Generate a circle (0 to $90^o$ ) of radius 4 width center located at (2, 2) in incremental co-ordinate.

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written 5.3 years ago by

teamques10 ★ 68k

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

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Parametric Representation of a ellipse:

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

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

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

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

Incremental:

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

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

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

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