648 lines
17 KiB
C++
648 lines
17 KiB
C++
#include <psemek/phys/engine_2d.hpp>
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#include <psemek/util/heterogeneous_container.hpp>
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#include <psemek/geom/constants.hpp>
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#include <psemek/geom/matrix.hpp>
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#include <psemek/geom/gauss.hpp>
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#include <psemek/geom/rotation.hpp>
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#include <psemek/geom/math.hpp>
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#include <psemek/util/profiler.hpp>
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#include <psemek/log/log.hpp>
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#include <optional>
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namespace psemek::phys2d
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{
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namespace
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{
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float shape_area(ball const & b)
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{
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return geom::pi * b.radius * b.radius;
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}
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float shape_inertia(ball const & b)
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{
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return shape_area(b) * b.radius * b.radius / 2.f;
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}
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float shape_area(half_space const &)
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{
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return std::numeric_limits<float>::infinity();
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}
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float shape_inertia(half_space const &)
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{
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return std::numeric_limits<float>::infinity();
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}
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float shape_area(box const & b)
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{
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return b.width * b.height;
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}
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float shape_inertia(box const & b)
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{
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return shape_area(b) * (b.width * b.width + b.height * b.height) / 12.f;
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}
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template <typename Shape>
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struct wrapped_shape
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{
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Shape shape;
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float area;
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float inertia;
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wrapped_shape(Shape const & shape)
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: shape{shape}
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, area(shape_area(shape))
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, inertia(shape_inertia(shape))
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{}
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};
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template <typename Shape>
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wrapped_shape<Shape> wrap(Shape const & shape)
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{
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return {shape};
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}
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// penetration points from object 1 to object 2
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struct collision
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{
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geom::point<float, 2> position;
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geom::vector<float, 2> penetration;
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};
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std::optional<collision> invert(std::optional<collision> c)
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{
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if (c)
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c->penetration *= -1.f;
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return c;
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}
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std::optional<collision> shape_collision(ball const & b1, static_state const & s1, ball const & b2, static_state const & s2)
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{
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auto const d = s2.position - s1.position;
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float const l = geom::length(d);
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if (l > b1.radius + b2.radius)
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return std::nullopt;
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auto const p = geom::lerp(s1.position, s2.position, (b1.radius + l - b2.radius) / 2.f / l);
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return collision{p, d * (b1.radius + b2.radius - l) / l};
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}
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std::optional<collision> shape_collision(ball const & b1, static_state const & s1, half_space const & b2, static_state const &)
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{
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float v = b2.normal[0] * s1.position[0] + b2.normal[1] * s1.position[1] - b2.value - b1.radius;
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if (v > 0.f)
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return std::nullopt;
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return collision{s1.position - b2.normal * b1.radius, v * b2.normal};
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}
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std::optional<collision> shape_collision(ball const & b1, static_state const & s1, box const & b2, static_state const & s2)
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{
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geom::vector ex{std::cos(s2.rotation), std::sin(s2.rotation)};
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geom::vector ey{-std::sin(s2.rotation), std::cos(s2.rotation)};
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float w = b2.width / 2.f;
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float h = b2.height / 2.f;
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auto r = s1.position - s2.position;
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float x = geom::dot(r, ex);
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float y = geom::dot(r, ey);
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if (std::abs(x) < w && std::abs(y) < h)
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{
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// ball center is inside the box
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float vx = w - std::abs(x);
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float vy = h - std::abs(y);
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if (vx < vy)
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{
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if (x > 0.f)
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{
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return collision{s1.position, geom::vector{-vx - b1.radius, 0.f}};
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}
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else
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{
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return collision{s1.position, geom::vector{vx + b1.radius, 0.f}};
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}
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}
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else
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{
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if (y > 0.f)
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{
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return collision{s1.position, geom::vector{0.f, -vy - b1.radius}};
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}
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else
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{
