About sphere equation $z = a+bx+cy+dx^2 +ey^2$
0
I'm trying to fit a sphere from points. I tried a first way to estimate the sphere but I'm not satisfied.
I saw in an article a way to get a best fitting sphere from the equation :
$z = a+bx+cy+dx^2 +ey^2$
Now, I have $a,b,c,d$ and $e$ values but I don't know what is the center of the sphere, radius ...
Do you have some explanation about this equation ?
Thank you.
least-squares
edited Jun 4 '14 at 21:44
Thomas
35.4k1056116
asked Jun 4 '14 at 19:32
usersssusersss
12
|
show 6 more comments
0
I'm trying to fit a sphere from points. I tried a first way to estimate the sphere but I'm not satisfied.
I saw in an article a way to get a best fitting sphere from the equation :
$z = a+bx+cy+dx^2 +ey^2$
Now, I have $a,b,c,d$ and $e$ values but I don't know what is the center of the sphere, radius ...
Do you have some explanation about this equation ?
Thank you.
least-squares
edited Jun 4 '14 at 21:44
Thomas
35.4k1056116
asked Jun 4 '14 at 19:32
usersssusersss
12
1
I believe it's a circle, not a sphere?
– Tunococ
Jun 4 '14 at 19:35
a $3-sphere$ ? as in the four dimensional analogue of the 'normal' sphere ?
– The very fluffy Panda
Jun 4 '14 at 19:36
How many point do you have?
– Mark Bennet
Jun 4 '14 at 19:37
I think @usersss meant to say 2-sphere, but probably doesn't understand what a 3-sphere really is.
– Rocket Man
Jun 4 '14 at 19:38
1
it's not a sphere unless it has $z^2$ in the equation
– PA6OTA
Jun 4 '14 at 19:41
|
show 6 more comments
0
0
0
I'm trying to fit a sphere from points. I tried a first way to estimate the sphere but I'm not satisfied.
I saw in an article a way to get a best fitting sphere from the equation :
$z = a+bx+cy+dx^2 +ey^2$
Now, I have $a,b,c,d$ and $e$ values but I don't know what is the center of the sphere, radius ...
Do you have some explanation about this equation ?
Thank you.
least-squares
edited Jun 4 '14 at 21:44
Thomas
35.4k1056116
asked Jun 4 '14 at 19:32
usersssusersss
12
I'm trying to fit a sphere from points. I tried a first way to estimate the sphere but I'm not satisfied.
I saw in an article a way to get a best fitting sphere from the equation :
$z = a+bx+cy+dx^2 +ey^2$
Now, I have $a,b,c,d$ and $e$ values but I don't know what is the center of the sphere, radius ...
Do you have some explanation about this equation ?
Thank you.
least-squares
least-squares
edited Jun 4 '14 at 21:44
Thomas
35.4k1056116
asked Jun 4 '14 at 19:32
usersssusersss
12
edited Jun 4 '14 at 21:44
Thomas
35.4k1056116
asked Jun 4 '14 at 19:32
usersssusersss
12
edited Jun 4 '14 at 21:44
Thomas
35.4k1056116
edited Jun 4 '14 at 21:44
Thomas
35.4k1056116
edited Jun 4 '14 at 21:44
Thomas
35.4k1056116
35.4k1056116
asked Jun 4 '14 at 19:32
usersssusersss
12
asked Jun 4 '14 at 19:32
usersssusersss
12
asked Jun 4 '14 at 19:32
usersssusersss
12
12
1
I believe it's a circle, not a sphere?
– Tunococ
Jun 4 '14 at 19:35
a $3-sphere$ ? as in the four dimensional analogue of the 'normal' sphere ?
– The very fluffy Panda
Jun 4 '14 at 19:36
How many point do you have?
– Mark Bennet
Jun 4 '14 at 19:37
I think @usersss meant to say 2-sphere, but probably doesn't understand what a 3-sphere really is.
