A minimal spring physics library for Unity

Implement multiple solvers for damped harmonic oscillator.

Solvers:

• [x] Closed-form solution for the ODE
• [x] Semi-implicit Euler method
• [x] Explicit Runge-Kutta 4th order aka RK4
• [x] Verlet Integration

Maybe not:

• [ ] Explicit Euler aka Forward Euler
• [ ] Implicit Euler aka Backward Euler
• [ ] Mid-point method
• [ ] Implicit Runge-Kutta 4th order aka RK4

Performance rough check with 2.6 GHz Intel Core i7:

Install

via Package Manager UI

ssh://[email protected]/thammin/unity-spring.git

via OpenUPM

openupm add com.thammin.unity-spring

Usage

Every solver is just a simple class with few fields.

using UnityEngine;
using Spring = UnitySpring.ClosedForm.Spring;

public class Ball : MonoBehaviour
{
    Spring spring;

    void Start()
    {
        // interpolate from -10f to 10f
        spring = new Spring()
        {
            startValue = -10f,
            endValue = 10f
        };
    }

    void Update()
    {
        var x = spring.Evaluate(Time.deltaTime);
        transform.position = new Vector3(x, 0f, 0f);
    }
}

Screenshot or demo

Visualizer:

FAQ

Unity SmoothDamp

Source code: link

Based on closed-form solution, but only modeling critically damped spring. Using tweaked Exponential approximation (up to Taylor 3rd order) which claims as roughly 80 times faster and approximate less than 0.1% error than exp function.

// tweaked coefficients
float exp = 1F / (1F + x + 0.48F * x * x + 0.235F * x * x * x);

References

Analytical:

• http://www.entropy.energy/scholar/node/damped-harmonic-oscillator
• https://doc.lagout.org/Others/Game%20Development/Programming/Game%20Programming%20Gems%204.pdf

Numerical:

• http://box2d.org/files/GDC2015/ErinCatto_NumericalMethods.pdf

General:

• https://hplgit.github.io/num-methods-for-PDEs/doc/pub/vib/pdf/vib-4print-A4-2up.pdf

License

MIT