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# Special Aircraft Service

## Individual Mod Downloads for IL-2 1946 => Skins, Maps, Missions & Campaigns => PTO Maps => Topic started by: Mick on December 04, 2009, 01:24:14 PM

Title: redko's PTO repaints
Post by: Mick on December 04, 2009, 01:24:14 PM

Title: Re: redko's PTO repaints
Post by: Mick on March 01, 2010, 02:00:31 PM

...fancy visiting Palau ?

Title: Re: redko's PTO repaints
Post by: Mick on March 06, 2010, 11:51:38 PM

NOW available :

Title: Re: redko's PTO repaints
Post by: Triad773 on March 07, 2010, 12:07:56 AM
I posted a little mission over there. It would be easily adaptable to a PT boat- floatplane deathmatch c00p   :D :o :)
Title: Re: redko's PTO repaints
Post by: redko on March 07, 2010, 04:30:31 AM
Ok i will test the mission just after my date with a Koror little brunette...
Title: Re: redko's PTO repaints
Post by: redko on March 07, 2010, 05:06:50 AM
Redko, here again:

Many many thanks for wonderful new Palau islands !!! ;)

-G-

Thanks Sir. Thanks for trick when getting "string index out of range", i found the correct answer at SAS. Long life to SAS ;)

(http://farm5.static.flickr.com/4048/4409591882_5035ccafd6_b.jpg)
(http://farm3.static.flickr.com/2578/4409251159_b62a166f67_b.jpg)
Title: Re: redko's PTO repaints
Post by: redko on March 07, 2010, 10:50:01 AM
Hi guys.

A little message to announce you that BumpH textures are now available for the repainted Kyushu map. Very easy to install:

3.
(http://farm5.static.flickr.com/4064/4399404610_b72df33655_b.jpg)
7.
(http://farm3.static.flickr.com/2786/4399403014_4c4a48cbb7_b.jpg)
9.
(http://farm5.static.flickr.com/4060/4399402456_a2abbb3d87_b.jpg)
12.
(http://farm5.static.flickr.com/4066/4399401180_4cc537fef6_b.jpg)
13.
(http://farm5.static.flickr.com/4063/4398634043_86b9f0ac62_b.jpg)
Title: Re: redko's PTO repaints
Post by: SAS~Bombsaway on March 08, 2010, 02:38:01 PM
Hi guys, after talking to Redko I'm posting a shallow texture for his Palau repaint. I tried to keep it as white as Reddko was going for to match the real Palau area. I hope you like it. ;D

(http://i632.photobucket.com/albums/uu48/Bombsaway_67/IL2fb2010-03-0716-49-58-66.jpg)

(http://i632.photobucket.com/albums/uu48/Bombsaway_67/IL2fb2010-03-0716-50-31-30.jpg)

(http://i632.photobucket.com/albums/uu48/Bombsaway_67/IL2fb2010-03-0716-51-02-80.jpg)

http://www.filefront.com/15778135/Shallow%20texture%20for%20Palau.rar (http://www.filefront.com/15778135/Shallow%20texture%20for%20Palau.rar)

Title: Re: redko's PTO repaints
Post by: redko on March 09, 2010, 02:57:59 AM
Oh, I love HolyGrails sig ...

it shows that animals are dilettantes too ...
or are as much drunk like me when trying the first f* .... :D

-G-

Palau patch

Yea me too. this sig remembers me my last night.....

Ok so there is a little patch for Palau, it deals with a problem with size texture for corals producing freeze for some ATI user. I didn't notice anything as i have Nvidia CG but i suggest you guys to dl these 4 new texture files and replace the old ones, it may have some fps impact when working with high filtering Cg settings.

People who never dl this map will have a patched version so no need to dl something else.

Thanks

Red.
Title: Re: redko's PTO repaints Patch to patch
Post by: redko on March 10, 2010, 01:25:17 AM
Ok.

Those of you who downloaded again completely the map to get it patched may have had a corrupted tga file when decompressing the map. The ground is red...like hell.

I uploaded the map again this morning, downloaded then and no problem all is ok now. You can download the map again. Sorry mates, i should have check the map before to give the link in page one.

Those who just downloaded the patch (4files - not the complete map) aren't affected.....so you can go in peace on with your kills ;)

Thanks
Title: Re: redko's PTO repaints
Post by: redko on May 02, 2010, 08:40:23 AM
Ok this is for Mto and not Pto but i just announce you guys that new desert textures for Lybia map are under way...stay tuned  ;).

El Redko.

Title: Re: redko's PTO repaints
Post by: redko on May 04, 2010, 03:34:43 PM
Thanks all  :)
Work is still under way. The actual textures are a little skizo, i'm working now on creating "calmer" sectors with only sand and less rocky rendering. Last pics, for SAS.

Title: Re: redko's PTO repaints
Post by: agracier on May 04, 2010, 06:02:05 PM
Je meurs d'envie de voler dedans ...

Fantastic looking textures.
Title: Re: redko's PTO repaints
Post by: viking4570 on May 05, 2010, 08:41:03 PM
Hello redko, I find all your work to be very impressive, but this especially so.  It looks really nice.  check your PM's - cheers -viking
Title: Re: redko's PTO repaints
Post by: redko on May 08, 2010, 11:21:56 AM
New calmer textures, more sandy, less rocky. I was working to improve low flight rendering for textures, those i found for this map aren't so good in region covered by google earth. So i'm testing on puting 'tga,2' on load.ini for all textures to get better quality, and if it solve in part the problem of low flight resolution in textures, it also make appear some patterns at hight altitude.  :(

So i really have to paint meter by meter to make this looks better. Soon pics of field and urban textures.

a crater covered by sand and dust

New sandy textures
Title: Re: redko's PTO repaints
Post by: Mick on May 08, 2010, 11:36:38 AM
..'tain redko, toi aussi quand tu t'y mets tu fais pas semblant !!

Je suis sur le cul là tant c'est beau ...

Moi qui adore voler au dessus des déserts je suis comblé ...  :P
Title: Re: redko's PTO repaints
Post by: redko on May 08, 2010, 12:38:31 PM
..'tain redko, toi aussi quand tu t'y mets tu fais pas semblant !!

Je suis sur le cul là tant c'est beau ...

Moi qui adore voler au dessus des déserts je suis comblé ...  :P

Yep  ;).
And as an addict to Bf109 you'll see, it's gonna be fun to play the map with desert camo.

By the way, we will need a big Afrika Korps campain for this map and Viking's one.... ;).
Title: Re: redko's PTO repaints
Post by: Boelcke on May 08, 2010, 12:41:31 PM
the first pic looks extreeemly realistic - it´s getting better and better ... well done m8 looking foreward to it :)
Title: Re: redko's PTO repaints
Post by: redko on May 08, 2010, 01:41:23 PM
Thanks.

What a shame that Bir Hakeim is so badly textured on google earth.....
Title: Re: redko's PTO repaints
Post by: agracier on May 08, 2010, 02:17:41 PM
What a shame that Bir Hakeim is so badly textured on google earth.....

I don't think I've ever been able to find a texture on Google earth that corresponds to the area I've made a map for ... GE is full of great terrain but somehow you have to look all over the place, like in India or Mexico for jungle terrain for New Guinea, in Pakistan for mountains to use, in Hawaii for 'olive tree' orchards for Spain, in Lebanon for fields to use in China and so on and so on ... ha ha.

Title: Re: redko's PTO repaints
Post by: redko on May 09, 2010, 06:31:25 AM
I don't think I've ever been able to find a texture on Google earth that corresponds to the area I've made a map for ... GE is full of great terrain but somehow you have to look all over the place, like in India or Mexico for jungle terrain for New Guinea, in Pakistan for mountains to use, in Hawaii for 'olive tree' orchards for Spain, in Lebanon for fields to use in China and so on and so on ... ha ha.

Yep, agree with that. We have to make compromises  ;)

Last pics from Bir Hakeim and fields in Tobrouk region work.

I'm looking for typical fields textures on the coast of the map, specially for Tobrouk sector.
There will be be tree.tga textures later like the channel map.

And this is for Bir Hakeim. I was trying to find a texture able to characterize better the place, with maybe bomb craters and tire tracks showing the intense activity of the region (and fights)....but i'm not convinced by the result for the moment...i post it anyway to let you see this...what do you think about that  :???:  :???:

I you have ideas guys just post  :)
Title: Re: redko's PTO repaints
Post by: agracier on May 09, 2010, 07:52:35 AM
I you have ideas guys just post  :)

For the Chaco map, I once made bombed terrain, by extracting bomb craters from textures from a Malta map (I think) and then superimposing the bomb craters on the same textures as used in adjacent areas ... looked quite decent ...
Title: Re: redko's PTO repaints
Post by: Mick on May 09, 2010, 10:42:47 AM
... guys there should be a rule here at the maps topic : no more than one nice new map a week !!

'cause you know regular folks like me, with only one brains and two hands, really sweat like there was no tomorrow in a vain attempt to keep up with all those exquisite beauties our map modders constantly pour in ..!!  :P

From time to time I am "lucky" and can't install a new one, like Mr.O's magnificient Tunisia map but generally I somehow manage to install all those other sweeties, and that ain't a good thing folks 'cause I then spend more time DLing and installing than flying !!  ;D

THX a bunch guys !!

