POV-Ray : Newsgroups : povray.off-topic : Too many pipes? Server Time
14 Oct 2026 11:20:36 EDT (-0400)
  Too many pipes? (Message 1 to 50 of 51)  
Goto Latest 50 Messages Next 1 Messages >>>
From: Invisible
Subject: Too many pipes?
Date: 21 Oct 2008 07:10:27
Message: <48fdb8a3@news.povray.org>
Thus far, I have had two seperate dreams involving pipe organs. While I 
was learning about organ terminology, I had a dream about playing a pipe 
organ. When I started learning about the stop names, I had a second 
dream in which I accidentally killed 3 people by choosing a powerful stop.

I just read that the speed of sound in air is around 340 m/s, and that 
an open pipe contains 1/2 of a wave while a stopped pipe contains 1/4 of 
a wave. (Not forgetting the end corrections due to the stationary air 
outside the pipe.) And also that long thin pipes have more harmonics 
than short wide pipes.

All of this has pretty much inevitably ended with... the wave equation.

Yah.

So apparently the wave equation tells us that the 2nd derivative of some 
physical quanitity "u" with respect to time is equal to the square of 
the wave propogation constant multiplied by the Laplacian of "u".

...which would probably mean something if I could figure out what a 
Laplacian is! :-S

According to Wikipedia, the Laplacian of u is the sum of all partial 2nd 
derivatives of u with respect to every coordinate axis.

...so...the total curvature then? ._.


Post a reply to this message

From: scott
Subject: Re: Too many pipes?
Date: 21 Oct 2008 07:19:38
Message: <48fdbaca@news.povray.org>
> All of this has pretty much inevitably ended with... the wave equation.

Hehe, I so knew that was coming.

> So apparently the wave equation tells us that the 2nd derivative of some 
> physical quanitity "u" with respect to time is equal to the square of the 
> wave propogation constant multiplied by the Laplacian of "u".
>
> ...which would probably mean something if I could figure out what a 
> Laplacian is! :-S
>
> According to Wikipedia, the Laplacian of u is the sum of all partial 2nd 
> derivatives of u with respect to every coordinate axis.
>
> ...so...the total curvature then? ._.

Pretty much yeh - the wave equation basically says that the 2nd differential 
in time is proportional to the 2nd differential in space.  Obviously the 2nd 
differential in "space" depends on how many dimensions you are working in, 
but you more or less just sum up the 2nd differential in each dimension.

Thinking of writing a simulator? ;-)


Post a reply to this message

From: Invisible
Subject: Re: Too many pipes?
Date: 21 Oct 2008 07:31:01
Message: <48fdbd75$1@news.povray.org>
scott wrote:
>> All of this has pretty much inevitably ended with... the wave equation.
> 
> Hehe, I so knew that was coming.

Yeah, pretty much.

>> ...so...the total curvature then? ._.
> 
> Pretty much yeh - the wave equation basically says that the 2nd 
> differential in time is proportional to the 2nd differential in space.  
> Obviously the 2nd differential in "space" depends on how many dimensions 
> you are working in, but you more or less just sum up the 2nd 
> differential in each dimension.

Hmm. Seems simple enough...

> Thinking of writing a simulator? ;-)

Well let's put it this way: What do you think my chances of building a 
working set of organ pipes are? :-P Last time I tried to cut wood, I 
couldn't even cut it straight! :-/ I figure I have far more chance of 
building an organ simulator...


Post a reply to this message

From: nemesis
Subject: Re: Too many pipes?
Date: 21 Oct 2008 08:45:00
Message: <web.48fdceae45093b7798a5bb110@news.povray.org>
Some dream, huh?  Only a math/musician to dream of organs and equations... :P


Post a reply to this message

From: Invisible
Subject: Re: Too many pipes?
Date: 21 Oct 2008 08:53:18
Message: <48fdd0be$1@news.povray.org>
nemesis wrote:
> Some dream, huh?  Only a math/musician to dream of organs and equations... :P

For the record: I have never had dreams about equations.

Dreaming about people being killed is unfortunately very typical for me 
though. :-S


Post a reply to this message

From: Invisible
Subject: Re: Too many pipes?
Date: 21 Oct 2008 08:54:57
Message: <48fdd121$1@news.povray.org>
Invisible wrote:

> Hmm. Seems simple enough...

Well, I just implemented it, tried it, and... it doesn't work at all. :-.

Oh, wait... *second* derivative! >_< Damnit...

Oh look, and I've also implemented u = c d2u/dx2 rather than d2u/dt2 = c 
d2u/dx2. I'm doing well here. :-/


Post a reply to this message

From: scott
Subject: Re: Too many pipes?
Date: 21 Oct 2008 09:22:38
Message: <48fdd79e@news.povray.org>
> Hmm. Seems simple enough...
>
>> Thinking of writing a simulator? ;-)
>
> Well let's put it this way: What do you think my chances of building a 
> working set of organ pipes are? :-P Last time I tried to cut wood, I 
> couldn't even cut it straight! :-/

Just practise, and you can buy (or make) some jigs that constrain the saw to 
move exactly straight.  THat way you will get perfect cuts every time.

