Re: Intersect Point of a 3D Parametric Line & B-Spline Surface
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- Subject: [mg132170] Re: Intersect Point of a 3D Parametric Line & B-Spline Surface
- From: Bob Hanlon <hanlonr357 at gmail.com>
- Date: Thu, 9 Jan 2014 01:50:50 -0500 (EST)
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- References: <20140108035226.99D546A06@smc.vnet.net>
paraLine = ParametricPlot3D[ {2 + t, 2 + 3 t, 2 t}, {t, -1, 1}, PlotRange -> {{0, 5}, {0, 5}, {-1, 1}}, PlotStyle -> {Red, Thickness[0.004]}, ViewPoint -> {4, 2, 1}, AxesLabel -> {"X", "Y", "Z"}, Background -> LightYellow, ImageSize -> 500]; 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`}}}; surf = Graphics3D[BSplineSurface[cpts]]; 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]]; ip = FindRoot[{ x == 2 + t == gx[u, v], y == 2 + 3 t == gy[u, v], z == 2 t == gz[u, v]}, {{x, 2}, {y, 2}, {z, 0}, {t, 0}, {u, .2, 0, 1}, {v, .2, 0, 1}}] {x -> 1.95648, y -> 1.86945, z -> -0.0870339, t -> -0.043517, u -> 0.191361, v -> 0.170743} {x, y, z} == {2 + t, 2 + 3 t, 2 t} == f[u, v] /. ip True Show[paraLine, surf] Show[paraLine, ParametricPlot3D[f[u, v], {u, 0, 1}, {v, 0, 1}]] Bob Hanlon On Tue, Jan 7, 2014 at 10:52 PM, Bill <WDWNORWALK at aol.com> wrote: > Hi: > > I have the following Mathematica 8.0.4. code that plots a parametric 3D > line and a surface using BSplineSurface. > > paraLine=ParametricPlot3D[{2+t,2+t 3,t 2}, {t,-1,1},PlotRange -> {{0, > 5},{0, 5},{-1, 1}}, PlotStyle->{Red,Thickness[0.004]},ViewPoint->{4,2,1}, > AxesLabel -> {"X", "Y", "Z"},Background->LightYellow,ImageSize->500]; > > cpts={{{1,1,-0.5740579178735179`},{1,2,0.3902669640296943`},{1,3,0.6162= 142022057271`},{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,-0.1969086942= 688163`},{3,2,0.7961076758026819`},{3,3,-0.060290070096196136`},{3,4,0.4866= 5856202059254`},{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`},{5,2,0.786581533= 6945703`},{5,3,-0.6672322036832838`},{5,4,0.5688838564868042`},{5,5,0.55410= 79809436917`}}}; > surf=Graphics3D[BSplineSurface[cpts]]; > Show[paraLine,surf] > > > Question: How can the intersect point coordinates of the line and surface > be found by using Mathematica? > > I think the Mathematica code maybe something like this: > > NSolve[x==2+t && y==2+t 3 && z==t 2 && (?),{x,y,z,t}] > > but I don't know how to enter the BSplineSurface. > > > Thanks, > > Bill W. > >
- References:
- Intersect Point of a 3D Parametric Line & B-Spline Surface
- From: Bill <WDWNORWALK@aol.com>
- Intersect Point of a 3D Parametric Line & B-Spline Surface