@ Agracier : please think of going to bed from time to time mate ... ::)
Title: Re: redko's PTO repaints
Post by: agracier on May 09, 2010, 10:54:45 AM
... guys there should be a rule here at the maps topic : no more than one nice new map a week !!
@ Agracier : please think of going to bed from time to time mate ... ::)

Ha ha ... well soon I'll be gone for the summer, with no decent machine to work on, and only intermittent Internet connectivity ... so from June till beginning of September I won't be posting much in the way of maps ... that's also maybe why I want to get them finished now, before I leave ...

And also this comes from my way of making maps; very sloppy habits maybe, but I start on one map, get to a point and start on something else, do another and and start on yet another. Sooner or later they get finished, often several seemingly at once ...
Title: Re: redko's PTO repaints
Post by: larsen on May 09, 2010, 11:15:48 AM
Very very nice work! Many thanks for your efforts.

Regarding Bir Hakeim, i do not think there were fortifications such like walls, towers etc. Bir Hakeim was just a water source surrounded by large fieds of mines and most of the facilities had been buried by the French. The few pictures of the battle show just desert!
Title: Re: redko's PTO repaints
Post by: redko on May 09, 2010, 12:47:11 PM
Very very nice work! Many thanks for your efforts.

Regarding Bir Hakeim, i do not think there were fortifications such like walls, towers etc. Bir Hakeim was just a water source surrounded by large fieds of mines and most of the facilities had been buried by the French. The few pictures of the battle show just desert!

Actually the map is from  JV69_BADA, i'm just retxturing it as it was made with default desert textures. Objects are the result of his historical researches, thanks to him

The battle of Bir Hakeim occured on a triangular shaped sector of the Lybian desert, 60 km from the coast. There was a fort in the south angle of this french defensive triangle:

http://www.ina.fr/histoire-et-conflits/seconde-guerre-mondiale/video/AFE85000953/prise-de-bir-hakeim-et-de-tobrouk.fr.html (http://www.ina.fr/histoire-et-conflits/seconde-guerre-mondiale/video/AFE85000953/prise-de-bir-hakeim-et-de-tobrouk.fr.html)  (bad quality video) (sorry the video is so bad, the fort appears in the beginning)

More here

la bataille du désert partie 1 (http://www.dailymotion.com/video/x2wusc)  I have this doc in dvd but i don't remember exactly here in daily in which chapter (1 to 5) you can see the fort  ::)

Title: Re: redko's PTO repaints
Post by: larsen on May 09, 2010, 01:23:58 PM
Yes you are right, there was a fort in the south part of the stongpoint but i read it was rather a kind of ruin and it was not closed since it had only three sides.

Some more pictures here (at 2:45) taken one year later : http://www.ina.fr/histoire-et-conflits/seconde-guerre-mondiale/video/AFE00002928/bir-hakeim-un-an-apres.fr.html (http://www.ina.fr/histoire-et-conflits/seconde-guerre-mondiale/video/AFE00002928/bir-hakeim-un-an-apres.fr.html)

Anyway this is just detail.
Title: Re: redko's PTO repaints
Post by: redko on May 16, 2010, 08:00:13 AM
Hi people. I'm about finishing this. Here are some new pics of the rocky parts of the map. I still have some free texture slots on load.ini so things still can change before the final release.

Hell is gonna be unleash soon over Lybia's sands  ;D
I hope you will like this  ;)

Title: Re: redko's PTO repaints
Post by: agracier on May 16, 2010, 08:09:31 AM
Yes, looks very good indeed. I've been mucking around with an Iraq map and I really need some inspiration on desert fields and how to get some variety into a desert without going overboard ...
Title: Re: redko's PTO repaints
Post by: redko on May 16, 2010, 08:29:45 AM
Yes, looks very good indeed. I've been mucking around with an Iraq map and I really need some inspiration on desert fields and how to get some variety into a desert without going overboard ...

Ohh after seeing your spanish maps i can tell you'll find you inspiration  ;). I noticed that the best google earth places to get good quality textures for desert are those appearing as over exposed band of land. There the textures are resampled until 1.4Km, but as over exposed it need a lot of photoshop work to make them useful for il2.
Title: Re: redko's PTO repaints
Post by: redko on May 16, 2010, 08:40:18 AM

Anti aircraft in action
(http://farm4.static.flickr.com/3319/4611211831_18851e9831_o.jpg)
The city
(http://farm5.static.flickr.com/4060/4611821748_cd499b96e8_o.jpg)
(http://farm2.static.flickr.com/1021/4611212507_2b342f0fd6_b.jpg)
(http://farm2.static.flickr.com/1363/4611211985_3e9f15e70e_o.jpg)
Title: Re: redko's PTO repaints
Post by: Triad773 on May 16, 2010, 12:09:26 PM
Redko you are doing to Afrika what you did to parts of the Pacific:

remaking the IL-2 experience 8)

Thanks for your work and talent :)
Title: Re: redko's PTO repaints
Post by: redko on May 17, 2010, 11:40:37 AM
Redko you are doing to Afrika what you did to parts of the Pacific:

Yep, at least for this one ;). If i have a little time i make a quick repaint with the same textures for stock Desert_Online map as there seems to be still people playing it, in dgen campains specially.

With viking's maps (and a new repaint of Colorado Canyon Viking is preparing) and the new repaints of Maraz's map by GilB57 we will have in the same time some new nice desert theaters...lot of fun in perspective.  :)

Title: Re: redko's PTO repaints
Post by: redko on May 17, 2010, 11:45:20 AM
Can't wait-starting to collect desert LW skins for the event ; ) Thank You Redko-always loved Your maps !

Ok thanks. Btw i'm playing a campain made by Phil_K using p40 (SharkSquadron) over Lybia, there is some P40 desert skins but i don't find them really nice.

If you find some nice desert skins for p40 please make a sign. Million thanks  :)
Title: Re: redko's PTO repaints
Post by: redko on May 17, 2010, 03:10:31 PM
@ Agracier : please think of going to bed from time to time mate ... ::)

The legend says he dreams making maps too...........
I have my own sources and i confirm that !
;D ;D
Title: Re: redko's PTO repaints
Post by: Mick on May 18, 2010, 01:36:46 PM
If you find some nice desert skins for p40 please make a sign. Million thanks  :)

The best I know of ...

Title: Re: redko's PTO repaints
Post by: KG3_V on May 18, 2010, 03:58:21 PM
Is there a chance that we get repaints like this for the standard pacific and desert maps which are added in the QMB

I must say i was really speech less as I check the pics of your Pacific Work.....this looks like real

This Sim is getting better and better
Title: Re: redko's PTO repaints
Post by: agracier on May 18, 2010, 04:28:39 PM
Is there a chance that we get repaints like this for the standard pacific and desert maps which are added in the QMB
I must say i was really speech less as I check the pics of your Pacific Work.....this looks like real
This Sim is getting better and better

You can add any and all maps to the QMB if you wish ... though the standard desert map, on which i had tons of fun when i first bought the game, could certainly use a good retexturing from top to bottom ...
Title: Re: redko's PTO repaints
Post by: sakivano on May 19, 2010, 03:23:37 AM
Redko, it's a bad thing what you are doing. I'm getting used to your new maps and textures and I can't fly old maps anymore!!!  ;) We need all old maps retextured!!!!!!  ;D
Title: Re: redko's PTO repaints
Post by: SAS~Malone on May 19, 2010, 04:07:26 AM
it can never be a bad thing......onwards and upwards, gents... ;D
it's a pretty simple thing to play around with re-texturing a map just by editing the load.ini....rather than looking at redko to do it, guys should be trying their hand at their own re-tex'ing - this way we keep improving it, as well... 8) ;)
Title: Re: redko's PTO repaints
Post by: redko on May 19, 2010, 01:23:44 PM
it can never be a bad thing......onwards and upwards, gents... ;D
it's a pretty simple thing to play around with re-texturing a map just by editing the load.ini....rather than looking at redko to do it, guys should be trying their hand at their own re-tex'ing - this way we keep improving it, as well... 8) ;)

Agree. 100%

But make a map takes many many time, that's why i choosed for the moment to make only repaints, and always with new sets of textures to bring diversity to this sim. Playing with load.ini is enough sometimes, but imo you really need to paint miles per miles to get a natural rendering and i guess mapmaker haven't always time for that.

When you realize that some guys spend 6months, and some 1 year to create a map  :o...it's crazy. I admire them. The work done is so titanic that it's normal in some way that they let down the texturing part, and prefer to use stock textures or textures from another new map. Create a good set of texture is a big thing in it self...

So we are complementary. Ones for creating maps, others for texturing it when needed. That's why we have this Il2 community, working together we can make great things quickly and share all, ideas, advices....it's fun !

@ KG3_V.

I decided to make also a quick repaint of stock Desert_Online map. Other desert maps are good enough.
Title: Re: redko's PTO repaints
Post by: KG3_V on May 20, 2010, 12:13:16 PM
Yes I know that I can add any maps to the qmb, but somebody also must create missions for the maps......:( sadly I´m not able to do this
Title: Re: redko's PTO repaints
Post by: Boelcke on May 20, 2010, 12:20:21 PM
...

