Collision_solver.cpp

#include "Collision_solver.h"
#include "Physics_object.h"
#include "Physics_model.h"
#include "Minkowski_vector.h"
#include "Minkowski_simplex.h"
#include "Minkowski_polytope.h"

#include <Vector_math.h>

#include <vector>
#include <list>
#include <tuple>

namespace Dubious {
namespace Physics {

namespace {

Math::Local_vector
support(const Physics_model& model, const Math::Local_vector& direction)
{
    Math::Local_vector result;
    float              max_dot = std::numeric_limits<float>::lowest();
    for (const auto& v : model.vectors()) {
        float dot = Math::dot_product(v, direction);
        if (dot > max_dot) {
            max_dot = dot;
            result  = v;
        }
    }
    return result;
}

// This function is used to check the top level models a and b.
// The children of these models are not tested at this level.
// The first step of this is to perform the GJK test to find if
// there is a collision, and then move on to EPA to find the
// collision point and normal.
// Children of models a and b are tested in other functions
bool
model_intersection(const Physics_model& a, const Math::Coordinate_space& ca, const Physics_model& b,
                   const Math::Coordinate_space& cb, Minkowski_simplex& simplex)
{
    if (a.vectors().empty() || b.vectors().empty()) {
        return false;
    }

    Math::Vector direction(1, 0, 0);
    Math::Vector support_a =
        ca.transform(support(a, ca.transform(direction))) + (Math::to_vector(ca.position()));
    Math::Vector support_b =
        cb.transform(support(b, cb.transform(direction * -1))) + (Math::to_vector(cb.position()));
    Math::Vector support_point = support_a - support_b;
    if (support_point == Math::Vector()) {
        // an empty simplex_point will result in an invalid direction, so try
        // another one.
        direction = Math::Vector(0, 1, 0);
        support_a =
            ca.transform(support(a, ca.transform(direction))) + (Math::to_vector(ca.position()));
        support_b = cb.transform(support(b, cb.transform(direction * -1))) +
                    (Math::to_vector(cb.position()));
        support_point = support_a - support_b;
    }
    simplex   = Minkowski_simplex(Minkowski_vector(support_point, support_a, support_b));
    direction = support_point * -1;

    // In a perfect world this would be an infinite loop. However in reality, we can get
    // into situations where we keep selecting the same faces over and over. If we don't
    // converge on a solution in 20 steps then just give up
    int i = 0;
    for (i = 0; i < 20; ++i) {
        support_a =
            ca.transform(support(a, ca.transform(direction))) + (Math::to_vector(ca.position()));
        support_b = cb.transform(support(b, cb.transform(direction * -1))) +
                    (Math::to_vector(cb.position()));
        support_point = support_a - support_b;
        // If this next check is < 0 then touching will be considered
        // a collision. If it's <= 0 then touching will not be a collision.
        // For EPA to work, our GJK must exit with a CONVEX tetrahedron. Therefore
        // if a contact point is directly on a line or triangle simplex (ie
        // a touching collision) then the resulting tetrahedron would end up
        // being flat (essentially 2D). This would cause some normal generation
        // to blow up. So we need for touching to not be considered a collision
        if (Math::dot_product(support_point, direction) <= 0) {
            return false;
        }
        simplex.push_back(Minkowski_vector(support_point, support_a, support_b));
        bool collision_found;
        std::tie(collision_found, direction) = simplex.build();
        if (collision_found) {
            return true;
        }
    }
    // for debugging
    if (i >= 20) {
        int debug = 5;
    }
    return false;
}

// Taken from http://hacktank.net/blog/?p=119 , which was apparently
// taken from Crister Erickson's Real-Time Collision Detection
std::tuple<float, float, float>
barycentric(const Math::Vector& p, const Math::Vector& a, const Math::Vector& b,
            const Math::Vector& c)
{
    Math::Vector v0    = b - a;
    Math::Vector v1    = c - a;
    Math::Vector v2    = p - a;
    float        d00   = Math::dot_product(v0, v0);
    float        d01   = Math::dot_product(v0, v1);
    float        d11   = Math::dot_product(v1, v1);
    float        d20   = Math::dot_product(v2, v0);
    float        d21   = Math::dot_product(v2, v1);
    float        denom = d00 * d11 - d01 * d01;
    float        v     = (d11 * d20 - d01 * d21) / denom;
    float        w     = (d00 * d21 - d01 * d20) / denom;
    float        u     = 1.0f - v - w;
    return std::make_tuple(u, v, w);
}

