oxijolt 1.1.0+jolt-5.6.0

Safe Rust API for Jolt Physics
Documentation
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
346
347
348
349
350
351
352
353
354
355
356
357
358
359
360
361
362
363
364
365
366
367
368
369
370
371
372
373
374
375
376
377
378
379
380
381
382
383
384
385
386
387
388
389
390
391
392
393
394
395
396
397
398
399
400
401
402
403
404
405
406
407
408
409
410
411
412
413
414
415
416
417
418
419
420
421
422
423
424
425
426
427
428
429
430
431
432
433
434
435
436
437
438
439
440
441
442
443
444
445
446
447
448
449
450
451
452
453
454
455
456
457
458
459
460
461
462
463
464
465
466
467
468
469
470
471
472
473
474
475
476
477
478
479
480
481
482
483
484
485
486
487
488
489
490
491
492
493
494
495
496
497
498
499
500
501
502
503
504
505
506
507
508
509
510
511
512
513
514
515
516
use super::super::tests::{bits3, curve_points, jolt_vec};
use super::*;
use crate::world::ensure_initialized;
use crate::{ObjectLayer, SpringSettings};

const LAYERS: u32 = 2;

/// A valid tank: three wheels per track, each track driven at its first wheel, a ray tester on
/// layer 1.
fn tank() -> TrackedVehicleSettings {
    let track = |x: f32| {
        let wheels = [1.0, 0.0, -1.0]
            .map(|z| TrackedWheelSettings::new(Vec3::new(x, -0.3, z)))
            .to_vec();
        VehicleTrackSettings::new(wheels, 0)
    };
    TrackedVehicleSettings::new(
        track(1.0),
        track(-1.0),
        VehicleCollisionTester::ray(ObjectLayer::new(1)),
    )
}

fn with_left(
    edit: impl Fn(VehicleTrackSettings) -> VehicleTrackSettings,
) -> TrackedVehicleSettings {
    let mut settings = tank();
    settings.left = edit(settings.left.clone());
    settings
}

fn with_inertias(left: f32, right: f32) -> TrackedVehicleSettings {
    let mut settings = with_left(|t| t.inertia(left));
    settings.right = settings.right.clone().inertia(right);
    settings
}

fn with_wheel(
    edit: impl Fn(TrackedWheelSettings) -> TrackedWheelSettings,
) -> TrackedVehicleSettings {
    let mut settings = tank();
    settings.right.wheels[1] = edit(settings.right.wheels[1].clone());
    settings
}

#[track_caller]
fn assert_refused(settings: TrackedVehicleSettings, rule: &str) {
    match settings.validate(LAYERS) {
        Err(VehicleError::InvalidValue(what)) => {
            assert!(
                what.contains(rule),
                "refused for {what:?}, expected {rule:?}"
            )
        }
        other => panic!("expected a refusal for {rule:?}, got {other:?}"),
    }
}

