How to find a cylinders axis from points on the surface.
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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
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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
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$begingroup$
Not if the points were colinear.
$endgroup$
– Jens
Dec 16 '18 at 1:31
1
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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
17.9k348107
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$begingroup$
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 |
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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
17.9k348107
$endgroup$
$begingroup$
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
17.9k348107
$endgroup$
$begingroup$
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
17.9k348107
$endgroup$
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
17.9k348107
edited Dec 16 '18 at 1:55
answered Dec 16 '18 at 1:48
Joseph O'RourkeJoseph O'Rourke
17.9k348107
answered Dec 16 '18 at 1:48
Joseph O'RourkeJoseph O'Rourke
17.9k348107
answered Dec 16 '18 at 1:48
Joseph O'RourkeJoseph O'Rourke
17.9k348107
17.9k348107
$begingroup$
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 |
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$begingroup$
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