Mixing
What is a non-concave and non-convex polygon called?
$begingroup$
I am writing a software function to plot the outer points of an n-sided polygon and I'm having trouble ensuring I use the correct terminology. The function I've written simply renders the calculated points of a predetermined polygon in two dimensional space. These polygons are neither convex nor concave and thus I believe the name I should give the function is Render Uniform Polygon; however, I believe uniform may not be the correct word and could end up in a debate over the name. The function itself performs three actions to achieve the goal:
- Calculate the angle of each point $theta_n$.
- Calculate the new position $P_n$.
- Render a 3px by 3px dot at the new position.
The math for calculating $theta_n$ is:
$$theta_n = frac{biggl(bigl(frac{360°}{p}bigr)n + phibiggr)pi}{180°}$$
Where:
$p$ is the number of points in the polygon.
$n$ is the current point.
$phi$ is the global rotation angle.
Once $theta_n$ has been calculated with the math above, I then use it to calculate the new position with the following:
$$P_{_n{x, y}} = C_{x, y} + (cos(theta_n), sin(theta_n))r$$
Where:
$P_n$ is current point's position.
$C_{x, y}$ is the center of the polygon.
$r$ is the radius of the polygon.
This method can be used to render any polygon with three sides or more, and since the radius is predefined there isn't a case where the polygon can be convex or concave.
What is a polygon that is neither convex nor concave called?
terminology polygons
edited Jan 21 at 18:25
Adrian Keister
5,27371933
asked Jan 21 at 18:20
PerpetualJPerpetualJ
1767
$endgroup$
add a comment |
$begingroup$
I am writing a software function to plot the outer points of an n-sided polygon and I'm having trouble ensuring I use the correct terminology. The function I've written simply renders the calculated points of a predetermined polygon in two dimensional space. These polygons are neither convex nor concave and thus I believe the name I should give the function is Render Uniform Polygon; however, I believe uniform may not be the correct word and could end up in a debate over the name. The function itself performs three actions to achieve the goal:
- Calculate the angle of each point $theta_n$.
- Calculate the new position $P_n$.
- Render a 3px by 3px dot at the new position.
The math for calculating $theta_n$ is:
$$theta_n = frac{biggl(bigl(frac{360°}{p}bigr)n + phibiggr)pi}{180°}$$
Where:
$p$ is the number of points in the polygon.
$n$ is the current point.
$phi$ is the global rotation angle.
Once $theta_n$ has been calculated with the math above, I then use it to calculate the new position with the following:
$$P_{_n{x, y}} = C_{x, y} + (cos(theta_n), sin(theta_n))r$$
Where:
$P_n$ is current point's position.
$C_{x, y}$ is the center of the polygon.
$r$ is the radius of the polygon.
This method can be used to render any polygon with three sides or more, and since the radius is predefined there isn't a case where the polygon can be convex or concave.
What is a polygon that is neither convex nor concave called?
terminology polygons
edited Jan 21 at 18:25
Adrian Keister
5,27371933
asked Jan 21 at 18:20
PerpetualJPerpetualJ
1767
$endgroup$
1
$begingroup$
All regular polygons are convex. As far as I know, a polygon that is neither convex nor concave is called "neither convex nor concave". I don't know of any special term for that.
$endgroup$
– Adrian Keister
Jan 21 at 18:22
$begingroup$
@AdrianKeister So simply Render Polygon should suffice in this case without causing any confusion?
$endgroup$
– PerpetualJ
Jan 21 at 18:23
1
$begingroup$
Sure! A regular polygon is a polygon, but not the reverse. So if you happen to be constructing regular polygons, aconstruct_polygon()method is a fine name for that.
$endgroup$
– Adrian Keister
Jan 21 at 18:25
2
$begingroup$
For me, a concave polygon is one that has at least one angle greater than $pi$ and a convex one has no angles greater than $pi$. In that case there are no polygons that are neither concave nor convex.
$endgroup$
– Ross Millikan
Jan 21 at 18:25
$begingroup$
@RossMillikan: Excellent point, I agree!
