omegapausestuck:highpriestmckickass:omegapausestuck:koobaxion:alphaplayfree:alienpapacy:you ever see
omegapausestuck:highpriestmckickass:omegapausestuck:koobaxion:alphaplayfree:alienpapacy:you ever see an image and think “i may see something as funny as this again, but never anything funnier”ALL RIGHT YOU LITTLE SHITS GET READY TO LEARN SOMETHINGyOU WANNA ROTATE TEXT?! well mod 5ider has got the fucking t r i c k s homieStep one: Type something.P E R F E C T.sTEP TWO: FIND THE RESIZE OPTION.You see that little resize button on your menu?Yeah, that’s the one. you can just click that shit!On older versions of MS Paint there isn’t this option, but you can always find it with a quick right-click.THERE IT FUCKING IS!!!!! STEP THREE: STRETCH AND SKEWWhen you click resize, this menu comes up.I’m sure you all have seen this menu before, but for those who don’t, I’ll clue you in. The top options control the length and respective width of your artwork. you can choose to alter them separately,or all togetherUsing that little “Maintain Aspect Ration” checkbox there, but that’s not important right now.wHat we’re focusing on is that skew option on the botttom.with that you can t i l t whatever image yuo have on your screen to the leftto the rightupand down.“BUT 5IDER!!!!!” you say, “THAT DOESN’T LOOK ROTATED AT ALL”wELL HOLD ON TO YOUR LUG NUTS BECAUSE I T ’ S T I M E F O RSTEP 4: ULTRA COMBOOOOOOOO!!!!!now, comes the fun part. unlike its aspect ratio locked cousin, the stretch and skew options work independently from one another. So, you can do things like andBut that’s neither here nor there… what gets REALLY interesting is when your ratios are in opposite directions..HOME RUN!Now, before I let you go, I found out through trial and error that an angle doesn’t exactly match up with its negative dimension…(Step 5: Angular ratios)See? there’s a little offset between vertical and horizontal if your expect your text to appear natural instead of tilted. The only places that this offset reaches zero is at 90° (of course) and the rare and extremely dangerous 45° rotations.Fortunately, I’ve already mapped out a few angles that I find are very useful in my works so, for your viewing pleasure… i present my handy dandy graphAll you have to do is match up your desired angle up to its respective complement and you have quickly and efficiently rotated your first word in MS Paint.Have fun!You know, you guys really seemed to enjoy this post.Should I do more MS Paint tutorials in the future?“I found out through trial and error that an angle doesn’t exactly match up with its negative dimension…”Kinda! It matches up, but only if you do a stretch between them.Since they’re linear, both these operations can be represented as a matrix. Stretching by a horizontally and b vertically is the matrix ((a, 0), (0, b)). Horizontal skew by an angle t turns a vertical line into a line that is t degrees from vertical, i.e., a line with slope cot t. So its matrix is ((1, tan t), (0, 1)). Likewise, a vertical skew by t is ((1, 0), (tan t, 1)).So, say we wanna rotate our image by t degrees (counterclockwise). If you remember your linear algebra (and if you don’t, props for still reading this far), you’ll recall the desired matrix is ((cos t, -sin t), (sin t, cos t)). Let’s do a horizontal skew, a stretch, and a vertical skew, and remember, the first operation to be applied goes on the right. We’ll let the parameters for the stretch be some unknown a and b, and solve for them.We’re looking good, we see some symmetric terms in the upper right and lower left. But we gotta deal with the ugly looking term in the lower right (it won’t be as bad as it seems.We want the upper left to be cos t, so we’ve gotta set a = cos t. Since cos(t) tan(t) = sin t, the upper right and lower left terms work out perfectly. (Thank goodness, or else we’d have to try a different pattern of stretches/skews.)This leaves the lower right term, which is now -cos(t) tan^2(t) + b = b - sin(t) tan(t). We want it to be cos(t), and we can tune b to get that.If cos t = b - sin(t) tan(t), then b must be cos(t) + sin(t) tan(t). This looks hairy, but if you put them as fractions over a common denominator, it becomes very pleasant:So, in summary, if you want to rotate by t degrees, you can skew horizontally by -t, and skew vertically by t, but the rotation only turns out perfect if you stretch by (cos t, 1/cos t) between those two skews.Notably, this is why the no-stretch method works well for small angles: that’s exactly when cos t is close to 1. And for 45 degrees, the stretch at its most imbalanced, at (71%, 141%). (Yes it gets more imbalanced after that, but if you’re turning more than 45, you can do a 90 degree turn and then turn less than 45. :P)(math! :D)seriously y’all, I think I’m in love -- source link