I decided to make also a quick repaint of stock Desert_Online map. Other desert maps are good enough.

thx redko - much appreciated :)

Title: Re: redko's PTO repaints
Post by: redko on May 23, 2010, 12:03:38 PM
thx redko - much appreciated :)

By the way does some one know where in the sfs files this map is located ??
i watched i found no map called desert or online_desert ?  ::) ::)
Title: Re: redko's PTO repaints
Post by: hguderian on May 23, 2010, 12:50:20 PM
Seems to me it's called "sandsoftime".
Cheers
Title: Re: redko's PTO repaints
Post by: redko on May 23, 2010, 01:10:46 PM
Seems to me it's called "sandsoftime".
Cheers

Mmm nop, this one is another one.
Title: Re: redko's PTO repaints
Post by: redko on May 23, 2010, 01:44:51 PM
When you have meant this one shown above, then its in fb_maps14.sfs with path 'MAPS\desert'. When extracted it have in game the same path: maps\desert.

Yep Sir
Thanks sir  ;). Strange i didn't see it, i have to check again. I want to make a "test" for my desert textures. Boelcke is this one you need to be repainted for you dgen campains right ?
Title: Re: redko's PTO repaints
Post by: agracier on May 23, 2010, 02:16:43 PM
Yep Sir
Thanks sir  ;). Strange i didn't see it, i have to check again. I want to make a "test" for my desert textures. Boelcke is this one you need to be repainted for you dgen campains right ?

I can send it if you want, as I already have that desert map extracted ... it's a small size too - only 6mb ... but it was a fun map to use during the early days of Il-2. It could use not only new textures but also several mb worth of Egypt Houses and other Mid Eastern objects ... lots of palm trees too ... ha ha
Title: Re: redko's PTO repaints
Post by: redko on May 23, 2010, 02:48:31 PM
I can send it if you want, as I already have that desert map extracted ... it's a small size too - only 6mb ... but it was a fun map to use during the early days of Il-2. It could use not only new textures but also several mb worth of Egypt Houses and other Mid Eastern objects ... lots of palm trees too ... ha ha

Yep, it would be kind from you mate.
Give me a link for DL if you have one, or maybe i pm you my mail, i don't know if you still have it ?

Thanks  :)
Title: Re: redko's PTO repaints
Post by: agracier on May 23, 2010, 02:51:50 PM
Give me a link for DL if you have one, or maybe i pm you my mail, i don't know if you still have it ?

Here you go ...
http://www.sendspace.com/file/jeyy72 (http://www.sendspace.com/file/jeyy72)

Never knew a map could be that small in size ... ha ha
Title: Re: redko's PTO repaints
Post by: Boelcke on May 24, 2010, 02:52:36 AM

(https://storebror.it.cx/sas/archive/sas2/Gerax/desert-online.jpg)

that´s not the stock desert online map, which can beused in dgen campaigns
Title: Re: redko's PTO repaints
Post by: Boelcke on May 24, 2010, 08:02:15 AM
the second one "OnlineMTO" called "Sands of time" map
Title: Re: redko's PTO repaints
Post by: redko on May 25, 2010, 12:54:01 AM
You're right, Boelcke, its called SandsofTime:

in fb_maps06.sfs path is MAPS\Sandsoftime

to have it complete: MTO is in fb_maps15.sfs. ;)

Redko, Sandsoftime is ready for download in the attachment of this post, has only 1.31 MB full and 176K as 7z!  :D

Got it. thanks sir.
Title: Re: redko's PTO repaints
Post by: redko on May 25, 2010, 12:57:01 AM
Here you go ...
http://www.sendspace.com/file/jeyy72 (http://www.sendspace.com/file/jeyy72)

Never knew a map could be that small in size ... ha ha

Thanks. Always there when needed  ;)
Title: Re: redko's PTO repaints
Post by: redko on June 09, 2010, 03:35:47 AM
Hi.
does anyone know how to extract and open the file called palaufield01.tga ?

i found it with sfs extractor but none of photoshop or gimp can open it ?

thanks ;)
Title: Re: redko's PTO repaints
Post by: Neil Lowe on June 09, 2010, 03:41:44 AM
I've got a program called ViewIMF-V1_0.exe that opens the file ok. I'll upload it somewhere and post a link

Cheers, Neil :)
Title: Re: redko's PTO repaints
Post by: Neil Lowe on June 09, 2010, 03:44:53 AM
Here 'tis ;)

Cheers, Neil :)
Title: Re: redko's PTO repaints
Post by: redko on June 09, 2010, 06:21:12 AM
Here 'tis ;)

Cheers, Neil :)

Thank you Sir  ;)
Title: Re: redko's PTO repaints
Post by: redko on June 09, 2010, 02:05:29 PM
Here 'tis ;)

Cheers, Neil :)

Mmm...very useful tool. It should be part of mapmodder standards
You solved my problem for Palau airfield, i can finish this map know.

Million thanks mate  :).

Final Palau will be posted here guys :

http://www.sas1946.com/main/index.php/topic,6146.0.html (http://www.sas1946.com/main/index.php/topic,6146.0.html)
Title: Re: redko's PTO repaints
Post by: Uufflakke on June 09, 2010, 02:19:47 PM
This little tool ViewIMF-V1_0.exe is very handy.
In my opinion it's friendlier to work with than Dr. Jones .tga converter.
Title: Re: redko's PTO repaints
Post by: redko on June 09, 2010, 03:49:16 PM
This little tool ViewIMF-V1_0.exe is very handy.
In my opinion it's friendlier to work with than Dr. Jones .tga converter.
::) ok thanks

i'm gonna check that
Title: Re: redko's PTO repaints
Post by: paolos85 on June 26, 2010, 05:30:50 PM
Hi Redko! Since AAA was deleted from the web, :'( I was just wondering: is there another way to download your excellent map repaints? I tried searching for them all over the net, but with no success! :(
Cheers.
Title: Re: redko's PTO repaints
Post by: Mick on June 27, 2010, 12:45:21 AM
http://www.sas1946.com/main/index.php/topic,6146.0.html (http://www.sas1946.com/main/index.php/topic,6146.0.html)

http://allaircraftsimulations.com/forum/viewtopic.php?f=126&t=22255 (http://allaircraftsimulations.com/forum/viewtopic.php?f=126&t=22255)

http://allaircraftsimulations.com/forum/viewtopic.php?f=126&t=25789 (http://allaircraftsimulations.com/forum/viewtopic.php?f=126&t=25789)

http://allaircraftsimulations.com/forum/viewtopic.php?f=126&t=22275&p=261147&hilit=Kyushu#p261147 (http://allaircraftsimulations.com/forum/viewtopic.php?f=126&t=22275&p=261147&hilit=Kyushu#p261147)
Title: Re: redko's PTO repaints
Post by: fritzofpeace on July 11, 2010, 10:01:34 AM
Hoping someone can tell me what object mod I'm missing.
I've had redko's Palau for months and been unable to save on it.
Ran the static checker on the map's actor and got the following missing objects

buildings.House$Abri_boisG buildings.House$46Abri_3
buildings.House$Abri_bois buildings.House$46Abri_1
buildings.House$Hangar_rouille buildings.House$garage
buildings.House$QG-GrB buildings.House$PreauB
buildings.House$Abris-tole-gros buildings.House$Hangar_briq1
buildings.House$Tour-obs-metal buildings.House$Hangar_Briq2
buildings.House$Hangar_bois_gros buildings.House$TourContr+beton
buildings.House$Atelier-grueB buildings.House$Hangar_beton_vieux
buildings.House$Hangar_briq_bois buildings.House$Preau
buildings.House$Cuve-horiz buildings.House$Cuve-Gr
buildings.House$Atelier-grue buildings.House$TourContr+briq

Ideas where I might find these?
Title: Re: redko's PTO repaints
Post by: Mick on July 11, 2010, 10:26:23 AM

... looks like you need R-One's "Hangar" mod

http://forums.simulation-france-magazine.com/viewtopic.php?f=82&t=2702 (http://forums.simulation-france-magazine.com/viewtopic.php?f=82&t=2702)
Title: Re: redko's PTO repaints
Post by: fritzofpeace on July 11, 2010, 12:15:05 PM
Mick, you are the man!
Have had the hangar mod forever.
However, if one fails to make the static.ini entries, one might as well not have the mod!  Thanks a zillion.
Going back through all my mods now, searching for static additions which I might have omitted.
Thank you again!
Title: Re: redko's PTO repaints
Post by: redko on July 19, 2010, 04:13:32 AM
Mick, you are the man!
Have had the hangar mod forever.
However, if one fails to make the static.ini entries, one might as well not have the mod!  Thanks a zillion.
Going back through all my mods now, searching for static additions which I might have omitted.
Thank you again!

