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switch to klipkonns algorithm to pos calculation
This commit is contained in:
Marcel Märtens
parent
34c5682485
commit
f17bc34883
@ -295,13 +295,44 @@ fn cant_run_during_fall() -> Result<(), Box<dyn Error>> {
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Ok(())
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}
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fn mass_c() -> (f64, f64) {
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let mass = 1.0;
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let air_friction_co = 0.9_f64;
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let air_friction_area = 0.75_f64;
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let air_density = 1.225_f64;
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let c = air_friction_co * air_friction_area * 0.5 * air_density * mass;
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(mass, c)
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#[derive(Clone, Copy)]
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struct FricParams {
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friction_co: f64,
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projected_area: f64,
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density: f64,
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mass: f64,
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}
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impl Default for FricParams {
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fn default() -> Self {
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Self {
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friction_co: 0.9_f64,
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projected_area: 0.75_f64,
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density: 1.225_f64,
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mass: 1.0_f64,
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}
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}
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}
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impl FricParams {
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const MAX_ACC: f64 = 9.2;
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// https://en.wikipedia.org/wiki/Drag_(physics)
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// Todo: old impl was (mass * acc.abs() / (friction_co * projected_area * 0.5 *
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// density * mass )).sqrt();
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fn v_term(&self, acc: f64) -> f64 {
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((2.0 * self.mass * acc.abs()) / (self.density * self.projected_area * self.friction_co))
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.sqrt()
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}
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}
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trait MathHelp {
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fn coth(&self) -> Self;
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fn acoth(&self) -> Self;
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}
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impl MathHelp for f64 {
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// coth(x) = 1/tanh(x)`
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fn coth(&self) -> Self { 1.0 / self.tanh() }
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// `acoth(x) = atanh(1/x)`
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fn acoth(&self) -> Self { (1.0 / self).atanh() }
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}
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fn test_run_helper(
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@ -311,16 +342,20 @@ fn test_run_helper(
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test_series: Vec<(/* acc */ f64, /* duration */ f64)>,
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) -> (f64, f64) {
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let dt = 1.0 / tps as f64;
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let (mass, c) = mass_c();
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let params = FricParams::default();
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let v_term = params.v_term(FricParams::MAX_ACC);
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println!("");
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println!("dt: {:0>4.4} - mass: {:0>4.4} - c: {:0>4.4}", dt, mass, c);
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println!(
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"dt: {:0>4.4} - mass: {:0>4.4} - v_term: {:0>4.4}",
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dt, params.mass, v_term
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);
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let (mut vel, mut pos) = (start_vel, start_pos);
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let mut i = 0;
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for (move_dir, duration) in test_series {
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let count = (duration / dt).round() as usize;
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println!("move_dir: {:0>4.4}", move_dir);
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for _ in 0..count {
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(vel, pos) = acc_with_frict_tick(i, move_dir, vel, pos, dt);
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(vel, pos) = acc_with_frict_tick(i, move_dir, vel, pos, dt, params);
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i += 1;
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}
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}
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@ -352,12 +387,15 @@ macro_rules! veriy_diffs {
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/// https://www.energie-lexikon.info/reibung.html
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/// https://sciencing.com/calculate-force-friction-6454395.html
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/// https://www.leifiphysik.de/mechanik/reibung-und-fortbewegung
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fn acc_with_frict_tick(i: usize, move_dir: f64, vel: f64, pos: f64, dt: f64) -> (f64, f64) {
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let (mass, c) = mass_c();
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const MAX_ACC: f64 = 9.2;
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let acc = MAX_ACC * move_dir; // btw: cant accelerate faster than gravity on foot
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let old_vel = vel;
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fn acc_with_frict_tick(
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i: usize,
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move_dir: f64,
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vel: f64,
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pos: f64,
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dt: f64,
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params: FricParams,
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) -> (f64, f64) {
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let acc = FricParams::MAX_ACC * move_dir; // btw: cant accelerate faster than gravity on foot
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// controller
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// I know what you think, wtf, yep: https://math.stackexchange.com/questions/1929436/line-integral-of-force-of-air-resistanc
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@ -366,41 +404,74 @@ fn acc_with_frict_tick(i: usize, move_dir: f64, vel: f64, pos: f64, dt: f64) ->
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// terminal velocity equals the maximum velocity that can be reached by acc
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// alone
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let vel_t = (mass * acc.abs() / c).sqrt();
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let _vel_tm = (mass * MAX_ACC / c).sqrt();
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let vel_t = acc.signum() * params.v_term(acc);
