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)

Re: Fitting a Parabolic Curve to 3D Data

Hello, lebronlin!

Quote:

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.

Re: Fitting a Parabolic Curve to 3D Data

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

Re: Fitting a Parabolic Curve to 3D Data

Quote:

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:

$\displaystyle Ax^2+Bxy+Cy^2+Dx+Ey+F=0$

2. If

$\displaystyle \Delta = \left| \begin{array}{ccc}A&\frac B2 & \frac D2 \\ \frac B2& C & \frac E2 \\ \frac D2 & \frac E2 & F\end{array} \right| \ne 0$ ... and ... $\displaystyle \delta = \left|\begin{array}{cc}A& \frac B2 \\ \frac B2&C\end{array}\right| = 0$

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.