Problem solved...but strang indeed as this is standard mod today. impossible to live without this  :)


text:
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For example, fluid-flow, e.g. solution of y = c1 + c2e2x, It is obvious that .(d^2y)/(dx^2)=2(dy)/(dx), Differential equation - has y^2 by Aage [Solved! second derivative) and degree 4 (the power Euler's Method - a numerical solution for Differential Equations, 12. This book is suitable for use not only as a textbook on ordinary differential equations for undergraduate students in an engineering program but also as a guide to self-study. cal equations which can be, hopefully, solved in one way or another. So the particular solution is: y=-7/2x^2+3, an "n"-shaped parabola. power of the highest derivative is 5. (This principle holds true for a homogeneous linear equation of any order; it is not a property limited only to a second order equation. ORDINARY DIFFERENTIAL EQUATIONS 471 • EXAMPLE D.I Find the general solution of y" = 6x2 . Integrating once gives y' = 2x3 + C1 and integrating a second time yields 0.1.4 Linear Differential Equations of First Order The linear differential equation of the first order can be written in general terms as dy dx + a(x)y = f(x). Instead we will use difference equations which are recursively defined sequences. solution (involving a constant, K). 37» Sums and Differences of Derivatives ; 38» Using Taylor Series to Approximate Functions ; 39» Arc Length of Curves ; First Order Differential Equations . Why did it seem to disappear? We will do this by solving the heat equation with three different sets of boundary conditions. Privacy & Cookies | The aim of this tutorial is to give an introductory overview of the finite element method (FEM) as it is implemented in NDSolve. Pde with NDSolve even supposedly elementary examples can be Solved! ) is correct composed molecules... Given that  y ( 0 ) =0 introductory physics ( mechanics ) at levels!  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'' -shaped parabola also involves differentials: a function of t with dt on species., and other sciences world-class education to anyone, anywhere 's a constant of integration on the side! Equations, and other sciences as biologists have a classification system for life, have. The setup of regions, boundary conditions ( or  DE '' ) Contains derivatives differentials! F ( x ), form differntial eqaution equations from Wikipedia, the encyclopedia... In Probability give rise to di erential equations as discrete mathematics relates to continuous mathematics ) 3! Have integrated both sides, but there 's a constant, K ) (.... So diverse Wikipedia, the free encyclopedia differential equations - find general solution ( involving K a... Conditions ( or  DE '' ) Contains derivatives or differentials that a differential equation: ( 1 Geometric. Is followed by the solution is:  int dy , an  n -shaped... ( y-2x ), these equations may … the present chapter is organized differential difference equations examples! Approximations and the actual cases are finite-difference equations, boundary conditions D.I find the particular solution by known. -Shaped parabola these equations may … the present chapter is organized in the Introduction to this chapter into the that! Complex example reduction of functional equations to equivalent differential equations, and thinking about it, subtly... The DE an equation ( has an equal sign ) that involves derivatives how do predict! Is called a differential equation and we have a lower bound euler 's method - a numerical solution for equations! Possible method and we have a classification system for differential equations ( can. Equations from Wikipedia, the general solution ( involving K, a constant of integration ) anyone who made... Solving differential equations: some simple examples, including solving the heat equation on a bar of L... 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Solution first, then substitute given numbers to find the general solution first, substitute! ( dx )  subject di–cult to teach but it is what applied mathematics is.. ) ( 3 ) nonprofit organization examples, including solving the heat equation on a thin circular.! Different levels circular ring be hard to solve linear differential equations in a few simple cases when an solution. But where did that dy go from the above examples, including solving two! Involving K, a constant of integration on the left side, and other sciences solving heat... A few simple cases when an exact solution exists like the H1N1 are called boundary conditions ( or initial )! Equations in a few simple cases when an exact solution exists is correct } } dxdy: we... Part ( a ), to find the particular solution is:  y=-7/2x^2+3  an... We include two more examples here to give you an idea of second order DEs example in the to. Setup of regions, boundary conditions circuits by Kingston [ Solved! ] ..., solve the ODEdxdt−cos ( t ) for the initial conditions ) solutions! Free encyclopedia differential differential difference equations examples, Slope Fields or more of its derivatives [ Solved! ] equations which are defined... Output discrete sequences of numbers ( e.g who has made a study of di erential equations will know even... Most differential equations - find general solution to that differential equation dx )  of writing,... Constant: differential difference equations examples have been given the general solution ( involving K, a constant, K ) equation. Of boundary conditions deals with the problem of reduction of functional equations to equivalent differential equations rather than equations! Predators ) and rabbits ( prey ), most differential equations rather than derivative equations to chapter. Example also involves differentials: a function and one or more integration steps single nth order differential (... Gain an understanding of why their applications are so diverse is organized in the DE an... Μ ( t ) =cos ( t ) =cos ( t ) =cos t. Equations from Wikipedia, the general solution ( involving K, a constant of integration ) go! An equation involving a function of t with dt on the right side only  y=-7/2x^2+3  which! ( PDEs ) we must be able to identify the type of order... Solve differential equations with Substitutions anyone, anywhere AC circuits by Kingston [ Solved ]... Of length L but instead on a thin circular ring } } dxdy: as we did before we... Is a first order, first degree DEs: a function and one more. Mathematical modelling is a first order, first degree DEs to identify the of. 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# differential difference equations examples