// Perform EPA to find the point of collision
void
find_collision_point(const Physics_model& a, const Math::Coordinate_space& ca,
                     const Physics_model& b, const Math::Coordinate_space& cb,
                     const Minkowski_simplex& simplex, Contact_manifold::Contact& contact)
{
    Minkowski_polytope polytope(simplex);
    // In a perfect world, this would always break out when the collision
    // point was found. In our world, we limit it
    for (int i = 0; i < 20; ++i) {
        float                        min_distance;
        Minkowski_polytope::Triangle triangle;
        std::tie(triangle, min_distance) = polytope.find_closest_triangle();
        Math::Vector direction(triangle.normal);
        Math::Vector support_a =
            ca.transform(support(a, ca.transform(direction))) + (Math::to_vector(ca.position()));
        Math::Vector support_b = cb.transform(support(b, cb.transform(direction * -1))) +
                                 (Math::to_vector(cb.position()));
        Math::Vector support_point = support_a - support_b;
        if (Math::dot_product(support_point, Math::Vector(triangle.normal)) <=
            min_distance + 0.001f) {
            contact.normal = triangle.normal;
            // http://box2d.org/2014/02/computing-a-basis/
            if (fabs(contact.normal.x()) >= 0.57735f) {
                contact.tangent1 = Math::Vector(contact.normal.y(), -contact.normal.x(), 0.0f);
            }
            else {
                contact.tangent1 = Math::Vector(0.0f, contact.normal.z(), -contact.normal.y());
            }
            contact.tangent2          = Math::cross_product(contact.normal, contact.tangent1);
            contact.penetration_depth = min_distance;
            Math::Point contact_point =
                Math::to_point(Math::Vector(triangle.normal) * min_distance);
            float u, v, w;
            std::tie(u, v, w) = barycentric(Math::to_vector(contact_point), triangle.a.v(),
                                            triangle.b.v(), triangle.c.v());
            contact_point = Math::to_point(triangle.a.support_a() * u + triangle.b.support_a() * v +
                                           triangle.c.support_a() * w);
            contact.contact_point_a = contact_point;
            contact.local_point_a   = ca.transform(contact_point);
            contact_point = Math::to_point(triangle.a.support_b() * u + triangle.b.support_b() * v +
                                           triangle.c.support_b() * w);
            contact.contact_point_b = contact_point;
            contact.local_point_b   = cb.transform(contact_point);
            return;
        }
        polytope.push_back(Minkowski_vector(support_point, support_a, support_b));
    }
}

bool
intersection_recurse_b(const Physics_model& a, const Math::Coordinate_space& ca,
                       const Physics_model& b, const Math::Coordinate_space& cb,
                       std::vector<Contact_manifold::Contact>& contacts)
{
    bool              ret_val = false;
    Minkowski_simplex simplex;
    if (model_intersection(a, ca, b, cb, simplex)) {
        Contact_manifold::Contact contact;
        find_collision_point(a, ca, b, cb, simplex, contact);
        contacts.push_back(contact);
        ret_val = true;
    }
    for (const auto& kid : b.kids()) {
        if (intersection_recurse_b(a, ca, *kid, cb, contacts)) {
            ret_val = true;
        }
    }

    return ret_val;
}

bool
intersection_recurse_a(const Physics_model& a, const Math::Coordinate_space& ca,
                       const Physics_model& b, const Math::Coordinate_space& cb,
                       std::vector<Contact_manifold::Contact>& contacts)
{
    bool ret_val = false;
    if (intersection_recurse_b(a, ca, b, cb, contacts)) {
        ret_val = true;
    }
    for (const auto& kid : a.kids()) {
        if (intersection_recurse_a(*kid, ca, b, cb, contacts)) {
            ret_val = true;
        }
    }

    return ret_val;
}

}  // namespace

bool
Collision_solver::broad_phase_intersection(const Physics_object& a, const Physics_object& b) const
{
    // If the sum of the radius squared is longer then the distance squared
    // then there's no way these can be touching
    // This is an optimisation I tested and resulted in a very good speed up.
    float distance_squared =
        (a.coordinate_space().position() - b.coordinate_space().position()).length_squared();
    float radius_sum = a.model().radius() + b.model().radius();
    return distance_squared <= radius_sum * radius_sum;
}

bool
Collision_solver::intersection(const Physics_object& a, const Physics_object& b,
                               std::vector<Contact_manifold::Contact>& contacts) const
{
    return intersection_recurse_a(a.model(), a.coordinate_space(), b.model(), b.coordinate_space(),
                                  contacts);
}

}  // namespace Physics
}  // namespace Dubious