POV-Ray : Newsgroups : povray.binaries.images : Visualizing camera view frustum Server Time: 25 Feb 2017 14:03:01 GMT
  Visualizing camera view frustum (Message 1 to 8 of 8)  
From: Bald Eagle
Subject: Visualizing camera view frustum
Date: 16 Jan 2017 15:20:01
Message: <web.587ce3fc782d1af2c437ac910@news.povray.org>
I worked a lot of what I needed out, and it mostly works the way I want it to.
Still a few small things that I haven't fixed / perfected.

But now I can plot out the camera's view frustum, and do some basic culling /
clipping.

Questions, comments, and suggestions for fixes & further developments welcome.


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viewfrustrumtest1.png


 

From: Bald Eagle
Subject: Re: Visualizing camera view frustum
Date: 16 Jan 2017 15:35:01
Message: <web.587ce70b1652a4dcc437ac910@news.povray.org>
meta-view:


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viewfrustumtest2.png


 

From: Bald Eagle
Subject: Re: Visualizing camera view frustum
Date: 16 Jan 2017 20:20:01
Message: <web.587d2a171652a4dcc437ac910@news.povray.org>
Working on some of this to do bounding boxes, and if that works, I might look
into octree culling.
Currently I need to figure out a quick and direct way to establish the p-vertex
and n-vertex.

https://books.google.com/books?id=CCqzMm_-WucC&pg=PA74&lpg=PA74&dq=ned+greene+frustum&source=bl&ots=mtnu29NEfj&sig=TvSJ
4OWFFaRb6c0RiSbtXD9pbww&hl=en&sa=X&ved=0ahUKEwjzsZm9mcfRAhVCOCYKHcBuCXYQ6AEIIjAB#v=onepage&q=ned%20greene%20frustum&f=f
alse


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From: Mike Horvath
Subject: Re: Visualizing camera view frustum
Date: 19 Jan 2017 03:51:45
Message: <588037d1$1@news.povray.org>
On 1/16/2017 10:17 AM, Bald Eagle wrote:
> I worked a lot of what I needed out, and it mostly works the way I want it to.
> Still a few small things that I haven't fixed / perfected.
>
> But now I can plot out the camera's view frustum, and do some basic culling /
> clipping.
>
> Questions, comments, and suggestions for fixes & further developments welcome.
>

Are you using a perspective camera or orthographic?

Mike


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From: Bald Eagle
Subject: Re: Visualizing camera view frustum
Date: 19 Jan 2017 13:00:01
Message: <web.5880b8311652a4dcc437ac910@news.povray.org>
Mike Horvath <mik### [at] gmailcom> wrote:


> Are you using a perspective camera or orthographic?


I had hoped that the diagram would clearly show the perspective camera's frustum
- an orthographic view frustum would appear as a rectangular solid instead of a
[truncated] square-base pyramid.

I found a good an very fast method of determining the p-vertex,
http://www.txutxi.com/?p=584
but I'm currently struggling with understanding _exactly_ how planes and their
normals get calculated.

I'm using equations from Paul Bourke's site to calculate the A, B, C and (-)D
coefficients in the plane equation,

#declare Point1 = <-1, 0.5, 1>;
#declare Point2 = <1, -0.25, 1>;
#declare Point3 = <0, -1, -1>;

cylinder {Point1, Point2 0.005 texture {pigment {Black}} }
cylinder {Point2, Point3 0.005 texture {pigment {Black}} }
cylinder {Point3, Point1 0.005 texture {pigment {Black}} }


// derive the plane equation
#declare A1 = Point1.y*(Point2.z-Point3.z) + Point2.y*(Point3.z-Point1.z) +
Point3.y*(Point1.z-Point2.z);
#declare B1 = Point1.z*(Point2.x-Point3.x) + Point2.z*(Point3.x-Point1.x) +
Point3.z*(Point1.x-Point2.x);
#declare C1 = Point1.x*(Point2.y-Point3.y) + Point2.x*(Point3.y-Point1.y) +
Point3.x*(Point1.y-Point2.y);
#declare D1 = -1*(Point1.x*(Point2.y*Point3.z-Point3.y*Point2.z) +
Point2.x*(Point3.y*Point1.z-Point1.y*Point3.z) +
Point3.x*(Point1.y*Point2.z-Point2.y*Point1.z));
#declare L = vlength (<A1, B1, C1>);

and after much fiddling, got the plane to pass through the three points, and the
p-vertex to be where I think it ought to be.

I'd like to figure out the length and direction of the normal vector of the
plane, and how to calculate the position of a point in the plane that is closest
to a point not in the plane (in this case, the p-vertex).

