sync

common/systems/src/phys.rs

@@ -791,9 +791,8 @@ impl<'a> PhysicsData<'a> {
                         .terrain
                         .contains_key(read.terrain.pos_key(pos.0.map(|e| e.floor() as i32)));
 
-                    // Don't move if we're not in a loaded chunk
+                    let move_dir = if vel.0.x != 0.0 || vel.0.y != 0.0 {
-                    let pos_delta = if in_loaded_chunk {
+                        Vec3::new(vel.0.x, vel.0.y, 0.0).normalized()
-                        vel.0 * read.dt.0
                     } else {
                         Vec3::zero()
                     };
@@ -815,7 +814,19 @@ impl<'a> PhysicsData<'a> {
                     // resolves these sort of things well anyway.
                     // At the very least, we don't do things that result in glitchy
                     // velocities or entirely broken position snapping.
-                    let mut tgt_pos = pos.0 + pos_delta;
+                    // Don't move if we're not in a loaded chunk
+                    let (tgt_vel, mut tgt_pos) = if in_loaded_chunk {
+                        acc_with_frict_tick(move_dir, vel.0, pos.0, read.dt.0 as f64, FricParams::default())
+                    } else {
+                        (vel.0, pos.0)
+                    };
+
+                    vel.0 = tgt_vel;
+
+                    let pos_delta = tgt_pos - pos.0;
+
+
+
 
                     let was_on_ground = physics_state.on_ground.is_some();
                     let block_snap =
@@ -1769,20 +1780,6 @@ fn box_voxel_collision<T: BaseVol<Vox = Block> + ReadVol>(
         physics_state.skating_active = true;
         vel.0 = Vec3::new(new_ground_speed.x, new_ground_speed.y, 0.0);
     } else {
-        let ground_fric = physics_state
-            .on_ground
-            .map(|b| b.get_friction())
-            .unwrap_or(0.0);
-        let wall_fric = if physics_state.on_wall.is_some() && climbing {
-            FRIC_GROUND
-        } else {
-            0.0
-        };
-        let fric = ground_fric.max(wall_fric);
-        if fric > 0.0 {
-            vel.0 *= (1.0 - fric.min(1.0) * fric_mod).powf(dt.0 * 60.0);
-            physics_state.ground_vel = ground_vel;
-        }
         physics_state.skating_active = false;
     }
 
@@ -1813,6 +1810,161 @@ fn box_voxel_collision<T: BaseVol<Vox = Block> + ReadVol>(
         });
 }
 
