Add second-order motion to any continuous value, useful for procedural animation of dynamic systems. Or interpolation without fixed start and end points.

Full credit for this belongs to t3ssel8r and this video on youtube (watch it!) explaining this is great detail. I only ported the code to Rust and made a simple example using Bevy (cargo run --release --example sphere).

The parameters are:

• f - Frequency in cycles per second. The speed at which the system will respond to changes in the input, and rate of vibration.
• ζ (zeta) - Damping coefficient. Controls how fast the system settles. 0 is no dampening. Less than 1, vibration is damped. Greater than 1, no vibration.
• r - Initial response. Lower values makes the system slower to react. Above 1, the response overshoots the target. Negative values anticipate motion.