Thread: Fitting a Parabolic Curve to 3D Data

Hi!

I'm trying to write code to fit a parabolic curve to three points that are each three dimensional, but I'm not really understanding the math behind it and could use some help.

Here are my three points:

(-0.000461,0.003841, -0.001400)
(0.000766, -0.002610, -0.001256)
(0.005331, -0.015542, -0.011193)

Could someone perhaps walk me through the process? (My math knowledge only extends up to BC calculus)

Hello, lebronlin!

I'm trying to write code to fit a parabolic curve to three points . . .

We need more than three points.

Unless there are more restrictions,
. . there is an infinite number of such parabolas.

Shouldn't there only be one parabola that fits these points? Since there is one plane for which these points all lie on and then couldn't I solve for the parabola in that plane

Originally Posted by lebronlin

Hi!

I'm trying to write code to fit a parabolic curve to three points that are each three dimensional, but I'm not really understanding the math behind it and could use some help.

Here are my three points:

(-0.000461,0.003841, -0.001400)
(0.000766, -0.002610, -0.001256)
(0.005331, -0.015542, -0.011193)

Could someone perhaps walk me through the process? (My math knowledge only extends up to BC calculus)

1. A parabola belongs to the conic sections whose general equation is:



2. If
... and ...

then the conic section is a parabola.

3. From the general equation you can see that you need 6 points to determine the co-efficients A to F.
That's what Soroban meant when he stated that we don't have enough informations.