OK, so I'm messing around with the size of the entire Nova universe by going through ConText->spreadsheet->ResStore conversion cycles to see how different modifications "feel". First I squeezed everything down to half-size by dividing all of the s˙st X and Y positions by 2. Cute, but all of the system names start running into each other - bleah. Then I tried expanding everything by 2X from the original. Hey now ... that isn't bad at all. If I use the Nova map scaling buttons on my 1024x768 screen to bring the universe down to the point where the names are not shown, it's a very workable display. I mean I've been playing around with this game long enough to know virtually all of the names by heart, so I wanted to get them out of the way with out having a super-tiny squigy little map to deal with. Expanding the universe to 2X did that nicely. Of course I had to then resize and relocate the nëbulas as well, but that was no biggy.

So then I decided to really mess with the s˙st locations by transposing everything in a mirror image. Like, the Aurorans are now all in the north and the Polaris are in the west. Makes for a slightly different mind-set while playing. I kept going the wrong way to get somewhere. This is where the conundrum occurred to me.

Conundrum:
You look in a mirror and everything in the reflected visual image is transposed left-to-right and right-to-left. Just hold a printed page up to a mirror and it's obvious.
So why isn't the reflected visual image also transposed top-to-bottom and bottom-to-top?

Now I'm no more stupid than average, but I couldn't think of an explanation for this apparent anomaly in the way a mirror works.
Anybody got a handle on this?

( I just know I'm gonna feel like a fool when somebody writes ... " Oh, it's simple. It's because _____" )

I'll just be sitting here polishing up my "D'Oh" while I'm waiting for that answer.

That's simple, because the mirror is flat. Incoming parallel rays are still parallel once they're reflected. That is to say, a reflected image of your right hand is still on your right hand side, and a reflected image of your head is still on your top side. It's not really transposed left-to-right, it's just what you would look like from behind, if you were transparent (if that makes any sense).

To demonstrate, let me use an example. Suppose I write the word "BELTHAZAR" on a piece of paper. Now, looking at the paper, I see that the B is on the left hand side, then the A is next to the right, then the L, then the T, etc etc. Now suppose I picked up the paper and turned it the other way around. (Edit)That is to say, so that the written side is now face-down.(/Edit) Now the word BELTHAZAR reads from right-to-left - I would be able to see this if I held the paper up to a light. The B is on the right-hand-side, with respect to my eyes (that is, my light receptors). When I hold the paper up to the mirror, the B remains on the right hand side, meaning that I read the word as RAZAHTLEB (albeit with reversed letters). The same deal applies for the vertical reflection - my feet remain on the bottom of my reflection because it reflects straight off the mirror.

If the mirror were a vertical concave curve (like the inside of a spoon), then the rays of light would cross over each other, and arrive on the opposite side. That is, when I hold up my BELTHAZAR paper, the B, which is on the right, crosses over to appear on the left-hand-side (and vice versa), meaning that the word once again reads BELTHAZAR. Same deal for a horizontally-curved mirror, just this time my feet are reflected upwards and my head downwards.

Just for a bit of fun, try holding up a piece of paper with a palindromic word made entirely of vertically symmetrical letters - the longest I can think of at the moment is "AHA", all the rest escape me. That should really blow your mind.

(This message has been edited by Belthazar (edited 06-23-2004).)

... D'Oh ...

Quote

Originally posted by Belthazar:
If the mirror were a vertical concave curve (like the inside of a spoon), then the rays of light would cross over each other, and arrive on the opposite side. That is, when I hold up my BELTHAZAR paper, the B, which is on the right, crosses over to appear on the left-hand-side (and vice versa), meaning that the word once again reads BELTHAZAR. Same deal for a horizontally-curved mirror, just this time my feet are reflected upwards and my head downwards.

That assumes that the focal point of said concave surface is between your eye and the mirror, otherwise, everything will just be elongated and otherwise distorted.
Joe

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"Life is tough, but it's even tougher when you're stupid."
-John Wayne

Quote

Originally posted by Arturo:
...So then I decided to really mess with the s˙st locations by transposing everything in a mirror image. Like, the Aurorans are now all in the north and the Polaris are in the west. Makes for a slightly different mind-set while playing. I kept going the wrong way to get somewhere. This is where the conundrum occurred to me...

