How can I get a mesh or a surface through the use of the two curves?

I have two questions.

The first question seems to be well simple:

1. How could I show two curves in distinct planes in the same graphic or plotting?

My attempts:

These are the points that define the first curve in the Plane XY

datacurve1={{0,0},{45,20},{90,-20},{135,0}};

Here I yields a equation that defines the relationship between values of X-axis and Y-axis

curve1=Fit[datacurve1,{1,x,x^2,x^3,x^4},x];

The curve 1 represents the values in the Plane XY

gr1=Plot[curve1,{x,0,135},AxesLabel->{X,Y},PlotLabel->"PlaneXY",LabelStyle->{GrayLevel}]

These are the points that define the first curve in the Plane ZY

datacurve2={{0,0},{25,15},{50,0},{100,15}}

Here I yields a equation that defines the relationship between values of Z-axis and Y-axis

curve2=Fit[datacurve2,{1,z,z^2,z^3,z^4},z]

The curve 2 represents the values in the PlaneZY

gr2=Plot[curve2,{z,0,100},AxesLabel->{Z,Y},PlotLabel->"PlaneZY",LabelStyle->{GrayLevel}]

This is the only way I know do to show the two plots, but this is not what I want. I tried to use Graphics3D, but I don´t know how do it

Show[gr1,gr2]

I would like that the result was something as shown in the image below: The second question is this:

1. How can I get a mesh or a surface through the use of these two curves as shown in image below? I tried to find the word suitable for this question, but I don´t know which would be... • The animation was unsuccessful. I will try to update later. – LCarvalho Aug 11 '16 at 13:58
• You can use GeometricTransformation and friends – Wjx Aug 11 '16 at 14:01

It seems to me this is what you want:

Plot3D[curve1 + curve2, {x, 0, 135}, {z, 0, 100}] Or perhaps this, if the shading is important:

Plot3D[curve1 + curve2, {x, 0, 135}, {z, 0, 100},
MeshShading -> {{Black, Gray}, {Gray, Black}}] If not, then please clarify the question.

• What I need to do to achieve a similar result to the first question image? – LCarvalho Aug 11 '16 at 20:56
• @Leandro, use ParametricPlot3D[] for space curves. – J. M. will be back soon Aug 11 '16 at 23:16
• I was referring to with this image: http://i.stack.imgur.com/mCTPD.jpg. If it was about her that said, forgive me but I don't understand how to use. – LCarvalho Aug 12 '16 at 14:16