[vtk-developers] Class design for spline visualizations

[Lin M]

Hi Dr.Thompson,

I added the method to insert a knot multiple times based on the algorithm
in the NURBS book. It supports knot insertion for 3-d patches if it works
correctly. I tested it in 1-d case and it works well.

Best,
Lin

On Wed, Jun 24, 2015 at 4:38 PM, Lin M <majcjc at gmail.com> wrote:

> Hi Dr. Thompson,
>
> I implemented the InserKnot() method. Currently the API is like:
>
> void InsertKnot(
>     vtkDataArray* pointsOut, int* knotsLenNew, double* knotsArrNew, int*
> ctrlPtsNumNew,
>     double tNew, int insertDim,
>     vtkDataArray* pointsIn, int* knotsLen, double* knotsArr, int*
> ctrlPtsNum);
>
> I have submitted the code to gitlab (
> https://gitlab.kitware.com/splines/vtk/merge_requests/4). Please take a
> look at it. Thanks.
>
> Best,
> Lin
>
> On Wed, Jun 24, 2015 at 10:43 AM, Lin M <majcjc at gmail.com> wrote:
>
>> Hi Dr. Thompson,
>>
>> I'm writing the knot insertion method InsertKnot() and I hope it can be
>> used to handle both 1-d, 2-d and 3-d cases.
>>
>> 1. One question is that when converting a nurbs curve to a bezier curve,
>> eaca segment of a nurbs curve will correspond to a new bezier curve. So we
>> need to repeatedly retrieve a subset of the control points and the knot
>> vector from the original nurbs curve. To make the InserKnot() method more
>> generally. I define the API as
>>
>> void InsertKnot(
>> vtkPoints* pointsOut,
>> double tNew, int dim,
>> vtkPoints* pointsIn, int* knotsLen, double* knotsArr)
>>
>> // pointsOut stores the new control points
>> // tNew is the new knot we want to insert
>> // dim is the dimension where the new knot is
>> // pointsIn is the old control points (which is probably a subset of the
>> original nurbs control points)
>> // knotsLen stores the number of entries of the knots vector in each
>> dimension (I'll assume it is always a 1*3 int array)
>> // knotsArr stores the knot vector for all dimensions
>>
>> Do you think this API is proper?
>>
>> 2. The second question is that, as described in the first question, a
>> p-degree nurbs curve with a given knot vector actually will generate a
>> series of bezier curve. Each of the them corresponds to a segment of the
>> original nurbs curve. How can I find the subset of the control points and
>> knot vector for a segment?
>>
>> Best,
>> Lin
>>
>> On Mon, Jun 22, 2015 at 6:54 PM, David Thompson <
>> david.thompson at kitware.com> wrote:
>>
>>> Hi Lin,
>>>
>>> > 1. The definition of knot vector seems to be a little different from
>>> the NURBS book. In the NURBS book, a knot vector is defined as U =
>>> {a,...,a,u_{p+1},...,u_{m-p-1},b,...,b} where a and b are repeated p+1
>>> times (p is the degree of NURBS curve). And since NURBS cruve  is defined
>>> as C(u) = sum_{i,n}(N_{i,p}(u)*P_{i}),  the endpoints seems to be
>>> interpolated as well.
>>>
>>> NURBS do not require any knot vector entries to be repeated. Many
>>> examples in the NURBS book *happen* to have repeated entries, but it is not
>>> a requirement.
>>>
>>> > ...
>>> > 2. The previous section of the wiki page writes "The number of knots
>>> is always equal to the number of control points plus curve degree plus one
>>> (i.e. number of control points plus curve order)." Should it be degree + N
>>> + 1 = K ?
>>>
>>> From the wikipedia entry: "Some modelers that use older algorithms for
>>> NURBS evaluation require two extra knot values for a total of (degree+N+1)
>>> knots.[7]"  You can use whichever you like. I would advise sticking with
>>> the NURBS book because it has many examples worked out in detail. (The
>>> NURBS book appears to use the degree + N + 1 = K formulation.)
>>>
>>> > 3. I think the inference is only for a single patch.  If there are
>>> several patches in the vtkStructuredGrid, we can not get the number of
>>> control points for a certain patch by vtkStructuredGrid->GetDimension()
>>> unless we know the number of patches and the number of control points are
>>> the same for all these patches.
>>>
>>>
>>> Nope, you can use GetDimension() to discover the number, N, of control
>>> points for all patches. That is related to the degree by the number of knot
>>> vector entries for all patches. We have not specified how the knot vector
>>> would be stored. If stored as an array in vtkFieldData, then   we would
>>> also have to store the number entries along each axis (the equivalent
>>> information as GetDimension() returns for the control points). Or we could
>>> store the degree along each axis and use that to determine the size of the
>>> knot vector along each axis... whichever you prefer.
>>>
>>>         David
>>
>>
>>
>
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