Re: Getting started with 3D cardioid

*To*: mathgroup at smc.vnet.net*Subject*: [mg111977] Re: Getting started with 3D cardioid*From*: Bill Rowe <readnews at sbcglobal.net>*Date*: Mon, 23 Aug 2010 02:37:49 -0400 (EDT)

On 8/22/10 at 8:10 AM, aetherwizard at gmail.com (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? To plot a basic cardioid: ParametricPlot[{2 Cos[t] - Cos[2 t], 2 Sin[t] - Sin[2 t]}, {t, 0, 2 Pi}] The same cardioid rotated 45 degrees counterclockwise about the origin m = TransformationMatrix[RotationTransform[\[Pi]/4]][[;; 2, ;; 2]]; ParametricPlot[m.{2 Cos[t] - Cos[2 t], 2 Sin[t] - Sin[2 t]}, {t, 0, 2 Pi}] The same cardioid rotated 45 degrees about the point {1,0} m = TransformationMatrix[RotationTransform[\[Pi]/4, {1, 0}]][[;; 2]]; ParametricPlot[m.{2 Cos[t] - Cos[2 t], 2 Sin[t] - Sin[2 t], 1}, {t, 0, 2 Pi}]