# curve on the surface [closed]

I have a bezier polygon aa=Table[{i^2.5, 2*Sqrt[i]}, {i, 1, 5}],is anyone can give me a example in Mathematica code that how to create another iso parametric curve on this bezier surface?Display the control polygon of this iso curve and the iso curve on the surface.

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## closed as off-topic by Yves Klett, rasher, george2079, Artes, m_goldbergApr 4 at 13:12

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The name of the product you're using is Mathematica, not Mathematic –  belisarius Apr 4 at 3:23
I don't understand your question. The table consists of 5 2D-Points, possibly the control points of a 2D Bézier curve. How do you make a 3D Bézier surface of a single row of 2D points? Please add more information to your question. –  gdir Apr 4 at 6:16
Thanks, I correct the mistake. I'm a totally rookie with using this product... –  user13368 Apr 4 at 6:16
The bezier polygon is:Table[{i, j, Cos[i]*Sin[j]}, {i, 5}, {j, 5}]] and parameter t.Would you please give me a example that how to create an iso parametric curve on this surface. Display the control polygon of this iso curve and curve on the surface. –  user13368 Apr 4 at 6:41
edit the question if you have information to add, but the is just a table of 2d points, not a surface –  george2079 Apr 4 at 11:42

Perhaps this is what you mean ( BezierFunction can be substituted instead of BSplineFunction ):

cpts = Table[{i, j, Cos[i]*Sin[j]}, {i, 5}, {j, 5}];

bss = BSplineFunction[cpts];

Show[

(* spline surface *)
ParametricPlot3D[bss[u, v], {u, 0, 1}, {v, 0, 1},
ColorFunction -> "Rainbow", PlotStyle -> Opacity[.5],
PlotPoints -> 35, MeshStyle -> Opacity[.5], MeshFunctions -> {#3 &}],

(* a curve on spline surface *)
ParametricPlot3D[bss[u, Sin[4 u^2]], {u, 0, 1}, PlotStyle -> Red] /.
Line[pts_, rest___] :> Tube[pts, 0.05, rest],

(* control points *)
Graphics3D[{{PointSize[Medium], Red, Map[Point, cpts]}, {Opacity[.5],
Line[cpts], Line[Transpose[cpts]]}}],

PlotRange -> All]


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nice, but a bit of work to go if the curve is itself a 2d bezier you need to map the one parameter space onto the other. –  george2079 Apr 4 at 12:24
@george2079 let's see what he says - too foggy to proceed without a beacon ;-) –  Vitaliy Kaurov Apr 4 at 12:30
@VitaliyKaurov The beacon at the end of the tunnel, you know... –  belisarius May 3 at 5:08