Followup to Atmospheric Scattering—Part 1

This post is the first in a series to fol­low-​up on my 2012 GPU Pro 3 arti­cle about atmos­pher­ic scat­ter­ing [11]. What I showed there was a full sin­gle-​scat­ter­ing solu­tion for a plan­e­tary atmos­phere run­ning in a pix­el shad­er, dynam­ic and in real time, with­out pre-​com­pu­ta­tion or sim­pli­fy­ing assump­tions. The key to this achieve­ment was a nov­el and effi­cient way to eval­u­ate the Chap­man func­tion [2], hence the title. In the time since then I have improved on the algo­rithm and extend­ed it to include aspects of mul­ti­ple scat­ter­ing. The lat­ter caus­es hor­i­zon­tal dif­fu­sion (twi­light sit­u­a­tions) and ver­ti­cal dif­fu­sion (deep atmos­pheres), and nei­ther can be ignored for a gen­er­al atmos­phere ren­der­er in a space game, for exam­ple.

I have writ­ten a Shader­toy that reflects the cur­rent state of affairs. It’s a mini flight sim­u­la­tor that also fea­tures clouds, and oth­er ren­der­ing good­ies. A WebGL2 capa­ble brows­er is need­ed to run it. Under Win­dows, the ANGLE/Direct3D trans­la­tor may take a long time to com­pile it (up to a minute is noth­ing unusu­al, but it runs fast after­wards). When suc­cess­ful­ly com­piled it should look like this:
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So, where are the stars?

In my pre­vi­ous rant about dynam­ic expo­sure in Elite Dan­ger­ous (which hon­est­ly applies to any oth­er space game made to date), I made a rough cal­cu­la­tion to pre­dict the bright­ness of stars as they should real­is­ti­cal­ly appear in pho­tos tak­en in out­er space. My pre­dic­tion was, that,

  • for an illu­mi­na­tion of sim­i­lar strength to that on earth,
  • if the sun­lit parts are prop­er­ly exposed,
  • and with an angu­lar res­o­lu­tion of about 2 arc min­utes per pix­el,

then the pix­el-val­ue of a promi­nent star should be in the order of 1 to 3 (out of 255, in 8-bit sRGB encod­ing). Since then I was curi­ous to find some real world val­i­da­tion for that fact, and it seems I have now found it.

ISS_and_Endeavour_EV+0

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Elite Dangerous: Impressions of Deep Space Rendering

I am a backer of the upcom­ing Elite Dan­ger­ous game and have par­tic­i­pat­ed in their pre­mi­um beta pro­gramme from the begin­ning, pos­i­tive­ly enjoy­ing what was there at the ear­ly time. ‘Pre­mi­um beta’ sounds like an oxy­moron, pay­ing a pre­mi­um for an unfin­ished game, but it is noth­ing more than pur­chas­ing the same backer sta­tus as that from the Kick­starter cam­paign.

I came into con­tact with the orig­i­nal Elite dur­ing christ­mas in 1985. Com­pared with the progress I made back then in just two days, my recent per­for­mance in ED is lousy; I think my com­bat rat­ing now would be ‘com­pe­tent’.

But this will not be a game­play review, instead I’m going to share thoughts that were inspired while play­ing ED, most­ly about graph­ics and shad­ing, things like dynam­ic range, sur­face mate­ri­als, phase curves, ‘real’ pho­tom­e­try, and so on; so … after I loaded the game and jumped through hyper­space for the first time (actu­al­ly the sec­ond time), I was greet­ed by this screen fill­ing disk of hot plas­ma:

ED001

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Journey into the Zone (Plates)

I have exper­i­ment­ed recent­ly with zone plates, which are the 2-D equiv­a­lent of a chirp. Zone plates make for excel­lent test images to detect defi­cien­cies in image pro­cess­ing algo­rithms or dis­play and cam­era cal­i­bra­tion. They have inter­est­ing prop­er­ties: Each point on a zone plate cor­re­sponds to a unique instan­ta­neous wave vec­tor, and also like a gauss­ian a zone plate is its own Fouri­er trans­form. A quick image search (google, bing) turns up many results, but I found all of them more or less unus­able, so I made my own.

Zone Plates Done Right

I made the fol­low­ing two 256×256 zone plates, which I am releas­ing into the pub­lic so they can be used by any­one freely.

Cosine zone plate with constrast weighting

Cosine zone plateCC0

Zone plates with contrast weighting

Sine zone plateCC0

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Cloud rendering and the relativity of whiteness

Here are some philo­soph­i­cal and ren­der­ing-relat­ed ques­tions that I took home from the last vaca­tion. What’s the col­or of clouds? The stan­dard answer would be, white.
What’s the col­or of snow? Again, white. Ok, then look at the fol­low­ing pic­ture, where the snow seems con­sid­er­ably whiter. This is the case in almost all pho­tos that I took.

There is an image on Wikipedia from the same gen­er­al area on which the bright­ness dif­fer­ence between clouds vs snow is even more pro­nounced. If you look at the direct­ly lit parts of the snow and con­sid­er it white (#ffffff), then the direct­ly lit parts of the clouds are at most 50% grey (#bbbbbb). Is that an evi­dence of air pol­lu­tion? Unlike­ly! (At least not in Tyrol).

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