       Re: How to plot the surface of revolution graphics

• To: mathgroup at smc.vnet.net
• Subject: [mg49283] Re: How to plot the surface of revolution graphics
• From: mathma18 at hotmail.com (Narasimham G.L.)
• Date: Sun, 11 Jul 2004 02:16:16 -0400 (EDT)
• References: <ccg4la\$osp\$1@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

```Firstly,you have to rotate axes if surface of revolution about an axis
other than x-axis is desired. I have given below for straight line
generators 4 sides of a rectangle, you see four cones. The four points
at rectangle corners are: {(0,4),(3,0),(11,6),(8,10)} which I assumed
for convenience. The four parts are same except choice of line extreme
points.[Hope someone suggests how to avoid repetition]. The meridian
has to be modified for other sections. HTH

Clear[r,z,r1,z1,r2,z2];
z1= 3; r1=0; z2=0; r2=4;
z= (r-r1) (z2-z1)/(r2-r1)+z1 ;
one=ParametricPlot3D[{r Cos[th],r Sin[th],z},{r,r1,r2},{th,0,Pi*1.5}];
Clear[r,z,r1,z1,r2,z2];
z1= 3; r1=0; z2=11; r2=6;
z= (r-r1) (z2-z1)/(r2-r1)+z1 ;
two=ParametricPlot3D[{r Cos[th],r Sin[th],z},{r,r1,r2},{th,0,Pi*1.5}];
Clear[r,z,r1,z1,r2,z2];
z1= 0; r1=4 ; z2=8; r2=10;
z= (r-r1) (z2-z1)/(r2-r1)+z1  ;
three=ParametricPlot3D[{r Cos[th],r
Sin[th],z},{r,r1,r2},{th,0,Pi*1.5}];
Clear[r,z,r1,z1,r2,z2];
z1= 8; r1=10; z2=11; r2=6;
z= (r-r1) (z2-z1)/(r2-r1)+z1 ;
four=ParametricPlot3D[{r Cos[th],r
Sin[th],z},{r,r1,r2},{th,0,Pi*1.5}];
Show[{one,two,three,four},ViewPoint->{1.5,-1.5,1},
PlotRange->{{-12,12},{0,12},{-4,12}}];

"CYSTERNA++" <e_cysterna at wp.pl> wrote in message news:<ccg4la\$osp\$1 at smc.vnet.net>...
> I would like to make graphics with many surfaces. All surfaces are surfaces
> of revolution. They are created through rotate specified countur about
> certain line. I cannot make these graphics.
> I have rectangle which is represented through 4 points which have following
> coordinates : (2,2), (6,6), (7,5), 3,1). This rectangle is rotated about
> line y(x) = x and is created cylindrical surface. How to create graph with
> this surface. I know this is a simple problem and I can used
> ParametricPlot3D[] function or another but in the real I have countours more
> complicated than rectangle and I would like use specified function to make
> graph surface of revolution.
>
> Thanks for all

```

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