How does Circlepoints function actually work when drawing a polygon?

up vote
3
down vote

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By reading that Circlepoints gives the positions of n points equally spaced around the unit circle, I understood that :

Graphics[Green, Polygon[CirclePoints[4]]]

is equivalent to draw a Polygon into a circumscribed circle of radius 1 and centered as 0, 0.

I don't understand what Circlepoints with a real number does:

look at the picture:

Graphics[Red, Polygon[CirclePoints[4.434335]], Green, 
 Polygon[CirclePoints[4]]]

enter image description here

What is the meaning of placing "4.434335" points around the unit circle ?How do they come equally spaced ?

Look at the red polygon, they are not equally spaced, but I don't understand how the perimeter of the inner circle would be split.

asked 3 hours ago

user305883

1658

add a commentÂ |Â

up vote
3
down vote

favorite

By reading that Circlepoints gives the positions of n points equally spaced around the unit circle, I understood that :

Graphics[Green, Polygon[CirclePoints[4]]]

is equivalent to draw a Polygon into a circumscribed circle of radius 1 and centered as 0, 0.

I don't understand what Circlepoints with a real number does:

look at the picture:

Graphics[Red, Polygon[CirclePoints[4.434335]], Green, 
 Polygon[CirclePoints[4]]]

enter image description here

What is the meaning of placing "4.434335" points around the unit circle ?How do they come equally spaced ?

Look at the red polygon, they are not equally spaced, but I don't understand how the perimeter of the inner circle would be split.

asked 3 hours ago

user305883

1658

add a commentÂ |Â

up vote
3
down vote

favorite

By reading that Circlepoints gives the positions of n points equally spaced around the unit circle, I understood that :

Graphics[Green, Polygon[CirclePoints[4]]]

is equivalent to draw a Polygon into a circumscribed circle of radius 1 and centered as 0, 0.

I don't understand what Circlepoints with a real number does:

look at the picture:

Graphics[Red, Polygon[CirclePoints[4.434335]], Green, 
 Polygon[CirclePoints[4]]]

enter image description here

What is the meaning of placing "4.434335" points around the unit circle ?How do they come equally spaced ?

Look at the red polygon, they are not equally spaced, but I don't understand how the perimeter of the inner circle would be split.

asked 3 hours ago

user305883

1658

By reading that Circlepoints gives the positions of n points equally spaced around the unit circle, I understood that :

Graphics[Green, Polygon[CirclePoints[4]]]

is equivalent to draw a Polygon into a circumscribed circle of radius 1 and centered as 0, 0.

I don't understand what Circlepoints with a real number does:

look at the picture:

Graphics[Red, Polygon[CirclePoints[4.434335]], Green, 
 Polygon[CirclePoints[4]]]

enter image description here

What is the meaning of placing "4.434335" points around the unit circle ?How do they come equally spaced ?

Look at the red polygon, they are not equally spaced, but I don't understand how the perimeter of the inner circle would be split.

geometry polygons

asked 3 hours ago

user305883

1658

asked 3 hours ago

user305883

1658

asked 3 hours ago

user305883

1658

asked 3 hours ago

user305883

1658

asked 3 hours ago

user305883

1658

add a commentÂ |Â

2 Answers
2

active

oldest

votes

up vote
2
down vote

The details section of the documentation says the following:

In CirclePoints[n], n does not have to be an exact integer. The angles between successive vectors are always $frac2pin$.

If the angle $theta_1$ is not given, it is assumed to be $pi/n - pi/2$, ...

($theta_1$ is the starting angle.)

Here is a simple implementation to test this:

circlePoints[n_] := Module[start, diff,
 start = Pi/n - Pi/2;
 diff = 2 Pi/n;
 Table[Cos[start + i diff], Sin[start + i diff], i, 0, Floor[n] - 1]
 ]

Graphics[
 Green,
 Polygon[CirclePoints[4.434335]],
 FaceForm[Transparent],
 EdgeForm[Red, Thick],
 Polygon[circlePoints[4.434335]]
 ]

Mathematica graphics

How do they come equally spaced?

