fit_trajectory
Fit polynomial to trajectory data for smoothing or deriving motion equations. Supports linear, quadratic, or cubic fits, returning coefficients and goodness-of-fit.
Instructions
Fit polynomial to trajectory data.
Useful for smoothing noisy data or finding trajectory equations.
Default fit_type="quadratic" fits parabolic trajectory (constant acceleration).
Args:
times: Time values in seconds (or JSON string)
positions: Position vectors [[x,y,z], ...] in meters (or JSON string)
fit_type: Polynomial type - "linear", "quadratic", or "cubic" (default "quadratic")
Returns:
Dict containing:
- coefficients_x: Polynomial coefficients for x(t)
- coefficients_y: Polynomial coefficients for y(t)
- coefficients_z: Polynomial coefficients for z(t)
- r_squared: R² goodness of fit (0-1)
- predicted_positions: Fitted positions [[x,y,z], ...]
Example - Projectile motion:
result = await fit_trajectory(
times=[0, 1, 2, 3],
positions=[[0,0,0], [10,15,0], [20,20,0], [30,15,0]],
fit_type="quadratic"
)
# Fits x(t) = c0 + c1*t + c2*t²Input Schema
TableJSON Schema
| Name | Required | Description | Default |
|---|---|---|---|
| times | Yes | ||
| positions | Yes | ||
| fit_type | No | quadratic |