> I figure I have far more chance of building an organ simulator...

You reckon? Thinking about it, I think you will need to use the 
Navier-Stokes equations, because you need to simulate the velocity of the 
fluid too, not just the pressure. (the velocity of the air stream is what 
causes the pressure differences which in turn cause the flow to oscillate 
between going out of the mouth and staying within the pipe).

Good luck :-)


Post a reply to this message

From: m a r c
Subject: Re: Too many pipes?
Date: 21 Oct 2008 09:30:14
Message: <48fdd966@news.povray.org>
"scott" <sco### [at] scottcom> a écrit dans le message de news: 
48fdd79e@news.povray.org...
> Just practise, and you can buy (or make) some jigs that constrain the saw 
> to move exactly straight.  That way you will get perfect cuts every time.

Let's add that a plane is always meant to be checkered :-)
Marc


Post a reply to this message

From: m a r c
Subject: Re: Too many pipes?
Date: 21 Oct 2008 09:34:11
Message: <48fdda53@news.povray.org>
"m_a_r_c" <jac### [at] wanadoofr> a écrit dans le message de news: 
48fdd966@news.povray.org...
>
> "scott" <sco### [at] scottcom> a écrit dans le message de news: 
> 48fdd79e@news.povray.org...
>> Just practise, and you can buy (or make) some jigs that constrain the saw 
>> to move exactly straight.  That way you will get perfect cuts every time.
>
> Let's add that a plane is always meant to be checkered :-)
> Marc
is NOT always :-s

Marc


Post a reply to this message

From: Invisible
Subject: Re: Too many pipes?
Date: 21 Oct 2008 09:39:14
Message: <48fddb82$1@news.povray.org>
>> Well let's put it this way: What do you think my chances of building a 
>> working set of organ pipes are? :-P Last time I tried to cut wood, I 
>> couldn't even cut it straight! :-/
> 
> Just practise, and you can buy (or make) some jigs that constrain the 
> saw to move exactly straight.  THat way you will get perfect cuts every 
> time.

Frankly, first I need to find a saw that isn't blunt.

(Actually, finding any kind of tool isn't easy. My mum *has* millions of 
tools - every time she goes to start another job, she can never find the 
tool she wants, so she buys a new one. It gets used once, and is never 
found again.)

>> I figure I have far more chance of building an organ simulator...
> 
> You reckon?

I said "chance". :-P

> Thinking about it, I think you will need to use the 
> Navier-Stokes equations.
> 
> Good luck :-)

Actually... it's possibly not directly related, but Wolfram showed a 
trivially simple cellular automaton which has no sophisticated 
properties encoded into it, and isn't even an accurate simulation of any 
physical system, and yet exhibits the same characteristics as a flowing 
liquid. (Most particularly, it has both laminar and turbulent flow.)

This is much simpler to model then exotic differential equations. OTOH, 
it's a few orders of magnitude less efficient too... ;-)


Post a reply to this message

From: Invisible
Subject: Sum ting wong
Date: 21 Oct 2008 10:38:38
Message: <48fde96e$1@news.povray.org>
Invisible wrote:

> All of this has pretty much inevitably ended with... the wave equation.

OK, so I simulated the wave equation and got... this?

Hmm. I started with a green square on a black background. The corners 
lit up, and plausibly wave-like projections radiated out from the 
corners. But... why only those two corners? Why not all four?

I think I must have done something rather wrong here... :-S


Post a reply to this message

From: Invisible
Subject: Re: Sum ting wong
Date: 21 Oct 2008 10:40:10
Message: <48fde9ca$1@news.povray.org>
Invisible wrote:

> OK, so I simulated the wave equation and got... this?

Try including the attachment, dork! :-P


Post a reply to this message


Attachments:
Download 'test.png' (4 KB)

Preview of image 'test.png'
test.png


 

From: scott
Subject: Re: Sum ting wong
Date: 21 Oct 2008 11:08:46
Message: <48fdf07e@news.povray.org>
>> OK, so I simulated the wave equation and got... this?
>
> Try including the attachment, dork! :-P

I made some POV code to simulate the wave equation a long time ago, see 
attached.  Maybe you can compare with your code and see where it's giving 
different answers?

BTW in my version it forces the central point to follow a sine wave up and 
down, and that then causes the circular "ripple" effect outwards.


Post a reply to this message


Attachments:
Download 'us-ascii' (3 KB) Download 'waves.png' (47 KB)

Preview of image 'waves.png'
waves.png


 

From: Invisible
Subject: Re: Sum ting wong
Date: 21 Oct 2008 11:23:58
Message: <48fdf40e$1@news.povray.org>
scott wrote:

> I made some POV code to simulate the wave equation a long time ago, see 
> attached.  Maybe you can compare with your code and see where it's 
> giving different answers?

