We have a start point (x, y) and a circle radius. There also exists an engine that can create a path from Bézier curve points.

How can I create a circle using Bézier curves?

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## Top Answer 1

Im not sure if i should open new question since this is about aproximation but Im interested in general formula to get control points for Bezier of any degree and I believe it fits within this question.

All solutions I found on the web are only for cubic curves or are paid or I dont even understand (Im not very good at math).

So I decided try to solve this on my own. I was study distance of the control point from center of a circle dependent on given angle and so far I found that:

Where

N

is number of control points for single curve and

α

is circle arc angle.

For quadratic curve it can be simplified to

l ≈ r + r * PI*0.1 * pow(α90, 2)

The

PI*0.1

is rather a guess I didnt calculate perfect value but its pretty close.

This works reasonably good for curve with 1-2 control points giving radius error about 0.2% for cubic curve. For higher degree curves loss of accuracy is noticable. With 3 control points curve look similar to quadratic so obviously Im miss something but I cant figure it out and this method generally fits my needs for now.

Here is demo.

## Top Answer 2

Im not sure if i should open new question since this is about aproximation but Im interested in general formula to get control points for Bezier of any degree and I believe it fits within this question.

All solutions I found on the web are only for cubic curves or are paid or I dont even understand (Im not very good at math).

So I decided try to solve this on my own. I was study distance of the control point from center of a circle dependent on given angle and so far I found that:

Where

N

is number of control points for single curve and

α

is circle arc angle.

For quadratic curve it can be simplified to

l ≈ r + r * PI*0.1 * pow(α90, 2)

The

PI*0.1

is rather a guess I didnt calculate perfect value but its pretty close.

This works reasonably good for curve with 1-2 control points giving radius error about 0.2% for cubic curve. For higher degree curves loss of accuracy is noticable. With 3 control points curve look similar to quadratic so obviously Im miss something but I cant figure it out and this method generally fits my needs for now.

Here is demo.

## Top Answer 3

Im not sure if i should open new question since this is about aproximation but Im interested in general formula to get control points for Bezier of any degree and I believe it fits within this question.

All solutions I found on the web are only for cubic curves or are paid or I dont even understand (Im not very good at math).

So I decided try to solve this on my own. I was study distance of the control point from center of a circle dependent on given angle and so far I found that:

Where

N

is number of control points for single curve and

α

is circle arc angle.

For quadratic curve it can be simplified to

l ≈ r + r * PI*0.1 * pow(α90, 2)

The

PI*0.1

is rather a guess I didnt calculate perfect value but its pretty close.

This works reasonably good for curve with 1-2 control points giving radius error about 0.2% for cubic curve. For higher degree curves loss of accuracy is noticable. With 3 control points curve look similar to quadratic so obviously Im miss something but I cant figure it out and this method generally fits my needs for now.

Here is demo.

## Top Answer 4

All solutions I found on the web are only for cubic curves or are paid or I dont even understand (Im not very good at math).

So I decided try to solve this on my own. I was study distance of the control point from center of a circle dependent on given angle and so far I found that:

Where

N

is number of control points for single curve and

α

is circle arc angle.

For quadratic curve it can be simplified to

l ≈ r + r * PI*0.1 * pow(α90, 2)

The

PI*0.1

This works reasonably good for curve with 1-2 control points giving radius error about 0.2% for cubic curve. For higher degree curves loss of accuracy is noticable. With 3 control points curve look similar to quadratic so obviously Im miss something but I cant figure it out and this method generally fits my needs for now.

Here is demo.

## Top Answer 5

All solutions I found on the web are only for cubic curves or are paid or I dont even understand (Im not very good at math).

So I decided try to solve this on my own. I was study distance of the control point from center of a circle dependent on given angle and so far I found that:

Where

N

is number of control points for single curve and

α

is circle arc angle.

For quadratic curve it can be simplified to

l ≈ r + r * PI*0.1 * pow(α90, 2)

The

PI*0.1

This works reasonably good for curve with 1-2 control points giving radius error about 0.2% for cubic curve. For higher degree curves loss of accuracy is noticable. With 3 control points curve look similar to quadratic so obviously Im miss something but I cant figure it out and this method generally fits my needs for now.

Here is demo.

## Top Answer 6

All solutions I found on the web are only for cubic curves or are paid or I dont even understand (Im not very good at math).

So I decided try to solve this on my own. I was study distance of the control point from center of a circle dependent on given angle and so far I found that:

Where

N

is number of control points for single curve and

α

is circle arc angle.

For quadratic curve it can be simplified to

l ≈ r + r * PI*0.1 * pow(α90, 2)

The

PI*0.1

This works reasonably good for curve with 1-2 control points giving radius error about 0.2% for cubic curve. For higher degree curves loss of accuracy is noticable. With 3 control points curve look similar to quadratic so obviously Im miss something but I cant figure it out and this method generally fits my needs for now.

Here is demo.

## Top Answer 7

All solutions I found on the web are only for cubic curves or are paid or I dont even understand (Im not very good at math).

So I decided try to solve this on my own. I was study distance of the control point from center of a circle dependent on given angle and so far I found that:

Where

N

is number of control points for single curve and

α

is circle arc angle.

For quadratic curve it can be simplified to

l ≈ r + r * PI*0.1 * pow(α90, 2)

The

PI*0.1

This works reasonably good for curve with 1-2 control points giving radius error about 0.2% for cubic curve. For higher degree curves loss of accuracy is noticable. With 3 control points curve look similar to quadratic so obviously Im miss something but I cant figure it out and this method generally fits my needs for now.

Here is demo.

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