#[test]
fn tracked_wheel_defaults_are_jolts() {
    assert!(ensure_initialized());
    let ours = TrackedWheelSettings::new(Vec3::ZERO);
    // SAFETY: Jolt is initialised; the guard owns the one reference joltc returns.
    let jolt = unsafe { Owned::from_raw(JPH_WheelSettingsTV_Create()) }.unwrap();
    let tv = jolt.as_ptr();
    let base: *mut JPH_WheelSettings = tv.cast();
    // SAFETY: the settings are live and only read; every output is a live local.
    unsafe {
        let direction = jolt_vec(|v| JPH_WheelSettings_GetSuspensionDirection(base, v));
        assert_eq!(bits3(direction), bits3(ours.base.suspension_direction));
        let axis = jolt_vec(|v| JPH_WheelSettings_GetSteeringAxis(base, v));
        assert_eq!(bits3(axis), bits3(ours.base.steering_axis));
        let up = jolt_vec(|v| JPH_WheelSettings_GetWheelUp(base, v));
        assert_eq!(bits3(up), bits3(ours.base.wheel_up));
        let forward = jolt_vec(|v| JPH_WheelSettings_GetWheelForward(base, v));
        assert_eq!(bits3(forward), bits3(ours.base.wheel_forward));
        assert!(!JPH_WheelSettings_GetEnableSuspensionForcePoint(base));
        assert_eq!(
            JPH_WheelSettings_GetSuspensionMinLength(base),
            ours.base.suspension_min_length
        );
        assert_eq!(
            JPH_WheelSettings_GetSuspensionMaxLength(base),
            ours.base.suspension_max_length
        );
        assert_eq!(
            JPH_WheelSettings_GetSuspensionPreloadLength(base),
            ours.base.suspension_preload_length
        );
        let mut spring = JPH_SpringSettings {
            mode: JPH_SpringMode_StiffnessAndDamping,
            frequencyOrStiffness: 0.0,
            damping: 0.0,
        };
        JPH_WheelSettings_GetSuspensionSpring(base, &mut spring);
        let expected = ours.base.suspension_spring.to_jph();
        assert_eq!(spring.mode, expected.mode);
        assert_eq!(spring.frequencyOrStiffness, expected.frequencyOrStiffness);
        assert_eq!(spring.damping, expected.damping);
        assert_eq!(JPH_WheelSettings_GetRadius(base), ours.base.radius);
        assert_eq!(JPH_WheelSettings_GetWidth(base), ours.base.width);
        assert_eq!(
            JPH_WheelSettingsTV_GetLongitudinalFriction(tv),
            ours.longitudinal_friction
        );
        assert_eq!(
            JPH_WheelSettingsTV_GetLateralFriction(tv),
            ours.lateral_friction
        );
    }
}

#[test]
fn track_defaults_are_jolts() {
    let ours = VehicleTrackSettings::new(Vec::new(), 0);
    // SAFETY: an all-zero `JPH_VehicleTrackSettings` is valid (integers, floats and a null
    // pointer); `_Init` fills it with Jolt's defaults and allocates nothing.
    let jolt = unsafe {
        let mut jolt: JPH_VehicleTrackSettings = std::mem::zeroed();
        JPH_VehicleTrackSettings_Init(&mut jolt);
        jolt
    };
    assert_eq!(jolt.drivenWheel, ours.driven_wheel);
    assert_eq!(jolt.inertia, ours.inertia);
    assert_eq!(jolt.angularDamping, ours.angular_damping);
    assert_eq!(jolt.maxBrakeTorque, ours.max_brake_torque);
    assert_eq!(jolt.differentialRatio, ours.differential_ratio);
}

#[test]
fn tracked_controller_defaults_are_jolts() {
    assert!(ensure_initialized());
    let engine = TrackedVehicleSettings::default_engine();
    let transmission = TrackedVehicleSettings::default_transmission();
    // SAFETY: Jolt is initialised; the guard owns the one reference joltc returns.
    let jolt = unsafe { Owned::from_raw(JPH_TrackedVehicleControllerSettings_Create()) }.unwrap();
    let ptr = jolt.as_ptr();
    // SAFETY: the settings are live and only read. `GetEngine` lends the settings' own torque
    // curve and `GetTransmission` the settings' own transmission; both are read while the guard
    // keeps the settings alive and never destroyed here.
    unsafe {
        let mut jolt_engine: JPH_VehicleEngineSettings = std::mem::zeroed();
        JPH_TrackedVehicleControllerSettings_GetEngine(ptr, &mut jolt_engine);
        assert_eq!(jolt_engine.maxTorque, engine.max_torque);
        assert_eq!(jolt_engine.minRPM, engine.min_rpm);
        assert_eq!(jolt_engine.maxRPM, engine.max_rpm);
        assert_eq!(jolt_engine.inertia, engine.inertia);
        assert_eq!(jolt_engine.angularDamping, engine.angular_damping);
        assert_eq!(
            curve_points(jolt_engine.normalizedTorque),
            engine.normalized_torque
        );

