gdalgorithms-list

[Algorithms] Best fit of polygon inside another polygon

[<Ste...@gm...>]

Hi,

I've been thinking about an algorithm which fits a given polygon into a  
quad. I've stumbled upon this while trying to fit the largest possible  
polygon out of a set of different polygons into a quadliteral. What I want  
to find is the best-fit-polygon which can be contained completely in the  
quadliteral. The polygon and quad can be assumed to be convex. An nice  
feature would be to calculate the error as a function of the area which  
doesn't fit into the quad for every polygon I throw at the quad.

I'm working in 2D right now, but might want to expand the problem for a  
later application into a 3D case (fit a polyhedra into a hexahedron).

Any ideas how to solve this problem?

Stefan

Re: [Algorithms] Best fit of polygon inside another polygon

[Fabian G. <f.g...@49...>]

Ste...@gm... wrote:
> Hi,
> 
> I've been thinking about an algorithm which fits a given polygon into a 
> quad. I've stumbled upon this while trying to fit the largest possible 
> polygon out of a set of different polygons into a quadliteral. What I 
> want to find is the best-fit-polygon which can be contained completely 
> in the quadliteral. The polygon and quad can be assumed to be convex. An 
> nice feature would be to calculate the error as a function of the area 
> which doesn't fit into the quad for every polygon I throw at the quad.
> 
> I'm working in 2D right now, but might want to expand the problem for a 
> later application into a 3D case (fit a polyhedra into a hexahedron).
> 
> Any ideas how to solve this problem?
> 
> Stefan

Which transformations are allowed? "Only translations", "translations 
and rotations", "translations, rotations and uniform scaling" and 
"general affine transformation" are all sensible choices but lead to 
very different approaches.

Also, is the quad a general convex quad, or is it a rectangle or 
parallelogram?

Kind regards,
-Fabian Giesen

Re: [Algorithms] Best fit of polygon inside another polygon

[Peter L. <pe...@to...>]

sounds like a question from one of my take-home final exams....

Ste...@gm... wrote:
> Hi,
>
> I've been thinking about an algorithm which fits a given polygon into 
> a quad. I've stumbled upon this while trying to fit the largest 
> possible polygon out of a set of different polygons into a 
> quadliteral. What I want to find is the best-fit-polygon which can be 
> contained completely in the quadliteral. The polygon and quad can be 
> assumed to be convex. An nice feature would be to calculate the error 
> as a function of the area which doesn't fit into the quad for every 
> polygon I throw at the quad.
>
> I'm working in 2D right now, but might want to expand the problem for 
> a later application into a 3D case (fit a polyhedra into a hexahedron).
>
> Any ideas how to solve this problem?
>
> Stefan
> ------------------------------------------------------------------------
>
> ------------------------------------------------------------------------------
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> the minds behind Google Creative Lab, Visual Complexity, Processing, & 
> iPhoneDevCamp asthey present alongside digital heavyweights like Barbarian
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Re: [Algorithms] Best fit of polygon inside another polygon

[Robin G. <rob...@gm...>]

On Fri, May 22, 2009 at 8:41 AM, Peter Lipson <pe...@to...> wrote:

> sounds like a question from one of my take-home final exams....
>
>
Welcome to the world of R&D, where it's like taking an exam every day of the
week.
Only there are no right answers, no scores at the end, and it's not clear
whether the question is even possible.

- R.

Re: [Algorithms] Best fit of polygon inside another polygon

[Emil P. <hu...@co...>]

I'm tired and I have a headache, but if I understand your problem right then
it sounds like a special case of a problem I just solved last night and
wrote a tool for:

http://www.humus.name/index.php?page=News
<http://www.humus.name/index.php?page=News&ID=266> &ID=266

 

So you'd just input your polygon directly (instead of inputting a particle
texture and generate a polygon from that) and optimize for 4 vertices and
that would solve it, no?