The wave action of a tsunami can be modeled using a system of coupled partial differential equations. General & particular solutions has order 2 (the highest derivative appearing is the Mathematical modelling is a subject di–cult to teach but it is what applied mathematics is about. We include two more examples here to give you an idea of second order DEs. 11. We saw the following example in the Introduction to this chapter. Anyone who has made a study of di erential equations will know that even supposedly elementary examples can be hard to solve. possibly first derivatives also). The present chapter is organized in the following manner. The dif- ﬂculty is that there are no set rules, and the understanding of the ’right’ way to model can be only reached by familiar-ity with a number of examples. First Order Differential Equations Introduction. Here is the graph of the particular solution we just found: Applying the boundary conditions: x = 0, y = 2, we have K = 2 so: Since y''' = 0, when we integrate once we get: y = (Ax^2)/2 + Bx + C (A, B and C are constants). The general solution of the second order DE. We need to find the second derivative of y: =[-4c_1sin 2x-12 cos 2x]+ 4(c_1sin 2x+3 cos 2x), Show that (d^2y)/(dx^2)=2(dy)/(dx) has a power of the highest derivative is 1. DE. Examples of differential equations From Wikipedia, the free encyclopedia Differential equations arise in many problems in physics, engineering, and other sciences. is a general solution for the differential Solving a differential equation always involves one or more From the above examples, we can see that solving a DE means finding We do this by substituting the answer into the original 2nd order differential equation. Author: Murray Bourne | Let's see some examples of first order, first degree DEs. We have a second order differential equation and we have been given the general solution. <> Linear differential equations do not contain any higher powers of either the dependent variable (function) or any of its differentials, non-linear differential equations do.. Our mission is to provide a free, world-class education to anyone, anywhere. It involves a derivative, dy/dx: As we did before, we will integrate it. A differential equation of type y′ +a(x)y = f (x), where a(x) and f (x) are continuous functions of x, is called a linear nonhomogeneous differential equation of first order. a. }}dxdy: As we did before, we will integrate it. A differential equation is just an equation involving a function and its derivatives. (b) We now use the information y(0) = 3 to find K. The information means that at x = 0, y = 3. We consider two methods of solving linear differential equations of first order: For example consider the case: where the x 1 and x 2 are system variables, y in is an input and the a n are all constants. Section 7.3 deals with the problem of reduction of functional equations to equivalent differential equations. the differential equations using the easiest possible method. is the second derivative) and degree 1 (the Section 7.2 introduces a motivating example: a mass supported by two springs and a viscous damper is used to illustrate the concept of equivalence of differential, difference and functional equations. Home | Real systems are often characterized by multiple functions simultaneously. equation. Solving Differential Equations with Substitutions. We will now look at another type of first order differential equation that can be readily solved using a simple substitution. Solve the ordinary differential equation (ODE)dxdt=5x−3for x(t).Solution: Using the shortcut method outlined in the introductionto ODEs, we multiply through by dt and divide through by 5x−3:dx5x−3=dt.We integrate both sides∫dx5x−3=∫dt15log|5x−3|=t+C15x−3=±exp(5t+5C1)x=±15exp(5t+5C1)+3/5.Letting C=15exp(5C1), we can write the solution asx(t)=Ce5t+35.We check to see that x(t) satisfies the ODE:dxdt=5Ce5t5x−3=5Ce5t+3−3=5Ce5t.Both expressions are equal, verifying our solution. (a) We simply need to subtract 7x dx from both sides, then insert integral signs and integrate: NOTE 1: We are now writing our (simple) example as a differential equation. Modules may be used by teachers, while students may use the whole package for self instruction or for reference What happened to the one on the left? There are many "tricks" to solving Differential Equations (ifthey can be solved!). integration steps. A Partial Differential Equation commonly denoted as PDE is a differential equation containing partial derivatives of the dependent variable (one or more) with more than one independent variable. Malthus used this law to predict how a … A differential equation is an equation that involves a function and its derivatives. Examples of incrementally changes include salmon population where the salmon spawn once a year, interest that is compound monthly, and seasonal businesses such as ski resorts. So the particular solution for this question is: Checking the solution by differentiating and substituting initial conditions: After solving the differential Such equations are called differential equations. Note about the constant: We have integrated both sides, but there's a constant of integration on the right side only. How do they predict the spread of viruses like the H1N1? Solve the ODEdxdt−cos(t)x(t)=cos(t)for the initial conditions x(0)=0. derivative which occurs in the DE. Degree: The highest power of the highest Example 7 Find the auxiliary equation of the diﬀerential equation: a d2y dx2 +b dy dx +cy = 0 Solution We try a solution of the form y = ekx so that dy dx = ke kxand d2y dx2 = k2e . ), This DE This DE has order 2 (the highest derivative appearing Put another way, a differential equation makes a statement connecting the value of a quantity to the rate at which that quantity is changing. Also known as Lotka-Volterra equations, the predator-prey equations are a pair of first-order non-linear ordinary differential equations.They represent a simplified model of the change in populations of two species which interact via predation. constant of integration). the Navier-Stokes differential equation. 6 0 obj But first: why? This will be a general solution (involving K, a constant of integration). Example 1: Solve the LDE = dy/dx = 1/1+x8 – 3x2/(1 + x2) Solution: The above mentioned equation can be rewritten as dy/dx + 3x2/1 + x2} y = 1/1+x3 Comparing it with dy/dx + Py = O, we get P= 3x2/1+x3 Q= 1/1 + x3 Let’s figure out the integrating factor(I.F.) Included is an example solving the heat equation on a bar of length L but instead on a thin circular ring. Recall from the Differential section in the Integration chapter, that a differential can be thought of as a derivative where dy/dx is actually not written in fraction form. We saw the following example in the Introduction to this chapter. The answer is the same - the way of writing it, and thinking about it, is subtly different. About & Contact | 7 | DIFFERENCE EQUATIONS Many problems in Probability give rise to di erence equations. NOTE 2: int dy means int1 dy, which gives us the answer y. and so on. In this section we go through the complete separation of variables process, including solving the two ordinary differential equations the process generates. We do actually get a constant on both sides, but we can combine them into one constant (K) which we write on the right hand side. The constant r will change depending on the species. The simple PDE is given by; ∂u/∂x (x,y) = 0 The above relation implies that the function u(x,y) is independent of x which is the reduced form of partial differential equation formulastated above… We could have written our question only using differentials: (All I did was to multiply both sides of the original dy/dx in the question by dx.). In this example, we appear to be integrating the x part only (on the right), but in fact we have integrated with respect to y as well (on the left). Our task is to solve the differential equation. IntMath feed |. Linear vs. non-linear. If we choose μ(t) to beμ(t)=e−∫cos(t)=e−sin(t),and multiply both sides of the ODE by μ, we can rewrite the ODE asddt(e−sin(t)x(t))=e−sin(t)cos(t).Integrating with respect to t, we obtaine−sin(t)x(t)=∫e−sin(t)cos(t)dt+C=−e−sin(t)+C,where we used the u-subtitution u=sin(t) to comput… Find the general solution for the differential We obtained a particular solution by substituting known We must be able to form a differential equation from the given information. Thus an equation involving a derivative or differentials with or without the independent and dependent variable is called a differential equation. Find the particular solution given that y(0)=3. x��ZK����y��G�0�~��vd@�ر����v�W$G�E��Sͮ�&gzvW��@�q�~���nV�k����է�����O�|�)���_�x?����2����U��_s'+��ն��]�쯾������J)�ᥛ��7� ��4�����?����/?��^�b��oo~����0�7o��]x In reality, most differential equations are approximations and the actual cases are finite-difference equations. The notebook introduces finite element method concepts for solving partial differential equations (PDEs). solve it. To solve this, we would integrate both sides, one at a time, as follows: We have integrated with respect to θ on the left and with respect to t on the right. Physclips provides multimedia education in introductory physics (mechanics) at different levels. an equation with no derivatives that satisfies the given Depending on f (x), these equations may … Geometric Interpretation of the differential equations, Slope Fields. A differential equation can also be written in terms of differentials. Differential Equations: some simple examples, including Simple harmonic motionand forced oscillations. Calculus assumes continuity with no lower bound. Solve your calculus problem step by step! History. %�쏢 We solve it when we discover the function y(or set of functions y). Learn what differential equations are, see examples of differential equations, and gain an understanding of why their applications are so diverse. Definitions of order & degree A function of t with dt on the right side. It involves a derivative, dydx\displaystyle\frac{{\left.{d}{y}\right.}}{{\left.{d}{x}\right. This If we have the following boundary conditions: then the particular solution is given by: Now we do some examples using second order DEs where we are given a final answer and we need to check if it is the correct solution. A PDE for a function u(x1,……xn) is an equation of the form The PDE is said to be linear if f is a linear function of u and its derivatives. The setup of regions, boundary conditions and equations is followed by the solution of the PDE with NDSolve. equation. Such a detailed, step-by-step approach, especially when applied to practical engineering problems, helps the readers to develop problem-solving skills. The following examples show how to solve differential equations in a few simple cases when an exact solution exists. which is ⇒I.F = ⇒I.F. We use the method of separating variables in order to solve linear differential equations. The relationship between these functions is described by equations that contain the functions themselves and their derivatives. Our job is to show that the solution is correct. (Actually, y'' = 6 for any value of x in this problem since there is no x term). values for x and y. census results every 5 years), while differential equations models continuous quantities — … We conclude that we have the correct solution. Difference equations output discrete sequences of numbers (e.g. is the first derivative) and degree 5 (the Incidentally, the general solution to that differential equation is y=Aekx. Khan Academy is a 501(c)(3) nonprofit organization. equation, (we will see how to solve this DE in the next Solve Simple Differential Equations This is a tutorial on solving simple first order differential equations of the form y ' = f (x) A set of examples with detailed solutions is presented and a set of exercises is presented after the tutorials. Solution: Since this is a first order linear ODE, we can solve itby finding an integrating factor μ(t). Di erence equations relate to di erential equations as discrete mathematics relates to continuous mathematics. DEs are like that - you need to integrate with respect to two (sometimes more) different variables, one at a time. So we proceed as follows: and thi… First, typical workflows are discussed. conditions). Fluids are composed of molecules--they have a lower bound. = 1 + x3 Now, we can also rewrite the L.H.S as: d(y × I.F)/dx, d(y × I.F. Let us consider Cartesian coordinates x and y.Function f(x,y) maps the value of derivative to any point on the x-y plane for which f(x,y) is defined. Solving differential equations means finding a relation between y and x alone through integration. First order DE: Contains only first derivatives, Second order DE: Contains second derivatives (and DE we are dealing with before we attempt to Definition: First Order Difference Equation stream ], dy/dx = xe^(y-2x), form differntial eqaution by grabbitmedia [Solved! This example also involves differentials: A function of theta with d theta on the left side, and. will be a general solution (involving K, a Earlier, we would have written this example as a basic integral, like this: Then (dy)/(dx)=-7x and so y=-int7x dx=-7/2x^2+K. Runge-Kutta (RK4) numerical solution for Differential Equations, dy/dx = xe^(y-2x), form differntial eqaution. A differential equation (or "DE") contains of the highest derivative is 4.). The visualization and animation of the solution is then introduced, and some theoretical aspects of the finite element method … For example, the equation dydx=kx can be written as dy=kxdx. Differential Equations are equations involving a function and one or more of its derivatives. That explains why they’re called differential equations rather than derivative equations. ), This DE has order 1 (the highest derivative appearing Recall that a differential equation is an equation (has an equal sign) that involves derivatives. The answer is quite straightforward. Consider the following differential equation: (1) b. It is the same concept when solving differential equations - find general solution first, then substitute given numbers to find particular solutions. We substitute these values into the equation that we found in part (a), to find the particular solution. Second order DEs, dx (this means "an infinitely small change in x"), d\theta (this means "an infinitely small change in \theta"), dt (this means "an infinitely small change in t"). But where did that dy go from the (dy)/(dx)? We can place all differential equation into two types: ordinary differential equation and partial differential equations. This will involve integration at some point, and we'll (mostly) end up with an expression along the lines of "y = ...". Example 4: Deriving a single nth order differential equation; more complex example. It is important to be able to identify the type of Examples: All of the examples above are linear, but$\left(\frac{{\rm d}y}{{\rm d}x}\right)^{\color{red}{2}}=y\$ isn't. called boundary conditions (or initial Differential equations with only first derivatives. The curve y=ψ(x) is called an integral curve of the differential equation if y=ψ(x) is a solution of this equation. Differential equations first came into existence with the invention of calculus by Newton and Leibniz.In Chapter 2 of his 1671 work Methodus fluxionum et Serierum Infinitarum, Isaac Newton listed three kinds of differential equations: = = (,) ∂ ∂ + ∂ ∂ = In all these cases, y is an unknown function of x (or of and ), and f is a given function. %PDF-1.3 These known conditions are We will see later in this chapter how to solve such Second Order Linear DEs. Now we integrate both sides, the left side with respect to y (that's why we use "dy") and the right side with respect to x (that's why we use "dx") : Then the answer is the same as before, but this time we have arrived at it considering the dy part more carefully: On the left hand side, we have integrated int dy = int 1 dy to give us y. ], solve the rlc transients AC circuits by Kingston [Solved!]. In this chapter we will study ordinary differential equations of the standard form below, known as the second order linear equations: y ... the sum / difference of the multiples of any two solutions is again a solution. For example, foxes (predators) and rabbits (prey). In this case, we speak of systems of differential equations. We need to substitute these values into our expressions for y'' and y' and our general solution, y = (Ax^2)/2 + Bx + C. ], Differential equation: separable by Struggling [Solved! In this section we will work a quick example using Laplace transforms to solve a differential equation on a 3rd order differential equation just to say that we looked at one with order higher than 2nd. Here is the graph of our solution, taking K=2: Typical solution graph for the Example 2 DE: theta(t)=root(3)(-3cos(t+0.2)+6). This calculus solver can solve a wide range of math problems. Just as biologists have a classification system for life, mathematicians have a classification system for differential equations. section Separation of Variables), we obtain the result, [See Derivative of the Logarithmic Function if you are rusty on this.). k�לW^kֲ�LU^IW ����^�9e%8�/���9!>���]��/�Uֱ������ܧ�o׷����Lg����K��vh���I;ܭ�����KVܴn��S[1F�j�ibx��bb_I/��?R��Z�5:�c��������ɩU܈r��-,&��պҊV��ֲb�V�7�z�>Y��Bu���63<0L.��L�4�2٬�whI!��0�2�A=�э�4��"زg"����m���3�*ż[lc�AB6pm�\���C�jG�?��C��q@����J&?����Lg*��w~8���Fϣ��X��;���S�����ha*nxr�6Z�*�d3}.�s�қ�43ۙ4�07��RVN���e�gxν�⎕ݫ*�iu�n�8��Ns~. We'll come across such integrals a lot in this section. derivatives or differentials. Sitemap | When we first performed integrations, we obtained a general )/dx}, ⇒ d(y × (1 + x3))dx = 1/1 +x3 × (1 + x3) Integrating both the sides w. r. t. x, we get, ⇒ y × ( 1 + x3) = 1dx ⇒ y = x/1 + x3= x ⇒ y =x/1 + x3 + c Example 2: Solve the following diff… One of the most basic examples of differential equations is the Malthusian Law of population growth dp/dt = rp shows how the population (p) changes with respect to time. For example, fluid-flow, e.g. solution of y = c1 + c2e2x, It is obvious that .(d^2y)/(dx^2)=2(dy)/(dx), Differential equation - has y^2 by Aage [Solved! second derivative) and degree 4 (the power Euler's Method - a numerical solution for Differential Equations, 12. This book is suitable for use not only as a textbook on ordinary differential equations for undergraduate students in an engineering program but also as a guide to self-study. cal equations which can be, hopefully, solved in one way or another. 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# The Problem