How did you arrive at

#local XD = waveHeight[X+1][Y] - 2*waveHeight[X][Y] + waveHeight[X-1][Y];

According to my calculations,

   (v[x-1] - v[x]) + (v[x] - v[x+1]) =
   v[x-1] - v[x] + v[x] - v[x+1] =
   v[x-1] - v[x+1]

which is completely different to what you have.


Post a reply to this message

From: Darren New
Subject: Re: Too many pipes?
Date: 21 Oct 2008 12:04:01
Message: <48fdfd71$1@news.povray.org>
Invisible wrote:
> Actually... it's possibly not directly related, but Wolfram showed a 
> trivially simple cellular automaton which has no sophisticated 
> properties encoded into it, and isn't even an accurate simulation of any 
> physical system, and yet exhibits the same characteristics as a flowing 
> liquid. (Most particularly, it has both laminar and turbulent flow.)

Cool. Where did you see this?   I couldn't track down anything obvious 
with Google, due to conflicting hits.

-- 
Darren New / San Diego, CA, USA (PST)


Post a reply to this message

From: Orchid XP v8
Subject: Re: Too many pipes?
Date: 21 Oct 2008 13:22:30
Message: <48fe0fd6$1@news.povray.org>
>> Actually... it's possibly not directly related, but Wolfram showed a 
>> trivially simple cellular automaton which has no sophisticated 
>> properties encoded into it, and isn't even an accurate simulation of 
>> any physical system, and yet exhibits the same characteristics as a 
>> flowing liquid. (Most particularly, it has both laminar and turbulent 
>> flow.)
> 
> Cool. Where did you see this?   I couldn't track down anything obvious 
> with Google, due to conflicting hits.

Wolfram's "A New Kind of Science".

Maddeningly, I've searched and searched the online version, but cannot 
find any reference to this experiment. It definitely appears in the 
paper copy I have though.

(As an aside, I found the book to be somewhat dissapointing. But there 
were one or two very interesting things to be found. This was one of them!)

-- 
http://blog.orphi.me.uk/
http://www.zazzle.com/MathematicalOrchid*


Post a reply to this message

From: Darren New
Subject: Re: Too many pipes?
Date: 21 Oct 2008 14:00:15
Message: <48fe18af$1@news.povray.org>
Orchid XP v8 wrote:
> Maddeningly, I've searched and searched the online version, but cannot 
> find any reference to this experiment. It definitely appears in the 
> paper copy I have though.

Cool. I'll dig thru the index.

> (As an aside, I found the book to be somewhat dissapointing. But there 
> were one or two very interesting things to be found. This was one of them!)

I thought a lot of it was pretty cool, and he did a good job of 
organizing it into "the part you read for fun" and "the part you read if 
you're actually going to do something technical with the results". 
(Unlike several other tomes of this sort I've read.) Altho, yeah, the 
hubris was rather astounding. :-)

I trust you've read Godel-Escher-Bach?

-- 
Darren New / San Diego, CA, USA (PST)


Post a reply to this message

From: Orchid XP v8
Subject: Re: Too many pipes?
Date: 21 Oct 2008 15:42:18
Message: <48fe309a$1@news.povray.org>
>> Maddeningly, I've searched and searched the online version, but cannot 
>> find any reference to this experiment. It definitely appears in the 
>> paper copy I have though.
> 
> Cool. I'll dig thru the index.

Chapter 8, "Implications for everyday systems", section title "Fluid 
Flow", page 376 in my hardback copy.

He shows a cellular automaton consisting of a hexagonal grid. Each cell 
may optionally contain a particle, which can have one of 6 possible 
velocities. (Note that all particles have unit momentum. There is no 
attempt to simulate varying particle speeds.)

When two neighboring cells both contain particles, a simple automaton 
rule defines the new velocities for those particles. (Again, casually 
glossing over a vast swathe of actual phenomina that occur with 
molecular collisions. Here there is no vague attempt at Newton's laws of 
motion, or even intuitive plausibility really.)

Viewed locally, all the particles dance around more or less at random. 
However, if you average over a very large number of particles, you what 
something looking suspiciously like fluid dynamics. Specifically, 
Wolfram demonstrates that if all the particles have random initial 
velocities, the overall net flow is zero. If a large minority of 
particles all move in one direction, and there is an obsticle in the 
way, you get trailing vorticies behind it. And if enough particles are 
made to move the same way, you get real turbulence behind the obsticle.

All this from just individual particles interacting in a very 
physically-incorrect manner. (OTOH, you have to average absurd numbers 
of particles to get this, so it's very ineffient stuff!)

>> (As an aside, I found the book to be somewhat dissapointing. But there 
>> were one or two very interesting things to be found. This was one of 
>> them!)
> 
> I thought a lot of it was pretty cool, and he did a good job of 
> organizing it into "the part you read for fun" and "the part you read if 
> you're actually going to do something technical with the results". 
> (Unlike several other tomes of this sort I've read.) Altho, yeah, the 
> hubris was rather astounding. :-)

It makes some valid points... it's just not very interesting to read.

> I trust you've read Godel-Escher-Bach?

Never heard of it.