        let jolt_transmission = JPH_TrackedVehicleControllerSettings_GetTransmission(ptr);
        assert_eq!(
            JPH_VehicleTransmissionSettings_GetMode(jolt_transmission),
            JPH_TransmissionMode_Auto
        );
        let forward: Vec<f32> =
            (0..JPH_VehicleTransmissionSettings_GetGearRatioCount(jolt_transmission))
                .map(|i| JPH_VehicleTransmissionSettings_GetGearRatio(jolt_transmission, i))
                .collect();
        assert_eq!(forward, transmission.gear_ratios);
        let reverse: Vec<f32> =
            (0..JPH_VehicleTransmissionSettings_GetReverseGearRatioCount(jolt_transmission))
                .map(|i| JPH_VehicleTransmissionSettings_GetReverseGearRatio(jolt_transmission, i))
                .collect();
        assert_eq!(reverse, transmission.reverse_gear_ratios);
        assert_eq!(
            JPH_VehicleTransmissionSettings_GetSwitchTime(jolt_transmission),
            transmission.switch_time
        );
        assert_eq!(
            JPH_VehicleTransmissionSettings_GetClutchReleaseTime(jolt_transmission),
            transmission.clutch_release_time
        );
        assert_eq!(
            JPH_VehicleTransmissionSettings_GetSwitchLatency(jolt_transmission),
            transmission.switch_latency
        );
        assert_eq!(
            JPH_VehicleTransmissionSettings_GetShiftUpRPM(jolt_transmission),
            transmission.shift_up_rpm
        );
        assert_eq!(
            JPH_VehicleTransmissionSettings_GetShiftDownRPM(jolt_transmission),
            transmission.shift_down_rpm
        );
        assert_eq!(
            JPH_VehicleTransmissionSettings_GetClutchStrength(jolt_transmission),
            transmission.clutch_strength
        );
    }
}

#[test]
fn built_tracked_wheels_reach_jolt() {
    assert!(ensure_initialized());
    let wheel = TrackedWheelSettings::new(Vec3::new(1.0, -0.3, 0.5))
        .radius(0.4)
        .longitudinal_friction(3.0)
        .lateral_friction(1.5);
    let jolt = wheel.create();
    let tv = jolt.as_ptr();
    // SAFETY: the settings are live and only read; outputs are live locals.
    unsafe {
        let position = jolt_vec(|v| JPH_WheelSettings_GetPosition(tv.cast(), v));
        assert_eq!(bits3(position), bits3(wheel.base.position));
        assert_eq!(JPH_WheelSettings_GetRadius(tv.cast()), 0.4);
        assert_eq!(JPH_WheelSettingsTV_GetLongitudinalFriction(tv), 3.0);
        assert_eq!(JPH_WheelSettingsTV_GetLateralFriction(tv), 1.5);
    }
    let built = tank().build();
    assert_eq!(built.wheels.len(), 6);
    assert_eq!(built.tracks, Some([0..3, 3..6]));
    assert!(matches!(built.controller, ControllerGuard::Tracked(_)));
}

#[test]
fn tracked_settings_are_validated() {
    assert!(ensure_initialized());
    assert_eq!(tank().validate(LAYERS), Ok(()));

    assert_refused(
        with_left(|t| VehicleTrackSettings::new(Vec::new(), 0).inertia(t.inertia)),
        "at least one wheel",
    );
    assert_refused(
        with_left(|t| VehicleTrackSettings {
            driven_wheel: 3,
            ..t
        }),
        "driven wheel",
    );
    assert_refused(
        with_left(|t| VehicleTrackSettings {
            driven_wheel: u32::MAX,
            ..t
        }),
        "driven wheel",
    );
    let below_min = f32::from_bits(limits::MIN_TRACK_INERTIA.to_bits() - 1);
    let above_max = f32::from_bits(limits::MAX_TRACK_INERTIA.to_bits() + 1);
    for inertia in [0.0, -1.0, f32::NAN, f32::INFINITY, below_min, above_max] {
        assert_refused(with_left(|t| t.inertia(inertia)), "track inertia");
    }
    for inertia in [limits::MIN_TRACK_INERTIA, limits::MAX_TRACK_INERTIA] {
        assert_eq!(with_inertias(inertia, inertia).validate(LAYERS), Ok(()));
    }
    assert_refused(with_left(|t| t.angular_damping(-0.1)), "angular damping");
    assert_refused(
        with_left(|t| t.max_brake_torque(f32::NAN)),
        "max brake torque",
    );
    for ratio in [0.0, -6.0, f32::INFINITY] {
        assert_refused(
            with_left(|t| t.differential_ratio(ratio)),
            "differential ratio",
        );
    }
    for friction in [-0.1, limits::MAX_FRICTION * 1.001, f32::NAN] {
        assert_refused(
            with_wheel(|w| w.longitudinal_friction(friction)),
            "friction",
        );
        assert_refused(with_wheel(|w| w.lateral_friction(friction)), "friction");
    }
    assert_eq!(
        with_wheel(|w| w
            .longitudinal_friction(limits::MAX_FRICTION)
            .lateral_friction(0.0))
        .validate(LAYERS),
        Ok(())
    );
    assert_refused(tank().up(Vec3::new(0.0, 2.0, 0.0)), "unit");
    assert_refused(tank().forward(Vec3::new(0.0, 0.6, 0.8)), "perpendicular");
    assert_refused(tank().max_pitch_roll_angle(-0.1), "pitch roll");
    assert_refused(
        tank().engine(TrackedVehicleSettings::default_engine().max_rpm(3000.0)),
        "shift up rpm",
    );
    assert_refused(
        tank().transmission(TrackedVehicleSettings::default_transmission().gear_ratios(vec![])),
        "gear ratios",
    );
    let mut far_layer = tank();
    far_layer.collision_tester = VehicleCollisionTester::ray(ObjectLayer::new(LAYERS));
    assert_refused(far_layer, "object layer");
}