 

-Emil

 

 

From: Ste...@gm... [mailto:Ste...@gm...] 
Sent: 22 May 2009 14:59
To: Game Development Algorithms
Subject: [Algorithms] Best fit of polygon inside another polygon

 

Hi,

I've been thinking about an algorithm which fits a given polygon into a
quad. I've stumbled upon this while trying to fit the largest possible
polygon out of a set of different polygons into a quadliteral. What I want
to find is the best-fit-polygon which can be contained completely in the
quadliteral. The polygon and quad can be assumed to be convex. An nice
feature would be to calculate the error as a function of the area which
doesn't fit into the quad for every polygon I throw at the quad.

I'm working in 2D right now, but might want to expand the problem for a
later application into a 3D case (fit a polyhedra into a hexahedron). 

Any ideas how to solve this problem?

Stefan

Re: [Algorithms] Best fit of polygon inside another polygon

[Stefan D. <ste...@gm...>]

Hi Emil,

that's not exactly the problem I am trying to solve. Maybe I have
stated it incorrectly. In my case the surrounding quad is of fixed
size. I have different polygons with varying shape and size and I want
to find the polygon and according transformation of the polygon which
best fits it into the given quad. The allowed transformations which
can be applied to the polygon are translation and scaling.

regards,

Stefan

On Fri, May 22, 2009 at 8:27 PM, Emil Persson <hu...@co...> wrote:
> I’m tired and I have a headache, but if I understand your problem right then
> it sounds like a special case of a problem I just solved last night and
> wrote a tool for:
>
> http://www.humus.name/index.php?page=News&ID=266
>
>
>
> So you’d just input your polygon directly (instead of inputting a particle
> texture and generate a polygon from that) and optimize for 4 vertices and
> that would solve it, no?
>
>
>
> -Emil
>
>
>
>
>
> From: Ste...@gm... [mailto:Ste...@gm...]
> Sent: 22 May 2009 14:59
> To: Game Development Algorithms
> Subject: [Algorithms] Best fit of polygon inside another polygon
>
>
>
> Hi,
>
> I've been thinking about an algorithm which fits a given polygon into a
> quad. I've stumbled upon this while trying to fit the largest possible
> polygon out of a set of different polygons into a quadliteral. What I want
> to find is the best-fit-polygon which can be contained completely in the
> quadliteral. The polygon and quad can be assumed to be convex. An nice
> feature would be to calculate the error as a function of the area which
> doesn't fit into the quad for every polygon I throw at the quad.
>
> I'm working in 2D right now, but might want to expand the problem for a
> later application into a 3D case (fit a polyhedra into a hexahedron).
>
> Any ideas how to solve this problem?
>
> Stefan
>
> ------------------------------------------------------------------------------
> Register Now for Creativity and Technology (CaT), June 3rd, NYC. CaT
> is a gathering of tech-side developers & brand creativity professionals.
> Meet
> the minds behind Google Creative Lab, Visual Complexity, Processing, &
> iPhoneDevCamp asthey present alongside digital heavyweights like Barbarian
> Group, R/GA, & Big Spaceship. http://www.creativitycat.com
> _______________________________________________
> GDAlgorithms-list mailing list
> GDA...@li...
> https://lists.sourceforge.net/lists/listinfo/gdalgorithms-list
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>



-- 
--
Stefan Daenzer
Körnerplatz 8
04107 Leipzig

Tel.: +49-176-61157550

"Work like you don't need the money, love like you've never been hurt
and dance like no one is watching." - Randall G Leighton

Re: [Algorithms] Best fit of polygon inside another polygon

[Jon W. <jw...@gm...>]

Stefan Dänzer wrote:
> size. I have different polygons with varying shape and size and I want
> to find the polygon and according transformation of the polygon which
> best fits it into the given quad. The allowed transformations which
> can be applied to the polygon are translation and scaling.
>   

But you could just as easily try to fit the rectangle around the 
polygon, using translation and rotation, and then just invert that 
transform to go from polygon to rectangle.

In general, I believe you can show that the optimal fit will have one 
side of the polygon parallel with one side of the rectangle. If that is 
indeed the case, a very straightforward algorithm (but slow) would be:

foreach polygon:
  foreach side in the polygon
    for lengthwise and heightwise sides in rectangle
      translate and rotate polygon so that it fits as well as possible 
with the polygon side snug to the rectangle side
      test whether fully inside, and calculate coverage

Then pick the one with the best coverage value while being fully inside.
To calculate the "snug fit" you rotate the polygon to match the side to 
the rectangle, rotate your frame of reference to make this side "right," 
and then slide it so that the uppermost vertex just touches the 
uppermost side of the rectangle.