-- 
http://blog.orphi.me.uk/
http://www.zazzle.com/MathematicalOrchid*


Post a reply to this message

From: Halbert
Subject: Re: Too many pipes?
Date: 21 Oct 2008 17:08:57
Message: <48fe44e9$1@news.povray.org>
> organ. When I started learning about the stop names, I had a second dream 
> in which I accidentally killed 3 people by choosing a powerful stop.
>

Good thing you haven't been learning bag-pipes. That would have been 
particularly grusome.

-- 
H²


Post a reply to this message

From: Darren New
Subject: Re: Too many pipes?
Date: 21 Oct 2008 19:59:32
Message: <48fe6ce4@news.povray.org>
Orchid XP v8 wrote:
> Chapter 8, "Implications for everyday systems", section title "Fluid 
> Flow", page 376 in my hardback copy.

Thank you!

> All this from just individual particles interacting in a very 
> physically-incorrect manner. (OTOH, you have to average absurd numbers 
> of particles to get this, so it's very ineffient stuff!)

BTW, if you liked Wolfram's thing and you like science fiction, check 
out "Permutation City" by Greg Egan. A very fun geeky read.

> It makes some valid points... it's just not very interesting to read.

I found it pretty interesting, but repetitive. I also really like CAs.

>> I trust you've read Godel-Escher-Bach?
> Never heard of it.

http://www.amazon.com/Godel-Escher-Bach-Eternal-Golden/dp/0465026567

Wow.  I'm not sure why it came up in the conversation, but it's a 
must-read for anyone who enjoys computers and waded thru Wolfram's stuff.

-- 
Darren New / San Diego, CA, USA (PST)


Post a reply to this message

From: scott
Subject: Re: Sum ting wong
Date: 22 Oct 2008 02:27:17
Message: <48fec7c5$1@news.povray.org>
> How did you arrive at
>
> #local XD = waveHeight[X+1][Y] - 2*waveHeight[X][Y] + waveHeight[X-1][Y];
>
> According to my calculations,
>
>   (v[x-1] - v[x]) + (v[x] - v[x+1]) =

That should be a "-" in the middle, because you are taking the differential 
of the differential.


Post a reply to this message

From: scott
Subject: Re: Sum ting wong
Date: 22 Oct 2008 02:30:33
Message: <48fec889$1@news.povray.org>
>   (v[x-1] - v[x]) + (v[x] - v[x+1]) =

Oh, and just for clarity, you should probably write that as:

(v[x+1]-v[x]) - (v[x]-v[x-1])

rather than:

(v[x-1]-v[x]) - (v[x]-v[x+1])

In your case it makes no difference because you are differentiating twice, 
but in general differentials are usually defined to be positive if v[x] 
increases with x.


Post a reply to this message

From: Invisible
Subject: Re: Too many pipes?
Date: 22 Oct 2008 04:15:16
Message: <48fee114$1@news.povray.org>
>> Chapter 8, "Implications for everyday systems", section title "Fluid 
>> Flow", page 376 in my hardback copy.
> 
> Thank you!

;-)

Well, go implement! :-P

>> It makes some valid points... it's just not very interesting to read.
> 
> I found it pretty interesting, but repetitive. I also really like CAs.

I find CAs to be dull and boring.

>>> I trust you've read Godel-Escher-Bach?
>> Never heard of it.
> 
> http://www.amazon.com/Godel-Escher-Bach-Eternal-Golden/dp/0465026567
> 
> Wow.  I'm not sure why it came up in the conversation, but it's a 
> must-read for anyone who enjoys computers and waded thru Wolfram's stuff.

I actually didn't bother finishing to read it. It didn't have anything 
much interesting to say.


Post a reply to this message

From: Invisible
Subject: Re: Sum ting wong
Date: 22 Oct 2008 04:16:51
Message: <48fee173$1@news.povray.org>
>> How did you arrive at
>>
>> #local XD = waveHeight[X+1][Y] - 2*waveHeight[X][Y] + waveHeight[X-1][Y];
>>
>> According to my calculations,
>>
>>   (v[x-1] - v[x]) + (v[x] - v[x+1]) =
> 
> That should be a "-" in the middle, because you are taking the 
> differential of the differential.

The above formula is only meant to be the 1st derivative. I run it twice 
to get the second derivative.

Except that, as noted, my code fails miserably, whereas the formula you 
used seems to work perfectly for some reason...


Post a reply to this message

From: Invisible
Subject: Re: Too many pipes?
Date: 22 Oct 2008 05:00:41
Message: <48feebb9@news.povray.org>
Darren New wrote:

> http://www.amazon.com/Godel-Escher-Bach-Eternal-Golden/dp/0465026567
> 
> Wow.  I'm not sure why it came up in the conversation, but it's a 
> must-read for anyone who enjoys computers and waded thru Wolfram's stuff.

If it's your thing, I must recommend:

http://www.amazon.co.uk/Linked-Everything-Connected-Business-Everyday/dp/0452284392

It's a really nice book. (E.g., did you know that the software marked is 
like a Bose-Einstine condensate? If you care about such things, you'll 
love this quirky little book...)


