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Intersect Point of a 3D Parametric Line & B-Spline Surface

• To: mathgroup at smc.vnet.net
• Subject: [mg132164] Intersect Point of a 3D Parametric Line & B-Spline Surface
• From: Bill <WDWNORWALK at aol.com>
• Date: Tue, 7 Jan 2014 22:52:26 -0500 (EST)
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• Delivered-to: l-mathgroup@wolfram.com
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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`},{1,3,0.6162142022057271`},{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]];
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.

• Follow-Ups:
  • Re: Intersect Point of a 3D Parametric Line & B-Spline
    • From: Itai Seggev <itais@wolfram.com>
  • Re: Intersect Point of a 3D Parametric Line & B-Spline Surface
    • From: Bob Hanlon <hanlonr357@gmail.com>