$endgroup$
– Adrian Keister
Jan 21 at 18:26
add a comment |
$begingroup$
I am writing a software function to plot the outer points of an n-sided polygon and I'm having trouble ensuring I use the correct terminology. The function I've written simply renders the calculated points of a predetermined polygon in two dimensional space. These polygons are neither convex nor concave and thus I believe the name I should give the function is Render Uniform Polygon; however, I believe uniform may not be the correct word and could end up in a debate over the name. The function itself performs three actions to achieve the goal:
- Calculate the angle of each point $theta_n$.
- Calculate the new position $P_n$.
- Render a 3px by 3px dot at the new position.
The math for calculating $theta_n$ is:
$$theta_n = frac{biggl(bigl(frac{360°}{p}bigr)n + phibiggr)pi}{180°}$$
Where:
$p$ is the number of points in the polygon.
$n$ is the current point.
$phi$ is the global rotation angle.
Once $theta_n$ has been calculated with the math above, I then use it to calculate the new position with the following:
$$P_{_n{x, y}} = C_{x, y} + (cos(theta_n), sin(theta_n))r$$
Where:
$P_n$ is current point's position.
$C_{x, y}$ is the center of the polygon.
$r$ is the radius of the polygon.
This method can be used to render any polygon with three sides or more, and since the radius is predefined there isn't a case where the polygon can be convex or concave.
What is a polygon that is neither convex nor concave called?
terminology polygons
edited Jan 21 at 18:25
Adrian Keister
5,27371933
asked Jan 21 at 18:20
PerpetualJPerpetualJ
1767
$endgroup$
I am writing a software function to plot the outer points of an n-sided polygon and I'm having trouble ensuring I use the correct terminology. The function I've written simply renders the calculated points of a predetermined polygon in two dimensional space. These polygons are neither convex nor concave and thus I believe the name I should give the function is Render Uniform Polygon; however, I believe uniform may not be the correct word and could end up in a debate over the name. The function itself performs three actions to achieve the goal:
- Calculate the angle of each point $theta_n$.
- Calculate the new position $P_n$.
- Render a 3px by 3px dot at the new position.
The math for calculating $theta_n$ is:
$$theta_n = frac{biggl(bigl(frac{360°}{p}bigr)n + phibiggr)pi}{180°}$$
Where:
$p$ is the number of points in the polygon.
$n$ is the current point.
$phi$ is the global rotation angle.
Once $theta_n$ has been calculated with the math above, I then use it to calculate the new position with the following:
$$P_{_n{x, y}} = C_{x, y} + (cos(theta_n), sin(theta_n))r$$
Where:
$P_n$ is current point's position.
$C_{x, y}$ is the center of the polygon.
$r$ is the radius of the polygon.
This method can be used to render any polygon with three sides or more, and since the radius is predefined there isn't a case where the polygon can be convex or concave.
What is a polygon that is neither convex nor concave called?
terminology polygons
terminology polygons
edited Jan 21 at 18:25
Adrian Keister
5,27371933
asked Jan 21 at 18:20
PerpetualJPerpetualJ
1767
edited Jan 21 at 18:25
Adrian Keister
5,27371933
asked Jan 21 at 18:20
PerpetualJPerpetualJ
1767
edited Jan 21 at 18:25
Adrian Keister
5,27371933
edited Jan 21 at 18:25
Adrian Keister
5,27371933
edited Jan 21 at 18:25
Adrian Keister
5,27371933
5,27371933
asked Jan 21 at 18:20
PerpetualJPerpetualJ
1767
asked Jan 21 at 18:20
PerpetualJPerpetualJ
1767
asked Jan 21 at 18:20
PerpetualJPerpetualJ
1767
1767
1
$begingroup$
All regular polygons are convex. As far as I know, a polygon that is neither convex nor concave is called "neither convex nor concave". I don't know of any special term for that.
$endgroup$
– Adrian Keister
Jan 21 at 18:22
$begingroup$
@AdrianKeister So simply Render Polygon should suffice in this case without causing any confusion?
$endgroup$
– PerpetualJ
Jan 21 at 18:23
1
$begingroup$
Sure! A regular polygon is a polygon, but not the reverse. So if you happen to be constructing regular polygons, aconstruct_polygon()method is a fine name for that.
$endgroup$
– Adrian Keister
Jan 21 at 18:25
2
$begingroup$
For me, a concave polygon is one that has at least one angle greater than $pi$ and a convex one has no angles greater than $pi$. In that case there are no polygons that are neither concave nor convex.