Post a reply to this message

From: scott
Subject: Re: Sum ting wong
Date: 22 Oct 2008 05:33:57
Message: <48fef385$1@news.povray.org>
>>>   (v[x-1] - v[x]) + (v[x] - v[x+1]) =
>>
>> That should be a "-" in the middle, because you are taking the 
>> differential of the differential.
>
> The above formula is only meant to be the 1st derivative. I run it twice 
> to get the second derivative.

To get the 1st derivative you just need:

v[x+1] - v[x]

What you are doing is to essentially average the differential of one point 
and the point before, which is going to blur out any sharp gradients.  (eg 
if you have points 5 0 5 the gradient your way will come out as zero)


Post a reply to this message

From: Mike Raiford
Subject: Re: Too many pipes?
Date: 22 Oct 2008 08:37:18
Message: <48ff1e7e@news.povray.org>
Invisible wrote:

> 
>> Thinking of writing a simulator? ;-)
> 
> Well let's put it this way: What do you think my chances of building a 
> working set of organ pipes are? :-P Last time I tried to cut wood, I 
> couldn't even cut it straight! :-/ I figure I have far more chance of 
> building an organ simulator...

Reminds me of something I had some time ago. It was a software synth 
based on the physical characteristics of the instrument, I think it was 
put out by Creative at the time, bundled with their sound card. I've 
since forgotten the name of it, though. Ahh, called WaveGuide:

http://en.wikipedia.org/wiki/Digital_waveguide_synthesis

Interesting technology. Good luck if you do produce a pipe organ simulator.



-- 
~Mike


Post a reply to this message

From: Invisible
Subject: Re: Too many pipes?
Date: 22 Oct 2008 09:00:38
Message: <48ff23f6$1@news.povray.org>
Mike Raiford wrote:

> Reminds me of something I had some time ago. It was a software synth 
> based on the physical characteristics of the instrument, I think it was 
> put out by Creative at the time, bundled with their sound card. I've 
> since forgotten the name of it, though. Ahh, called WaveGuide:
> 
> http://en.wikipedia.org/wiki/Digital_waveguide_synthesis
> 
> Interesting technology. Good luck if you do produce a pipe organ simulator.

The Reaktor product from Native Instruments features a sound module 
named "Steam Pipe" which uses a (1D) digital waveguide to simulate 
string and wind instruments. It does a delightful flute sound. ;-)

(What can I say? I like flutes!)

It's really interesting. You can "over-blow" the flute just like a real 
one. It sounds ever so believable.

Of course, Steam Pipe does all this using a few non-physical shortcuts. 
(E.g., instead of a true gas turbulence engine, it uses a simple 
nonlinear waveshaper to produce wave saturation.) The next step would be 
to move to 2D or even 3D with real turbulence simulation. I suspect this 
would result in an instrument that takes weeks to simulate and doesn't 
sound all that much different.


Post a reply to this message

From: Darren New
Subject: Re: Too many pipes?
Date: 22 Oct 2008 10:50:24
Message: <48ff3db0@news.povray.org>
Invisible wrote:
> I actually didn't bother finishing to read it. It didn't have anything 
> much interesting to say.

Wow. OK.  I'll note that it took me several readings to even realize it 
was two books in one cover, for example, in spite of the author telling 
you so several times.  It's a rather complex tome.  But if it's not your 
thing, I can understand that... :-)

 > http://www.amazon.co.uk/Linked- ...

I'll check it out, thanks!

-- 
Darren New / San Diego, CA, USA (PST)


Post a reply to this message

From: Mike Raiford
Subject: Re: Too many pipes?
Date: 22 Oct 2008 12:42:54
Message: <48ff580e$1@news.povray.org>
Invisible wrote:

> Of course, Steam Pipe does all this using a few non-physical shortcuts. 
> (E.g., instead of a true gas turbulence engine, it uses a simple 
> nonlinear waveshaper to produce wave saturation.) The next step would be 
> to move to 2D or even 3D with real turbulence simulation. I suspect this 
> would result in an instrument that takes weeks to simulate and doesn't 
> sound all that much different.

To do things in realtime, you must take shortcuts :)

Wonder if there's a sound card out there that has a programmable DSP 
that's got enough parallelism to add as much realism to your simulation 
as possible.
-- 
~Mike


Post a reply to this message

From: Orchid XP v8
Subject: Re: Too many pipes?
Date: 22 Oct 2008 15:48:48
Message: <48ff83a0$1@news.povray.org>
>> Reminds me of something I had some time ago. It was a software synth 
>> based on the physical characteristics of the instrument, I think it 
>> was put out by Creative at the time, bundled with their sound card. 
>> I've since forgotten the name of it, though. Ahh, called WaveGuide:
> 
> The Reaktor product from Native Instruments features a sound module 
> named "Steam Pipe" which uses a (1D) digital waveguide to simulate 
> string and wind instruments. It does a delightful flute sound. ;-)

Here ya go:

http://download.orphi.me.uk/Music/G3/Silhouettes.ogg

This entire piece of music was created using *only* Steam Pipe. 
Everything you hear is a digital waveguide simulation.

