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}]