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Re: BSplineSurface & BSplineFunction_Extracting Data

• To: mathgroup at smc.vnet.net
• Subject: [mg132230] Re: BSplineSurface & BSplineFunction_Extracting Data
• From: Bob Hanlon <hanlonr357 at gmail.com>
• Date: Tue, 21 Jan 2014 03:01:28 -0500 (EST)
• Delivered-to: l-mathgroup@mail-archive0.wolfram.com
• Delivered-to: l-mathgroup@wolfram.com
• Delivered-to: mathgroup-outx@smc.vnet.net
• Delivered-to: mathgroup-newsendx@smc.vnet.net
• References: <20140120090005.1529C69D2@smc.vnet.net>

cpts = {
   {{1, 1, -0.5740579178735179`}, {1, 2, 0.3902669640296943`},
    {1, 3, 0.6162142022057271`}, {1, 4, -0.11572153782589911`},
    {1, 5, 0.436662579150056`}},
   {{2, 1, 0.8096824307907462`}, {2, 2, -0.7419265507701529`},
    {2, 3, -0.8659156744537175`}, {2, 4, -0.0998628811371658`}, {2,
     5, -0.24185346526195106`}},
   {{3, 1, -0.1969086942688163`}, {3, 2, 0.7961076758026819`},
    {3, 3, -0.060290070096196136`}, {3, 4, 0.48665856202059254`},
    {3, 5, -0.013419247141178037`}},
   {{4, 1, 0.6573342854316904`}, {4, 2, -0.9170657725998455`},
    {4, 3, 0.9830103505987027`}, {4, 4, -0.8759376369982923`},
    {4, 5, -0.03030297194593956`}},
   {{5, 1, -0.549653902873303`}, {5, 2, 0.7865815336945703`},
    {5, 3, -0.6672322036832838`}, {5, 4, 0.5688838564868042`},
    {5, 5, 0.5541079809436917`}}};


f = BSplineFunction[cpts];


>From documentation for SplineWeights (
http://reference.wolfram.com/mathematica/ref/SplineWeights.html):
"SplineWeights->Automatic makes all weights equal, yielding polynomial
splines."


Consequently, you can use any value.


splineWts=ConstantArray[Random[],Most[Dimensions[cpts]]];


Graphics3D[

BSplineSurface[cpts,

SplineKnots->f[[6]],

SplineDegree->3,

SplineWeights->splineWts]]



Bob Hanlon




On Mon, Jan 20, 2014 at 4:00 AM, Bill <WDWNORWALK at aol.com> wrote:

> Hi:
>
> I have the following Mathematica 8.0.4. code which plots the following:
>
> In[1]:=
>  cpts={{{1,1,-0.5740579178735179`},{1,2,0.3902669640296943`},{1,3,0.616=
2142022057271`},{1,4,-0.11572153782589911`},{1,5,0.436662579150056`}},{{2,1=
,0.8096824307907462`},{2,2,-0.7419265507701529`},{2,3,-0.8659156744537175`}=
,{2,4,-0.0998628811371658`},{2,5,-0.24185346526195106`}},{{3,1,-0.196908694=
2688163`},{3,2,0.7961076758026819`},{3,3,-0.060290070096196136`},{3,4,0.486=
65856202059254`},{3,5,-0.013419247141178037`}},{{4,1,0.6573342854316904`},{=
4,2,-0.9170657725998455`},{4,3,0.9830103505987027`},{4,4,-0.875937636998292=
3`},{4,5,-0.03030297194593956`}},{{5,1,-0.549653902873303`},{5,2,0.78658153=
36945703`},{5,3,-0.6672322036832838`},{5,4,0.5688838564868042`},{5,5,0.5541=
079809436917`}}};
> surf1=Graphics3D[BSplineSurface[cpts]];
>
> (*Plot omitted.*)
>
> I then used the following code to extract data:  Note "Automatic" at the
> end in Out[4].
>
> In[3]:=  f=BSplineFunction[cpts]
>
> Out[3]=  BSplineFunction[{{0.,1.},{0.,1.}},<>]
>
> In[4]:= f[[5]],f[[6]]
>
> Out[4]=
> {{{{1.,1.,-0.574058},{1.,2.,0.390267},{1.,3.,0.616214},{1.,4.,-0.115722},=
{1.,5.,0.436663}},{{2.,1.,0.809682},{2.,2.,-0.741927},{2.,3.,-0.865916},{2.=
,4.,-0.0998629},{2.,5.,-0.241853}},{{3.,1.,-0.196909},{3.,2.,0.796108},{3.,=
3.,-0.0602901},{3.,4.,0.486659},{3.,5.,-0.0134192}},{{4.,1.,0.657334},{4.,2=
.,-0.917066},{4.,3.,0.98301},{4.,4.,-0.875938},{4.,5.,-0.030303}},{{5.,1.,-=
0.549654},{5.,2.,0.786582},{5.,3.,-0.667232},{5.,4.,0.568884},{5.,5.,0.5541=
08}}},Automatic}
>
> Out[5]=
> {{0.,0.,0.,0.,0.5,1.,1.,1.,1.},{0.,0.,0.,0.,0.5,1.,1.,1.,1.}}
>
> In[6]:= {uk,vk}=%;
>
> In[7]:=surf2=Graphics3D[{BSplineSurface[cpts,SplineKnots->{uk,vk},Spl=
ineDegree->3,SplineWeights
> ->Automatic];
>
> (*Plot omitted.*)
>
> Question:  Is there some way to extract the SplineWeights values that
> Mathematica used for "SplineWeights ->Automatic"?
>
>
> Thanks,
>
> Bill W.
>
>

• References:
  • BSplineSurface & BSplineFunction_Extracting Data
    • From: Bill <WDWNORWALK@aol.com>