$endgroup$
– Ross Millikan
Jan 21 at 18:25
$begingroup$
@RossMillikan: Excellent point, I agree!
$endgroup$
– Adrian Keister
Jan 21 at 18:26
add a comment |
1
$begingroup$
All regular polygons are convex. As far as I know, a polygon that is neither convex nor concave is called "neither convex nor concave". I don't know of any special term for that.
$endgroup$
– Adrian Keister
Jan 21 at 18:22
$begingroup$
@AdrianKeister So simply Render Polygon should suffice in this case without causing any confusion?
$endgroup$
– PerpetualJ
Jan 21 at 18:23
1
$begingroup$
Sure! A regular polygon is a polygon, but not the reverse. So if you happen to be constructing regular polygons, aconstruct_polygon()method is a fine name for that.
$endgroup$
– Adrian Keister
Jan 21 at 18:25
2
$begingroup$
For me, a concave polygon is one that has at least one angle greater than $pi$ and a convex one has no angles greater than $pi$. In that case there are no polygons that are neither concave nor convex.
$endgroup$
– Ross Millikan
Jan 21 at 18:25
$begingroup$
@RossMillikan: Excellent point, I agree!
$endgroup$
– Adrian Keister
Jan 21 at 18:26
1
1
$begingroup$
All regular polygons are convex. As far as I know, a polygon that is neither convex nor concave is called "neither convex nor concave". I don't know of any special term for that.
$endgroup$
– Adrian Keister
Jan 21 at 18:22
$begingroup$
All regular polygons are convex. As far as I know, a polygon that is neither convex nor concave is called "neither convex nor concave". I don't know of any special term for that.
$endgroup$
– Adrian Keister
Jan 21 at 18:22
$begingroup$
@AdrianKeister So simply Render Polygon should suffice in this case without causing any confusion?
$endgroup$
– PerpetualJ
Jan 21 at 18:23
$begingroup$
@AdrianKeister So simply Render Polygon should suffice in this case without causing any confusion?
$endgroup$
– PerpetualJ
Jan 21 at 18:23
1
1
$begingroup$
Sure! A regular polygon is a polygon, but not the reverse. So if you happen to be constructing regular polygons, a
construct_polygon() method is a fine name for that.$endgroup$
– Adrian Keister
Jan 21 at 18:25
$begingroup$
Sure! A regular polygon is a polygon, but not the reverse. So if you happen to be constructing regular polygons, a
construct_polygon() method is a fine name for that.$endgroup$
– Adrian Keister
Jan 21 at 18:25
2
2
$begingroup$
For me, a concave polygon is one that has at least one angle greater than $pi$ and a convex one has no angles greater than $pi$. In that case there are no polygons that are neither concave nor convex.
$endgroup$
– Ross Millikan
Jan 21 at 18:25
$begingroup$
For me, a concave polygon is one that has at least one angle greater than $pi$ and a convex one has no angles greater than $pi$. In that case there are no polygons that are neither concave nor convex.
$endgroup$
– Ross Millikan
Jan 21 at 18:25
$begingroup$
@RossMillikan: Excellent point, I agree!
$endgroup$
– Adrian Keister
Jan 21 at 18:26
$begingroup$
@RossMillikan: Excellent point, I agree!
$endgroup$
– Adrian Keister
Jan 21 at 18:26
add a comment |
1 Answer
1
active
oldest
votes
$begingroup$
As far as I can see your polygon is convex. It's a regular polygon whose vertices are equidistant on the circle with radius $r$ and center $C$.
