Struct CASpring 

pub struct CASpring {
    pub response: f32,
    pub damping_ratio: f32,
}

Authentic macOS CoreAnimation damped harmonic oscillator spring model.

Matches Apple’s CASpringAnimation and SwiftUI .spring(response:dampingRatio:). Provides exact closed-form analytical solutions for underdamped ($\zeta < 1$), critically damped ($\zeta = 1$), and overdamped ($\zeta > 1$) regimes without numerical Euler drift or floating-point overflow.

Example

use egui_macview::CASpring;

// Create a responsive spring (0.35s period, 0.85 damping ratio)
let spring = CASpring::new(0.35, 0.85);

// Evaluate position x(t) in [0.0, 1.0]
let x_start = spring.evaluate(0.0);
let x_mid = spring.evaluate(0.15);
let x_settled = spring.evaluate(spring.settling_duration());

assert_eq!(x_start, 0.0);
assert!(x_mid > 0.0 && x_mid < 1.1);
assert!((x_settled - 1.0).abs() < 0.005);

Fields

response: f32

Perceptual oscillation period $T_0$ in seconds ($\ge 0.0001$).

damping_ratio: f32

Dimensionless damping ratio $\zeta$ ($\ge 0.0$).

• $\zeta < 1.0$: Underdamped (oscillates with decaying overshoot).
• $\zeta = 1.0$: Critically damped (fastest decay with zero overshoot).
• $\zeta > 1.0$: Overdamped (smooth monotonic decay without oscillation).

Implementations

impl CASpring

pub fn new(response: f32, damping_ratio: f32) -> Self

Creates a new CASpring from cycle period response (in seconds) and dimensionless damping_ratio ($\zeta$).

pub fn from_perceptual(response: f32, damping_ratio: f32) -> Self

Creates a CASpring using Apple SwiftUI / AppKit perceptual parameters response (in seconds) and damping_ratio.

pub fn from_frequency(omega_0: f32, damping_ratio: f32) -> Self

Creates a CASpring from undamped angular frequency $\omega_0$ (in rad/s) and damping ratio $\zeta$.

pub fn from_physical(mass: f32, stiffness: f32, damping: f32) -> Self

Creates a CASpring from physical mass $m$, stiffness $k$, and damping $c$.

pub fn omega_0(&self) -> f32

Undamped natural angular frequency $\omega_0 = \frac{2\pi}{\text{response}}$ in rad/s.

pub fn omega_d(&self) -> f32

Damped angular frequency $\omega_d = \omega_0 \sqrt{|1 - \zeta^2|}$ in rad/s.

pub fn settling_duration(&self) -> f32

Analytical settling duration $t_{\text{settle}} = \frac{-\ln(\epsilon)}{\zeta \omega_0} = \frac{6.907755}{\zeta \omega_0}$ for underdamped/critically damped oscillators ($\zeta \le 1$), and the dominant pole $\frac{6.907755}{\zeta \omega_0 - \omega_d}$ for overdamped systems ($\zeta > 1$), to within $\epsilon = 0.001$ (0.1%) of target resting state.

pub fn animate_f32(&self, ctx: &Context, id: Id, target: f32) -> f32

Evaluates a stateful CASpring transition toward target using egui temporary memory, requesting a repaint only while (target - start_val).abs() > f32::EPSILON and elapsed < self.settling_duration().

pub fn animate_f32_at( &self, ctx: &Context, id: Id, target: f32, now: f64, frame_paced: bool, ) -> f32

Evaluates a stateful CASpring transition toward target at explicit timestamp now, performing zero spring math or IdTypeMap write locks when settled at rest.

pub fn position_at(&self, t: f32) -> f32

Evaluates displacement $x(t) \in [0.0, 1.0]$ at time $t$ in seconds.

pub fn overshoot_ratio(&self) -> f32

Theoretical peak overshoot ratio over resting state (0.0 if critically or overdamped).

pub fn evaluate(&self, t: f32) -> f32

Evaluates displacement $x(t) \in [0.0, 1.0]$ at time $t$ in seconds.

pub fn velocity(&self, t: f32) -> f32

Analytical velocity derivative $\dot{x}(t)$ at time $t$ in seconds.

Trait Implementations

impl Clone for CASpring

fn clone(&self) -> Self

Returns a duplicate of the value.

fn clone_from(&mut self, source: &Self)

Performs copy-assignment from source.

impl Copy for CASpring

impl Debug for CASpring

fn fmt(&self, f: &mut Formatter<'_>) -> Result

Formats the value using the given formatter.

impl Default for CASpring

fn default() -> Self

Returns the “default value” for a type.

impl<'de> Deserialize<'de> for CASpring

fn deserialize<__D>(__deserializer: __D) -> Result<Self, __D::Error>

where __D: Deserializer<'de>,

Deserialize this value from the given Serde deserializer.

impl PartialEq for CASpring

fn eq(&self, other: &Self) -> bool

Equality operator ==.

fn ne(&self, other: &Rhs) -> bool

Inequality operator !=.

impl Serialize for CASpring

fn serialize<__S>(&self, __serializer: __S) -> Result<__S::Ok, __S::Error>

where __S: Serializer,

Serialize this value into the given Serde serializer.

impl StructuralPartialEq for CASpring