Page: Generate a circle (0 to $90^o$ ) of radius 4 width center located at (2, 2) in incremental co-ordinate.
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Sr No $\theta$ $x_i$ $y_i$ $x = x_c + rcos \theta$ $y = y_c + rsin \theta$
1 $0^o$ - - 6 2
2 $35^o$ 6 2 5.464 4
1 $60^o$ 5.464 4 3.999 5.464
1 $90^o$ 4 5.464 2 6

Parametric Representation of a ellipse:

$x=x_{c}+a \cos \theta \quad 0 \leq \theta \leq 2 \pi$

$y=y_{c}+\operatorname{asin} \theta$

$\cos \theta=\frac{x-x_{c}}{a}$

$\sin \theta=\frac{y-y_{c}}{b}$

Incremental:

\begin{aligned} x_{i+1} &=x_{c}+\operatorname{acos}(\theta+\delta \theta) \\ &=x_{c}+\mathrm{a}[\cos \theta \cdot \cos \delta \theta-\sin \theta \cdot \sin \delta \theta] \end{aligned}

$\therefore x_{i+1}=x_{c}+\left[\left(x_{i}-x_{c}\right) \cos \delta \theta+\frac{a}{b}\left(y_{i}-y_{c}\right) \sin \delta \theta\right]$

$\therefore y_{i+1}=y_{c}+\left[\left(y_{i}-y_{c}\right) \cos \delta \theta+\frac{b}{a}\left(x_{i}-x_{c}\right) \sin \delta \theta\right]$

page circle - ellipse • 25 views