Neat, isn't it?

-- 
http://blog.orphi.me.uk/
http://www.zazzle.com/MathematicalOrchid*


Post a reply to this message

From: triple r
Subject: Re: Too many pipes?
Date: 22 Oct 2008 19:35:00
Message: <web.48ffb77345093b77e0c9e9540@news.povray.org>
Invisible <voi### [at] devnull> wrote:

> So apparently the wave equation tells us that the 2nd derivative of some
> physical quanitity "u" with respect to time is equal to the square of
> the wave propogation constant multiplied by the Laplacian of "u".
>
> ...which would probably mean something if I could figure out what a
> Laplacian is! :-S
>
> According to Wikipedia, the Laplacian of u is the sum of all partial 2nd
> derivatives of u with respect to every coordinate axis.
>
> ...so...the total curvature then? ._.

In a realistic setting, this could be pressure and velocity, in which case they
usually just differ by a phase of 90 degrees, if I recall correctly.

Or, think of it as a string under tension.  If it has a positive second
derivative, then it is curved upward and that part of the string will tend to
accelerate upward. According to Newton's 2nd law, F=ma, so if the curvature
acts as a force, then it is proportional to the acceleration, a=d^2(u)/dt^2.
Using the constant c^2, which happens to end up as the wave speed, this gives
the 1-D wave equation:

d^2(u)/dt = c^2 * d^2(u)/dx^2.

For two dimensions, you just have curvature acting in two directions, so you add
them up and

d^2(u)/dt^2 = c^2 * ( d^2(u)/dx^2 + d^2(u)/dy^2 ) = c^2 * Laplacian(u)

To solve this, remember that the second derivative can be written discretely as

d^2(f)/dx^2  =  ( f(i+1) - 2*f(i) + f(i-1) ) / ( dx^2 )

where f(i+1) and f(i-1) are the neighboring grid points and dx is the grid
spacing.  Applying this to the time and space derivatives across a
two-dimensional grid, (assuming dx=dy),

( u(n+1) - 2*u(n) + u(n-1) ) / dt^2 = c^2 * ( u(i+1,j) + u(i-1,j) + u(i,j+1) +
u(i,j-1) - 4*u(i,j) ) / dx^2

Assuming you know the previous two time steps and that the right-hand side is
evaluated at time level n, just solve for u(n+1):

u(n+1) = 2*u(n) - u(n-1) + (c*dt/dx)^2 * ( u(i+1,j) + u(i-1,j) + u(i,j+1) +
u(i,j-1) - 4*u(i,j) )

So to solve the equation, make three grids.  Set grids (n-1) and (n) to zero.
Solve for (n+1).  Then transfer (n)->(n-1) and (n+1)->n.  Now you're back where
you started so just repeat over and over.  This should be stable as long as
(c*dt/dx) < 1.  This is called the CFL number and ensures that waves don't
travel across more than one cell per time step.

To make it interesting, just say instead that

d^2(u)/dt^2 - c^2*Laplacian(u) = f(x,y,t)

where f(x,y,t) is just any old forcing function that can depend on space and
time and makes it actually move.

Sorry.  That got a little long.  Hope it's remotely useful...

 - Ricky


Post a reply to this message

From: scott
Subject: Re: Too many pipes?
Date: 23 Oct 2008 02:54:32
Message: <49001fa8@news.povray.org>
> To do things in realtime, you must take shortcuts :)
> 
> Wonder if there's a sound card out there that has a programmable DSP 
> that's got enough parallelism to add as much realism to your simulation 
> as possible.

I imagine a GPU would be quite good at this sort of thing.


Post a reply to this message

From: Michael Zier
Subject: Re: Too many pipes?
Date: 23 Oct 2008 03:51:07
Message: <49002ceb@news.povray.org>
Am Tue, 21 Oct 2008 12:30:58 +0100 schrieb Invisible:

> 
>> Thinking of writing a simulator? ;-)
> 
> Well let's put it this way: What do you think my chances of building a
> working set of organ pipes are? :-P Last time I tried to cut wood, I
> couldn't even cut it straight! :-/ I figure I have far more chance of
> building an organ simulator...

Maybe this is something for you: http://www.kokkinizita.net/linuxaudio/
aeolus

Haven't tried it yet, but looks interesting.


Post a reply to this message

From: Mike Raiford
Subject: Re: Too many pipes?
Date: 23 Oct 2008 08:49:21
Message: <490072d1$1@news.povray.org>
scott wrote:
>> To do things in realtime, you must take shortcuts :)
>>
>> Wonder if there's a sound card out there that has a programmable DSP 
>> that's got enough parallelism to add as much realism to your 
>> simulation as possible.
> 
> I imagine a GPU would be quite good at this sort of thing.
> 

I suspect you're right. It has built-in support for parallel operations. 
Can you repurpose a GPU for that sort of thing?

