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coorection
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fang
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You can use the following ways to find the control points of a cubic Bezier curve for approximating a circular arc with end points $P_0$, $P_1$, radius R and angular span A:

Denoting the control points as $Q_0$, $Q_1$, $Q_2$ and $Q_3$, then

$Q_0=P_0$,
$Q_3=P_1$,
$Q_1=P_0 + LT_0$
$Q_2=P_1 - LT_1$

where $T_0$ and $T_1$ are the unit tangent vector of the circular arc at $P_0$ and $P_1$ and $L = \frac{4}{3}tan(\frac{A}{4})$$L = \frac{4R}{3}tan(\frac{A}{4})$.

Please note that above formula will give you a pretty good approximation for the circular arc. But it is not "the best" approximation. We can achieve an even better approximation with more complicated formula for the $L$ value. But for practical purpose, above formula is typically good enough.

You can use the following ways to find the control points of a cubic Bezier curve for approximating a circular arc with end points $P_0$, $P_1$, radius R and angular span A:

Denoting the control points as $Q_0$, $Q_1$, $Q_2$ and $Q_3$, then

$Q_0=P_0$,
$Q_3=P_1$,
$Q_1=P_0 + LT_0$
$Q_2=P_1 - LT_1$

where $T_0$ and $T_1$ are the unit tangent vector of the circular arc at $P_0$ and $P_1$ and $L = \frac{4}{3}tan(\frac{A}{4})$.

Please note that above formula will give you a pretty good approximation for the circular arc. But it is not "the best" approximation. We can achieve an even better approximation with more complicated formula for the $L$ value. But for practical purpose, above formula is typically good enough.

You can use the following ways to find the control points of a cubic Bezier curve for approximating a circular arc with end points $P_0$, $P_1$, radius R and angular span A:

Denoting the control points as $Q_0$, $Q_1$, $Q_2$ and $Q_3$, then

$Q_0=P_0$,
$Q_3=P_1$,
$Q_1=P_0 + LT_0$
$Q_2=P_1 - LT_1$

where $T_0$ and $T_1$ are the unit tangent vector of the circular arc at $P_0$ and $P_1$ and $L = \frac{4R}{3}tan(\frac{A}{4})$.

Please note that above formula will give you a pretty good approximation for the circular arc. But it is not "the best" approximation. We can achieve an even better approximation with more complicated formula for the $L$ value. But for practical purpose, above formula is typically good enough.

Source Link
fang
  • 3.6k
  • 1
  • 14
  • 13

You can use the following ways to find the control points of a cubic Bezier curve for approximating a circular arc with end points $P_0$, $P_1$, radius R and angular span A:

Denoting the control points as $Q_0$, $Q_1$, $Q_2$ and $Q_3$, then

$Q_0=P_0$,
$Q_3=P_1$,
$Q_1=P_0 + LT_0$
$Q_2=P_1 - LT_1$

where $T_0$ and $T_1$ are the unit tangent vector of the circular arc at $P_0$ and $P_1$ and $L = \frac{4}{3}tan(\frac{A}{4})$.

Please note that above formula will give you a pretty good approximation for the circular arc. But it is not "the best" approximation. We can achieve an even better approximation with more complicated formula for the $L$ value. But for practical purpose, above formula is typically good enough.