How to find a cylinders axis from points on the surface.
$begingroup$
Is it possible to find the axis of a cylinder with a known diameter in 3D space from points on its surface?
I would guess that at least 3 points would be required.
geometry
asked Dec 16 '18 at 1:25
o0dv0oo0dv0o
61
$endgroup$
add a comment |
$begingroup$
Is it possible to find the axis of a cylinder with a known diameter in 3D space from points on its surface?
I would guess that at least 3 points would be required.
geometry
asked Dec 16 '18 at 1:25
o0dv0oo0dv0o
61
$endgroup$
$begingroup$
Not if the points were colinear.
$endgroup$
– Jens
Dec 16 '18 at 1:31
1
$begingroup$
I assume you refer to a right circular cylinder. With 3 non-collinear points a circum-circle can be made which lies in a plane perpendicular to cylinder axis. With 5 collinear points a conic can be made. If it is an ellipse then $cos^{-1}(b/a) $ is its inclination to cylinder axis
$endgroup$
– Narasimham
Dec 16 '18 at 6:48
add a comment |
$begingroup$
Is it possible to find the axis of a cylinder with a known diameter in 3D space from points on its surface?
I would guess that at least 3 points would be required.
geometry
asked Dec 16 '18 at 1:25
o0dv0oo0dv0o
61
$endgroup$
Is it possible to find the axis of a cylinder with a known diameter in 3D space from points on its surface?
I would guess that at least 3 points would be required.
geometry
geometry
asked Dec 16 '18 at 1:25
o0dv0oo0dv0o
61
asked Dec 16 '18 at 1:25
o0dv0oo0dv0o
61
asked Dec 16 '18 at 1:25
o0dv0oo0dv0o
61
asked Dec 16 '18 at 1:25
o0dv0oo0dv0o
61
asked Dec 16 '18 at 1:25
o0dv0oo0dv0o
61
61
$begingroup$
Not if the points were colinear.
$endgroup$
– Jens
Dec 16 '18 at 1:31
1
$begingroup$
I assume you refer to a right circular cylinder. With 3 non-collinear points a circum-circle can be made which lies in a plane perpendicular to cylinder axis. With 5 collinear points a conic can be made. If it is an ellipse then $cos^{-1}(b/a) $ is its inclination to cylinder axis
$endgroup$
– Narasimham
Dec 16 '18 at 6:48
add a comment |
$begingroup$
Not if the points were colinear.
$endgroup$
– Jens
Dec 16 '18 at 1:31
1
$begingroup$
I assume you refer to a right circular cylinder. With 3 non-collinear points a circum-circle can be made which lies in a plane perpendicular to cylinder axis. With 5 collinear points a conic can be made. If it is an ellipse then $cos^{-1}(b/a) $ is its inclination to cylinder axis
$endgroup$
– Narasimham
Dec 16 '18 at 6:48
$begingroup$
Not if the points were colinear.
$endgroup$
– Jens
Dec 16 '18 at 1:31
$begingroup$
Not if the points were colinear.
$endgroup$
– Jens
Dec 16 '18 at 1:31
1
1
$begingroup$
I assume you refer to a right circular cylinder. With 3 non-collinear points a circum-circle can be made which lies in a plane perpendicular to cylinder axis. With 5 collinear points a conic can be made. If it is an ellipse then $cos^{-1}(b/a) $ is its inclination to cylinder axis
$endgroup$
– Narasimham
Dec 16 '18 at 6:48
$begingroup$
I assume you refer to a right circular cylinder. With 3 non-collinear points a circum-circle can be made which lies in a plane perpendicular to cylinder axis. With 5 collinear points a conic can be made. If it is an ellipse then $cos^{-1}(b/a) $ is its inclination to cylinder axis
$endgroup$
– Narasimham
Dec 16 '18 at 6:48
add a comment |
1 Answer
1
active
oldest
votes
$begingroup$
These references concern the same question but without a known diameter.
(1) Perhaps take a look at NLREG:
Cylindrical Regression—Fit a Cylinder to Data Points
(2) See "Cylinders Through Five Points: Computational Algebra and
Geometry" (PDF download), by Daniel Lichtblau, for theoretical background
and Mathematica code.
answered Dec 16 '18 at 1:48
Joseph O'RourkeJoseph O'Rourke
18k349109
$endgroup$
$begingroup$
Your link doesn't appear to take into account that the diameter is known.
$endgroup$
– Jens
Dec 16 '18 at 1:53
$begingroup$
@Jens: You are correct; thanks. I will so indicate.
