Compute projected radii of a rotated elliptic paraboloid
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I'm working of a set of datapoints known to be an elliptic paraboloid on which I best fit the general quadric
$$ax²+bxy+cy²+dx+ey+f=0$$
Then I work with what I call radii projected on x an y defined as:
$$R_x=-frac{1}{2a}, R_y=-frac{1}{2c}$$
Now I have a dataset for which the rotational term $bxy$ is far from neglectable and I would like to compute $Rx'$ and $Ry'$ along the ellipsoid natural axes. How can I do that? I suppose I should rewrite equation with something like this?
$$u=xcos(t)+ysin(t)$$
$$v=xsin(t)+ycos(t)$$
quadrics
asked Jan 7 at 14:13
Julien MJulien M
1113
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add a comment |
$begingroup$
I'm working of a set of datapoints known to be an elliptic paraboloid on which I best fit the general quadric
$$ax²+bxy+cy²+dx+ey+f=0$$
Then I work with what I call radii projected on x an y defined as:
$$R_x=-frac{1}{2a}, R_y=-frac{1}{2c}$$
Now I have a dataset for which the rotational term $bxy$ is far from neglectable and I would like to compute $Rx'$ and $Ry'$ along the ellipsoid natural axes. How can I do that? I suppose I should rewrite equation with something like this?
$$u=xcos(t)+ysin(t)$$
$$v=xsin(t)+ycos(t)$$
quadrics
asked Jan 7 at 14:13
Julien MJulien M
1113
$endgroup$
$begingroup$
How are you fitting a planar equation two a surface in 3-d?
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– amd
Jan 8 at 1:54
add a comment |
$begingroup$
I'm working of a set of datapoints known to be an elliptic paraboloid on which I best fit the general quadric
$$ax²+bxy+cy²+dx+ey+f=0$$
Then I work with what I call radii projected on x an y defined as:
$$R_x=-frac{1}{2a}, R_y=-frac{1}{2c}$$
Now I have a dataset for which the rotational term $bxy$ is far from neglectable and I would like to compute $Rx'$ and $Ry'$ along the ellipsoid natural axes. How can I do that? I suppose I should rewrite equation with something like this?
$$u=xcos(t)+ysin(t)$$
$$v=xsin(t)+ycos(t)$$
quadrics
asked Jan 7 at 14:13
Julien MJulien M
1113
$endgroup$
I'm working of a set of datapoints known to be an elliptic paraboloid on which I best fit the general quadric
$$ax²+bxy+cy²+dx+ey+f=0$$
Then I work with what I call radii projected on x an y defined as:
$$R_x=-frac{1}{2a}, R_y=-frac{1}{2c}$$
Now I have a dataset for which the rotational term $bxy$ is far from neglectable and I would like to compute $Rx'$ and $Ry'$ along the ellipsoid natural axes. How can I do that? I suppose I should rewrite equation with something like this?
$$u=xcos(t)+ysin(t)$$
$$v=xsin(t)+ycos(t)$$
quadrics
quadrics
asked Jan 7 at 14:13
Julien MJulien M
1113
asked Jan 7 at 14:13
Julien MJulien M
1113
asked Jan 7 at 14:13
Julien MJulien M
1113
asked Jan 7 at 14:13
Julien MJulien M
1113
asked Jan 7 at 14:13
Julien MJulien M
1113
1113
$begingroup$
How are you fitting a planar equation two a surface in 3-d?
$endgroup$
– amd
Jan 8 at 1:54
add a comment |
$begingroup$
How are you fitting a planar equation two a surface in 3-d?
$endgroup$
– amd
Jan 8 at 1:54
$begingroup$
How are you fitting a planar equation two a surface in 3-d?
$endgroup$
– amd
Jan 8 at 1:54
$begingroup$
How are you fitting a planar equation two a surface in 3-d?
$endgroup$
– amd
Jan 8 at 1:54
add a comment |
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$begingroup$
How are you fitting a planar equation two a surface in 3-d?
$endgroup$
– amd
Jan 8 at 1:54