– Rocket Man
Jun 4 '14 at 19:38
1
it's not a sphere unless it has $z^2$ in the equation
– PA6OTA
Jun 4 '14 at 19:41
|
show 6 more comments
1
I believe it's a circle, not a sphere?
– Tunococ
Jun 4 '14 at 19:35
a $3-sphere$ ? as in the four dimensional analogue of the 'normal' sphere ?
– The very fluffy Panda
Jun 4 '14 at 19:36
How many point do you have?
– Mark Bennet
Jun 4 '14 at 19:37
I think @usersss meant to say 2-sphere, but probably doesn't understand what a 3-sphere really is.
– Rocket Man
Jun 4 '14 at 19:38
1
it's not a sphere unless it has $z^2$ in the equation
– PA6OTA
Jun 4 '14 at 19:41
1
1
I believe it's a circle, not a sphere?
– Tunococ
Jun 4 '14 at 19:35
I believe it's a circle, not a sphere?
– Tunococ
Jun 4 '14 at 19:35
a $3-sphere$ ? as in the four dimensional analogue of the 'normal' sphere ?
– The very fluffy Panda
Jun 4 '14 at 19:36
a $3-sphere$ ? as in the four dimensional analogue of the 'normal' sphere ?
– The very fluffy Panda
Jun 4 '14 at 19:36
How many point do you have?
– Mark Bennet
Jun 4 '14 at 19:37
How many point do you have?
– Mark Bennet
Jun 4 '14 at 19:37
I think @usersss meant to say 2-sphere, but probably doesn't understand what a 3-sphere really is.
– Rocket Man
Jun 4 '14 at 19:38
I think @usersss meant to say 2-sphere, but probably doesn't understand what a 3-sphere really is.
– Rocket Man
Jun 4 '14 at 19:38
1
1
it's not a sphere unless it has $z^2$ in the equation
– PA6OTA
Jun 4 '14 at 19:41
it's not a sphere unless it has $z^2$ in the equation
– PA6OTA
Jun 4 '14 at 19:41
|
show 6 more comments
1 Answer
1
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oldest
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This is an extract (translated) from pp.17-18 http://fr.scribd.com/doc/14819165/Regressions-coniques-quadriques-circulaire-spherique
answered Jun 4 '14 at 21:00
JJacquelinJJacquelin
42.8k21750
1
I now have better results. Merci beaucoup.
– usersss
Jun 4 '14 at 21:11
@Chris : Thank you very much for your remark about the sign of $A_0$ in the equation for $R$. You are right, this was a typo. I rejected your corrected page because it is better to make the correction directly in the joint image instead of in an additional comment. Moreover, there was another typo in the 4X4 matrix, now fixed. All this was already mentioned by Alan Magnuson who I thank too. But sorry, up to now, I neglected to made the correction.
– JJacquelin
Jul 26 '18 at 15:03
add a comment |
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This is an extract (translated) from pp.17-18 http://fr.scribd.com/doc/14819165/Regressions-coniques-quadriques-circulaire-spherique
answered Jun 4 '14 at 21:00
JJacquelinJJacquelin
42.8k21750
1
I now have better results. Merci beaucoup.
– usersss
Jun 4 '14 at 21:11
@Chris : Thank you very much for your remark about the sign of $A_0$ in the equation for $R$. You are right, this was a typo. I rejected your corrected page because it is better to make the correction directly in the joint image instead of in an additional comment. Moreover, there was another typo in the 4X4 matrix, now fixed. All this was already mentioned by Alan Magnuson who I thank too. But sorry, up to now, I neglected to made the correction.
– JJacquelin
Jul 26 '18 at 15:03
add a comment |
0
This is an extract (translated) from pp.17-18 http://fr.scribd.com/doc/14819165/Regressions-coniques-quadriques-circulaire-spherique
answered Jun 4 '14 at 21:00
JJacquelinJJacquelin
42.8k21750
1
I now have better results. Merci beaucoup.