$endgroup$
– Joseph O'Rourke
Dec 16 '18 at 13:38
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%2f3042137%2fhow-to-find-a-cylinders-axis-from-points-on-the-surface%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
$begingroup$
These references concern the same question but without a known diameter.
(1) Perhaps take a look at NLREG:
Cylindrical Regression—Fit a Cylinder to Data Points
(2) See "Cylinders Through Five Points: Computational Algebra and
Geometry" (PDF download), by Daniel Lichtblau, for theoretical background
and Mathematica code.
answered Dec 16 '18 at 1:48
Joseph O'RourkeJoseph O'Rourke
18k349109
$endgroup$
$begingroup$
Your link doesn't appear to take into account that the diameter is known.
$endgroup$
– Jens
Dec 16 '18 at 1:53
$begingroup$
@Jens: You are correct; thanks. I will so indicate.
$endgroup$
– Joseph O'Rourke
Dec 16 '18 at 13:38
add a comment |
$begingroup$
These references concern the same question but without a known diameter.
(1) Perhaps take a look at NLREG:
Cylindrical Regression—Fit a Cylinder to Data Points
(2) See "Cylinders Through Five Points: Computational Algebra and
Geometry" (PDF download), by Daniel Lichtblau, for theoretical background
and Mathematica code.
answered Dec 16 '18 at 1:48
Joseph O'RourkeJoseph O'Rourke
18k349109
$endgroup$
$begingroup$
Your link doesn't appear to take into account that the diameter is known.
$endgroup$
– Jens
Dec 16 '18 at 1:53
$begingroup$
@Jens: You are correct; thanks. I will so indicate.
$endgroup$
– Joseph O'Rourke
Dec 16 '18 at 13:38
add a comment |
$begingroup$
These references concern the same question but without a known diameter.
(1) Perhaps take a look at NLREG:
Cylindrical Regression—Fit a Cylinder to Data Points
(2) See "Cylinders Through Five Points: Computational Algebra and
Geometry" (PDF download), by Daniel Lichtblau, for theoretical background
and Mathematica code.
answered Dec 16 '18 at 1:48
Joseph O'RourkeJoseph O'Rourke
18k349109
$endgroup$
These references concern the same question but without a known diameter.
(1) Perhaps take a look at NLREG:
Cylindrical Regression—Fit a Cylinder to Data Points
(2) See "Cylinders Through Five Points: Computational Algebra and
Geometry" (PDF download), by Daniel Lichtblau, for theoretical background
and Mathematica code.
answered Dec 16 '18 at 1:48
Joseph O'RourkeJoseph O'Rourke
18k349109
edited Dec 16 '18 at 1:55
answered Dec 16 '18 at 1:48
Joseph O'RourkeJoseph O'Rourke
18k349109
answered Dec 16 '18 at 1:48
Joseph O'RourkeJoseph O'Rourke
18k349109
answered Dec 16 '18 at 1:48
Joseph O'RourkeJoseph O'Rourke
18k349109
18k349109
$begingroup$
Your link doesn't appear to take into account that the diameter is known.
$endgroup$
– Jens
Dec 16 '18 at 1:53
$begingroup$
@Jens: You are correct; thanks. I will so indicate.
$endgroup$
– Joseph O'Rourke
Dec 16 '18 at 13:38
add a comment |
$begingroup$
Your link doesn't appear to take into account that the diameter is known.
$endgroup$
– Jens
Dec 16 '18 at 1:53
$begingroup$
@Jens: You are correct; thanks. I will so indicate.
$endgroup$
– Joseph O'Rourke
Dec 16 '18 at 13:38
$begingroup$
Your link doesn't appear to take into account that the diameter is known.
$endgroup$
– Jens
Dec 16 '18 at 1:53
$begingroup$
Your link doesn't appear to take into account that the diameter is known.
$endgroup$
– Jens
Dec 16 '18 at 1:53
$begingroup$
@Jens: You are correct; thanks. I will so indicate.
$endgroup$
– Joseph O'Rourke
Dec 16 '18 at 13:38
$begingroup$
@Jens: You are correct; thanks. I will so indicate.
$endgroup$
– Joseph O'Rourke
Dec 16 '18 at 13:38
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%2f3042137%2fhow-to-find-a-cylinders-axis-from-points-on-the-surface%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
$begingroup$
Not if the points were colinear.
$endgroup$
– Jens
Dec 16 '18 at 1:31
1
$begingroup$
I assume you refer to a right circular cylinder. With 3 non-collinear points a circum-circle can be made which lies in a plane perpendicular to cylinder axis. With 5 collinear points a conic can be made. If it is an ellipse then $cos^{-1}(b/a) $ is its inclination to cylinder axis
$endgroup$
– Narasimham
Dec 16 '18 at 6:48