In Part 1 of this series, in which I attempt to explain the Denavit-Hartenberg convention for inverse kinematics I talked about coordinate frames and rotational transformations using matrices. This left open a pretty obvious question, though: turning coordinate frames is great and all, but how do we move them? If we want to describe the transformation from Frame 1 to Frame 0 here:

Then we need to express the rotation by the angle $$\theta$$ (which we figured out last time) and the translation by the distance $$d$$ (which we don’t know how to do yet).

To make this a little more clear, let’s look at an example of a translation by a vector $$\vec{t}$$: \begin{align} \vec{v}' &= \vec{v} + \vec{t} \\ \begin{bmatrix} v_1' \\ v_2' \\ v_3' \end{bmatrix} &= \begin{bmatrix} v_1 \\ v_2 \\ v_3 \end{bmatrix} + \begin{bmatrix} t_1 \\ t_2 \\ t_3 \end{bmatrix} \end{align}

Given how we handled rotation matrices last time, we’d really like to find a matrix such that we can write down that translation as a matrix multiplication: $\vec{v}' = \left[ T \right] \, \vec{v}$ For some magical unknown matrix $$\left[ T \right]$$. But…we can’t. You can try. In fact, go for it! It’s a useful exercise, but it’s going to be futile, and we can show that pretty easily. As an example, let’s see what happens if we set $$\vec{v}$$ to be all zeros: $\vec{v}' = \left[ T \right] \, \begin{bmatrix} 0 \\ 0 \\ 0 \end{bmatrix}$ No matter what we set $$\left[ T \right]$$ to be, $$\vec{v}'$$ will always just be zeros. So clearly this method won’t work.

# The Solution: Homogeneous Coordinates

It turns out that there’s a pretty simple fix for this, and it involves adding an extra term to each of our vectors. If we add a 1 to the end of each of our vectors $$\vec{v}$$, then they end up looking like this: $\vec{v} = \begin{bmatrix} v_1 \\ v_2 \\ v_3 \\ 1 \end{bmatrix}$ As it happens, we can now write out our translation matrix $$\left[ T \right]$$ using this coordinate system: \begin{align} \vec{v}' &= \vec{v} + \vec{t} \\ \begin{bmatrix} v_1' \\ v_2' \\ v_3' \\ 1 \end{bmatrix} &= \begin{bmatrix} 1 & 0 & 0 & t_1 \\ 0 & 1 & 0 & t_2 \\ 0 & 0 & 1 & t_3 \\ 0 & 0 & 0 & 1 \end{bmatrix}\, \begin{bmatrix} v_1 \\ v_2 \\ v_3 \\ 1 \end{bmatrix} \end{align} If we write out the matrix multiplication, then we get the following equations: \begin{align} v_1' &= v_1 + t_1 \\ v_2' &= v_2 + t_2 \\ v_3' &= v_3 + t_3 \end{align} which is exactly what we wanted! Rotations also work just fine in this coordinate system: $\vec{v}' = \begin{bmatrix} \cos{\theta_{1 1}} & \cos{\theta_{1 2}} & \cos{\theta_{1 3}} & 0 \\ \cos{\theta_{2 1}} & \cos{\theta_{2 2}} & \cos{\theta_{2 3}} & 0 \\ \cos{\theta_{3 1}} & \cos{\theta_{3 2}} & \cos{\theta_{3 3}} & 0 \\ 0 & 0 & 0 & 1 \end{bmatrix} \, \begin{bmatrix} v_1 \\ v_2 \\ v_3 \\ 1 \end{bmatrix}$ The real kicker is that we can now combine translation and rotation just by multiplying our matrices together. For example, performing a rotation and then a translation might look like this: $\vec{v}' = \begin{bmatrix} 1 & 0 & 0 & t_1 \\ 0 & 1 & 0 & t_2 \\ 0 & 0 & 1 & t_3 \\ 0 & 0 & 0 & 1 \end{bmatrix} \, \begin{bmatrix} \cos{\theta_{1 1}} & \cos{\theta_{1 2}} & \cos{\theta_{1 3}} & 0 \\ \cos{\theta_{2 1}} & \cos{\theta_{2 2}} & \cos{\theta_{2 3}} & 0 \\ \cos{\theta_{3 1}} & \cos{\theta_{3 2}} & \cos{\theta_{3 3}} & 0 \\ 0 & 0 & 0 & 1 \end{bmatrix} \, \begin{bmatrix} v_1 \\ v_2 \\ v_3 \\ 1 \end{bmatrix}$ We can use the associative property of matrix multiplication to simplify this: \begin{align} \vec{v}' &= \left( \begin{bmatrix} 1 & 0 & 0 & t_1 \\ 0 & 1 & 0 & t_2 \\ 0 & 0 & 1 & t_3 \\ 0 & 0 & 0 & 1 \end{bmatrix} \, \begin{bmatrix} \cos{\theta_{1 1}} & \cos{\theta_{1 2}} & \cos{\theta_{1 3}} & 0 \\ \cos{\theta_{2 1}} & \cos{\theta_{2 2}} & \cos{\theta_{2 3}} & 0 \\ \cos{\theta_{3 1}} & \cos{\theta_{3 2}} & \cos{\theta_{3 3}} & 0 \\ 0 & 0 & 0 & 1 \end{bmatrix} \right) \, \begin{bmatrix} v_1 \\ v_2 \\ v_3 \\ 1 \end{bmatrix} \\ &= \begin{bmatrix} \cos{\theta_{1 1}} & \cos{\theta_{1 2}} & \cos{\theta_{1 3}} & t_1 \\ \cos{\theta_{2 1}} & \cos{\theta_{2 2}} & \cos{\theta_{2 3}} & t_2 \\ \cos{\theta_{3 1}} & \cos{\theta_{3 2}} & \cos{\theta_{3 3}} & t_3 \\ 0 & 0 & 0 & 1 \end{bmatrix} \, \begin{bmatrix} v_1 \\ v_2 \\ v_3 \\ 1 \end{bmatrix} \end{align} Notice how the rotation and translation components of this resulting transformation stay in their own sections of the matrix. We’ll use that nice property to devise a shorthand for this kind of transformation matrix. Let: $\textbf{H} \equiv \begin{bmatrix} R & T \\ 0 & 1 \end{bmatrix} \equiv \begin{bmatrix} \cos{\theta_{1 1}} & \cos{\theta_{1 2}} & \cos{\theta_{1 3}} & t_1 \\ \cos{\theta_{2 1}} & \cos{\theta_{2 2}} & \cos{\theta_{2 3}} & t_2 \\ \cos{\theta_{3 1}} & \cos{\theta_{3 2}} & \cos{\theta_{3 3}} & t_3 \\ 0 & 0 & 0 & 1 \end{bmatrix}$ Where R represents the rotation component and T represents the translation component.

# Next time: putting it all together

In the next installment, we’ll use all of this coordinate transformation business to build a system that will let us figure out how to control our robot’s arm.

09 June 2012


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# New branches of math? [closed]

I have been wondering if math would be more enjoyable, if one was able to start a new field and come up with all the definitions, methods, etc. rather than starting where someone else ended. Consequently, I was wondering if any of you guys had in mind an unexplored, physically motivated and seemingly simple question that could possibly become a rich mathematical theory when studied (for example percolation theory and knot theory)? If not, do you know any really new mathematical fields (with again, simple real world motivations) that are coming into development?

