Re: Getting started with 3D cardioid
- To: mathgroup at smc.vnet.net
- Subject: [mg112035] Re: Getting started with 3D cardioid
- From: David Thomson <aetherwizard at gmail.com>
- Date: Thu, 26 Aug 2010 06:47:35 -0400 (EDT)
- References: <i4r4ab$jt2$1@smc.vnet.net> <i4t54d$fgj$1@smc.vnet.net>
On Aug 23, 1:40 am, Helen Read <h... at together.net> wrote: > On 8/22/2010 8:14 AM,David Thomsonwrote: > > > 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 Thank you, Helen. That worked beautifully. Not only did it produce the 3D shape I was looking for, but also with the proper proportions. I tried to use a different geometry, but the parametric equation did not give the results I was expecting. r[t_] = t^-1 Sin[t + 1] PolarPlot[r[t], {t, 0, 2 \[Pi]}] In the above case, I'm looking for something with the appearance of a horn. Afterward, I want to learn how to position the cardioid origin on top of the point of the horn. This is a project I am actually building and would like to use Mathematica to model it so I can make illustrations. Dave