The key here is that successive vectors are equally spaced. The angle between the first and last vectors is not the same as the other angles unless $n$ is an integer.

edited 3 hours ago

answered 3 hours ago

C. E.

48.2k392194

Does RegularPolygon have the same behavior?
â€“Â J. M. is somewhat okay.â™¦
1 min ago

add a commentÂ |Â

up vote
1
down vote

here is how CirclePoints work

enter image description here

try this..

Graphics[Point@CirclePoints[40.99]]

enter image description here

the above misses a point

see this one

Graphics[Point@CirclePoints[41]]

enter image description here

now

Graphics[Point@CirclePoints[4.43]]

enter image description here

misses the fifth point...

this one

Graphics[Point@CirclePoints[5]]

enter image description here

edited 2 hours ago

answered 3 hours ago

J42161217

1,686216

add a commentÂ |Â

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2 Answers
2

active

oldest

votes

2 Answers
2

active

oldest

votes

up vote
2
down vote

The details section of the documentation says the following:

In CirclePoints[n], n does not have to be an exact integer. The angles between successive vectors are always $frac2pin$.

If the angle $theta_1$ is not given, it is assumed to be $pi/n - pi/2$, ...

($theta_1$ is the starting angle.)

Here is a simple implementation to test this:

circlePoints[n_] := Module[start, diff,
 start = Pi/n - Pi/2;
 diff = 2 Pi/n;
 Table[Cos[start + i diff], Sin[start + i diff], i, 0, Floor[n] - 1]
 ]

Graphics[
 Green,
 Polygon[CirclePoints[4.434335]],
 FaceForm[Transparent],
 EdgeForm[Red, Thick],
 Polygon[circlePoints[4.434335]]
 ]

Mathematica graphics

How do they come equally spaced?

The key here is that successive vectors are equally spaced. The angle between the first and last vectors is not the same as the other angles unless $n$ is an integer.

edited 3 hours ago

answered 3 hours ago

C. E.

48.2k392194

Does RegularPolygon have the same behavior?
â€“Â J. M. is somewhat okay.â™¦
1 min ago

add a commentÂ |Â

up vote
2
down vote

The details section of the documentation says the following:

In CirclePoints[n], n does not have to be an exact integer. The angles between successive vectors are always $frac2pin$.

If the angle $theta_1$ is not given, it is assumed to be $pi/n - pi/2$, ...

($theta_1$ is the starting angle.)

Here is a simple implementation to test this:

circlePoints[n_] := Module[start, diff,
 start = Pi/n - Pi/2;
 diff = 2 Pi/n;
 Table[Cos[start + i diff], Sin[start + i diff], i, 0, Floor[n] - 1]
 ]

Graphics[
 Green,
 Polygon[CirclePoints[4.434335]],
 FaceForm[Transparent],
 EdgeForm[Red, Thick],
 Polygon[circlePoints[4.434335]]
 ]

Mathematica graphics

How do they come equally spaced?

The key here is that successive vectors are equally spaced. The angle between the first and last vectors is not the same as the other angles unless $n$ is an integer.

edited 3 hours ago

answered 3 hours ago

C. E.

48.2k392194

Does RegularPolygon have the same behavior?
â€“Â J. M. is somewhat okay.â™¦
1 min ago

add a commentÂ |Â

up vote
2
down vote

The details section of the documentation says the following:

In CirclePoints[n], n does not have to be an exact integer. The angles between successive vectors are always $frac2pin$.

If the angle $theta_1$ is not given, it is assumed to be $pi/n - pi/2$, ...

($theta_1$ is the starting angle.)

Here is a simple implementation to test this:

circlePoints[n_] := Module[start, diff,
 start = Pi/n - Pi/2;
 diff = 2 Pi/n;
 Table[Cos[start + i diff], Sin[start + i diff], i, 0, Floor[n] - 1]
 ]

Graphics[
 Green,
 Polygon[CirclePoints[4.434335]],
 FaceForm[Transparent],
 EdgeForm[Red, Thick],
 Polygon[circlePoints[4.434335]]
 ]

Mathematica graphics

How do they come equally spaced?

