Quick question: when you bring the centre of balance closer to a sword's guard, does it make the sword more suited to cutting or thrusting?

In addition to what Nathan said...

The answer is complex because of two things :
1) It's difficult to find criteria to judge wether a sword is suited for thrusting or cutting
2) The point of balance does not tell the whole story (not even from the pure dynamics point of view, i.e. when you consider your weapon as perfectly rigid). You have to take the inertia of the sword into account.

Assuming the inertia does not vary, having a point of balance far from the hand puts more mass in the blade, making it more difficult to rotate from the wrist. However, it allows an easier acceleration of the sword in rotation, thus maybe favouring powerful cuts. Since the blade is more massive it might be more difficult to parry as well.

When thrusting, what you need is mainly tip control. This can be enhanced by moving the center of balance closer to the hand. But moving it too close can also result in really awkward weapons. It's my opinion that the tip control is best when the pivot point associated to your index is close to the tip, and that the tip control does not depend much on where your point of balance is located. At least it's something I verified on modern fencing weapons (epees and foils), which are used in conditions that favour tip control...

The answer also depends on what you mean by "bringing closer" the center of balance. It could be by moving the hand, in this case not modifying the inertia, or by adding (or removing) mass somewhere, which can heavily modify it. In the second case the answer would be yet more complicated, depending on how and where you add the mass.

Quick question, long answer, as usual :)

Hi

The BP on a sword is easy to measure and gives a quick reference point in comparison to other swords. The placement of the BP in IMHO is less important that other factors in the blade and hilt. The points made above are all good and I would expand on one of Vincent's to comment that the BP to close to the hand makes tip control more difficult. This is due to the fact that a bit of resistance is needed to give a blade some "feel", i.e. so there is enough presence in that hand to note were the blade is and allow the user to get the tip to track with the moment of his hand in a way that they can expect and instinctively get to incorporate into their muscle memory. This is why certain swords will fell "right" to different people. This can be seen in even the lightest blades like Smallswords.

Best
Craig