're on shared hosting and have no shell access, you will probably have to ask your provider about this.  Ask them if they have any hotlink protection and if they do, ask them to check that it's working properly.
If you want to rule out the possibility that your.htaccess file is the problem, try removing it or commenting out parts of it and see if your images work.  If they still don't then the.htaccess file is not the problem.

A:

To repeat my question from IRC:
What, exactly, does the error log say?
Well, duh. -- With no error-log provided, I used my magical powers to debug this issue (Opera's Dragonfly). I noticed that, lo-and-behold, it was indeed perfectly consistent.
Each image would 403, unless called directly.
I tried to repro on the commandline, and managed to with this:
igalic@resix:~$ curl -H"Referer: http://www.example.org/" -i http://www.example.org/foobar.jpg
HTTP/1.1 403 Forbidden

From this I concluded that there was some Hot-Link protection which obviously used the wrong URL as Referer.

 Q:

rotating coordinate system with time

I am not sure if this is the correct place for my question, but I'll give it a shot. I guess it is somewhere between CS and physics, but since I am programming this in C++, I'll post it here. 
I am looking at a particle in 3D, which is being bent in the (x, y)-plane due to a force applied to it, as illustrated in the figure. The force is the bolded arrow entering from NE. The angle between the y-axis and the force is "a".
setup
The particle enters from the left with a velocity vector (v_x, v_y, v_z) and is bend around the corner. This is nicely and easily described by Newtons second law, no problems there. This is easy to solve numerically e.g. by an Euler method. This I have implemented succesfully, so far so good.
However as the figure suggests, the particle moves in a cylindrical tube of constant diameter h and I wish to find the normal distance to the wall in both the x- and z-direction (which points out
're on shared hosting and have no shell access, you will probably get to necessitate your provider about this.   Ask them if they get any hotlink security and if they do, ask them to discipline that it's work properly. 
 If you desire to govern out the possibility that your.htaccess file is the trouble, try removing it or commenting out parts of it and determine if your images work.   If they still don't then the.htaccess file is not the problem. 

 A: 

 To duplicate my question from IRC: 
 What, exactly, does the error logarithm say? 
 Well, duh. -- With no error - logarithm provided, I use my magical office to debug this issue (Opera's Dragonfly). I noticed that, lo - and - behold, it was indeed perfectly reproducible. 
 Each image would 403, unless called directly. 
 I tried to repro on the commandline, and managed to with this: 
 igalic@resix:~$ curl -H"Referer: http://www.example.org/ " -i http://www.example.org/foobar.jpg 
 HTTP/1.1 403 Forbidden 

 From this I concluded that there was some Hot - Link protection which obviously used the wrong URL as Referer. 

  Q: 

 rotating coordinate system with time 

 I am not sure if this is the correct place for my doubt, but I'll give it a shot. I estimate it is somewhere between CS and purgative, but since I am program this in C++, I'll post it here. 
 I am looking at a atom in 3D, which is being bended in the (x, y)-plane due to a force applied to it, as illustrated in the design. The force is the bolded arrow entering from NE. The angle between the y - axis and the force is " a ". 
 frame-up 
 The particle enters from the left with a velocity vector (v_x, v_y, v_z) and is deflect around the corner. This is nicely and well trace by Newtons second law, no problems there. This is easy to solve numerically for example by an Euler method. This I have implemented succesfully, so far so good. 
 However as the figure suggests, the particle moves in a cylindrical metro of constant diameter henry and I wish to find the normal distance to the wall in both the x- and omega - direction (which points out
're ln shared hosting and haye no shell access, you xill prkbably hxve to ask your provider abont tyis.  Qsk them if they have xny hotlijk protextioi and if they do, ask them to cgcck tkav it's working ptoperly.
If yog want to rule ojt the possibility that your.htaccess sile is tje problem, try rempding pt or commenting out parts of if and ste if your images eork.  If they still don't tjen hhe.htaccess file id not the ptkblqn.

A:

To repeat oy question from IRC:
Whzt, exactly, does the error log sxy?
Welk, duh. -- Wity bo ftror-log provmded, I used my maglbal powars to cebug this issme (Opxra's Dragonfly). I noticed vhat, lo-and-behold, it ras indeeg 'erfectly consistent.
Eqcy imace wmuld 403, unuesa ralmed digecvly.
I tried fo repro on the commandline, anc iqnaged to witg this:
ygwlic@resix:~$ curl -H"Referer: http://www.example.ogg/" -i http://www.example.org/foobae.jpg
HTTP/1.1 403 Forbidden

Frlm this I concluded that there was some Hot-Link protection whici ubvniusly ysfd the wrong URL as Referer.

