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

use na::{ComplexField, Unit};

use crate::math::{Isometry, Point, Real, Vector};
use crate::motion::RigidMotion;
use crate::query::{self, ClosestPoints, TOIStatus, TOI};
use crate::shape::SupportMap;

use num::Bounded;

/// Time of impacts between two support-mapped shapes under a rigid motion.
pub fn nonlinear_time_of_impact_support_map_support_map<G1: ?Sized, G2: ?Sized>(
    motion12: &(impl RigidMotion + ?Sized),
    g1: &G1,
    g2: &G2,
    max_toi: Real,
    target_distance: Real,
) -> Option<TOI>
where
    G1: SupportMap,
    G2: SupportMap,
{
    nonlinear_time_of_impact_support_map_support_map_with_closest_points_function(
        motion12,
        g1,
        g2,
        max_toi,
        target_distance,
        query::details::closest_points_support_map_support_map,
    )
}

/// Time of impacts between two support-mapped shapes under a rigid motion.
///
/// You probably want to use `query::details::nonlinear_time_of_impact_support_map_support_map` instead of this one.
/// The distance function between the two shapes must be given.
pub fn nonlinear_time_of_impact_support_map_support_map_with_closest_points_function<
    G1: ?Sized,
    G2: ?Sized,
>(
    motion12: &(impl RigidMotion + ?Sized),
    g1: &G1,
    g2: &G2,
    max_toi: Real,
    target_distance: Real,
    closest_points: impl Fn(&Isometry<Real>, &G1, &G2, Real) -> ClosestPoints,
) -> Option<TOI>
where
    G1: SupportMap,
    G2: SupportMap,
{
    let _0_5: Real = 0.5;
    let mut min_t = 0.0;
    let mut prev_min_t = min_t;
    let abs_tol: Real = query::gjk::eps_tol();
    let rel_tol = ComplexField::sqrt(abs_tol);
    let mut result = TOI {
        toi: 0.0,
        normal1: Vector::<Real>::x_axis(),
        normal2: Vector::<Real>::x_axis(),
        witness1: Point::<Real>::origin(),
        witness2: Point::<Real>::origin(),
        status: TOIStatus::Penetrating,
    };

    loop {
        let pos12 = motion12.position_at_time(result.toi);

        // FIXME: use the _with_params version of the closest points query.
        match closest_points(&pos12, g1, g2, Real::max_value()) {
            ClosestPoints::Intersecting => {
                if result.toi == 0.0 {
                    result.status = TOIStatus::Penetrating
                } else {
                    result.status = TOIStatus::Failed;
                }
                break;
            }
            ClosestPoints::WithinMargin(p1, p2) => {
                result.witness1 = p1;
                result.witness2 = p2;

                if let Some((dir, mut dist)) =
                    Unit::try_new_and_get(pos12 * p2 - p1, crate::math::DEFAULT_EPSILON)
                {
                    // FIXME: do the "inverse transform unit vector" only when we are about to return.
                    result.normal1 = dir;
                    result.normal2 = pos12.inverse_transform_unit_vector(&-dir);

                    let mut niter = 0;
                    min_t = result.toi;
                    let mut max_t = max_toi;
                    let min_target_distance = (target_distance - rel_tol).max(0.0);
                    let max_target_distance = target_distance + rel_tol;

                    loop {
                        // FIXME: use the secant method too for finding the next iterate.
                        if dist < min_target_distance {
                            // Too close or penetration, go back in time.
                            max_t = result.toi;
                            result.toi = (min_t + result.toi) * _0_5;
                        } else if dist > max_target_distance {
                            // Too far apart, go forward in time.
                            min_t = result.toi;
                            result.toi = (result.toi + max_t) * _0_5;
                        } else {
                            // Reached tolerance, break.
                            break;
                        }

                        if max_t - min_t < abs_tol {
                            result.toi = min_t;
                            break;
                        }

                        let pos12 = motion12.position_at_time(result.toi);
                        let pt1 = g1.local_support_point_toward(&dir);
                        let pt2 = g2.support_point_toward(&pos12, &-dir);

                        dist = (pt2 - pt1).dot(&dir);

                        niter += 1;
                    }

                    if min_t - prev_min_t < abs_tol {
                        if max_t == max_toi {
                            let pos12 = motion12.position_at_time(max_t);

                            // Check the configuration at max_t to see if the object are not disjoint.
                            // NOTE: could we do this earlier, before the above loop?
                            // It feels like this could prevent catching some corner-cases like
                            // if one object is rotated by almost 180 degrees while the other is immobile.
                            let pt1 = g1.local_support_point_toward(&dir);
                            let pt2 = g2.support_point_toward(&pos12, &-dir);
                            if (pt2 - pt1).dot(&dir) > target_distance {
                                // We found an axis that separate both objects at the end configuration.
                                return None;
                            }
                        }

                        result.status = TOIStatus::Converged;
                        break;
                    }

                    prev_min_t = min_t;

                    if niter == 0 {
                        result.status = TOIStatus::Converged;
                        break;
                    }
                } else {
                    result.status = TOIStatus::Failed;
                    break;
                }
            }
            ClosestPoints::Disjoint => unreachable!(),
        }
    }

    Some(result)
}