#[test]
fn tracked_wheels_share_the_wheel_rules() {
    assert_refused(with_wheel(|w| w.radius(0.0)), "wheel radius");
    assert_refused(with_wheel(|w| w.width(-0.1)), "wheel width");
    assert_refused(
        with_wheel(|w| w.suspension_direction(Vec3::new(0.0, -1.1, 0.0))),
        "wheel directions",
    );
    assert_refused(
        with_wheel(|w| w.wheel_up(Vec3::new(0.0, 0.0, 1.0))),
        "perpendicular",
    );
    assert_refused(with_wheel(|w| w.suspension_min_length(-0.1)), "min length");
    assert_refused(with_wheel(|w| w.suspension_max_length(0.2)), "max length");
    assert_refused(with_wheel(|w| w.suspension_preload_length(-0.1)), "preload");
    assert_refused(
        with_wheel(|w| w.suspension_force_point(Some(Vec3::new(f32::NAN, 0.0, 0.0)))),
        "force point",
    );
    assert_refused(
        with_wheel(|w| {
            w.suspension_spring(SpringSettings::FrequencyAndDamping {
                frequency: 0.0,
                damping: 0.5,
            })
        }),
        "suspension spring",
    );
    let extent = limits::MAX_SHAPE_EXTENT;
    assert_refused(
        with_wheel(|_| TrackedWheelSettings::new(Vec3::new(extent * 1.001, 0.0, 0.0))),
        "wheel position",
    );
    // The cylinder tester needs positive widths, as for wheeled vehicles.
    let mut settings = with_wheel(|w| w.width(0.0));
    assert_eq!(settings.validate(LAYERS), Ok(()));
    settings.collision_tester = VehicleCollisionTester::cast_cylinder(ObjectLayer::new(1));
    assert_refused(settings, "cylinder tester");
}

#[test]
fn track_wheel_radii_stay_within_max_ratio_of_the_driven_wheel() {
    const RULE: &str = "wheel radii";
    let radii = |driven: f32, other: f32| {
        let mut settings = tank();
        settings.left.wheels[0] = settings.left.wheels[0].clone().radius(driven);
        settings.left.wheels[2] = settings.left.wheels[2].clone().radius(other);
        settings
    };
    assert_eq!(radii(1.0, 1.0e-4).validate(LAYERS), Ok(()));
    assert_refused(radii(1.0, 0.99e-4), RULE);
    assert_eq!(radii(1.0e-3, 10.0).validate(LAYERS), Ok(()));
    assert_refused(radii(1.0e-3, 10.1), RULE);
    // The review's counter-example: a 1e-36 m wheel next to a 0.3 m driven wheel would turn at
    // 1200 rad/s · 0.3 / 1e-36, which overflows.
    assert_refused(radii(0.3, 1.0e-36), RULE);
}

