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May 21, 2024 22:27
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Spring delta time equation [Godot]
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## Translated from EgoMoose tutorial of deriving formula for Unity | |
## https://youtu.be/FZekwtIO0I4 | |
## https://gist.github.com/EgoMoose/777ed827e89b69d479ea407e79261b97 | |
class_name SpringMath | |
extends Node | |
## zeta = damping ratio | |
## omega = angular frequency | |
static func vec1(value:float, target:float, velocity:float, delta:float, zeta:float = 0.3, omega:float = 20.0)->Array[float]: | |
if zeta >= 1: | |
return [target, velocity] | |
if zeta < 0: | |
zeta = 0.0 | |
var x0:float = value - target | |
var omega_zeta:float = omega * zeta | |
var alpha:float = omega * sqrt(1.0 - zeta * zeta) | |
var _exp:float = exp(-delta * omega_zeta) | |
var _cos:float = cos(delta * alpha) | |
var _sin:float = sin(delta * alpha) | |
var c2:float = (velocity + x0 * omega_zeta) / alpha | |
var position:float = target + _exp * (x0 * _cos + c2 * _sin) | |
var _velocity:float = -_exp * ((x0 * omega_zeta - c2 * alpha) * _cos + (x0 * alpha + c2 * omega_zeta) * _sin) | |
return [position, _velocity] | |
## zeta = damping ratio | |
## omega = angular frequency | |
static func vec2(value:Vector2, target:Vector2, velocity:Vector2, delta:float, zeta:float = 0.3, omega:float = 20.0)->Array[Vector2]: | |
if zeta >= 1: | |
return [target, velocity] | |
if zeta < 0: | |
zeta = 0.0 | |
var x0:Vector2 = value - target | |
var omega_zeta:float = omega * zeta | |
var alpha:float = omega * sqrt(1.0 - zeta * zeta) | |
var _exp:float = exp(-delta * omega_zeta) | |
var _cos:float = cos(delta * alpha) | |
var _sin:float = sin(delta * alpha) | |
var c2:Vector2 = (velocity + x0 * omega_zeta) / alpha | |
var position:Vector2 = target + _exp * (x0 * _cos + c2 * _sin) | |
var _velocity:Vector2 = -_exp * ((x0 * omega_zeta - c2 * alpha) * _cos + (x0 * alpha + c2 * omega_zeta) * _sin) | |
return [position, _velocity] | |
## zeta = damping ratio | |
## omega = angular frequency | |
static func vec3(value:Vector3, target:Vector3, velocity:Vector3, delta:float, zeta:float = 0.9, omega:float = 0.1)->Array[Vector3]: | |
if zeta >= 1: | |
return [target, velocity] | |
if zeta < 0: | |
zeta = 0.0 | |
var x0:Vector3 = value - target | |
var omega_zeta:float = omega * zeta | |
var alpha:float = omega * sqrt(1.0 - zeta * zeta) | |
var _exp:float = exp(-delta * omega_zeta) | |
var _cos:float = cos(delta * alpha) | |
var _sin:float = sin(delta * alpha) | |
var c2:Vector3 = (velocity + x0 * omega_zeta) / alpha | |
var position:Vector3 = target + _exp * (x0 * _cos + c2 * _sin) | |
var _velocity:Vector3 = -_exp * ((x0 * omega_zeta - c2 * alpha) * _cos + (x0 * alpha + c2 * omega_zeta) * _sin) | |
return [position, _velocity] |
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