Question about Estimation of Local Differential Properties

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Question about Estimation of Local Differential Properties

graphicsRat
Hello -

I'm looking to use the jet-fitting algorithm to compute the principal
curvature and directions at various non-vertex points of a (triangular
mesh) i.e. my points of interest lie on the faces of a mesh, and by
definition, do not coincide with its vertexes.

My question however concerns the method used by the implementation of
the jet-fitting algorithm in this case. I would like to confirm if the
jet-fitting algorithm uses an (a) interpolation or (b) approximation
approach to compute the differential properties at such no-vertex points
-- the former would be preferred.

I'm aware that this issue was discussed on page 12 of "Jet fitting 3: A
Generic C++ Package for Estimating the Differential Properties on
Sampled Surfaces via Polynomial Fitting", but I found the reading a bit
confusing probably because I'm only just learning the algorithm.

Thanks,

- Olumide


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Re: Question about Estimation of Local Differential Properties

Marc Pouget
Hello,

i summarize here the discussion we had by phone:

you can use interpolation with the jet fitting if you give exactly  
the nb of points that correspond to the nb of constraints.

Then, by default, the differential quantities returned are those  
computed at the projection of the first point you have given on the  
fitted polynomial surface.

If you want to compute the quantities for another point p, and you  
dont want this point to be taken into account to do the fitting  
(either-wise just give this point first and you are done); you can  
just project this point on the fitted surface (that is given by the  
monge form in the monge coordinate system) and compute the diff  
quantities by classical diff geo formula.

I may consider adding this functionality in the future ...

best
Marc


On 28 , May , 2008, at 06:42 , Olumide wrote:

> Hello -
>
> I'm looking to use the jet-fitting algorithm to compute the  
> principal curvature and directions at various non-vertex points of  
> a (triangular mesh) i.e. my points of interest lie on the faces of  
> a mesh, and by definition, do not coincide with its vertexes.
>
> My question however concerns the method used by the implementation  
> of the jet-fitting algorithm in this case. I would like to confirm  
> if the jet-fitting algorithm uses an (a) interpolation or (b)  
> approximation approach to compute the differential properties at  
> such no-vertex points -- the former would be preferred.
>
> I'm aware that this issue was discussed on page 12 of "Jet fitting  
> 3: A Generic C++ Package for Estimating the Differential Properties  
> on Sampled Surfaces via Polynomial Fitting", but I found the  
> reading a bit confusing probably because I'm only just learning the  
> algorithm.
>
> Thanks,
>
> - Olumide
>
>
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> You are currently subscribed to cgal-discuss.
> To unsubscribe or access the archives, go to
> https://lists-sop.inria.fr/wws/info/cgal-discuss

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Is there an existing function to get the bbox of a polyhedron_3

Max-151
hi,

I want to get the (axis aligned) bounding box of a given polyhedron_3.
I don't know if there is an existing funtion to do this.

thanks for any hints.

B/Rgds
Max

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Re: Is there an existing function to get the bbox of a polyhedron_3

andreas.fabri
Max wrote:

> hi,
>
> I want to get the (axis aligned) bounding box of a given polyhedron_3.
> I don't know if there is an existing funtion to do this.
>
> thanks for any hints.
>
> B/Rgds
> Max
>

Hi Max,

There is no bbox() member function that caches and updates
the bbox whenever you change the Polyhedron_3.

The most compact piece of code for computing the bbox in linear time
looks like this


#include <CGAL/bounding_box.h>

Polyhedron_3 poly;


CGAL Bbox_3 bb  = CGAL::bounding_box(poly.points_begin(), points_end()).bbox();


andreas
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Re: Re: Is there an existing function to get the bboxof a polyhedron_3

Max-151
>Hi Max,
>
>There is no bbox() member function that caches and updates
>the bbox whenever you change the Polyhedron_3.
>
>The most compact piece of code for computing the bbox in linear time
>looks like this
>
>
>#include <CGAL/bounding_box.h>
>
>Polyhedron_3 poly;
>
>
>CGAL Bbox_3 bb  = CGAL::bounding_box(poly.points_begin(), points_end()).bbox();
>
>
>andreas

Hello andreas,

Thank you very much for your quick and detailed reply.
That's enough for my current demand.

B/Rgds
Max

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Re: Is there an existing function to get the bboxof a polyhedron_3

Max-151
>Hello andreas,
>
>Thank you very much for your quick and detailed reply.
>That's enough for my current demand.
>
>B/Rgds
>Max

Just one more question - suppose I have a bunch of bbox_3,
what is the convenient way to get the 'union' of them.

Thanks and B/Rgds.
Max


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Re: Is there an existing function to get the bboxof

Ashwin Nanjappa-2
Max wrote:
>
> Just one more question - suppose I have a bunch of bbox_3,
> what is the convenient way to get the 'union' of them.

There doesn't seem to be a function that does this. But, using the values
of x/y/z-min(), x/y/z-max(), you can easily create a function that does
this for your bbox_3 list.

Regards,
~ash
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Re: Is there an existing function to get the bboxof

Sylvain Pion
Administrator
Ashwin Nanjappa a écrit :
> Max wrote:
>> Just one more question - suppose I have a bunch of bbox_3,
>> what is the convenient way to get the 'union' of them.
>
> There doesn't seem to be a function that does this. But, using the values
> of x/y/z-min(), x/y/z-max(), you can easily create a function that does
> this for your bbox_3 list.

Maybe std::accumulate ?

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Sylvain Pion
INRIA Sophia-Antipolis
Geometrica Project-Team
CGAL, http://cgal.org/


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Re: Is there an existing function to get the bboxof

Ashwin Nanjappa-2
Sylvain Pion wrote:
> Ashwin Nanjappa a écrit :
>> Max wrote:
>>> Just one more question - suppose I have a bunch of bbox_3,
>>> what is the convenient way to get the 'union' of them.
>> There doesn't seem to be a function that does this. But, using the values
>> of x/y/z-min(), x/y/z-max(), you can easily create a function that does
>> this for your bbox_3 list.
>
> Maybe std::accumulate ?

That would be an elegant way to implement it! Thanks for the suggestion, I
wasn't aware of this STL function.

Regards,
~ash

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