[vtk-developers] Class design for spline visualizations

[Lin M]

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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