– usersss
Jun 4 '14 at 21:11
@Chris : Thank you very much for your remark about the sign of $A_0$ in the equation for $R$. You are right, this was a typo. I rejected your corrected page because it is better to make the correction directly in the joint image instead of in an additional comment. Moreover, there was another typo in the 4X4 matrix, now fixed. All this was already mentioned by Alan Magnuson who I thank too. But sorry, up to now, I neglected to made the correction.
– JJacquelin
Jul 26 '18 at 15:03
add a comment |
0
0
0
This is an extract (translated) from pp.17-18 http://fr.scribd.com/doc/14819165/Regressions-coniques-quadriques-circulaire-spherique
answered Jun 4 '14 at 21:00
JJacquelinJJacquelin
42.8k21750
This is an extract (translated) from pp.17-18 http://fr.scribd.com/doc/14819165/Regressions-coniques-quadriques-circulaire-spherique
answered Jun 4 '14 at 21:00
JJacquelinJJacquelin
42.8k21750
edited Jul 26 '18 at 14:44
answered Jun 4 '14 at 21:00
JJacquelinJJacquelin
42.8k21750
answered Jun 4 '14 at 21:00
JJacquelinJJacquelin
42.8k21750
answered Jun 4 '14 at 21:00
JJacquelinJJacquelin
42.8k21750
42.8k21750
1
I now have better results. Merci beaucoup.
– usersss
Jun 4 '14 at 21:11
@Chris : Thank you very much for your remark about the sign of $A_0$ in the equation for $R$. You are right, this was a typo. I rejected your corrected page because it is better to make the correction directly in the joint image instead of in an additional comment. Moreover, there was another typo in the 4X4 matrix, now fixed. All this was already mentioned by Alan Magnuson who I thank too. But sorry, up to now, I neglected to made the correction.
– JJacquelin
Jul 26 '18 at 15:03
add a comment |
1
I now have better results. Merci beaucoup.
– usersss
Jun 4 '14 at 21:11
@Chris : Thank you very much for your remark about the sign of $A_0$ in the equation for $R$. You are right, this was a typo. I rejected your corrected page because it is better to make the correction directly in the joint image instead of in an additional comment. Moreover, there was another typo in the 4X4 matrix, now fixed. All this was already mentioned by Alan Magnuson who I thank too. But sorry, up to now, I neglected to made the correction.
– JJacquelin
Jul 26 '18 at 15:03
1
1
I now have better results. Merci beaucoup.
– usersss
Jun 4 '14 at 21:11
I now have better results. Merci beaucoup.
– usersss
Jun 4 '14 at 21:11
@Chris : Thank you very much for your remark about the sign of $A_0$ in the equation for $R$. You are right, this was a typo. I rejected your corrected page because it is better to make the correction directly in the joint image instead of in an additional comment. Moreover, there was another typo in the 4X4 matrix, now fixed. All this was already mentioned by Alan Magnuson who I thank too. But sorry, up to now, I neglected to made the correction.
– JJacquelin
Jul 26 '18 at 15:03
@Chris : Thank you very much for your remark about the sign of $A_0$ in the equation for $R$. You are right, this was a typo. I rejected your corrected page because it is better to make the correction directly in the joint image instead of in an additional comment. Moreover, there was another typo in the 4X4 matrix, now fixed. All this was already mentioned by Alan Magnuson who I thank too. But sorry, up to now, I neglected to made the correction.
– JJacquelin
Jul 26 '18 at 15:03
add a comment |
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1
I believe it's a circle, not a sphere?
– Tunococ
Jun 4 '14 at 19:35
a $3-sphere$ ? as in the four dimensional analogue of the 'normal' sphere ?
– The very fluffy Panda
Jun 4 '14 at 19:36
How many point do you have?
– Mark Bennet
Jun 4 '14 at 19:37
I think @usersss meant to say 2-sphere, but probably doesn't understand what a 3-sphere really is.
– Rocket Man
Jun 4 '14 at 19:38
1
it's not a sphere unless it has $z^2$ in the equation
– PA6OTA
Jun 4 '14 at 19:41