       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}]

```

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