-- 
~Mike


Post a reply to this message

From: Mike Raiford
Subject: Re: Too many pipes?
Date: 23 Oct 2008 08:51:13
Message: <49007341$1@news.povray.org>
Orchid XP v8 wrote:
>>> Reminds me of something I had some time ago. It was a software synth 
>>> based on the physical characteristics of the instrument, I think it 
>>> was put out by Creative at the time, bundled with their sound card. 
>>> I've since forgotten the name of it, though. Ahh, called WaveGuide:
>>
>> The Reaktor product from Native Instruments features a sound module 
>> named "Steam Pipe" which uses a (1D) digital waveguide to simulate 
>> string and wind instruments. It does a delightful flute sound. ;-)
> 
> Here ya go:
> 
> http://download.orphi.me.uk/Music/G3/Silhouettes.ogg
> 

I'll download and listen when I get home ...

> This entire piece of music was created using *only* Steam Pipe. 
> Everything you hear is a digital waveguide simulation.
> 
> Neat, isn't it?
> 

It is. I know the AWE64 software synth portion was quite nice. guitars 
sounded like guitars, etc ..

-- 
~Mike


Post a reply to this message

From: Invisible
Subject: Re: Too many pipes?
Date: 23 Oct 2008 08:54:08
Message: <490073f0@news.povray.org>
Mike Raiford wrote:

> Can you repurpose a GPU for that sort of thing?

Probably.

The math isn't even that complex - there's just *a lot* of it.


Post a reply to this message

From: scott
Subject: Re: Too many pipes?
Date: 23 Oct 2008 09:49:30
Message: <490080ea$1@news.povray.org>
>>> Wonder if there's a sound card out there that has a programmable DSP 
>>> that's got enough parallelism to add as much realism to your simulation 
>>> as possible.
>>
>> I imagine a GPU would be quite good at this sort of thing.
>>
>
> I suspect you're right. It has built-in support for parallel operations. 
> Can you repurpose a GPU for that sort of thing?

A GPU is basically very fast if you want to perform exactly the same 
function on big arrays of data.  Nowadays there are very few limitations on 
what you can and can't do, and the few remaining are easily got around by 
using temporary arrays and multiple functions.

Even if your algorithm apparently doesn't work on huge arrays of data, it 
can often be forced to do so in order to get a big speed up.  eg With an IFS 
program that transforms one point repeatedly to generate a picture, on the 
GPU you can transform millions of points in parallel and you get the same 
result.


Post a reply to this message

From: Darren New
Subject: Re: Too many pipes?
Date: 23 Oct 2008 13:50:09
Message: <4900b951$1@news.povray.org>
Mike Raiford wrote:
> It is. I know the AWE64 software synth portion was quite nice. guitars 
> sounded like guitars, etc ..

There's an artist named Larry Fast who has a one-man band called 
"Synergy."  He produces what was called "electronic music" a few decades 
ago, more rock than trance-like. In the liner notes of his first album 
talking about what instruments he used, he lists a dozen synthesizers 
and such, and ends with "and no guitars." In his second album, other 
synthesizers, and "and still no guitars."  Third album the same. Fourth 
album, one of the synthesizers is "Madrong M-500 guitar synthesizer."[1] 
And at the bottom, he adds "Finally, guitars, sort of."

[1] I don't know the exact brand offhand, no. :-) Don't google "madrong".

-- 
Darren New / San Diego, CA, USA (PST)


Post a reply to this message

From: Mike Raiford
Subject: Re: Too many pipes?
Date: 23 Oct 2008 16:28:03
Message: <4900de53$1@news.povray.org>
Darren New wrote:

> 
> [1] I don't know the exact brand offhand, no. :-) Don't google "madrong".
> 

Oh, good. it doesn't come up with anything nasty, thankfully.

(And just what did you think I was gonna do if you said don't google for 
[X] ... Google it, of course ;) )
-- 
~Mike


Post a reply to this message

From: Orchid XP v8
Subject: Re: Too many pipes?
Date: 23 Oct 2008 16:31:14
Message: <4900df12$1@news.povray.org>
Mike Raiford wrote:

> (And just what did you think I was gonna do if you said don't google for 
> [X] ... Google it, of course ;) )

Don't google "bukkake". Especially not at work.

-- 
http://blog.orphi.me.uk/
http://www.zazzle.com/MathematicalOrchid*


Post a reply to this message

From: Mike Raiford
Subject: Re: Too many pipes?
Date: 23 Oct 2008 16:48:14
Message: <4900e30e$1@news.povray.org>
Orchid XP v8 wrote:

> 
> Don't google "bukkake". Especially not at work.
> 

Errrrr ....

-- 
~Mike


Post a reply to this message

From: Orchid XP v8
Subject: Re: Too many pipes?
Date: 23 Oct 2008 16:54:02
Message: <4900e46a@news.povray.org>
>> Don't google "bukkake". Especially not at work.
> 
> Errrrr ....