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// if our old_vel is bigger than vel_t we can use `coth(x) = 1/tanh(x)` and
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// `acoth(x) = atanh(1/x)`
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let revert_fak = if vel_t != 0.0 {
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old_vel / vel_t
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// thanks to kilpkonn for figuring this out
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// https://en.wikipedia.org/wiki/Drag_(physics)
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//
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// upper and lower are upper and lower bound for integral
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let revert_fak = vel / vel_t;
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let (vel, pos) = if acc.abs() < f64::EPSILON {
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// https://www.wolframalpha.com/input?i=m%2F%28Cx+%2B+m%2FV%29+dx+integrate
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let c = params.density * params.projected_area * params.friction_co;
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let lower = params.mass * params.mass.ln() / c;
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let upper = params.mass * (c * vel * dt + params.mass).ln() / c;
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let pos = pos + (upper - lower);
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let vel = params.mass
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/ (params.density * params.projected_area * params.friction_co * dt
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+ params.mass / vel);
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(vel, pos)
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} else if revert_fak <= 0.0 {
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// Handle passing through 0 differently as the function changes
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// https://www.wolframalpha.com/input?i=V*tan%28x*g%2FV+%2B+atan%28v%2FV%29%29+%3D+0+solve+for+x
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let dt_to_zero = vel_t * (vel / vel_t).atan() / acc.abs();
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if dt_to_zero < dt {
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// Step with only part of dt that is left after reaching 0 vel
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let lower = vel_t.powi(2) * (vel / vel_t).atan().cos().ln() / acc;
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let upper =
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-vel_t.powi(2) * (acc * dt_to_zero / vel_t + (vel / vel_t).atan()).cos().ln() / acc;
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let pos = pos + (upper - lower);
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let dt = dt - dt_to_zero;
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// https://www.wolframalpha.com/input?i=V+*+tanh%28xg%2FV%29+dx+integrate
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// lower bound is 0
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let pos = pos + vel_t.powi(2) * (acc * dt / vel_t).cosh().ln() / acc;
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let vel = vel_t * (dt * acc / vel_t).tanh();
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(vel, pos)
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} else {
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// https://www.wolframalpha.com/input?i=V+*+tan%28xg%2FV+%2B+atan%28v%2FV%29%29+dx+integrate
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let lower = -vel_t.powi(2) * (vel / vel_t).atan().cos().ln() / acc;
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let upper = -vel_t.powi(2) * (acc * dt / vel_t + (vel / vel_t).atan()).cos().ln() / acc;
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let pos = pos + (upper - lower);
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let vel = vel_t * (dt * acc / vel_t + (vel / vel_t).atan()).tan();
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(vel, pos)
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}
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} else if revert_fak >= 1.0 {
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// https://www.wolframalpha.com/input?i=V+*+coth%28xg%2FV+%2B+acoth%28v%2FV%29%29+dx+integrate
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let lower = (vel_t.powi(2) * (vel / vel_t).acoth().cosh().ln()
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+ (vel / vel_t).acoth().tanh().ln())
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/ acc;
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let upper = (vel_t.powi(2) * (acc * dt / vel_t + (vel / vel_t).acoth()).cosh().ln()
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+ (acc * dt / vel_t + (vel / vel_t).acoth()).tanh().ln())
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/ acc;
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let pos = pos + (upper - lower);
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let vel = vel_t * (dt * acc / vel_t + (vel / vel_t).acoth()).coth();
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(vel, pos)
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} else {
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1337.0
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// https://www.wolframalpha.com/input?i=V+*+tanh%28xg%2FV+%2B+atanh%28v%2FV%29%29+dx+integrate
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let lower = vel_t.powi(2) * ((vel / vel_t).atanh()).cosh().ln() / acc;
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let upper = vel_t.powi(2) * (acc * dt / vel_t + (vel / vel_t).atanh()).cosh().ln() / acc;
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let pos = pos + (upper - lower);
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let vel = vel_t * (dt * acc / vel_t + (vel / vel_t).atanh()).tanh();
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(vel, pos)
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};
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let vel = if revert_fak.abs() >= 1.0 {
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vel_t / ((1.0 / revert_fak).atanh() + acc.signum() * (c * acc.abs()).sqrt() * dt).tanh()
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} else {
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vel_t * ((revert_fak).atanh() + acc.signum() * (c * acc.abs()).sqrt() * dt).tanh()
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};
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//physics
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let distance_last = mass / c * (((old_vel * (c / acc / mass).sqrt()).atanh()).cosh()).ln();
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let distance = mass / c
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* (((old_vel * (c / acc / mass).sqrt()).atanh() + dt * (c * acc / mass).sqrt()).cosh())
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.ln();
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let diff = distance - distance_last;
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let diff = if !diff.is_finite() { 0.0 } else { diff };
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let pos = pos + diff;
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let ending = ((i + 1) as f64 * dt * 100.0).round() as i64;
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let line = format!(
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"[{:0>2.2}]: acc: {:0>5.4}, revert_fak: {:0>4.4}, vel: {:0>4.4}, dist: \
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{:0>7.4}, pos: {:0>7.4}",
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"[{:0>2.2}]: acc: {:0>5.4}, revert_fak: {:0>4.4}, vel: {:0>4.4}, pos: {:0>7.4}",
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(i + 1) as f64 * dt,
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acc,
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revert_fak,
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vel,
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distance,
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pos
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);
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if ending % 10 != 0 {
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