Sincerely,

jw

Re: [Algorithms] Best fit of polygon inside another polygon

[Stefan D. <ste...@gm...>]

Sorry Jon, I stated the allowed transformations incorrectly in my last
email. The following part:
"The allowed transformations which can be applied to the polygon are
translation and scaling"

should read:

The allowed transformations which can be applied to the polygon are
translation and rotation."

Sorry for the confusion.

On Sun, May 24, 2009 at 6:42 PM, Jon Watte <jw...@gm...> wrote:

> Stefan Dänzer wrote:
> > size. I have different polygons with varying shape and size and I want
> > to find the polygon and according transformation of the polygon which
> > best fits it into the given quad. The allowed transformations which
> > can be applied to the polygon are translation and scaling.
> >
>
> But you could just as easily try to fit the rectangle around the
> polygon, using translation and rotation, and then just invert that
> transform to go from polygon to rectangle.
>
> In general, I believe you can show that the optimal fit will have one
> side of the polygon parallel with one side of the rectangle. If that is
> indeed the case, a very straightforward algorithm (but slow) would be:
>
> foreach polygon:
>  foreach side in the polygon
>    for lengthwise and heightwise sides in rectangle
>      translate and rotate polygon so that it fits as well as possible
> with the polygon side snug to the rectangle side
>      test whether fully inside, and calculate coverage
>
> Then pick the one with the best coverage value while being fully inside.
> To calculate the "snug fit" you rotate the polygon to match the side to
> the rectangle, rotate your frame of reference to make this side "right,"
> and then slide it so that the uppermost vertex just touches the
> uppermost side of the rectangle.
>
> Sincerely,
>
> jw
>
>
>
> ------------------------------------------------------------------------------
> Register Now for Creativity and Technology (CaT), June 3rd, NYC. CaT
> is a gathering of tech-side developers & brand creativity professionals.
> Meet
> the minds behind Google Creative Lab, Visual Complexity, Processing, &
> iPhoneDevCamp asthey present alongside digital heavyweights like Barbarian
> Group, R/GA, & Big Spaceship. http://www.creativitycat.com
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-- 
--
Stefan Daenzer
Körnerplatz 8
04107 Leipzig

Tel.: +49-176-61157550

"Work like you don't need the money, love like you've never been hurt and
dance like no one is watching." - Randall G Leighton

Re: [Algorithms] Best fit of polygon inside another polygon

[Jon W. <jw...@gm...>]

That's what I actually thought, so that's what I answered.

