Re: How to draw such 3D surface?

• To: mathgroup at smc.vnet.net
• Subject: [mg32661] Re: [mg32649] How to draw such 3D surface?
• From: BobHanlon at aol.com
• Date: Sat, 2 Feb 2002 01:19:37 -0500 (EST)
• Sender: owner-wri-mathgroup at wolfram.com

```In a message dated 2/1/02 5:11:25 PM, gzgear at yahoo.com writes:

>I want to draw a 3D surface defined by the following equations :
>
>r1=8;h=10/180*Pi;
>p=r1*Tan[h];
>x[u_,v_]:=r1*Cos[v] + u*Cos[h]*Sin[v];
>y[u_,v_]:=r1*Sin[v] - u*Cos[h]*Cos[v];
>z[u_,v_]:=p*v-u*Sin[h];
>R[u_, v_]= {x[u, v], y[u, v], z[u, v]};
>0 <= v <= Pi;
>u <= v*r1/Cos[h];
>R[u,v] is a space vector that is able to describe a 3D surface.
>
>I want to use the following procedure to draw it but failed, what should
>I do?
><< Graphics`ParametricPlot3D`
>  ParametricPlot3D[{r1*Cos[v] + u*Cos[h]*Sin[v],
>      r1*Sin[v] - u*Cos[h]*Cos[v],
>     p*v-u*Sin[h]}, {v, 0, Pi/2}, {u, 0,
>      v*r1/Cos[h]}]
>

r1=8;
h=10/180*Pi;
p=r1*Tan[h];
x[u_,v_]:=r1*Cos[v]+u*Cos[h]*Sin[v];
y[u_,v_]:=r1*Sin[v]-u*Cos[h]*Cos[v];
z[u_,v_]:=p*v-u*Sin[h];

let u = v*t

ParametricPlot3D[{x[v*t,v],y[v*t,v],z[v*t,v]},
{v,0,Pi},{t,0,r1/Cos[h]},

AxesLabel->{"x","y","z"},ImageSize->400];

Bob Hanlon
Chantilly, VA  USA

```

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