higher dimensions.

This made me decide that a multi-dimensional Virasoro algebra had to exist and I went out to find it. That it really does exist and has natural realizations on p-jets was very satisfying, but completing this task took a long time and I ran out of funding in the process. Moreover, it is only a limited success, because important pieces of the puzzle are still missing.

• There are operators acting on a vector space, but I haven't found a nice way to identify this space with its dual. So there is no known inner product and we can not discuss unitarity.
• The vector space is too big because momenta and velocities are not identified, which they should be.
• This is a purely kinematical theory, like tensor calculus. To use it in physics we should introduce dynamics in some form, with a Lagrangian, a Hamiltonian, or equations of motion. Doing this for p-jets is surprisingly difficult, or at least it was for me.

Because of these shortcomings I haven't been able to apply this theory to physics. Nevertheless, the math exists which made the effort worthwhile in itself, and I hope that somebody will make progress on the above problems one day.

But even if much remains to be done, some physics insights can still be extracted. The Virasoro extension depends on the observer's trajectory, and therefore we need a theory with an explicit physical observer. Since the observer's position is an operator, we must measure it to know its value, and that measurements is subject to quantum fluctuations. This is really enough to rule out every approach to quantum gravity which does not take horizontal fuzziness into account, because the lack of horizontal fuzziness amounts to a hidden assumption about an infinite mass.

<Previous    <<First

Four Dimensions?

Recall how we constructed representations of the multi-dimensional Virasoro algebra last week.

• Start from a classical representation acting on a tensor field, which corresponds to a representation of the general linear algebra \(gl(d)\).
• Make a Taylor expansion around the observer's location and truncate at order \(p\), i.e. pass to \(p\)-jet space.
• Consider trajectories in \(p\)-jet space.
• Introduce a vacuum state that is annihilated by all negative frequency modes, and normal order.

The "abelian charges", i.e. the coefficients in front of the extensions, depend both on the choice of \(gl(d)\) representation and on the trunctation order \(p\). They are polynomials in \(p\) of order \(d\), which means that they diverge in the limit \(p \to \infty\). This is not surprising. We passed to \(p\)-jets because the extension becomes infinite if we start from fields. By taking the limit \(p \to \infty\) we come back to the field we started from, insofar as an infinite Taylor series can be identified with the field itself, and the extension becomes infinite again.

Even if expected, having an infinite extension is undesirable and should be avoided. How to do that? We started from a bosonic field, but if we start from a fermionic field instead, we get the same extension but negative. So one way to avoid infinities is to have a perfect symmetry between bosons and fermions. However, such a symmetry is not seen in nature, and we saw yesterday that we lose locality if the total extension vanishes.

There is another way to cancel the leading terms, only leaving abelian changes that are independent of \(p\). Add more jets of order \(p-1\), \(p-2\) etc, both bosonic and fermionic. With a clever choice of field content, we can cancel all terms that depend on \(p\). For this to work in \(d\) dimensions, we need jets down to order \(p-d\). A similar hierarchy appears in gauge theory, where the lower-order jets would come from equations of motion and gauge conditions (continuity equations). Since those add derivatives, their jet order must be smaller, so the total number of derivatives does not exceed \(p\). So we start from

• Bosons, fermions, and gauge fields at order \(p\).
• Fermionic equations of motion at order \(p-1\).
• Bosonic equations of motion at order \(p-2\).
• Gauge conditions at order \(p-3\).

Then we can arrange the field content so that the divergent terms cancel if \(d=3\). We can further identify the time parameter \(t\) with one of the coordinates, and we naturally are led to the conclusion that the dimension of spacetime must be \(d+1 = 4\).

Unfortunately, a more detailed version of this argument seems to suggest things that disagree with observation, so the results are inconclusive. Nevertheless, I find it promising that the multi-dimensional Virasoro algebra seems to predict not only the number of spacetime dimensions, but actually the observed number of dimensions.

<Previous    Next>

Locality in Quantum Gravity

Today I argue that quantum gravity must be a local theory. However, a well-known theorem asserts that there are no local observables in quantum gravity. How can these statements be reconciled?

The thing to notice is that theorems have axioms. If one of the axioms is violated, the theorem does not apply. The relevant axiom in this case is the assumption that classical and quantum gravity have the same sets of gauge symmetries. If the group of spacetime diffeomorphisms acquires an extension upon quantization, that assumption fails. The multi-dimensional Virasoro algebra is that extension on the Lie algebra level.

Hence a theory of quantum gravity with local observables can not be a QFT. It must be a theory with horizontal fuzziness, i.e. QJT.

The same argument applies to theories with infinite conformal symmetry, because the infinite conformal group is isomorphic to the diffeomorphism group in one complex dimension. Hence there can be no local observables in a theory with infinite conformal symmetry. But this is not a problem in conformal field theory, because the relevant symmetry is not infinite conformal symmetry but rather the Virasoro symmetry with a nonzero central charge. 

If there are local observables, the symmetry group acts in a non-trivial way on them. A necessary condition for locality is thus that the symmetry group has nontrivial unitary representations. Indeed, the centerless Virasoro algebra does not have any of those, and hence there can't be any local observables if the central charge vanishes. If the central charge is nonzero there are many nontrivial representations, and hence local observables are possible. The same thing happens with gravity. If the spacetime diffeomorphism group does not have an extension, it remains a gauge symmetry and there are no local observables. When it has extensions described by the multi-dimensional Virasoro algebra, it becomes an ordinary symmetry and local observables are no longer ruled out.

Another way to see the need for locality is that correlation functions diverge in the same way when points coalesce, whether gravity is present or not. Correlation functions in flat space (ignoring gravity) typically diverge when spacetime points \(x\) and \(y\) approach each other in the following manner:
\[
<\phi(x) \phi(y)> \ \cong\ |x-y|^{-2\Delta}.
\]
The distance between the two points depends on the metric \(g_{\mu\nu}\):
\[
|x-y|^2 = g_{\mu\nu} (x^\mu - y^\mu) (x^\nu - y^\nu)
\]
In flat space the metric is the constant Minkowski metric. In the presence of gravity the physical metric is the gravitational field, and it is unclear what the distance would mean. However, we don't have to use the physical metric to define this distance; any metric would do. Of course the distance and hence the correlation function depends on the choice of unphysical metric, but the leading singularity does not. This is because the scaling dimension is the eigenvalue of the dilatation operator
\[
D = x^\mu {\partial \over \partial x^\mu}
\]
This is the contraction of an upper and lower index and hence independent of the metric. The scaling dimension only depends on the smooth structure. Since the correlation functions diverge in flat space, they must diverge in the presence of gravity as well.

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