Sincerely,

jw

Stefan Dänzer wrote:
> Sorry Jon, I stated the allowed transformations incorrectly in my last 
> email. The following part:
>
> "The allowed transformations which can be applied to the polygon are 
> translation and scaling"
>
> should read:
>
> The allowed transformations which can be applied to the polygon are 
> translation and rotation."
>
> Sorry for the confusion.
>
> On Sun, May 24, 2009 at 6:42 PM, Jon Watte <jw...@gm... 
> <mailto:jw...@gm...>> wrote:
>
>     Stefan Dänzer wrote:
>     > size. I have different polygons with varying shape and size and
>     I want
>     > to find the polygon and according transformation of the polygon
>     which
>     > best fits it into the given quad. The allowed transformations which
>     > can be applied to the polygon are translation and scaling.
>     >
>
>     But you could just as easily try to fit the rectangle around the
>     polygon, using translation and rotation, and then just invert that
>     transform to go from polygon to rectangle.
>
>     In general, I believe you can show that the optimal fit will have one
>     side of the polygon parallel with one side of the rectangle. If
>     that is
>     indeed the case, a very straightforward algorithm (but slow) would be:
>
>     foreach polygon:
>      foreach side in the polygon
>        for lengthwise and heightwise sides in rectangle
>          translate and rotate polygon so that it fits as well as possible
>     with the polygon side snug to the rectangle side
>          test whether fully inside, and calculate coverage
>
>     Then pick the one with the best coverage value while being fully
>     inside.
>     To calculate the "snug fit" you rotate the polygon to match the
>     side to
>     the rectangle, rotate your frame of reference to make this side
>     "right,"
>     and then slide it so that the uppermost vertex just touches the
>     uppermost side of the rectangle.
>
>     Sincerely,
>
>     jw
>
>
>     ------------------------------------------------------------------------------
>     Register Now for Creativity and Technology (CaT), June 3rd, NYC. CaT
>     is a gathering of tech-side developers & brand creativity
>     professionals. Meet
>     the minds behind Google Creative Lab, Visual Complexity, Processing, &
>     iPhoneDevCamp asthey present alongside digital heavyweights like
>     Barbarian
>     Group, R/GA, & Big Spaceship. http://www.creativitycat.com
>     _______________________________________________
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>     GDA...@li...
>     <mailto:GDA...@li...>
>     https://lists.sourceforge.net/lists/listinfo/gdalgorithms-list
>     Archives:
>     http://sourceforge.net/mailarchive/forum.php?forum_name=gdalgorithms-list
>
>
>
>
> -- 
> --
> Stefan Daenzer
> Körnerplatz 8
> 04107 Leipzig
>
> Tel.: +49-176-61157550
>
> "Work like you don't need the money, love like you've never been hurt 
> and dance like no one is watching." - Randall G Leighton
> ------------------------------------------------------------------------
>
> ------------------------------------------------------------------------------
> Register Now for Creativity and Technology (CaT), June 3rd, NYC. CaT
> is a gathering of tech-side developers & brand creativity professionals. Meet
> the minds behind Google Creative Lab, Visual Complexity, Processing, & 
> iPhoneDevCamp asthey present alongside digital heavyweights like Barbarian
> Group, R/GA, & Big Spaceship. http://www.creativitycat.com 
> ------------------------------------------------------------------------
>
> _______________________________________________
> GDAlgorithms-list mailing list
> GDA...@li...
> https://lists.sourceforge.net/lists/listinfo/gdalgorithms-list
> Archives:
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Re: [Algorithms] Best fit of polygon inside another polygon

[Nicholas \Indy\ R. <ar...@gm...>]

Without scaling this seems to be an odd request... as what defines any
one fit better then another, so long as the polygon does fit within
the quad, there lacks a metric for "best" as any fit will take the
same area and have the same excess area.

Indy

On Sun, May 24, 2009 at 3:52 PM, Stefan Dänzer <ste...@gm...> wrote:
> Sorry Jon, I stated the allowed transformations incorrectly in my last
> email. The following part:
> "The allowed transformations which can be applied to the polygon are
> translation and scaling"
> should read:
> The allowed transformations which can be applied to the polygon are
> translation and rotation."
> Sorry for the confusion.
>
> On Sun, May 24, 2009 at 6:42 PM, Jon Watte <jw...@gm...> wrote:
>>
>> Stefan Dänzer wrote:
>> > size. I have different polygons with varying shape and size and I want
>> > to find the polygon and according transformation of the polygon which
>> > best fits it into the given quad. The allowed transformations which
>> > can be applied to the polygon are translation and scaling.
>> >
>>
>> But you could just as easily try to fit the rectangle around the
>> polygon, using translation and rotation, and then just invert that
>> transform to go from polygon to rectangle.
>>
>> In general, I believe you can show that the optimal fit will have one
>> side of the polygon parallel with one side of the rectangle. If that is
>> indeed the case, a very straightforward algorithm (but slow) would be:
>>
>> foreach polygon:
>>  foreach side in the polygon
>>    for lengthwise and heightwise sides in rectangle
>>      translate and rotate polygon so that it fits as well as possible
>> with the polygon side snug to the rectangle side
>>      test whether fully inside, and calculate coverage
>>
>> Then pick the one with the best coverage value while being fully inside.
>> To calculate the "snug fit" you rotate the polygon to match the side to
>> the rectangle, rotate your frame of reference to make this side "right,"
>> and then slide it so that the uppermost vertex just touches the
>> uppermost side of the rectangle.
>>
>> Sincerely,
>>
>> jw
>>
>>
>>
>> ------------------------------------------------------------------------------
>> Register Now for Creativity and Technology (CaT), June 3rd, NYC. CaT
>> is a gathering of tech-side developers & brand creativity professionals.
>> Meet
>> the minds behind Google Creative Lab, Visual Complexity, Processing, &
>> iPhoneDevCamp asthey present alongside digital heavyweights like Barbarian
>> Group, R/GA, & Big Spaceship. http://www.creativitycat.com
>> _______________________________________________
>> GDAlgorithms-list mailing list
>> GDA...@li...
>> https://lists.sourceforge.net/lists/listinfo/gdalgorithms-list
>> Archives:
>> http://sourceforge.net/mailarchive/forum.php?forum_name=gdalgorithms-list
>
>
>
> --
> --
> Stefan Daenzer
> Körnerplatz 8
> 04107 Leipzig
>
> Tel.: +49-176-61157550
>
> "Work like you don't need the money, love like you've never been hurt and
> dance like no one is watching." - Randall G Leighton
>
> ------------------------------------------------------------------------------
> Register Now for Creativity and Technology (CaT), June 3rd, NYC. CaT
> is a gathering of tech-side developers & brand creativity professionals.
> Meet
> the minds behind Google Creative Lab, Visual Complexity, Processing, &
> iPhoneDevCamp asthey present alongside digital heavyweights like Barbarian
> Group, R/GA, & Big Spaceship. http://www.creativitycat.com
> _______________________________________________
> GDAlgorithms-list mailing list
> GDA...@li...
> https://lists.sourceforge.net/lists/listinfo/gdalgorithms-list
> Archives:
> http://sourceforge.net/mailarchive/forum.php?forum_name=gdalgorithms-list
>

