OverviewFirst off, if you can avoid curving your weapon, do so. The process is annoying, can lead to some injury, and at best slightly degrades the durability of your weapon. Also, if you're as much of a perfectionist as I am, you'll never quite be happy with the curve. I'll give instructions for bending a katana, but this can be adapted to any weapon type.
I'll preface this all with a few important words of advice that you should keep in mind throughout the construction of your curvy weapon. Trust me, I don't know anyone who's made as many katanas I have for Mystic Realms® or any other LARP. I'm not proud of that, but I am proud of the fact that none of my Mongorian NPCs come armed with European-looking swords.
Heat It SlowlyFirst off, the more you heat the weapon, the quicker it bends. Since you're not a machine, this will cause you to make mistakes faster, and much more dramatically. Furthermore, extreme heat will melt and warp the pipe, both weakening it and giving it an odd shape. (I've made a couple weapons almost a half an inch thinner in parts during my early days of katana construction.) Suffice it to say, don't heat it up too much.
If your PVC begins charring on the bottom, your best bet is to scrap it and start over again. Charred pipe tends to break easier. Light browning is acceptable. If any smoke comes off of the weapon, don't inhale it.
Bend It OnceKeep a picture of the kind of weapon you're making handy so that you can get the curve as close to correct as possible, but don't be obsessed with getting it just right the first time. As long as you don't over-bend, minor flaws can be corrected. A slight "list" either left or right is common. Sometimes you can correct this; sometimes you'll end up with a mess trying to correct it.
If you're marginally satisfied with what you've done, remember these words of wisdom: Don't fix it if it ain't broke. This would have saved me many hours and lots of precious, precious weapon-constructing supply.
Things You'll NeedPVC pipe about 6" less than the finished weapon length. (When you heat weapons and curve them, they have a tendency to stretch.) Also, you will need a marker, a straight edge, oven mitts, and a stove (preferably gas).
Mark the Inside of the CurveUse some kind of straight edge to draw a line along the length of the PVC. This is the line along which you will curve the weapon. For a katana, it is the back of the weapon where there is no cutting edge.
Mark the Pommel, Grip, and Blade
For a katana (technically, a Mystic Realms® 50" Sword IV: long sword), mark the PVC 2" and 13" from the hilt end to allow for an 11" grip. Make sure to clearly mark the 13" point.
Heat the StoveStart heating your stove up (I turn it up about half way). Pretend you're making an omelet. Imagine the omelet, and how much happier you'd be if you were making an omelet to eat. Now, remember that you're making a foam weapon for a LARP. Hit yourself with a frying pan.
Grip the Hilt of the WeaponPut your oven mitts on. I know you have oven mitts, you sissy.
You're going to grasp the PVC in your dominant hand, hilt toward you, so that the top of your hand reaches the 13" point (or wherever the top of the grip will be). You're not going to move this hand, ever, or you will mess up.
Align the line that goes the length of the PVC so that you can comfortably hold it straight up. Take a lot of time orienting it right, or you'll get a curve that is off by a few degrees. This error will drive you slowly insane at events, turning every glance your way into an attack on your weapon-construction skill. Don't make this mistake, or we might find you having hung yourself with duct tape and wearing socks on your hands.
Heat the PipeGrip the other end of the pipe at the tip, and hold it over the stove. Hopefully you're wearing billowy sleeves and have caught on fire. If you haven't, continue reading. You're going to sit here for a few minutes, thinking good and hard again about what you're doing. The reason you're holding it with two hands, in case you're wondering, is because the weapon will begin to droop on its own, and then counter-bending later will make your weapon less sassy (and more prone to breakage). Anyway, I took chemistry so I can say that I'm pretty sure the PVC will get warm all over.
Bend the PipeWhen you feel the PVC getting warm through the mitts, you can start bending.
Now, in your dominant hand you're holding the PVC so that your hand ends at the 13" point. With your off hand, grasp the PVC two-thirds up the blade (if we're dealing with a 44" piece of PVC, this will be approximately 33" from the pommel end). Bend upward, keeping the line straight. Don't pull too hard.
If it kinks at a point, congratulations, you've screwed up. You won't need the first derivative test to figure out that your PVC is now discontinuous. Throw out this PVC, or just give up altogether.
Check the CurveIf it doesn't bend at a point, and you get a more gradual curve, you're on the way to winning life. Step away from the stove and quickly hold the weapon out at arm's length. Compare it to something with some kind of pattern, like floor tiles, to see if there are any problems. Having a friend handy to look at it is also helpful.
Cool the PipeIf you like the curve you see, you're pretty much screwed, because when it cools it won't stay exactly the same. Run to the sink and, holding it to maintain the curve you like, run cool water over the length. Then run water through the length of the PVC. Set it down, turn off the stove, and run away. There's nothing more you can do for now.
Come back after, at the very least, 15 minutes. Pick the PVC up, see if you think it looks right. If it could use more bending, go ahead. If it could use less bending, decide whether or not it really needs less bending, because if you try to un-bend it you will most likely screw it up.