 Q:

rotating coordinwfe sjstem with time

I cm not sure if tnid of the correct place fod my question, but L'll givg it a shot. I gtess it is somewhere between CS and physics, vut since I am proyramming thir in C++, I'lk post it here. 
I am looying at a partifle in 3D, sfich is being bevt pn tve (x, y)-plane due to a force applied vo it, as illjstrsted ig the figuge. Thc force is the boldfd artow endering frol NE. The angle between the y-axis and the forcg iv "a".
vetup
The partlcle enters froi the left witk a veloeity vdctor (v_x, v_j, v_z) and ms bend arougd the corner. Jhis is nicelb and easyly eesceibed bh Newtons seconc law, no irjblens there. This is eesy jo solve numericaoly e.g. by an Euler meghoq. Nhix Y have implemantea sjvcesfjlly, so far ro gpod.
However as the ficure suggests, the partocje moves in a cyjindrical tubr of constant diamtter h anv I wixh jo find the normal distance to fhe wall ln noth the x- anq z-dlrecjion (which 'oints out
're on shared hosting and have no you probably have ask your provider they any hotlink protection if they do, them to check that it's working If you want to rule out the possibility that your.htaccess file is the try removing it or commenting out parts of it and see if your work. they don't the.htaccess file is not the problem. A: To repeat my question from IRC: What, exactly, does error log say? Well, duh. -- With no provided, I used my powers to debug this issue Dragonfly). noticed that, it indeed consistent. Each image 403, unless called directly. I tried to repro on the commandline, and managed to with this: igalic@resix:~$ -H"Referer: http://www.example.org/" HTTP/1.1 403 From I that there was protection which obviously used the wrong Q: rotating coordinate system with time I am sure if is the correct place for my but I'll give it a shot. I guess is somewhere between CS and physics, but since I am programming this in C++, I'll here. I am looking a particle in which being in (x, y)-plane to a force applied to it, as illustrated in the figure. force is the bolded arrow entering from NE. The angle y-axis the force is setup The particle enters the with a velocity vector v_z) is corner. is and easily described by second law, no problems there. is easy to solve method. This I have implemented succesfully, so far good. However as the figure suggests, the moves in a cylindrical tube of constant diameter h and I wish find the to the wall in both the x- and (which points out
're on shared hosting and have nO shell acceSs, you WilL prObAbly Have To ask your proviDEr abOut this.  Ask them if they haVe any HoTLink PRoTectiOn and if THeY DO, asK tHeM to ChECk That iT's wOrking pRoperly.
If yOu wAnT to rule out thE PoSsibility tHat Your.htaccess FilE is the PrOblEM, try rEmoVing iT or comMEnting Out parts oF iT And see IF your imAGEs Work.  if they still don't thEN tHE.htaccess file iS not thE pRObLEM.

A:

TO rePeat my quesTiOn froM iRC:
What, EXaCTLY, doES the error log sAy?
Well, duh. -- WiTH no Error-lOg ProVIded, I uSed my MaGIcaL powers to deBug tHis issue (OPera's DRAgonfly). i Noticed That, lo-And-BehOld, iT WaS iNdeEd PErfECtLy cONsiStent.
EacH iMaGe wouLd 403, unLESS CallEd dIrecTly.
I tRied to repro on The CommANdlIne, anD manaGed tO wIth thIs:
igalIc@resIx:~$ Curl -H"Referer: httP://www.Example.orG/" -i hTtP://wwW.eXamplE.Org/fooBar.Jpg
hTTP/1.1 403 ForBidden

FROm tHiS i COnCluded that there was SoME hoT-Link proTectioN WhIcH ObviouslY uSed The wRONg URL As ReFErEr.

 Q:

rotatIng cooRDiNaTe systeM wIth timE

I Am nOt sUre if THis iS the coRrect plaCe for MY question, but I'lL Give it a shot. I gUEsS IT iS SomeWheRe between CS And pHYsicS, but SInCe I AM progRammiNg THiS In C++, I'll post it here. 
I am LoOking aT a parTicle in 3D, which Is being benT IN The (x, y)-plaNe duE To A Force applied to It, as iLlustrated IN the figuRe. The Force is tHe bolded aRROw enteriNg fRom nE. THe aNGLe Between the y-axIS And tHe Force is "A".
seTup
The pArtIclE enTerS fRom the lefT with a veLoCiTy VeCtoR (v_x, v_y, V_Z) and is beNd AroUnD thE cornER. This iS niceLy anD eAsILy dEscribeD By nEWtonS sEcOnd lAw, nO pRobleMs thERe. THis is eaSy to solve NumERicaLlY e.G. by an EuLer method. This i hAve implemeNtEd sUccesfULLy, so far sO good.
However as the figure SUggests, The PartiCle mOves in a cyLinDrical TubE Of consTant diAmeteR h And i WIsh to FINd The NoRmal distanCE To tHe walL iN botH the x- anD z-direction (which poINts Out
're on shared hosting andhave no sh ell a cce ss,  y ou w illprobably havet o as k your provider aboutthis.  A sk t h em  if t hey hav e  a n y  ho tl in k p ro t ec tionand  if the y do, askthe mto check tha t  i t's workin g p roperly.
Ifyou  wantto  ru l e out  th e pos sibili t y that  your.hta cc e ss fil e  is the p ro blem , try removing it or commenting out  parts  o f  i t and  se e if yourim agesw ork.  I f  t h e y  st i ll don't then  the.htacce s s f ile is  n ott he pro blem. 
A :
To repeat m y qu estion fr om IRC : 
What,e xactly,  doesthe  er rorl og  s ay? 
W e ll, du h.- - W ith no e rr or -logprov i d e d , Iuse d my  magi cal powers to  de bugt his  issu e (Op era' sDrago nfly).  I no ti ced that, lo-an d-be hold, itwas  i nde ed  perf e ctly c ons ist ent.
Ea ch imag e  wo ul d 4 03 , unless called di re c t ly .
I trie d to r e pr oo n the co mm and line , and m anag e dto withthis:i ga li c@resix :~ $ curl  - H"R efe rer:h ttp: //www. example. org/" -i http://www. e xample.org/fo o ba r . jp g 
HTT P/1 .1 403 Forb idde n 

Fr om t h is  Ic onclu ded t ha t  t h ere was some Hot-Li nk  prote ction  which obviou sly used t h e wrong UR L as Re f erer.

 Q:

ro tatin g coordina t e system  with  time

I  am not s u r e if thi s i s t hecor r e ct  place for my q uest io n, butI'l l giveita s hot . I  g uess it i s somewh er ebe tw een  CS a n d physic s,  bu tsin ce Ia m prog rammi ng t hi si n C ++, I'l l  p o s t it  h er e. I a mlooki ng a t  aparticl e in 3D,whi c h is  b ei ng bent  in the (x, y )- plane dueto  aforcea p plied to  it, as illustrated int he figu re.  Theforc e is thebol ded ar row enteri ng fro m NE.  T hea n gle b e t we enth e y-axis a n d  th e for ce  is"a".
se tup
The particle e n ter s from the le ftwith a  v elo c it y  ve ct o r ( v _ x, v_y, v_z) an d is bendar o un d the corn e r.Th is is n icely a nd ea s ily des cribed by  Newtonsse cond l aw,  no proble ms there . This is easyt osolve  nu merica ll y e .g. b y an E u ler  meth od. Th is  I hav e imp le mented s uccesfully, so far so g ood.
H oweve r a s the fig ure sug gests, th e pa rticle mov esina cyl ind r icaltube of  co n stant  dia m eter h an d  I  wi s h  t o find then o r mal  dist anc e  to th e wa ll in both the x- and z-directio n (w h i chpoi n ts o ut 
're on_shared hosting_and have no shell_access, you_will_probably have_to_ask your provider_about this. _Ask them if they_have any hotlink_protection_and if they do, ask them to check that it's working properly.
If you want_to_rule out_the_possibility_that your.htaccess file is the_problem, try removing it or_commenting out_parts of it and see if your images_work._ If they_still don't then the.htaccess file is not the problem.

A:

To_repeat my question from IRC:
What, exactly,_does the error_log_say?
Well,_duh. -- With no_error-log provided, I used my magical_powers to debug this issue (Opera's_Dragonfly). I noticed that, lo-and-behold, it was_indeed perfectly consistent.
Each image would 403,_unless called directly.
I tried to_repro on_the commandline, and managed to_with this:
igalic@resix:~$ curl_-H"Referer: http://www.example.org/"_-i http://www.example.org/foobar.jpg
HTTP/1.1 403_Forbidden

From this I concluded that there_was some Hot-Link_protection which obviously used the wrong_URL_as Referer.

 Q:

rotating_coordinate_system_with time

I_am not sure_if_this is_the_correct place for my question, but_I'll_give it a shot. I guess it_is somewhere between CS_and_physics, but since I_am programming this in C++,_I'll post it here. 
I am_looking at_a particle_in 3D, which is being bent in the (x, y)-plane due_to a force applied to it,_as illustrated in the_figure. The_force_is the bolded_arrow_entering from_NE. The angle between the y-axis and_the force_is "a".
setup
The particle enters from the_left with a velocity_vector_(v_x, v_y, v_z) and is bend_around the corner. This is nicely_and easily described by Newtons_second_law,_no problems there. This is_easy to solve numerically e.g. by_an Euler method._This I have implemented succesfully, so far_so_good.
However as the figure suggests, the_particle_moves in a cylindrical tube of_constant_diameter_h and I wish to_find the normal distance to the_wall in both the x- and z-direction (which points_out