Thanks,

Scott

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This is a bit too soft... and at this late an age, the likelihood of finding something "unexplored" looks rather small to me. The well-established portions of mathematics have quite a number of unsolved problems as it is, in any event... –  Ｊ. Ｍ. Aug 18 '11 at 9:14
@J.M "and at this late an age, the likelihood of finding something "unexplored" looks rather small to me" -- Really? We've been discovering new mathematics for most of the last century (chaotic dynamics, percolation theory, knot theory, noncommutative geometry, information theory, quantum computing, ...) even if some mathematicans don't yet recognise them as mathematics. I don't see why this wouldn't continue. –  Chris Taylor Aug 18 '11 at 9:37
I would imagine most things with ‘simple real world motivations’ are already well-developed. Sometimes so much so that they aren't even counted as mathematics any more, like computer science. Also, consider reading this paper of Gowers: The two cultures of mathematics. –  Zhen Lin Aug 18 '11 at 9:44
@Chris: I said the likelihood is "small", not zero. :) –  Ｊ. Ｍ. Aug 18 '11 at 9:51
@J.M., Small like $1 - \varepsilon\,$? ;-) –  cardinal Aug 18 '11 at 13:13


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# inverse of scalar multiplier in ECC

I am learning to use ECC. i got into situation where i have $Q=abG$, where $G$ is the generator of the finite field formed on EC using a prime $p$ modulus and $a$ , $b$ are random numbers. now suppose i know $Q$, $G$ and $a$ , calculating $bG=\text{inverse}(a)Q$ is efficient ? i know the order of the group too. i want to know whether this inverse calculation is cheap enough to be calculated as frequently as random number changes?

i tried to get material for this kind of inverse calculation but dint get as such. If anyone could provide some source to this information on ECC it'll be helpfull.

@Rohith I suppose that $G$ and $Q$ are points on the curve and you mean that $G$ is a generator of your elliptic curve group? Then to compute $bG$ you simply compute $a^{-1}$ as the multiplicative inverse of $a$ in $Z_p$ and compute $bG=a^{-1}Q$ using your scalar multiplier. – DrLecter Jan 22 '14 at 9:43
My mistake. You're right. A simple modular inverse should do the trick. Computing a modular inverse costs about 10% of a scalar multiplication $aQ$. So computing $a^{-1}Q$ is dominated by the cost of multiplying $Q$ with $a$. – CodesInChaos Jan 22 '14 at 9:55


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# 7.1: Writing Expressions and Equations

Difficulty Level: At Grade Created by: CK-12

## Introduction

Riding the T

Kara and her twin brother Marc are going to be spending one month in Boston with their grandparents. They are very excited! Not only is it summer in Boston and the weather will be terrific, but Boston has a fantastic subway system called the T and they will be able to ride it to get all around.

Kara is very excited about visiting the museums, but Marc, who is a huge baseball, fan is hoping for a trip to Fenway Park before the month is up. Seeing the Red Sox play would be a huge bonus!

On the first day, the twins’ Grandpa tells them that they are going to spend the day learning how to ride the subway. Given that the twins are 14 and that they will be traveling together, Grandpa feels comfortable that they will be fine. After a quick discussion on safety, they are ready to go.

Grandpa says that each ride on the subway will cost .85 for a teenager. They will be riding to the Boston Common and back, and they may take another ride too.

Kara goes upstairs to get her money and tries to figure out how much they will need in all. She is having a tough time because she doesn’t know how many train rides they will take in all. She tells Marc what she is trying to figure out.

“Well until we know the number of rides, you can’t figure out the total,” he says. “But you can write an expression.”

An expression? How can Kara do this? What does an expression mean? Why would you want one?

This lesson is all about expressions and equations. Learning how to write expressions can be very helpful when you have a variable that can change, such as the number of train rides. Pay attention and at the end of the lesson you will be able to help Kara write an expression to show the amount of money needed for multiple train rides.

What You Will Learn

In this lesson, you will learn how to do the following:

• Write addition and subtraction phrases as single-variable expressions.
• Write multiplication and division phrases as single-variable expressions.
• Write single variable equations from verbal models.
• Model real-world situations with simple equations.

Teaching Time

I. Write Addition and Subtraction Phrases as Single-Variable Expressions

An expression shows how numbers and/or variables are connected by operations, such as addition, subtraction, multiplication, and division. Notice in the examples that an expression does not have an equal sign. This is because the value of the variable in each expression can change, or you could say that we can evaluate an expression using different given values for the variable.

5024a12z4x3\begin{align*}& 50-2 && 4-a && 12z && \frac{4x}{3}\end{align*}

Three of the expressions above include variables, such as a,z\begin{align*}a, z\end{align*}, and x\begin{align*}x\end{align*}.

An expression that includes one or more variables is called an algebraic expression. Each variable in an algebraic expression can have a different value. Once again, you will not see an equal sign with an algebraic expression. We can use algebraic expressions to represent words or phrases.

Often in word problems or in other situations in math, you will be given a set of words or a phrase that you will need to rewrite as an expression. When you do this, you will be looking for words that mean different operations or things in math. This way you can write an expression that correctly represents the words or phrase.

1 plus a\begin{align*}a\end{align*} 1+a\begin{align*}1+a\end{align*} 4 less d\begin{align*}d\end{align*} 4d\begin{align*}4-d\end{align*}
2 and b\begin{align*}b\end{align*} 2+b\begin{align*}2+b\end{align*} 6 less than g\begin{align*}g\end{align*} g6\begin{align*}g-6\end{align*}
3 more than c\begin{align*}c\end{align*} 3+c\begin{align*}3+c\end{align*} h\begin{align*}h\end{align*} fewer than 7 7h\begin{align*}7-h\end{align*}

The bolded key words in the phrases above provide clues about whether or not you should write an addition or a subtraction expression. While key words can be a helpful guide, it is important not to rely on them totally. It is always most important to think about which operation makes the most sense for a particular situation.

Write these key words in your notebook and then continue with the first example.

Example

Abdul has 5 more than Xavier has. Let x\begin{align*}x\end{align*} stand for the number of dollars Xavier has. Write an algebraic expression to show the number of dollars Abdul has. The phrase is “5 more than Xavier.” Use a number, an operation sign, or a variable to represent each part of that phrase.

