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https://github.com/thammin/unity-spring
A minimal spring physics library for Unity
https://github.com/thammin/unity-spring
damp oscillator unity unity3d
Last synced: about 2 months ago
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A minimal spring physics library for Unity
- Host: GitHub
- URL: https://github.com/thammin/unity-spring
- Owner: thammin
- License: mit
- Created: 2019-09-18T06:47:02.000Z (over 5 years ago)
- Default Branch: master
- Last Pushed: 2021-12-08T01:44:02.000Z (about 3 years ago)
- Last Synced: 2024-09-24T15:10:52.289Z (3 months ago)
- Topics: damp, oscillator, unity, unity3d
- Language: C#
- Homepage:
- Size: 1.86 MB
- Stars: 102
- Watchers: 5
- Forks: 8
- Open Issues: 4
-
Metadata Files:
- Readme: README.md
- License: LICENSE.md
Awesome Lists containing this project
README
# A minimal spring physics library for Unity
Implement multiple solvers for damped harmonic oscillator.
Solvers:
- [x] [Closed-form solution for the ODE](http://www.ryanjuckett.com/programming/damped-springs/)
- [x] [Semi-implicit Euler method](https://en.wikipedia.org/wiki/Semi-implicit_Euler_method)
- [x] [Explicit Runge-Kutta 4th order aka RK4](https://en.wikipedia.org/wiki/Runge%E2%80%93Kutta_methods)
- [x] [Verlet Integration](https://en.wikipedia.org/wiki/Verlet_integration)
Maybe not:
- [ ] [Explicit Euler aka Forward Euler](https://en.wikipedia.org/wiki/Euler_method)
- [ ] [Implicit Euler aka Backward Euler](https://en.wikipedia.org/wiki/Backward_Euler_method)
- [ ] [Mid-point method](https://en.wikipedia.org/wiki/Midpoint_method)
- [ ] [Implicit Runge-Kutta 4th order aka RK4](https://en.wikipedia.org/wiki/Runge%E2%80%93Kutta_methods#Implicit_Runge%E2%80%93Kutta_methods)
Performance rough check with 2.6 GHz Intel Core i7:
# Install
via Package Manager UI
```
ssh://[email protected]/thammin/unity-spring.git
```
via [OpenUPM](https://openupm.com/packages/com.thammin.unity-spring/)
```
openupm add com.thammin.unity-spring
```
# Usage
Every solver is just a [simple class](https://github.com/thammin/unity-spring/blob/master/Runtime/SpringBase.cs) with few fields.
```cs
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](https://github.com/Unity-Technologies/UnityCsReference/blob/2019.3/Runtime/Export/Math/Mathf.cs#L302-L331)
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.
```cs
// 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