#[test]
fn track_inertias_stay_within_max_track_inertia_ratio() {
    let ratio = limits::MAX_TRACK_INERTIA_RATIO;
    for lighter in [limits::MIN_TRACK_INERTIA, 10.0, 1.0e3] {
        let heavier = ratio * lighter;
        let above = f32::from_bits(heavier.to_bits() + 1);
        assert_eq!(with_inertias(lighter, heavier).validate(LAYERS), Ok(()));
        assert_eq!(with_inertias(heavier, lighter).validate(LAYERS), Ok(()));
        assert_refused(with_inertias(lighter, above), "inertia ratio");
        assert_refused(with_inertias(above, lighter), "inertia ratio");
    }
}

#[test]
fn tracked_drive_envelope_bounds_the_drivetrain() {
    const ENVELOPE: &str = "drive envelope";
    let engine = TrackedVehicleSettings::default_engine;
    let transmission = TrackedVehicleSettings::default_transmission;
    let torque = |value: f32| engine().max_torque(value);
    // Valid one by one: a huge max torque, heavy tracks, gear and differential ratios of 100.
    let mut counter_example = with_inertias(1.0e6, 1.0e6)
        .engine(torque(1.0e20).normalized_torque(vec![(0.0, limits::MAX_NORMALIZED_TORQUE)]))
        .transmission(transmission().gear_ratios(vec![100.0]));
    counter_example.left = counter_example.left.clone().differential_ratio(100.0);
    assert_refused(counter_example, ENVELOPE);

    // Each factor alone, a decade inside and a decade outside.
    assert_eq!(tank().engine(torque(1.0e18)).validate(LAYERS), Ok(()));
    assert_refused(tank().engine(torque(1.0e19)), ENVELOPE);
    let tenfold = vec![(0.0, limits::MAX_NORMALIZED_TORQUE)];
    assert_refused(
        tank().engine(torque(1.0e18).normalized_torque(tenfold)),
        ENVELOPE,
    );
    let gear = |ratio: f32| transmission().gear_ratios(vec![ratio, 1.0]);
    assert_eq!(
        tank()
            .engine(torque(1.0e17))
            .transmission(gear(100.0))
            .validate(LAYERS),
        Ok(())
    );
    assert_refused(
        tank().engine(torque(1.0e18)).transmission(gear(100.0)),
        ENVELOPE,
    );
    // A reverse gear counts as much as a forward one.
    assert_refused(
        tank()
            .engine(torque(1.0e18))
            .transmission(transmission().reverse_gear_ratios(vec![-100.0])),
        ENVELOPE,
    );
    // The speed limit grows as the smallest gear shrinks.
    assert_eq!(tank().transmission(gear(1.0e-13)).validate(LAYERS), Ok(()));
    assert_refused(tank().transmission(gear(1.0e-14)), ENVELOPE);
    assert_refused(
        tank().transmission(
            transmission()
                .gear_ratios(vec![1.0e-36])
                .reverse_gear_ratios(vec![-1.0e-36]),
        ),
        "underflows",
    );
    // Two light tracks of unequal inertia: the synchronisation bounds the torque.
    let light = |torque_value: f32| {
        let mut settings = tank().engine(torque(torque_value));
        settings.left = settings.left.clone().inertia(limits::MIN_TRACK_INERTIA);
        settings.right = settings
            .right
            .clone()
            .inertia(2.0 * limits::MIN_TRACK_INERTIA);
        settings
    };
    assert_eq!(light(1.0e11).validate(LAYERS), Ok(()));
    assert_refused(light(1.0e34), ENVELOPE);
    // The brake: its impulse over the inertia and its torque over the smallest wheel radius.
    assert_eq!(
        with_left(|t| t.max_brake_torque(1.0e29)).validate(LAYERS),
        Ok(())
    );
    assert_refused(with_left(|t| t.max_brake_torque(1.0e30)), ENVELOPE);
    let mut small_wheel = with_left(|t| t.max_brake_torque(1.0e25));
    small_wheel.left.wheels[2] = small_wheel.left.wheels[2].clone().radius(3.1e-5);
    assert_eq!(small_wheel.validate(LAYERS), Ok(()));
    small_wheel.left.max_brake_torque = 1.0e26;
    assert_refused(small_wheel, ENVELOPE);
    // The max rpm sets the speed limit too.
    assert_refused(tank().engine(engine().max_rpm(1.0e20)), ENVELOPE);
}