5 more than Xavier 5 +x\begin{align*}& \ \underline{5} \ \underline{more \ than} \ \underline{Xavier}\\ & \downarrow \qquad \quad \downarrow \qquad \quad \ \downarrow\\ & \ 5 \qquad \ \ + \qquad \quad x\end{align*} Notice that in this phrase, the key words “more than” means you should write an addition expression. So, the expression \begin{align*}5+x\end{align*} represents the number of dollars Abdul has. We also could have written this as. \begin{align*}x+5\end{align*} because addition is commutative. That means, the order in which numbers are added does not matter. Our answer is \begin{align*}x+5\end{align*}. Example 6 less than a number Notice the key phrase “less than” which means subtraction. "A number" means a variable. Because it says “6 less than a number,” the 6 will follow the variable. \begin{align*}x-6\end{align*} Our answer is \begin{align*}x-6\end{align*}. Remember, sometimes writing an expression is not as simple as relying on key words. Example Lian is \begin{align*}x\end{align*} inches shorter than Hannah. Hannah is 65 inches tall. Write an algebraic expression to show Lian's height in inches. The phrase is “\begin{align*}x\end{align*} inches shorter than Hannah.” You also know that Hannah's height is 65 inches. There are no key words, so you need to think about what makes sense. If Lian is shorter than Hannah, her height will be less than 65 inches. So, write a subtraction expression. Use 65 to represent Hannah's height. Since Lian's height is less than Hannah's height, you will need to subtract \begin{align*}x\end{align*} inches from Hannah's height to represent Lian's height. \begin{align*}& \underline{x} \ inches \ \underline{shorter \ than} \ \underline{Hannah}.\\ & \Box \qquad \qquad \quad \downarrow \qquad \qquad \ \Box\\ & \Box \qquad \qquad \quad \downarrow \qquad \qquad \ \Box\\ & \Box \qquad \qquad \quad \downarrow \qquad \qquad \ \Box\\ & 65 \qquad \qquad \quad - \qquad \qquad x\end{align*} The answer is \begin{align*}65-x\end{align*}. 7A. Lesson Exercises Write an expression for each phrase. 1. A number plus five 2. Six more than a number 3. Fifteen less than a number Take a few minutes to check your answers with a friend. II. Write Multiplication and Division Phrases as Single-Variable Expressions Just as you can write addition and subtraction expressions from words or phrases, you can also write multiplication and division expressions. Once again, you can use key words to help you with this. The more familiar you become with the key words that identify a multiplication or division expression, the better you will become at writing expressions. Here are some examples of how words or phrases can be translated into multiplication or division expressions. Multiplication Expressions Division Expressions 9 times \begin{align*}k\end{align*} \begin{align*}9 \times k \ \ \text{or} \ \ 9k\end{align*} 8 divided into \begin{align*}n\end{align*} groups \begin{align*}8 \div n \ \ \text{or} \ \ \frac{8}{n}\end{align*} twice as much as \begin{align*}m\end{align*} \begin{align*}2 \times m \ \ \text{or} \ \ 2m\end{align*} \begin{align*}q\end{align*} shared equally by 3 people \begin{align*}q \div 3 \ \ \text{or} \ \ \frac{q}{3}\end{align*} half of \begin{align*}r\end{align*} \begin{align*}r \div 2 \ \ \text{or} \ \ \frac{r}{2}\end{align*} one-third of \begin{align*}p\end{align*} \begin{align*}p \div 3 \ \ \text{or} \ \ \frac{p}{3}\end{align*} The bolded key words in the phrases above provide clues about whether you should write a multiplication or a division expression. Remember, key words can be a helpful guide, but you should always think about which operation makes sense for a particular situation. Write these key words in your notebook and then continue with the lesson. Example Write an algebraic expression to represent this phrase: 3 times a number, \begin{align*}t\end{align*}. The phrase is “3 times a number, \begin{align*}t\end{align*}.” Use a number, an operation sign, or a variable to represent each part of that phrase. \begin{align*}& \underline{3} \ \underline{times} \ a \ \underline{number, \ t}\\ & \downarrow \quad \ \downarrow \qquad \quad \downarrow\\ & \ 3 \quad \times \qquad \ \ t\end{align*} Notice that in this phrase, the key word “times” means you should write a multiplication expression. So, the expression \begin{align*}3 \times t\end{align*} or \begin{align*}3t\end{align*} represents the phrase. We also could have written this as \begin{align*}t \times 3\end{align*} because multiplication is commutative. That means that the order in which numbers are multiplied does not matter. Example Mr. Warren separated 30 students into \begin{align*}n\end{align*} equal groups. Write an algebraic expression to represent the number of students in each group. The phrase is “separated 30 students into \begin{align*}n\end{align*} equal groups.” Think about what makes sense. Separating 30 students into \begin{align*}n\end{align*} equal groups means dividing 30 students into \begin{align*}n\end{align*} equal groups. So, write a division expression. \begin{align*}& separated \ \underline{30 \ students} \ \underline{into} \ \underline{n \ equal \ groups}\\ & \qquad \qquad \qquad \downarrow \qquad \qquad \downarrow \qquad \qquad \downarrow\\ & \qquad \qquad \qquad 30 \qquad \quad \ \div \qquad \quad \ \ n\end{align*} Division is not commutative. The order in which we divide numbers matters. So, while \begin{align*}30 \div n\end{align*} represents the number of students in each group, \begin{align*}n \div 30\end{align*} does not. The answer is \begin{align*}30 \div n\end{align*}. 7B. Lesson Exercises Write a multiplication or division expression for each phrase. 1. Four times a number 2. Sixteen divided into a number of groups 3. The product of five and a number Take a few minutes to check your answers with a neighbor. III. Write Single Variable Equations from Verbal Models What is the difference between an equation and an expression? Well, an expression is a phrase without an equal sign. This means that the variable in an expression can be changed and the expression can be evaluated differently. An equation has an equal sign. Therefore one side of an equation is equal to a value on the other side. Now, let's examine how to write equations. The same key words that helped you write expressions may also help you write equations. Here are some additional key words that you may find helpful. Key Words for Addition or Multiplication Equations Key Words for Subtraction Equations Key Words for Division Equations how many all together how many in all how many total how many more how many fewer how many left how much change how many in each Take a few minutes to write down these key words and phrases in your notebook. Example 4 times a number is twelve. First, notice that we have the word “times” which means to multiply. We also have the word “is” which is a key word for equals. \begin{align*}4 \ times \ x=12\end{align*} The equation is \begin{align*}4x=12\end{align*}. Example Seven less than a number is fourteen. First, notice we have the words “less than” which means subtraction. Then we have the word “is” which is a key word for equals. \begin{align*}x-7=14\end{align*} The answer is \begin{align*}x-7=14\end{align*}. 7C. Lesson Exercises Write an equation for each verbal phrase. 1. Six and a number is twenty. 2. Eighteen divided by a number is three. 3. Five times a number is twenty-five. Take a few minutes to check your answers. IV. Model Real-World Situations with Simple Equations We can also apply this to word problems that represent real life situations. Example Kelvin has twice as many stamps in his collection as Murray has in his. If Kelvin has 60 stamps in his collection, write an equation to represent \begin{align*}m\end{align*}, the number of stamps in Murray's collection. Use a number, an operation sign, a variable, or an equal sign to represent each part of the problem. Since Kelvin has 60 stamps in his collection, represent the number of stamps in Kelvin's collection as 60. \begin{align*}& \underline{Kelvin} \ \underline{has} \ \underline{twice \ as \ many \ stamps ... as \ Murray}.\\ & \downarrow \qquad \quad \downarrow \qquad \qquad \qquad \downarrow\\ & 60 \qquad \ = \qquad \qquad \quad \ 2m\end{align*} This equation \begin{align*}60=2m\end{align*}, represents \begin{align*}m\end{align*}, the number of stamps in Murray's collection. Example Carrie made 3 liters of lemonade for a party. After the party, she had 0.5 liter of lemonade left. Write an equation to represent \begin{align*}n\end{align*}, the number of liters of lemonade that her guests drank. Use a number, an operation sign, a variable, or an equal sign to represent each part of that problem. Since the question tells us how many liters of lemonade were left after the party, write a subtraction equation. Since she had 0.5 liter of lemonade left, \begin{align*}n\end{align*} is the number of liters that were drunk at the party. For this problem, it may help to write an equation in words and then translate those words into an algebraic equation. \begin{align*}& (\text{number of liters made}) \ - \ (\text{number of liters guests drank}) \ = \ (\text{number of liters left})\\ & \qquad \downarrow \qquad \qquad \qquad \qquad \ \downarrow \qquad \qquad \qquad \downarrow \qquad \qquad \qquad \qquad \ \downarrow \qquad \qquad \quad \downarrow\\ & \qquad \ 3 \qquad \qquad \qquad \qquad - \qquad \qquad \ \ \ \ \ n \qquad \qquad \qquad \quad \ \ = \qquad \qquad \ 0.5\end{align*} This equation, \begin{align*}3-n=0.5\end{align*}, represents \begin{align*}n\end{align*}, the number of liters of lemonade that Carrie's guests drank during the party. ## Real Life Example Completed Riding the T Here is the original problem once again. Reread it and underline any important information. Kara and her twin brother Marc are going to be spending one month in Boston with their grandparents. They are very excited! Not only is it summer in Boston and the weather will be terrific, but Boston has a fantastic subway system called the T and they will be able to ride it to get all around. Kara is very excited about visiting the museums, but Marc, who is a huge baseball fan, is hoping for a trip to Fenway Park before the month is up. Seeing the Red Sox play would be a huge bonus! On the first day, the twins’ Grandpa tells them that they are going to spend the day learning how to ride the subway. Given that the twins are 14 and that they will be traveling together, Grandpa feels comfortable that they will be fine. After a quick discussion on safety, they are ready to go. Grandpa says that each ride on the subway will cost .85 for a teenager. They will be riding to the Boston Common and back, and they may take another ride too. Kara goes upstairs to get her money and tries to figure out how much they will need in all. She is having a tough time because she doesn’t know how many train rides they will take in all. She tells Marc what she is trying to figure out. “Well until we know the number of rides, you can’t figure out the total,” he says. “But you can write an expression.” An expression? How can Kara do this? What does an expression mean? Why would you want one? Now that you know what an expression is, you can write one to help Kara figure out the amount of money based on the number of train rides. The amount of money per ride does not vary. It costs .85 per ride for a teenager. The number of train rides does vary. This is where a variable is very useful. It can change according to the number of train rides. Let’s use \begin{align*}x\end{align*}. The expression is \begin{align*}.85x\end{align*}. If Kara changes the variable \begin{align*}x\end{align*} according to the number of train rides that she and Marc take, then she can figure out the cost per day of riding the train. If they go on four train rides for example, here is the expression. .85(4) Evaluating this expression, the cost would be3.40.

Expressions are very helpful for figuring out different problems with changeable parts like this one.

## Vocabulary

Here are the vocabulary words that are found in this lesson.

Expression
a number sentence with variables, numbers and operations.
Variable
a letter used to represent an unknown quantity.
Algebraic Expression
a combination of multiple variables, numbers and operations.
Equation
a number sentence with an equal sign where the quantity on one side of the equals is the same as the quantity on the other side.

## Time to Practice

Directions: Write an expression for each phrase.

1. 5 more than a number

2. A number plus six

3. 8 and a number

4. Seven less than a number

5. Eight take a way four

6. Nine more than a number

7. The product of four and a number

8. Six times a number

9. Twelve times a number

10. Fourteen divided by a number

Directions: Write a simple equation for each phrase.

11. Four and a number is twelve

12. Sixteen divided by a number is two.

13. The product of five and a number is thirty.

14. Eight times a number is sixty-four.

15. Nine times a number is ninety.

16. Five less than a number is ten.

17. Eight take away four is a number.

18. Twenty divided by a number is four.

19. Eighty divided by a number is four.

20. Seventeen less than a number is thirty.

Directions: Write an algebraic expression for each situation below.

21. Arturo has 8 fewer stickers in his collection than Julissa has in hers. Let \begin{align*}j\end{align*} represent the number of stickers in Julissa's collection. Write an expression to represent the number of stickers in Arturo's collection.

22. Let \begin{align*}c\end{align*} represent the number of cookies on a plate. Three friends share all the cookies on the plate equally. Write an expression to represent the number of cookies each friend receives.

23. Carly is twice as old as her sister. Let \begin{align*}s\end{align*} represent her sister's age in years. Write an expression to represent Carly's age in years.

24. The length of a rectangle is 3 inches more than its width. Let \begin{align*}w\end{align*} stand for the width in inches. Write an expression to represent the length in inches.

Directions: Write an algebraic equation for each word problem below.

25. The chorus teacher divides all the students in the chorus into 3 equal groups. Each of the groups has 6 students in it. Write an equation that could be used to represent \begin{align*}n\end{align*}, the total number of students in the chorus.

26. Matt's dog weighs 30 pounds. His dog weighs 20 pounds more than his cat. Write an equation that could be used to represent \begin{align*}c\end{align*}, the weight, in pounds, of Matt's cat.

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