Re: [Algorithms] Best fit of polygon inside another polygon

[Peter L. <pe...@to...>]

not at all - if you think of the physical world rather than a 
mathematical one, this search for 'best fit' is one that a child might 
use playing with a set of odd-shape blocks and a box.  Ask him which 
shape 'best fits' in the box and he won't think of scale...

Nicholas "Indy" Ray wrote:
> Without scaling this seems to be an odd request... as what defines any
> one fit better then another, so long as the polygon does fit within
> the quad, there lacks a metric for "best" as any fit will take the
> same area and have the same excess area

Re: [Algorithms] Best fit of polygon inside another polygon

[Peter L. <pe...@to...>]

-- I thought I should quote from the problem definition, too:

I have different polygons with varying shape and size and I want
> to find the polygon and according transformation of the polygon which
> best fits it into the given quad. 

  -- so it's not a question of "find the tightest bounding quadrilateral on a given polygon". It's "find the polygon that matches the given quad".



Peter Lipson wrote:
> not at all - if you think of the physical world rather than a 
> mathematical one, this search for 'best fit' is one that a child might 
> use playing with a set of odd-shape blocks and a box.  Ask him which 
> shape 'best fits' in the box and he won't think of scale...
>
> Nicholas "Indy" Ray wrote:
>> Without scaling this seems to be an odd request... as what defines any
>> one fit better then another, so long as the polygon does fit within
>> the quad, there lacks a metric for "best" as any fit will take the
>> same area and have the same excess area
>

Re: [Algorithms] Best fit of polygon inside another polygon

[Osman, B. <BO...@vv...>]

So what's your precise metric for "best fit"? Earlier you mentioned the area of the polygon that doesn't fit into the quad... But if scale (even uniform scale) is a permitted transformation then that must only be part of the metric. It's trivial to scale all polygons down to a point, such that they all fit perfectly into ANY quadrilateral.