/// A 4000 kg chassis with principal inverse inertia `inverse_inertia`, its principal frame
/// turned from body space by `body_to_principal`, its centre of mass at `center`.
fn chassis(inverse_inertia: [f64; 3], body_to_principal: Quat, center: Vec3) -> ChassisMass {
    ChassisMass {
        mass: PrincipalMass {
            inverse_mass: 1.0 / 4000.0,
            inverse_inertia,
        },
        body_to_principal,
        center_of_mass: center,
    }
}

/// The largest `√((r × d)ᵀ M (r × d))` over 3600 directions `d` in the y/z plane, for the
/// symmetric `M` given by its rows.
fn sampled_plane_lever(m: [[f64; 3]; 3], r: [f64; 3]) -> f64 {
    (0..3600)
        .map(|k| {
            let (sin, cos) = (f64::from(k) * std::f64::consts::PI / 1800.0).sin_cos();
            let c = limits::cross(r, [0.0, sin, cos]);
            (0..3)
                .flat_map(|i| (0..3).map(move |j| (i, j)))
                .map(|(i, j)| c[i] * m[i][j] * c[j])
                .sum::<f64>()
                .sqrt()
        })
        .fold(0.0, f64::max)
}

#[test]
fn track_mass_ratio_takes_the_chassis_inertia_at_the_farthest_contact() {
    let (a, b, c): (f64, f64, f64) = (1.0 / 1500.0, 1.0 / 4000.0, 1.0 / 2000.0);
    let center = Vec3::new(0.3, -0.5, 0.0);
    // `tank()`'s wheels: x = ±1, y = −0.3, z = 1, 0, −1, up +Y and forward +Z, so every ground
    // normal gives a longitudinal direction in the y/z plane. Jolt's 10 kg·m² tracks on 0.3 m
    // wheels, every contact within 0.5 + √(0.3² + 0.05²) of the attachment, where a unit lever
    // weighs at most the largest inverse inertia.
    let reach = 0.5 + 0.3_f64.hypot(0.05);
    let per_metre = a.max(b).max(c).sqrt();
    let track_mass = 10.0 / (0.3_f64 * 0.3);
    for angle in [0.0_f64, 0.4, -0.4] {
        let (half_sin, half_cos) = (0.5 * angle).sin_cos();
        let to_principal = Quat::from_xyzw(0.0, 0.0, half_sin as f32, half_cos as f32);
        // The body-space inverse inertia Rᵀ D R, with R the turn by `angle` about z.
        let (sin, cos) = angle.sin_cos();
        let xx = a * cos * cos + b * sin * sin;
        let yy = a * sin * sin + b * cos * cos;
        let xy = sin * cos * (b - a);
        let body = [[xx, xy, 0.0], [xy, yy, 0.0], [0.0, 0.0, c]];
        let expected = [1.0_f64, -1.0]
            .into_iter()
            .flat_map(|x| [1.0_f64, 0.0, -1.0].map(|z| [x - 0.3, -0.3 + 0.5, z]))
            .map(|r| {
                let lever = sampled_plane_lever(body, r) + reach * per_metre;
                track_mass * (1.0 / 4000.0 + lever * lever)
            })
            .fold(0.0, f64::max);
        let ratio = tank().largest_track_mass_ratio(&chassis([a, b, c], to_principal, center));
        assert!(
            (ratio - expected).abs() <= 1e-5 * expected,
            "angle {angle}: {ratio} vs {expected}"
        );
    }
    // A suspension force point far below the contacts sets the lever.
    let mut settings = tank();
    settings.left.wheels[0] = settings.left.wheels[0]
        .clone()
        .suspension_force_point(Some(Vec3::new(1.0, -5.0, 0.0)));
    let principal = [[a, 0.0, 0.0], [0.0, b, 0.0], [0.0, 0.0, c]];
    let lever = sampled_plane_lever(principal, [0.7, -4.5, 0.0]);
    let expected = track_mass * (1.0 / 4000.0 + lever * lever);
    let ratio = settings.largest_track_mass_ratio(&chassis([a, b, c], Quat::IDENTITY, center));
    assert!(
        (ratio - expected).abs() <= 1e-5 * expected,
        "{ratio} vs {expected}"
    );
}