Wow, interesting thread.
It almost turned into a Jerry Springer type brawl of repitition, but now it seems to have cooled down.
Ian. I see you thinking over there. Your games ideas are cool. I like the fighting one, but there's something you should realize.
Everyone of those games would be better with the NRC and nunchuck attachment. Every single one.
Let me demonstrate since I am the self elected game control specialist.
3-D shooter
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With the NRC you can posess any vehicle and command it through reflex.
I am guessing you are talking about a game more in tune with Rouge Squadron and not Starfox is terms of display. This would mean that the ship is fixed into the middle of the screen at all times.
The nunchuck attachment's analogue stick would control how fast your fighter flys. Holding forward is very vast, while back is a smooth slow glide.
For the next part, let's imagine the ship is flying around on earth.
Imagine holding the NRC like a remote, with the front pointed towards the tv. The NRC will control nose of the ship as well as the body. For example, if you point down then you will fall towards the ground. Now twisting the NRC will make the ship twist. So to get through a tight spot, you may twist the controller to orientate yourself vertically. No need for shoulder buttons, this solution is far more intuitive.
The "b" button would fire. To make tight turns you simply slow down, point and twist left.
That's all. Simple yet perfectly intuitive. Also, it would be fun just to throw the damn thing in the air to see what happens. As fun as that game sounds on the cube, the REV has it beat in everyway.
Weapon's fighting game
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I would enjoy playing a Zelda-esque fighter. Ever since playing OOT, I've had this "want" to play a more tactical, more strategic fighting game. This game could be incredibly engrossing with the NRC; much more realistic than anything before it.
The controls would be simple. The nunchuck attachment is for movement, shield, and crouching. The NRC is for your sword, other items, evasion, and magic.
You attack with the NRC. The sword will mimmick whatever you do in real life. If you want to block a high blow with your sword instead of your sheild you can (and you may have to). However, your sword can be given either complicated arm movements, or pre-configured wrist flicks. The difference is this: you can either make your own move, such as a stab or wide horizontal stroke; re-oreintate your sword; or, flick your wrist in the angle you would like the sword to slash. This is the defining mechanic of the game.
When you put up your sheild, by holding one of the trigger buttons on the nunchuck, the NRC will allow you complete control. This would be helpful in blocking certian sword strokes or batting a sword stroke away so you can counter. Also, crouching and shielding will allow you to withstand more powerful blows. This could turn out to be a very rewarding aspect of the game.
The d-pad will handle items and magic which is fully-customizable. I don't know what the B-trigger could be used for, maybe firing your item or magic attacks.
The "A" button would handle evasion very similar to Zelda. However, rolling would be done by crouching and moving the analogue stick left or right.
That's all.
Police Chase Game
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Basically what Kairon described. The view would go into over-the shoulder when holding one of the nun-chuck's triggers down. The camera would swivel from left to right as you aim your NRC. Pressing "B" fires.
When just plain driving (handled by the joystick, with "A" as gas, "B" as the handbrake), the NRC would allow you to look left and right by simply pointing left and right. This will give you a chance not only to see who is left and right of you, but to setup the camera before you enter "shooting mode".
The only problem I see is that you can't hit the handbrake and shoot at the sametime. That's not such a big problem since you can't do that in real life anyways.
And there it is........proof that each game would work alot better than it's traditional counterpart. That last sentence is the reason why we want the REV to suceed and why we have so much faith in the "reinventing of the wheel."