answered Jan 21 at 18:25
lightxbulblightxbulb
1,055311
$endgroup$
add a comment |
Your Answer
StackExchange.ifUsing("editor", function () {
return StackExchange.using("mathjaxEditing", function () {
StackExchange.MarkdownEditor.creationCallbacks.add(function (editor, postfix) {
StackExchange.mathjaxEditing.prepareWmdForMathJax(editor, postfix, [["$", "$"], ["\\(","\\)"]]);
});
});
}, "mathjax-editing");
StackExchange.ready(function() {
var channelOptions = {
tags: "".split(" "),
id: "69"
};
initTagRenderer("".split(" "), "".split(" "), channelOptions);
StackExchange.using("externalEditor", function() {
// Have to fire editor after snippets, if snippets enabled
if (StackExchange.settings.snippets.snippetsEnabled) {
StackExchange.using("snippets", function() {
createEditor();
});
}
else {
createEditor();
}
});
function createEditor() {
StackExchange.prepareEditor({
heartbeatType: 'answer',
autoActivateHeartbeat: false,
convertImagesToLinks: true,
noModals: true,
showLowRepImageUploadWarning: true,
reputationToPostImages: 10,
bindNavPrevention: true,
postfix: "",
imageUploader: {
brandingHtml: "Powered by u003ca class="icon-imgur-white" href="https://imgur.com/"u003eu003c/au003e",
contentPolicyHtml: "User contributions licensed under u003ca href="https://creativecommons.org/licenses/by-sa/3.0/"u003ecc by-sa 3.0 with attribution requiredu003c/au003e u003ca href="https://stackoverflow.com/legal/content-policy"u003e(content policy)u003c/au003e",
allowUrls: true
},
noCode: true, onDemand: true,
discardSelector: ".discard-answer"
,immediatelyShowMarkdownHelp:true
});
}
});
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
StackExchange.ready(
function () {
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f3082207%2fwhat-is-a-non-concave-and-non-convex-polygon-called%23new-answer', 'question_page');
}
);
Post as a guest
Required, but never shown
1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
$begingroup$
As far as I can see your polygon is convex. It's a regular polygon whose vertices are equidistant on the circle with radius $r$ and center $C$.
answered Jan 21 at 18:25
lightxbulblightxbulb
1,055311
$endgroup$
add a comment |
$begingroup$
As far as I can see your polygon is convex. It's a regular polygon whose vertices are equidistant on the circle with radius $r$ and center $C$.
answered Jan 21 at 18:25
lightxbulblightxbulb
1,055311
$endgroup$
add a comment |
$begingroup$
As far as I can see your polygon is convex. It's a regular polygon whose vertices are equidistant on the circle with radius $r$ and center $C$.
answered Jan 21 at 18:25
lightxbulblightxbulb
1,055311
$endgroup$
As far as I can see your polygon is convex. It's a regular polygon whose vertices are equidistant on the circle with radius $r$ and center $C$.
answered Jan 21 at 18:25
lightxbulblightxbulb
1,055311
answered Jan 21 at 18:25
lightxbulblightxbulb
1,055311
answered Jan 21 at 18:25
lightxbulblightxbulb
1,055311
answered Jan 21 at 18:25
lightxbulblightxbulb
1,055311
1,055311
add a comment |
add a comment |
Thanks for contributing an answer to Mathematics Stack Exchange!
- Please be sure to answer the question. Provide details and share your research!
But avoid …
- Asking for help, clarification, or responding to other answers.
- Making statements based on opinion; back them up with references or personal experience.
Use MathJax to format equations. MathJax reference.
To learn more, see our tips on writing great answers.
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
StackExchange.ready(
function () {
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f3082207%2fwhat-is-a-non-concave-and-non-convex-polygon-called%23new-answer', 'question_page');
}
);
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
1
$begingroup$
All regular polygons are convex. As far as I know, a polygon that is neither convex nor concave is called "neither convex nor concave". I don't know of any special term for that.
$endgroup$
– Adrian Keister
Jan 21 at 18:22
$begingroup$
@AdrianKeister So simply Render Polygon should suffice in this case without causing any confusion?
$endgroup$
– PerpetualJ
Jan 21 at 18:23
1
$begingroup$
Sure! A regular polygon is a polygon, but not the reverse. So if you happen to be constructing regular polygons, a
construct_polygon()method is a fine name for that.$endgroup$
– Adrian Keister
Jan 21 at 18:25
2
$begingroup$
For me, a concave polygon is one that has at least one angle greater than $pi$ and a convex one has no angles greater than $pi$. In that case there are no polygons that are neither concave nor convex.
$endgroup$
– Ross Millikan
Jan 21 at 18:25
$begingroup$
@RossMillikan: Excellent point, I agree!
$endgroup$
– Adrian Keister
Jan 21 at 18:26