[vtk-developers] Class design for spline visualizations

[David Thompson]

Hi Lin,

That sounds great. While I take a look at it, perhaps you could work on generating triangle strips for surfaces? Then we will be ready to render 2D versions as part of the test for knot insertion.

Do you need more information on triangle strips in VTK or was my last message enough?

	Thanks,
	David

> On Jun 25, 2015, at 7:04 PM, Lin M <majcjc at gmail.com> wrote:
> 
> 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
> 
> 
>