-Brian

-----Original Message-----
From: Stefan Dänzer [mailto:ste...@gm...] 
Sent: Saturday, May 23, 2009 12:08 PM
To: Game Development Algorithms
Subject: Re: [Algorithms] Best fit of polygon inside another polygon

Hi Emil,

that's not exactly the problem I am trying to solve. Maybe I have
stated it incorrectly. In my case the surrounding quad is of fixed
size. I have different polygons with varying shape and size and I want
to find the polygon and according transformation of the polygon which
best fits it into the given quad. The allowed transformations which
can be applied to the polygon are translation and scaling.

regards,

Stefan

On Fri, May 22, 2009 at 8:27 PM, Emil Persson <hu...@co...> wrote:
> I'm tired and I have a headache, but if I understand your problem right then
> it sounds like a special case of a problem I just solved last night and
> wrote a tool for:
>
> http://www.humus.name/index.php?page=News&ID=266
>
>
>
> So you'd just input your polygon directly (instead of inputting a particle
> texture and generate a polygon from that) and optimize for 4 vertices and
> that would solve it, no?
>
>
>
> -Emil
>
>
>
>
>
> From: Ste...@gm... [mailto:Ste...@gm...]
> Sent: 22 May 2009 14:59
> To: Game Development Algorithms
> Subject: [Algorithms] Best fit of polygon inside another polygon
>
>
>
> Hi,
>
> I've been thinking about an algorithm which fits a given polygon into a
> quad. I've stumbled upon this while trying to fit the largest possible
> polygon out of a set of different polygons into a quadliteral. What I want
> to find is the best-fit-polygon which can be contained completely in the
> quadliteral. The polygon and quad can be assumed to be convex. An nice
> feature would be to calculate the error as a function of the area which
> doesn't fit into the quad for every polygon I throw at the quad.
>
> I'm working in 2D right now, but might want to expand the problem for a
> later application into a 3D case (fit a polyhedra into a hexahedron).
>
> Any ideas how to solve this problem?
>
> Stefan
>
> ------------------------------------------------------------------------------
> Register Now for Creativity and Technology (CaT), June 3rd, NYC. CaT
> is a gathering of tech-side developers & brand creativity professionals.
> Meet
> the minds behind Google Creative Lab, Visual Complexity, Processing, &
> iPhoneDevCamp asthey present alongside digital heavyweights like Barbarian
> Group, R/GA, & Big Spaceship. http://www.creativitycat.com
> _______________________________________________
> GDAlgorithms-list mailing list
> GDA...@li...
> https://lists.sourceforge.net/lists/listinfo/gdalgorithms-list
> Archives:
> http://sourceforge.net/mailarchive/forum.php?forum_name=gdalgorithms-list
>



-- 
--
Stefan Daenzer
Körnerplatz 8
04107 Leipzig

Tel.: +49-176-61157550

"Work like you don't need the money, love like you've never been hurt
and dance like no one is watching." - Randall G Leighton

------------------------------------------------------------------------------
Register Now for Creativity and Technology (CaT), June 3rd, NYC. CaT
is a gathering of tech-side developers & brand creativity professionals. Meet
the minds behind Google Creative Lab, Visual Complexity, Processing, & 
iPhoneDevCamp asthey present alongside digital heavyweights like Barbarian
Group, R/GA, & Big Spaceship. http://www.creativitycat.com 
_______________________________________________
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Archives:
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Re: [Algorithms] Best fit of polygon inside another polygon

[Fabian G. <f.g...@49...>]

> Without scaling this seems to be an odd request... as what defines any
> one fit better then another, so long as the polygon does fit within
> the quad, there lacks a metric for "best" as any fit will take the
> same area and have the same excess area.

Same goes for scaling though - just let the scaling factor run towards 0 
and your metric will look better and better.

-Fabian Giesen

Re: [Algorithms] Best fit of polygon inside another polygon

[Nicholas \Indy\ R. <ar...@gm...>]

Except with Scaling you can define best fit to be the fit that takes
up the most amount of area, which is a pretty standard metric for best
fit, no such standard metric exists without scaling IMO.

Nicholas "Indy" Ray

On Mon, May 25, 2009 at 2:04 AM, Fabian Giesen <f.g...@49...> wrote:
>> Without scaling this seems to be an odd request... as what defines any
>> one fit better then another, so long as the polygon does fit within
>> the quad, there lacks a metric for "best" as any fit will take the
>> same area and have the same excess area.
>
> Same goes for scaling though - just let the scaling factor run towards 0
> and your metric will look better and better.
>
> -Fabian Giesen
>
> ------------------------------------------------------------------------------
> Register Now for Creativity and Technology (CaT), June 3rd, NYC. CaT
> is a gathering of tech-side developers & brand creativity professionals. Meet
> the minds behind Google Creative Lab, Visual Complexity, Processing, &
> iPhoneDevCamp asthey present alongside digital heavyweights like Barbarian
> Group, R/GA, & Big Spaceship. http://www.creativitycat.com
> _______________________________________________
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> https://lists.sourceforge.net/lists/listinfo/gdalgorithms-list
> Archives:
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>

