Split and extend unit tests for vec_roll_to_mat3_normalized.

Separate the huge test into huge logical parts and add more cases
to check. Also add a utility to check that the matrix is orthogonal,
with arbitrary epsilon values and calculations in double.

A couple of tests deliberately fail, to be fixed in following commits.

Ref D9551

Fix precision issues and a bug in vec_roll_to_mat3_normalized.

When the input vector gets close to -Y, y and theta becomes totally
unreliable. It is thus necessary to compute the result in a different
way based on x and z. The code already had a special case, but:

- The threshold for using the special case was way too low.
- The special case was not precise enough to extend the threshold.
- The special case math had a sign error, resulting in a jump.

This adds tests for the computation precision and fixes the issues
by adjusting the threshold, and replacing the special case with one
based on a quadratic Taylor expansion of sqrt instead of linear.

Replacing the special case fixes the bug and results in a compatibility
break, requiring versioning for the roll of affected bones.

Differential Revision: https://developer.blender.org/D9551

Fix precision issues and a bug in vec_roll_to_mat3_normalized.

When the input vector gets close to -Y, y and theta becomes totally
unreliable. It is thus necessary to compute the result in a different
way based on x and z. The code already had a special case, but:

- The threshold for using the special case was way too low.
- The special case was not precise enough to extend the threshold.
- The special case math had a sign error, resulting in a jump.

This adds tests for the computation precision and fixes the issues
by adjusting the threshold, and replacing the special case with one
based on a quadratic Taylor expansion of sqrt instead of linear.

Replacing the special case fixes the bug and results in a compatibility
break, requiring versioning for the roll of affected bones.

Differential Revision: https://developer.blender.org/D9551

Split and extend unit tests for vec_roll_to_mat3_normalized.

Separate the huge test into huge logical parts and add more cases
to check. Also add a utility to check that the matrix is orthogonal,
with arbitrary epsilon values and calculations in double.

A couple of tests deliberately fail, to be fixed in following commits.

Ref D9551

Python API: implement `PoseBone.children` via `Bone.children`.

Currently `PoseBone.children` is implemented by a linear scan of
the list of armature bones. This is doubly inefficient, since
not only is it scanning all bones, the `obj.data.bones` list
is actually synthetic and generated from Bone children lists.

Instead, use the `Bone.children` native RNA property.

Differential Revision: https://developer.blender.org/D12727

Animation: support filtering for curves that don't match the action cycle.

Since the looping behavior is defined per curve rather than at
action level, it is possible for curve loop periods to get out of
sync with each other. This commit adds an option to compare curves
against the frame range specified in the action, and treat any
mismatches as errors for the purpose of F-Curve filtering.

When enabled, the check verifies that curves within the action
have valid cyclic extrapolation, the action period evenly
divides by the curve period (since a curve looping at e.g. half
of the action period length still repeats in sync with the action),
and the end values match if the cycle is supposed to be perfect.

Differential Revision: https://developer.blender.org/D11803

Force Fields: implement new true power and custom falloff options.

The 'power' falloff option in Blender force fields does not actually
generate a true power falloff function, as pointed out in D2389.
However, that patch adds a special 'gravity' falloff option to Force
fields, without addressing the shortcoming in the common options.

The reason for not using the true curve in the options, as far as
one can tell, is that the power curve goes up to infinity as the
distance is reduced to 0, while the falloff options are designed
so that the maximum value of the curve is 1.

However, in reality forces with a power falloff don't actually go
to infinity, because real objects have a nonzero size, and the force
reaches its maximum at the surface of the object. This can be used
to integrate an option to use a true power falloff with the design
of falloff settings, if it requires a nonzero 'minimum' distance
to be set, and uses a curve that reaches 1 at that distance.

Since this is adding a new feature to the minimum distance value,
it is also a good opportunity to add a feature to the maximum
distance. Specifically, the new options can be used to apply
arbitrary brush-style falloff curves between min and max,
including a fully custom curve option. When used together with
power falloff, the two curves are multiplied together.

While the true power option allows creating more physically
correct forces, the custom curves aid artistic effects.

Differential Revision: https://developer.blender.org/D8075

Depsgraph: connect up drivers on various physics properties.

It seems drivers for physics properties weren't being linked to
evaluation nodes. This connects settings used by modifiers
to Geometry; particle settings and rigid body data to Transform
which seems to contain rigid body evaluation; and force fields
to object Transform, since fields can exist on empties.

Differential Revision: https://developer.blender.org/D10088

Constraints: refactor the D7437 patch adding Custom Space for constraints.

As mentioned in the comments to that patch, I had an idea for
a different way to do some technical aspects, but it was too
complicated to force changes in the original patch. Thus I submit
this follow up patch.

First, instead of modifying all the get_constraint_targets and
flush_constraint_targets callbacks, introduce wrapper functions
for accessing constraint targets, convert all code to use them,
and handle the new reference there uniformly for all constraints.

This incidentally revealed a place in the Collada exporter that
didn't clean up after retrieving the targets.

Also, tag the special target with a flag so other code can
handle it appropriately where necessary. This for instance
allows dependency graph to know that the Use B-Bone Shape
option doesn't affect this specific target.

Finally, rename and simplify the function for initializing the
custom space, and make sure it is called everywhere necessary.

Differential Revision: https://developer.blender.org/D9732

Armature: apply Y scale to B-Bone segments.

This fixes a strange behavior where the segments were not actually
scaled in the Y direction to match their actual length, thus
producing gaps or overlap depending on the shape of the curve. For
transformation the change should be very small if enough segments
are used, but this will affect the results of the Copy Transforms
and Armature constraints, so a backwards compatibility option is
provided. Newly created bones default to the new behavior.