Re: Distance Between a B-Spline Surface & Point
- To: mathgroup at smc.vnet.net
- Subject: [mg132243] Re: Distance Between a B-Spline Surface & Point
- From: Bob Hanlon <hanlonr357 at gmail.com>
- Date: Wed, 22 Jan 2014 03:31:06 -0500 (EST)
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- References: <20140121080248.A720969E5@smc.vnet.net>
This is a correction to my previous response. Additional constraints need to be included to get the minimum distance. cpts = {{{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}}}; f = BSplineFunction[cpts]; gx[u_?NumericQ, v_?NumericQ] := f[u, v][[1]]; gy[u_?NumericQ, v_?NumericQ] := f[u, v][[2]]; gz[u_?NumericQ, v_?NumericQ] := f[u, v][[3]]; zmin = NMinimize[{gz[u, v], 0 <= u <= 1, 0 <= v <= 1}, {u, v}, Method -> "DifferentialEvolution"][[1]] -0.574058 zmax = NMaximize[{gz[u, v], 0 <= u <= 1, 0 <= v <= 1}, {u, v}, Method -> "DifferentialEvolution"][[1]] 0.554369 pt = {2, 3, 4}; {dist, sol} = NMinimize[{Norm[pt - {x, y, z}], gx[u, v] == x, gy[u, v] == y, gz[u, v] == z, 0 <= u <= 1, 0 <= v <= 1, 1 <= x <= 5, 1 <= y <= 5, zmin <= z <= zmax}, {x, y, z, u, v}, Method -> "DifferentialEvolution"] // Chop {3.72822, {x -> 1., y -> 2.75868, z -> 0.416516, u -> 0, v -> 0.420237}} surfPt = {x, y, z} /. sol {1., 2.75868, 0.416516} f[u, v] /. sol {1., 2.75868, 0.416515} Norm[pt - surfPt] == dist True (f[u, v] /. sol) {1., 2.75868, 0.416515} Show[ParametricPlot3D[f[u, v], {u, 0, 1}, {v, 0, 1}], Graphics3D[{Thick, Line[{pt, surfPt}], Red, AbsolutePointSize[6], Point[{pt, surfPt}]}], PlotRange -> {{1, 5}, {1, 5}, {-1, 4}}] Bob Hanlon On Tue, Jan 21, 2014 at 3:41 PM, Bob Hanlon <hanlonr357 at gmail.com> wrote: > cpts={ > {{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}}}; > > f=BSplineFunction[cpts]; > > gx[u_?NumericQ,v_?NumericQ]:=f[u,v][[1]]; > gy[u_?NumericQ,v_?NumericQ]:=f[u,v][[2]]; > gz[u_?NumericQ,v_?NumericQ]:=f[u,v][[3]]; > > pt={2,3,4}; > > {dist,sol}=NMinimize[{Norm[pt-{x,y,z}], > gx[u,v]==x,gy[u,v]==y,gz[u,v]==z, > 0<=u<=1,0<=v<=1}, > {x,y,z,u,v}] > > {4.13757,{x->2.24681,y->1.00001,z->0.386337,u->0.266016,v->8.48701*10^-7}= } > > (Norm[pt-{x,y,z}]/.sol)==dist > > True > > f[u,v]/.sol > > {2.24681,1.00001,0.386337} > > surfPt={x,y,z}/.sol > > {2.24681,1.00001,0.386337} > > Show[ > ParametricPlot3D[f[u,v],{u,0,1},{v,0,1}], > Graphics3D[{ > Thick,Line[{pt,surfPt}], > Red,AbsolutePointSize[6],Point[{pt,surfPt}]}], > PlotRange->All] > > > Bob Hanlon > > > > On Tue, Jan 21, 2014 at 3:02 AM, Bill <WDWNORWALK at aol.com> wrote: > >> Hi: >> >> My objective: Find the Distance Between a B-Spline Surface and a Point, >> {2,3,4}. >> >> (Note: The point {2,3,4}, is not on the B-spline surface.) >> >> >> Below is the Mathematica 8.0.4. code I used to try and find the closest >> point on the B-spline surface to the point {2,3,4}: >> >> >> cpts={{{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,-0.0998= 629},{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,-0.66= 7232},{5,4,0.568884},{5,5,0.554108}}}; >> >> f=BSplineFunction[cpts]; >> >> gx[u_?NumericQ,v_?NumericQ]:=f[u,v][[1]] >> gy[u_?NumericQ,v_?NumericQ]:=f[u,v][[2]] >> gz[u_?NumericQ,v_?NumericQ]:=f[u,v][[3]] >> >> NMinimize[{(x-2)^2 +(y-3)^2+(z-4)^2<=5 && x==gx && y==gy && >> z==gz},{x,y,z,u,v}] >> >> Out(Error message.) >> >> >> Questions: Can this be done using NMinimize? If so, how should this be >> coded? If not, how can this be done using Mathematica. >> >> >> Thanks again, >> >> Bill W. >> >> >
- References:
- Distance Between a B-Spline Surface & Point
- From: Bill <WDWNORWALK@aol.com>
- Distance Between a B-Spline Surface & Point