Re: [Help-gsl] Using GSL to draw a 2D B-Spline path using unevenly spaced points

[Michael Petrie]

There is also an in depth answer by Vinicius Miranda on Stack Overflow if
anyone's interested for future reference.

http://stackoverflow.com/questions/24194909/using-gnu-scientific-library-gsl-to-draw-a-2d-b-spline-path-using-unevenly-spa

Best,

Michael


2014-06-16 9:31 GMT+12:00 Michael Petrie <address@hidden>:

> Hi Foivos,
>
> Thank you very much for your in depth reply. It's great to have someone
> who has some experience in this area point me in the right direction. Also,
> the links you have provided look very helpful. It's clear that I need to do
> some more learning before being able to exactly what I want with GSL. In
> the mean time, I'll give openNURBS a go - it does seem more suited to what
> I would like to achieve.
>
> Many thanks,
>
> Michael
>
>
> 2014-06-13 19:47 GMT+12:00 Foivos Diakogiannis <
> address@hidden>:
>
> Hi Michael and all,
>>
>> I am not a GSL software engineer, but I've been using heavily BSplines
>> and GSL for scientific purposes.
>> To your questions:
>>
>> It is possible to create any geometric shape with BSplines. The
>> implementation in GSL has some limitations (with regards to knot
>> distributions, multiplicity of knots, fixed multiplicity in first/last
>> knots etc) but - at least for scientific applications - I have found all
>> that I need. So your geometric shape (purple points) it is feasible to be
>> constructed with a 2D BSpline representation. Unfortunately I don't think
>> you can reconstruct the purple line with only the red points -
>> statistically speaking you have very little information. By the way for 2D
>> BSplines you'll have to do it "by hand" so you'll really need to study the
>> theory of BSplines. Check this link for more info a d references therein:
>> http://www.cs.mtu.edu/~shene/COURSES/cs3621/NOTES/
>>
>> As for the appropriate knot distribution for this, in my experience there
>> is no single choice and there is ongoing research int this direction. The
>> best method seems to be be implementing Genetic Algorithms in order to find
>> the best distribution of knots for a particular data set (am writing a
>> codel for this, slowly ...) . See
>> http://www.sciencedirect.com/science/article/pii/S001044850300006X
>>
>> If you need BSplines for scientific purposes I think GSL is great!! You
>> may need to tweak it a bit, see the .h and .c files of the distribution,
>> they have a lot of comments and you'll understand more the theory of
>> BSplines. If you want for computer design and graphics, BSplines are not
>> the standard any more, you'll have to pass to NURBS, and a nice library is
>> this:
>>
>> http://www.rhino3d.com/opennurbs
>>
>> in general with a search for nurbs you'll find many more things for
>> computer design.
>>
>>
>> Hope the above help,
>> Cheers,
>> Foivos
>>
>>
>>
>> On Fri, Jun 13, 2014 at 6:56 AM, Michael Petrie <address@hidden
>> > wrote:
>>
>>> Hi, my name's Michael, and I'm new to the mailing list, so forgive me if
>>> I'm asking this question in the wrong place.
>>>
>>> I'm trying to using the GNU Scientific Library (GSL) to draw a smooth
>>> path
>>> from A to B. I'm using an API that returns a small number (8 in this
>>> case)
>>> of irregularly spaced points (in red), that you can see picture [1].
>>>
>>> The purple points represent the points that I would like to see returned
>>> from GSL.
>>>
>>> Firstly, is this kind of 2D B-Spline shape obtainable by using GSL? I
>>> don't
>>> know much about B-Splines, let alone 2D B-Splines. I was able to get the
>>> B-Splines example at link [2] running and creating a smooth .ps file
>>> without problem, but that example uses uniform breakpoints with the
>>> following code:
>>>
>>>     /* use uniform breakpoints on [0, 15] */
>>>     gsl_bspline_knots_uniform(0.0, 15.0, bw);
>>>
>>> In my case, given that the data I'm given is erratic and not evenly
>>> spaced,
>>> would I have to use non-uniform knots? I tried using
>>> `gsl_bspline_knots()`,
>>> in order to use non uniform breakpoints within the following test code,
>>> but
>>> I'm really not sure if this is the right direction or not.
>>>
>>>     #define NCOEFFS 8 // not sure what this number should be - number of
>>> data points?
>>>     #define NBREAK   (NCOEFFS - 2)
>>>     const size_t nbreak = NBREAK;
>>>
>>>     int main (void) {
>>>
>>>         // (example code)...
>>>
>>>         gsl_vector *non_uniform = gsl_vector_alloc(nbreak);
>>>
>>>         // create some random breakpoint values
>>>         for (i=0; i<nbreak; i++) {
>>>             double val = gsl_ran_gaussian(r, 2.0);
>>>             printf("val: %f\n", val);
>>>             gsl_vector_set(non_uniform, i, val);
>>>         }
>>>
>>>         gsl_bspline_knots(non_uniform, bw);
>>>
>>>         // (more example code)...
>>>     }
>>>
>>> Further more, how would I translate the above example for drawing
>>> B-Splines
>>> in a 2D x/y coordinate space? If GNU Scientific Library is not suitable
>>> for
>>> this, could someone make a recommendation for a more suitable C/C++
>>> library?
>>>
>>> Any help or pointers in the direction would be much appreciated.
>>>
>>>   [1]: http://i.stack.imgur.com/mpxbx.png
>>>   [2]:
>>>
>>> http://www.gnu.org/software/gsl/manual/html_node/Example-programs-for-B_002dsplines.html#Example-programs-for-B_002dsplines
>>>
>>> PS, I have also asked this question at Stack Overflow too:
>>>
>>> http://stackoverflow.com/questions/24194909/using-gnu-scientific-library-gsl-to-draw-a-2d-b-spline-path-using-unevenly-spa
>>>
>>> --
>>> Michael Petrie
>>> Mobile Developer
>>> +64 21 022 99121
>>> address@hidden
>>>
>>>
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>>
>>
>
>
> --
> Michael Petrie
> Mobile Developer
> +64 21 022 99121
> address@hidden
>
>
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>



-- 
Michael Petrie
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