WIN!!!!!eleven! :-D

-- 
http://blog.orphi.me.uk/
http://www.zazzle.com/MathematicalOrchid*


Post a reply to this message

From: andrel
Subject: Re: Too many pipes?
Date: 23 Oct 2008 17:17:58
Message: <4900EA58.5080409@hotmail.com>
On 23-Oct-08 22:26, Mike Raiford wrote:
> Darren New wrote:
> 
>>
>> [1] I don't know the exact brand offhand, no. :-) Don't google "madrong".
>>
> 
> Oh, good. it doesn't come up with anything nasty, thankfully.
> 
> (And just what did you think I was gonna do if you said don't google for 
> [X] ... Google it, of course ;) )

I think it was just a way to bring the power of google again to the 
attention of our mascot. Most of the more obvious ways seem to have 
failed too often. ;)


Post a reply to this message

From: Mike Raiford
Subject: Re: Too many pipes?
Date: 24 Oct 2008 08:33:57
Message: <4901c0b5$1@news.povray.org>
Orchid XP v8 wrote:

> 
> http://download.orphi.me.uk/Music/G3/Silhouettes.ogg
> 

I've heard this tune before. I think you might have posted it a while 
back, but yes... neat. All waveguide? one patch sounded kind of 
electronic, too.

-- 
~Mike


Post a reply to this message

From: Invisible
Subject: Re: Too many pipes?
Date: 24 Oct 2008 08:59:00
Message: <4901c694$1@news.povray.org>
>> http://download.orphi.me.uk/Music/G3/Silhouettes.ogg
>>
> 
> I've heard this tune before. I think you might have posted it a while 
> back

Indeed yes.

> but yes... neat. All waveguide? one patch sounded kind of 
> electronic, too.

All waveguides. Just different settings of the sliders. ;-)

There's a sound in there which actually runs two notes very slightly out 
of tune for a phasing effect; it sounds moderately electronic.


Post a reply to this message

From: Stephen
Subject: Re: Too many pipes?
Date: 24 Oct 2008 12:13:11
Message: <jts3g41te6vg1h3hogsfq6o8sa9cfu2phn@4ax.com>
On Fri, 24 Oct 2008 07:32:32 -0500, Mike Raiford <"m[raiford]!at"@gmail.com>
wrote:

>I've heard this tune before.

It was used as a pop tune decades ago. I can't remember the name.

Andrew, your touch is getting better. :D
-- 

Regards
     Stephen


Post a reply to this message

From: Orchid XP v8
Subject: Re: Too many pipes?
Date: 24 Oct 2008 14:25:34
Message: <4902131e@news.povray.org>
>> I've heard this tune before.
> 
> It was used as a pop tune decades ago. I can't remember the name.

It was called - wait for it - Silhouettes.

http://artists.letssingit.com/hermans-hermits-lyrics-silhouettes-xbj5f89

(A favourite tune of mine, BTW.)

> Andrew, your touch is getting better. :D

Heh, sadly not. This is purely sequenced. ;-)

-- 
http://blog.orphi.me.uk/
http://www.zazzle.com/MathematicalOrchid*


Post a reply to this message

From: Stephen
Subject: Re: Too many pipes?
Date: 24 Oct 2008 16:31:29
Message: <9ub4g4t17b163im4i07var2hvqqb21b6pb@4ax.com>
On Fri, 24 Oct 2008 19:25:37 +0100, Orchid XP v8 <voi### [at] devnull> wrote:

>>> I've heard this tune before.
>> 
>> It was used as a pop tune decades ago. I can't remember the name.
>
>It was called - wait for it - Silhouettes.
>
>http://artists.letssingit.com/hermans-hermits-lyrics-silhouettes-xbj5f89
>
>(A favourite tune of mine, BTW.)
>

I played it to my wife (Delphi the oracle) and she not only told me it was
Silhouettes on the shade by Herman's Hermits (January 1965), she sang all the
verses 
Then I saw your link when I was replying. 
I was 14 when it reached #3.

>> Andrew, your touch is getting better. :D
>
>Heh, sadly not. This is purely sequenced. ;-)

Opps!   One more time, with feeling :)
-- 

Regards
     Stephen


Post a reply to this message

From: Orchid XP v8
Subject: Re: Too many pipes?
Date: 24 Oct 2008 16:34:49
Message: <49023169$1@news.povray.org>
>> It was called - wait for it - Silhouettes.
>>
>> http://artists.letssingit.com/hermans-hermits-lyrics-silhouettes-xbj5f89
>>
>> (A favourite tune of mine, BTW.)
> 
> I played it to my wife (Delphi the oracle) and she not only told me it was
> Silhouettes on the shade by Herman's Hermits (January 1965), she sang all the
> verses 
> Then I saw your link when I was replying. 
> I was 14 when it reached #3.

Heh. I hadn't even been born yet. (But I can still sing all the lyrics...)

>>> Andrew, your touch is getting better. :D
>> Heh, sadly not. This is purely sequenced. ;-)
> 
> Opps!   One more time, with feeling :)

;-)

-- 
http://blog.orphi.me.uk/
http://www.zazzle.com/MathematicalOrchid*


Post a reply to this message

Goto Latest 50 Messages Next 1 Messages >>>

Copyright 2003-2023 Persistence of Vision Raytracer Pty. Ltd.