Re: Getting started with 3D cardioid
- To: mathgroup at smc.vnet.net
- Subject: [mg111991] Re: Getting started with 3D cardioid
- From: Helen Read <hpr at together.net>
- Date: Mon, 23 Aug 2010 02:40:22 -0400 (EDT)
- References: <i4r4ab$jt2$1@smc.vnet.net>
- Reply-to: HPR <read at math.uvm.edu>
On 8/22/2010 8:14 AM, David Thomson wrote:
> I'm new to Mathematica, sorry. I would like to draw a cardioid
> rotated about its polar axis. I checked the Mathematica wiki and it
> did not cover this topic (that I could find). Can someone help me to
> understand how to do this in Mathematica?
The thing to do is represent the cardioid parametrically.
For example, if you start with this cardioid:
r[t_] = 1 - Cos[t]
PolarPlot[r[t], {t, 0, 2 \[Pi]}]
Then express the polar curve parametrically, like so.
x[t_] = r[t] Cos[t];
y[t_] = r[t] Sin[t];
Note that due to symmetry, you need only revolve the top half (t from 0
to Pi) around the polar axis.
RevolutionPlot3D[{x[t], y[t]}, {t, 0, \[Pi]}, RevolutionAxis -> x]
--
Helen Read
University of Vermont