+
+
+#[derive(Clone, Copy)]
+struct FricParams {
+    friction_co: f32,
+    projected_area: f32,
+    density: f32,
+    mass: f32,
+    max_acc: f32,
+}
+impl Default for FricParams {
+    fn default() -> Self {
+        Self {
+            friction_co: 0.98_f32,
+            projected_area: 0.75_f32,
+            density: 1.225_f32,
+            mass: 1.0_f32,
+            max_acc: 9.2_f32, /* on ground the maximum speed you can get by walking is the speed
+                               * of gravity */
+        }
+    }
+}
+impl FricParams {
+    // https://en.wikipedia.org/wiki/Drag_(physics)
+    // Todo: old impl was (mass * acc.abs() / (friction_co * projected_area * 0.5 *
+    // density * mass )).sqrt();
+    fn v_term(&self, acc: f32) -> f32 {
+        ((2.0 * self.mass * acc.abs()) / (self.density * self.projected_area * self.friction_co))
+            .sqrt()
+    }
+}
+trait MathHelp {
+    fn coth(&self) -> Self;
+    fn acoth(&self) -> Self;
+}
+impl MathHelp for f32 {
+    // coth(x) = 1/tanh(x)`
+    fn coth(&self) -> Self { 1.0 / self.tanh() }
+
+    // `acoth(x) = atanh(1/x)`
+    fn acoth(&self) -> Self { (1.0 / self).atanh() }
+}
+
+/// ROLLING_FRICTION_FORCE + AIR_FRICTION_FORCE + TILT_FRICT_FORCE + ACCEL_FORCE
+/// = TOTAL_FORCE
+///
+/// TILT_FRICT_FORCE = 0.0
+/// TOTAL_FORCE = depends on char = const
+/// ACCEL_FORCE = TOTAL_FORCE - ROLLING_FRICTION_FORCE - AIR_FRICTION_FORCE
+/// ACCEL = ACCEL_FORCE / MASS
+///
+/// ROLLING_FRICTION_FORCE => Indepent of vel
+/// AIR_FRICTION_FORCE => propotional to vel²
+///
+/// https://www.energie-lexikon.info/fahrwiderstand.html
+/// https://www.energie-lexikon.info/reibung.html
+/// https://sciencing.com/calculate-force-friction-6454395.html
+/// https://www.leifiphysik.de/mechanik/reibung-und-fortbewegung
+fn acc_with_frict_tick(
+    move_dir: Vec3<f32>,
+    vel: Vec3<f32>,
+    pos: Vec3<f32>,
+    dt: f64,
+    params: FricParams,
+) -> (Vec3<f32>, Vec3<f32>) {
+    let acc = move_dir * params.max_acc; // btw: cant accelerate faster than gravity on foot
+
+    // controller
+    // I know what you think, wtf, yep: https://math.stackexchange.com/questions/1929436/line-integral-of-force-of-air-resistanc
+    // basically an integral of the air resistance formula which scales with v^2
+    // transformed with an ODE.
+
+    // terminal velocity equals the maximum velocity that can be reached by acc
+    // alone
+    let vel_t = acc.map(|xyz| xyz.signum() * params.v_term(xyz));
+
+    // thanks to kilpkonn for figuring this out
+    // https://en.wikipedia.org/wiki/Drag_(physics)
+    //
+    // upper and lower are upper and lower bound for integral
+    let revert_fak = vel / vel_t;
+
+    let (mut pos, mut vel) = (pos, vel);
+    for i in 0..2 {
+        let dt = dt as f32;
+        let (v, p) = {
+            let acc = acc[i];
+            let vel = vel[i];
+            let pos = pos[i];
+            let vel_t = vel_t[i];
+            let revert_fak = revert_fak[i];
+            if acc.abs() < f32::EPSILON {
+                // https://www.wolframalpha.com/input?i=m%2F%28Cx+%2B+m%2FV%29+dx+integrate
+                let c = params.density * params.projected_area * params.friction_co;
+                let lower = params.mass * params.mass.ln() / c;
+                let upper = params.mass * (c * vel * dt + params.mass).ln() / c;
+                let pos = pos + (upper - lower);
+                let vel = params.mass
+                    / (params.density * params.projected_area * params.friction_co * dt
+                    + params.mass / vel);
+                (vel, pos)
+            } else if revert_fak <= 0.0 {
+                // Handle passing through 0 differently as the function changes
+                // https://www.wolframalpha.com/input?i=V*tan%28x*g%2FV+%2B+atan%28v%2FV%29%29+%3D+0+solve+for+x
+                let dt_to_zero = vel_t * (vel / vel_t).atan() / acc.abs();
+                if dt_to_zero < dt {
+                    // Step with only part of dt that is left after reaching 0 vel
+                    let lower = vel_t.powi(2) * (vel / vel_t).atan().cos().ln() / acc;
+                    let upper = -vel_t.powi(2)
+                        * (acc * dt_to_zero / vel_t + (vel / vel_t).atan()).cos().ln()
+                        / acc;
+                    let pos = pos + (upper - lower);
+                    let dt = dt - dt_to_zero;
+                    // https://www.wolframalpha.com/input?i=V+*+tanh%28xg%2FV%29+dx+integrate
+                    // lower bound is 0
+                    let pos = pos + vel_t.powi(2) * (acc * dt / vel_t).cosh().ln() / acc;
+                    let vel = vel_t * (dt * acc / vel_t).tanh();
+                    (vel, pos)
+                } else {
+                    // https://www.wolframalpha.com/input?i=V+*+tan%28xg%2FV+%2B+atan%28v%2FV%29%29+dx+integrate
+                    let lower = -vel_t.powi(2) * (vel / vel_t).atan().cos().ln() / acc;
+                    let upper =
+                        -vel_t.powi(2) * (acc * dt / vel_t + (vel / vel_t).atan()).cos().ln() / acc;
+                    let pos = pos + (upper - lower);
+                    let vel = vel_t * (dt * acc / vel_t + (vel / vel_t).atan()).tan();
+                    (vel, pos)
+                }
+            } else if revert_fak >= 1.0 {
+                // https://www.wolframalpha.com/input?i=V+*+coth%28xg%2FV+%2B+acoth%28v%2FV%29%29+dx+integrate
+                let lower = (vel_t.powi(2) * (vel / vel_t).acoth().cosh().ln()
+                    + (vel / vel_t).acoth().tanh().ln())
+                    / acc;
+                let upper = (vel_t.powi(2)
+                    * (acc * dt / vel_t + (vel / vel_t).acoth()).cosh().ln()
+                    + (acc * dt / vel_t + (vel / vel_t).acoth()).tanh().ln())
+                    / acc;
+                let pos = pos + (upper - lower);
+                let vel = vel_t * (dt * acc / vel_t + (vel / vel_t).acoth()).coth();
+                (vel, pos)
+            } else {
+                // https://www.wolframalpha.com/input?i=V+*+tanh%28xg%2FV+%2B+atanh%28v%2FV%29%29+dx+integrate
+                let lower = vel_t.powi(2) * ((vel / vel_t).atanh()).cosh().ln() / acc;
+                let upper =
+                    vel_t.powi(2) * (acc * dt / vel_t + (vel / vel_t).atanh()).cosh().ln() / acc;
+                let pos = pos + (upper - lower);
+                let vel = vel_t * (dt * acc / vel_t + (vel / vel_t).atanh()).tanh();
+                (vel, pos)
+            }
+        };
+        vel[i] = v;
+        pos[i] = p;
+    }
+    (vel, pos)
+}
+
 fn voxel_collider_bounding_sphere(
     voxel_collider: &VoxelCollider,
     pos: &Pos,