Re: [Algorithms] Best fit of polygon inside another polygon

[Fabian G. <f.g...@49...>]

> not at all - if you think of the physical world rather than a 
> mathematical one, this search for 'best fit' is one that a child might 
> use playing with a set of odd-shape blocks and a box.  Ask him which 
> shape 'best fits' in the box and he won't think of scale...

The basic point remains though that this is still just a binary test as 
requested (i.e. using translation and rotation only). Either the other 
polygon fits into the quad or it doesn't, but when it does, the 
remaining area is always Area(Quad)-Area(Polygon), since neither 
translation nor rotation of the polygon will change its area. So the 
remaining area is not helpful at all in comparing which is a better fit.

-Fabian Giesen

Re: [Algorithms] Best fit of polygon inside another polygon

[Jon W. <jw...@gm...>]

Fabian Giesen wrote:
> translation nor rotation of the polygon will change its area. So the 
> remaining area is not helpful at all in comparing which is a better fit.
>   

If the point is that you have many polygons to choose from, then the 
largest polygon that fits would "fit best."

Sincerely,

jw

[Algorithms] Thermal infrared techniques?

[Ron H. <rh...@cy...>]

Anyone have points to papers/tutorials/explanations of some algorithms 
for rendering a scene as it would appear through a thermal IR camera?  
As in military operations stuff.  Anything ranging from "good enough" to 
a decent approximation of reality is usable.

Thanks!

Re: [Algorithms] Thermal infrared techniques?

[Andy F. <an...@si...>]

Ron Hay wrote:
> Anyone have points to papers/tutorials/explanations of some algorithms 
> for rendering a scene as it would appear through a thermal IR camera?  
> As in military operations stuff.  Anything ranging from "good enough" to 
> a decent approximation of reality is usable.
>
> Thanks!
>
>   

Intuitively, render luminance (0.0 - 1.0) mapped to green with some 
overbrightness / glow effect.  How do you think that would work?

andy

Re: [Algorithms] Thermal infrared techniques?

[Jon W. <jw...@gm...>]

Ron Hay wrote:
> Anyone have points to papers/tutorials/explanations of some algorithms 
> for rendering a scene as it would appear through a thermal IR camera?  
> As in military operations stuff.  Anything ranging from "good enough" to 
> a decent approximation of reality is usable.
>   

What the military guys do is generally build a second set of textures 
for everything, where the texture values correspond to frequencies in 
the IR spectrum instead of the visible RGB spectrum. Additionally, as 
this is usually done for night vision, you render without lighting, but 
instead using fullbright (or some variation thereof) textures. The 
reason for this is that materials typically have very different behavior 
in the IR spectrum than in the visible spectrum -- a lawn, a garden 
hose, and a painted metal grate can all be "green," but they behave 
really differently in IR.
Depending on what kind of simulation you're doing, you might want to use 
a texture channel or two for parameters such as "decay," such that you 
can pass in a parameter like "time since last exposure to sunlight" and 
get a better emulation of how a scene will change over time -- different 
materials cool differently.
Finally, if you want to emulate the "look" of a particular IR sensor or 
display, you should get a copy of the real thing, or barring that, some 
video of the real thing, and add whatever artifacts you can see 
(striping, bright bands, knock-out, ringing, etc) as shader effects, 
until it's close enough.

Sincerely,

jw

Re: [Algorithms] Thermal infrared techniques?