I't not exactly a mirror image then, rather a 180° (or 200° or π/2, depending on your angle religious preferences) rotation. You just transformed both coordinate (i.e. X and Y) to its opposite, right?

One could try more convoluted transforms, such as scaling the X by a fraction but the Y by another - should be real funny. Or attempt to rotate everything to a certain angle, but then the new X coordinate depend on both the former X and Y ones, and the Y too, so you have to find a way to store the old ones to make the calculations or do all at once.

And if you really wish to go mad and non-linear (all the aforementioned ones are linear, i.e. the image of the sum of two positions is the sum of the images of the two positions), you can attempt an inversion: instead of X you put Xconst^2/(X^2+Y^2), and instead of Y, Yconst^2/(X^2+Y^2) (const is the distance from 0,0 you want to leave unchanged, which should be the average distance from 0,0).

The best thing is that the system coordinates have just two uses: the map (so it's actually just player interaction, not something having consequences gameplay-wise) and the direction you go when you enter hyperspace. Nothing else depends on them (though the engine my have problems if you attempt to have two systems at the exact same coordinates at the same time). Therefore, we can play with them as we like.

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Quote

Originally posted by Zacha Pedro:
đ/2

Ok, I'll bite. Just how did you write that pi? Should be just pi, incidentally, not pi/2

Quote

Originally posted by Arturo:
Now I'm no more stupid than average, but I couldn't think of an explanation for this apparent anomaly in the way a mirror works.
Anybody got a handle on this?

A good way to think of it is that things in a mirror are not backwards, they are inside out. It is just like how a right-handed glove, when turned inside out, will fit on the left hand.

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Who's the what now?

A π like this? What about a σ or a δ ?

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(This message has been edited by Echoboom (edited 06-26-2004).)

(This message has been edited by Echoboom (edited 06-26-2004).)

(This message has been edited by Echoboom (edited 06-26-2004).)

No, I mean an apple pie - yes I mean a pi like that! What else would I mean? If you're just going to sit there and gloat and not answer my question, then needn't bother.

You write π, just like that. Interestingly enough, in your quote of my post I see some kind of delta, and echoboom's one squared omegas instead of delta and a sigma. By the way, if you're not writing your special chars with &something; (i.e. you just enter it), it will likely not be consistent across computers, browsers and the such. I've seen people post special chars but other than the fact it's a special char I have no idea of which one they attempted to post. That's why we post & i uml; for ï, (replace i by the other vowels for the others) so that everyone sees the same thing.

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The (url="http://"https://secure.ambrosiasw.com/cgi-bin/store/hazel.cgi?action=serve&item;=breakdown.html&BREAKDOWN;_SKUID=1480")Ambrosia Mac CD(/url) with other registrations - 5$. Paying for (url="http://"http://www.ambrosiasw.com/games/evn/")EV Nova(/url) as it's such a great game - 30$.
The (url="http://"http://www.ambrosiasw.com/games/evn/tshirts.html")1337 EV Nova T-shirt(/url)(url="http://"http://www.ambrosiasw.com/webboard/Forum25/HTML/000003.html#ZachaPedro05-18-200409:42AM") (/url) - 22$. The (url="http://"http://w00tware.ev-nova.net/")NovaTools(/url) by wOOtWare to tinker with your Nova - FREE!
The feeling you're a Nova geek - priceless.
There are things money can't buy or that are free, for everything else, there's indeed Mastercard.

Arturo

If you want to have some more fun, try rotating the galaxy by various amounts. It's easy if you are using a spreadsheet like Excel.

Apply these formulae, where theta is the degree of rotation (+ or -):

new X coord = ROUND((Xcos(thetaPI()/180))+(Ysin(thetaPI()/180),0)
new Y coord = ROUND((Ycos(thetaPI()/180))-(Xsin(thetaPI()/180),0)

the (*PI()/180) is necessary in Excel because Excel performs trig calculations in radians rather than degrees. If you have a spreadsheet program that calculates in degrees, you don't need this.

You may have to experiment a bit with the plus and minus. I haven't tried real large rotations, so I am not sure what the effect is of rotating out of one quadrant into another. But this works fine up to +- 89 degrees.

For your complete translation, you could rotate by 180 degrees, which would turn your universe upside down!

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