Hipocicloids e Hipotrochoids
Hipocicloids, [;r,R >0;] e [; \omega=\frac{R-r}{r} ;]:
[;
\underline{\textbf{r}}(t)
=
\begin{pmatrix}
(R+r)\cos{t}+r \cos{\omega t}\\
(R+r)\sin{t}-r \sin{\omega t}\\
\end{pmatrix}, \quad t \in \mathbb{R}
;]
Hipotrocoids, [; r,R >0, b \in \mathbb{R};]:
[;
\underline{\textbf{r}}(t)
=
\begin{pmatrix}
(R+r)\cos{t}+(r+b) \cos{\omega t}\\
(R+r)\sin{t}-(r+b) \sin{\omega t}\\
\end{pmatrix}, \quad t \in \mathbb{R}
;]
- Desenhe os Hipocicloids para [;R=1;] e [;r=3,2,1,1/2,1/3;]
- Desenhe os Hipotrocoids para [;R=1=;], [;r=3,2,1,1/2,1/3;]
e [;b=3,2,1,1/2,1/3,0,-1/3,-1/2,-1,-2,-3;].