[Ron H. <rh...@cy...>]

Thanks for the response - to answer some questions, it's the "colorful" 
variant of IR that's probably going to be emulated.  They additionally 
want night vision (which is an easier effect, in general).  I'm looking 
for a bit more than a different set of textures, which is, as Jon 
stated, pretty much all they have been doing.  We want to do it better, 
so I was try to edu-macate myself on some other possibilities using 
"modern" (aka "not 10 years old") hardware.  Some of the ideas you 
through out are a good start Jon :)

    Ron

Jon Watte wrote:
> Ron Hay wrote:
>   
>> Anyone have points to papers/tutorials/explanations of some algorithms 
>> for rendering a scene as it would appear through a thermal IR camera?  
>> As in military operations stuff.  Anything ranging from "good enough" to 
>> a decent approximation of reality is usable.
>>   
>>     
>
> What the military guys do is generally build a second set of textures 
> for everything, where the texture values correspond to frequencies in 
> the IR spectrum instead of the visible RGB spectrum. Additionally, as 
> this is usually done for night vision, you render without lighting, but 
> instead using fullbright (or some variation thereof) textures. The 
> reason for this is that materials typically have very different behavior 
> in the IR spectrum than in the visible spectrum -- a lawn, a garden 
> hose, and a painted metal grate can all be "green," but they behave 
> really differently in IR.
> Depending on what kind of simulation you're doing, you might want to use 
> a texture channel or two for parameters such as "decay," such that you 
> can pass in a parameter like "time since last exposure to sunlight" and 
> get a better emulation of how a scene will change over time -- different 
> materials cool differently.
> Finally, if you want to emulate the "look" of a particular IR sensor or 
> display, you should get a copy of the real thing, or barring that, some 
> video of the real thing, and add whatever artifacts you can see 
> (striping, bright bands, knock-out, ringing, etc) as shader effects, 
> until it's close enough.
>
> Sincerely,
>
> jw
>
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Re: [Algorithms] Thermal infrared techniques?

[Jon W. <jw...@gm...>]

Ron Hay wrote:
> stated, pretty much all they have been doing.  We want to do it better, 
> so I was try to edu-macate myself on some other possibilities using 
> "modern" (aka "not 10 years old") hardware.  Some of the ideas you 
> through out are a good start Jon :)
>   

The "colorful" IR is simply a palette map at the end of the shader. Once 
you have "intensity" then you map that to the S texture coordinate of a 
color ramp texture, and out comes the display color. Depending on which 
piece of hardware you want to emulate, typically you apply bloom BEFORE 
the palettization, which means you need some render target ping-pong-ing.

Sincerely,

jw

[Algorithms] Formula for Damping f times

[Zafar Q. <zaf...@co...>]

Hi,
This is a semi-trivial but I can't quite remember the answer, even
though I've done it before.

I have an update function sort of like this..

void updateX( float deltaTime)
{
	x = x*k;
}

k is a constant less than 1.0.

Now to do the damping properly I need to perform "x=x*k" deltaTime
times, where deltaTime is a fraction.

Can anyone help with this please? I recall it just being a log or
something.

Cheers
Zafar Qamar
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Re: [Algorithms] Formula for Damping f times

[Fabian G. <f.g...@49...>]

> Hi,
> This is a semi-trivial but I can't quite remember the answer, even
> though I've done it before.
> 
> I have an update function sort of like this..
> 
> void updateX( float deltaTime)
> {
> 	x = x*k;
> }
> 
> k is a constant less than 1.0.
> 
> Now to do the damping properly I need to perform "x=x*k" deltaTime
> times, where deltaTime is a fraction.
> 
> Can anyone help with this please? I recall it just being a log or
> something.

x *= pow(k,deltaTime);

Kind regards,
-Fabian Giesen

Re: [Algorithms] Formula for Damping f times

[<Pau...@sc...>]

-----BEGIN PGP SIGNED MESSAGE-----
Hash: SHA256

> Hi,
> This is a semi-trivial but I can't quite remember the answer, even
> though I've done it before.
> 
> I have an update function sort of like this..
> 
> void updateX( float deltaTime)
> {
>    x = x*k;
> }
> 
> k is a constant less than 1.0.
> 
> Now to do the damping properly I need to perform "x=x*k" deltaTime
> times, where deltaTime is a fraction.
> 
> Can anyone help with this please? I recall it just being a log or
> something.

We just do something very simple:

x *= 1.0f-(k*deltaTime);

So k = 1 = damped to zero velocity over 1 second at 30fps.

Cheers, Paul.
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