The key here is that successive vectors are equally spaced. The angle between the first and last vectors is not the same as the other angles unless $n$ is an integer.

edited 3 hours ago

answered 3 hours ago

C. E.

48.2k392194

The details section of the documentation says the following:

In CirclePoints[n], n does not have to be an exact integer. The angles between successive vectors are always $frac2pin$.

If the angle $theta_1$ is not given, it is assumed to be $pi/n - pi/2$, ...

($theta_1$ is the starting angle.)

Here is a simple implementation to test this:

circlePoints[n_] := Module[start, diff,
 start = Pi/n - Pi/2;
 diff = 2 Pi/n;
 Table[Cos[start + i diff], Sin[start + i diff], i, 0, Floor[n] - 1]
 ]

Graphics[
 Green,
 Polygon[CirclePoints[4.434335]],
 FaceForm[Transparent],
 EdgeForm[Red, Thick],
 Polygon[circlePoints[4.434335]]
 ]

Mathematica graphics

How do they come equally spaced?

The key here is that successive vectors are equally spaced. The angle between the first and last vectors is not the same as the other angles unless $n$ is an integer.

edited 3 hours ago

answered 3 hours ago

C. E.

48.2k392194

edited 3 hours ago

answered 3 hours ago

C. E.

48.2k392194

answered 3 hours ago

C. E.

48.2k392194

answered 3 hours ago

C. E.

48.2k392194

Does RegularPolygon have the same behavior?
â€“Â J. M. is somewhat okay.â™¦
1 min ago

add a commentÂ |Â

Does RegularPolygon have the same behavior?
â€“Â J. M. is somewhat okay.â™¦
1 min ago

Does RegularPolygon have the same behavior?
â€“Â J. M. is somewhat okay.â™¦
1 min ago

add a commentÂ |Â

up vote
1
down vote

here is how CirclePoints work

enter image description here

try this..

Graphics[Point@CirclePoints[40.99]]

enter image description here

the above misses a point

see this one

Graphics[Point@CirclePoints[41]]

enter image description here

now

Graphics[Point@CirclePoints[4.43]]

enter image description here

misses the fifth point...

this one

Graphics[Point@CirclePoints[5]]

enter image description here

edited 2 hours ago

answered 3 hours ago

J42161217

1,686216

add a commentÂ |Â

up vote
1
down vote

here is how CirclePoints work

enter image description here

try this..

Graphics[Point@CirclePoints[40.99]]

enter image description here

the above misses a point

see this one

Graphics[Point@CirclePoints[41]]

enter image description here

now

Graphics[Point@CirclePoints[4.43]]

enter image description here

misses the fifth point...

this one

Graphics[Point@CirclePoints[5]]

enter image description here

edited 2 hours ago

answered 3 hours ago

J42161217

1,686216

add a commentÂ |Â

up vote
1
down vote

here is how CirclePoints work

enter image description here

try this..

Graphics[Point@CirclePoints[40.99]]

enter image description here

the above misses a point

see this one

Graphics[Point@CirclePoints[41]]

enter image description here

now

Graphics[Point@CirclePoints[4.43]]

enter image description here

misses the fifth point...

this one

Graphics[Point@CirclePoints[5]]

enter image description here

edited 2 hours ago

answered 3 hours ago

J42161217

1,686216

here is how CirclePoints work

enter image description here

try this..

Graphics[Point@CirclePoints[40.99]]

enter image description here

the above misses a point

see this one

Graphics[Point@CirclePoints[41]]

enter image description here

now

Graphics[Point@CirclePoints[4.43]]

enter image description here

misses the fifth point...

this one

Graphics[Point@CirclePoints[5]]

enter image description here

edited 2 hours ago

answered 3 hours ago

J42161217

1,686216

edited 2 hours ago

answered 3 hours ago

J42161217

1,686216

answered 3 hours ago

J42161217

1,686216

answered 3 hours ago

J42161217

1,686216

add a commentÂ |Â

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