Likely there's a way to use POV-Ray's vector functions, and macros, with
rotations and translations, but I'd like to use a direct calculation - something
that would be straight out of analytical geometry.
(I looked through Friedrich Lohmueller's site and his analytical_g.inc file, but
I didn't find exactly what I was looking for - maybe I missed it)

[I am, admittedly, probably not thinking about this in the right way, and am
thus overcomplicating it for myself as usual]


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From: Bald Eagle
Subject: Re: Visualizing camera view frustum
Date: 19 Jan 2017 17:55:01
Message: <web.5880fc4d1652a4dcc437ac910@news.povray.org>
Whee!

Thanks to:
http://math.stackexchange.com/questions/723937/find-the-point-on-a-plane-3x-4y-z-1-that-is-closest-to-1-0-1

I worked out:

sphere {Pvertex 0.05 texture {pigment {Red} finish {specular 0.6}} }

// for plane A1*x+B1*y+C1*z=D1, what is closest point on plane to Pvertex?
// Normal vector to plane is <A1, B1, C1>
// closest point is some multiple of <A1, B1, C1> added to <Pvertex.x,
Pvertex.y, Pvertex.z>
// P = <Pvertex.x, Pvertex.y, Pvertex.z> + c*<A1, B1, C1> = <(Pvertex.x+c*A1),
(Pvertex.y+c*B1), (Pvertex.z+c*C1)>
// substitute this into the plane equation
// A1*(Pvertex.x+c*A1) + B1*(Pvertex.y+c*B1) + C1*(Pvertex.z+c*C1)> = D1
// A1*Pvertex.x+pow(A1,2)*c) + B1*Pvertex.y+pow(B1,2)*c) +
C1*Pvertex.z+pow(C1,2)*c) = D1
// (A1*Pvertex.x) + (B1*Pvertex.y) + (C1*Pvertex.z) + pow(A1,2)*c) +
pow(B1,2)*c) + pow(C1,2)*c) = D1
// pow(A1,2)*c) + pow(B1,2)*c) + pow(C1,2)*c) = D1 - ( (A1*Pvertex.x) +
(B1*Pvertex.y) + (C1*Pvertex.z) )
// c = D1 - ( (A1*Pvertex.x) + (B1*Pvertex.y) + (C1*Pvertex.z) ) / ( pow(A1,2) +
pow(B1,2) + pow(C1,2) )
#declare c = (D1 - ( (A1*Pvertex.x) + (B1*Pvertex.y) + (C1*Pvertex.z) ) ) / (
pow(A1,2) + pow(B1,2) + pow(C1,2) );
#debug concat ("c = ", str(c, 3, 3), "\n")
#declare P = Pvertex + (c*<A1, B1, C1>);
#debug concat ("Point on plane is: <", vstr(3, P, ", ", 3, 3), ">  \n")

sphere {P 0.05 texture {pigment {Green} finish {specular 0.6}} }
cylinder {P, Pvertex, 0.025 texture {pigment {Green} finish {specular 0.6} }}


and this looks good.  (finally)

Hopefully I'll have more time to work out some more of the code, optimize the
macros, and make a nice test scene.


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From: Bald Eagle
Subject: Re: Visualizing camera view frustum
Date: 20 Jan 2017 15:10:00
Message: <web.588227ff1652a4dcc437ac910@news.povray.org>
Mike Horvath <mik### [at] gmailcom> wrote:

> Are you using a perspective camera or orthographic?

I re-read this, and:
The camera for the native scene - using screen.inc, is perspective.
I have rear, side, and orthographic views that use an orthographic camera to
view the native perspective camera's frustum in the "meta-scene"
The side-rear view of the perspective frustum uses a perspective camera.

I've seen some references that define other frustrums (frusta?) that reshape the
perspective frustum into a rectangular solid ("clipping frustum") I suppose for
easier handling of the data.
That uses a matrix to transform the perspective frustum and object coordinates.

I don't see why a frustum for the native scene couldn't be orthographic - future
work.   :)


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From: Mike Horvath
Subject: Re: Visualizing camera view frustum
Date: 24 Jan 2017 21:31:34
Message: <5887c7b6$1@news.povray.org>
On 1/20/2017 10:08 AM, Bald Eagle wrote:
> Mike Horvath <mik### [at] gmailcom> wrote:
>
>> Are you using a perspective camera or orthographic?
>
> I re-read this, and:
> The camera for the native scene - using screen.inc, is perspective.
> I have rear, side, and orthographic views that use an orthographic camera to
> view the native perspective camera's frustum in the "meta-scene"
> The side-rear view of the perspective frustum uses a perspective camera.
>
> I've seen some references that define other frustrums (frusta?) that reshape the
> perspective frustum into a rectangular solid ("clipping frustum") I suppose for
> easier handling of the data.
> That uses a matrix to transform the perspective frustum and object coordinates.
>
> I don't see why a frustum for the native scene couldn't be orthographic - future
> work.   :)
>
>
>


I made a habit of using direction, location, up and right instead of 
look_at, angle and sky. This makes such calculations a lot easier.

Mike


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