Final fix for [#31017] Particles not generated on Grid Distribution
* In some cases a quad would be intersected twice so particles near this double-intersection point were not generated in grid distribution due to being marked as outside the surface.

Fix for #32162 psys rotation causes size issues for particle instances
- The original scaling of the object wasn't taken into account when not using the particle dupliobject rotation option.

Fix for [#30445] Particle simulation, rekey crashes blender
- Entering particle mode crashed due to missing checks if a particle didn't have any baked keys.
- The rekey functionality is only supported for hair, so replaced the operator poll function with the correct one.
- Also replaced a couple of other "only hair" operator poll functions to the correct ones.

Some advanced particle rotation modes and reorganization of the rotation panel:
- More angular velocity modes to support creative effects.
- Renamed "Initial Rotation" to "Initial Orientation" to better reflect the functionality
- Renamed "Spin" angular velocity mode to "Velocity".
- Organized the rotation panel a bit better.
- Also some better names and tooltips for the different rotation values.

"Fix" for [#30098] Particle rotation wrong / explode modifier
- The main problem was that in order to be accurate all particle
rotations have to be calculated incrementally so the only working
solution is to store rotations to the point cache (previously
this was only done for dynamic rotations). This can nearly double
the point cache size so it's not ideal to have this as a default
as in many cases you don't care about particle rotations.
- Particle rotation panel now has a new "enable" checkbox that
enables rotation calculations and the storing of rotations to
point cache.
- Old files will have rotations enabled via do_versions so that in
the worst case old files will only get bigger point caches, but no
sudden loss of particle rotations.

Bug fix: Explode modifier created invalid faces if "unborn", "alive" or "dead" setting was unchecked
* Exploded faces that were meant to be hidden were still created with invalid vertices (0,0,0,0).
* In normal cases this went unnoticed, but for example edge split modifier crashed when it encountered these faces.

Fix [#29737] Can't edit particle hair if particle count is 0.
* Hair wasn't flagged as "done" if particle count was 0 before setting particles as hair, so particle edit mode didn't work.

Fix [#29530] Changing to particle mode could crash in some cases
* If a baked particle didn't have any cached keys creating an edit path for it crashed.

Fix [#29265] Particle Instance: Create Along Paths + Children inconsistent with actual children hair particles
* Hair particle rotations weren't calculated properly for particle locations along a path and the "particle on path" calculations were not correct in many other ways too.
* Now the particle's location along a path is interpolated directly from the cached paths if it exist. These paths are always correctly calculated.
* Paths are now cached if a particle instance modifier using the particle system with the path option exists.

Particle dupliobject rotation changes:
There has been quite a bit of fuss about particle dupliobject rotation in 2.59, so here are some changes to make things work a bit more consistently and predictably in 2.60.

Much of the confusion has been about what the "Initial rotation" for particles actually means. Simply put it's just a vector that that the particles (and the dupliobjects) are aligned to and around which they can be rotated with the phase controls. I've now renamed these controls under a label "Rotation axis".

In 2.59 and previous versions the dupliobject's global x-axis was aligned to the particle rotation axis for non-hair particles. This meant that the object's own rotation (in addition to the particle rotation) could effect the dupliobjects' rotations. This old behavior can still be used with the "Rotation" option in the particle render panel when object/group is set as the visualization. This option is also activated automatically for old files to maintain backwards compatibility.

Now the default dupliobject rotations ignore the object's own rotation completely and align the object's tracking axis to the particle rotation axis. The tracking axis can be found under the Object tab -> Animation Hacks panel.

In 2.58 the way of calculating the rotation for hair didn't work as intended and enabled many non-functional combinations of options. For this reason I removed most of the rotation options for hair in 2.59. Now the options have been reimplemented better and the dupliobject's tracking axis is aligned to the hair direction by default (Rotation axis = Velocity / Hair). All the other axis options work too along with the phase controls.