Re: BSplineSurface & BSplineFunction_Extracting Data

*To*: mathgroup at smc.vnet.net*Subject*: [mg132239] Re: BSplineSurface & BSplineFunction_Extracting Data*From*: Itai Seggev <itais at wolfram.com>*Date*: Tue, 21 Jan 2014 03:48:35 -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>

On Mon, Jan 20, 2014 at 04:00:05AM -0500, Bill 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`},{1,3,0.6162142022057271`},{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`}}}; > 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.,0.554108}}},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},SplineDegree->3,SplineWeights ->Automatic]; > > (*Plot omitted.*) > > Question: Is there some way to extract the SplineWeights values that Mathematica used for "SplineWeights ->Automatic"? That is documented to weight all points equally, so it is effecively equal to ConstantArray[1, Most @ Dimensions[cpts]]. -- Itai Seggev Mathematica Algorithms R&D

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