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return collision{s1.position, geom::vector{0.f, vy + b1.radius}};
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}
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}
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}
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else
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{
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float cx = geom::clamp(x, {-w, w});
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float cy = geom::clamp(y, {-h, h});
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geom::vector n = ex * (cx - x) + ey * (cy - y);
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float l = geom::length(n);
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if (l < b1.radius)
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{
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float v = b1.radius - l;
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n = n / l;
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return collision{s1.position + n * (b1.radius - v / 2.f), n * v};
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}
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}
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return std::nullopt;
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}
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std::optional<collision> shape_collision(half_space const & b1, static_state const & s1, ball const & b2, static_state const & s2)
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{
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return invert(shape_collision(b2, s2, b1, s1));
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}
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std::optional<collision> shape_collision(half_space const &, static_state const &, half_space const &, static_state const &)
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{
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return std::nullopt;
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}
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std::optional<collision> shape_collision(half_space const & b1, static_state const &, box const & b2, static_state const & s2)
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{
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geom::vector a{ b2.width / 2.f, b2.height / 2.f};
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geom::vector b{-b2.width / 2.f, b2.height / 2.f};
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auto const rot = geom::plane_rotation<float, 2>(0, 1, s2.rotation);
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a = rot(a);
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b = rot(b);
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float v = b1.normal[0] * s2.position[0] + b1.normal[1] * s2.position[1] - b1.value;
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geom::vector<float, 2> d;
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float va = geom::dot(a, b1.normal);
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float vb = geom::dot(b, b1.normal);
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v -= std::max(std::abs(va), std::abs(vb));
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if (std::abs(va) > std::abs(vb))
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{
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if (va > 0.f)
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d = -a;
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else
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d = a;
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}
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else if (std::abs(vb) > std::abs(va))
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{
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if (vb > 0.f)
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d = -b;
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else
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d = b;
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}
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else
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{
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// multiple points of contact
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auto da = (va > 0.f) ? -a : a;
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auto db = (vb > 0.f) ? -b : b;
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d = da * 0.5f + db * 0.5f;
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}
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if (v > 0.f)
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return std::nullopt;
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return collision{s2.position + d, - v * b1.normal};
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}
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std::optional<collision> shape_collision(box const & b1, static_state const & s1, ball const & b2, static_state const & s2)
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{
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return invert(shape_collision(b2, s2, b1, s1));
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}
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std::optional<collision> shape_collision(box const & b1, static_state const & s1, half_space const & b2, static_state const & s2)
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{
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return invert(shape_collision(b2, s2, b1, s1));
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}
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std::optional<collision> shape_collision(box const & b1, static_state const & s1, box const & b2, static_state const & s2)
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{
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geom::vector<float, 2> ex1{ std::cos(s1.rotation), std::sin(s1.rotation)};
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geom::vector<float, 2> ey1{-std::sin(s1.rotation), std::cos(s1.rotation)};
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geom::vector<float, 2> ex2{ std::cos(s2.rotation), std::sin(s2.rotation)};
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geom::vector<float, 2> ey2{-std::sin(s2.rotation), std::cos(s2.rotation)};
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float w1 = b1.width / 2.f;
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float h1 = b1.height / 2.f;
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float w2 = b2.width / 2.f;
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float h2 = b2.height / 2.f;
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float dxx = geom::dot(ex1, ex2);
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float dxy = geom::dot(ex1, ey2);
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float dyx = geom::dot(ey1, ex2);
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float dyy = geom::dot(ey1, ey2);
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// SAT collision detector, hand-optimized for boxes
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geom::vector<float, 2> normal{0.f, 0.f};
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float penetration = -std::numeric_limits<float>::infinity();
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geom::point<float, 2> point{0.f, 0.f};
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auto side = [&](geom::vector<float, 2> const & n, geom::point<float, 2> const & a, float vx, float vy, geom::point<float, 2> const & c, geom::vector<float, 2> const & ex, geom::vector<float, 2> const & ey, bool invert)
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{
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float vc = geom::dot((c - a), n);
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float v = vc - std::abs(vx) - std::abs(vy);
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if (v > penetration)
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{
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penetration = v;
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point = c - geom::sign(vx) * ex - geom::sign(vy) * ey;
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normal = invert ? -n : n;
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}
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};
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// dot(n, c +/- ex +/- ey) = dot(n, c) +/- dot(n, ex) +/- dot(n, ey)
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// box2 vs box1 +x
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side(ex1, s1.position + ex1 * w1, dxx * w2, dxy * h2, s2.position, ex2 * w2, ey2 * h2, false);
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if (penetration > 0.f) return std::nullopt;
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// box2 vs box1 -x
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side(-ex1, s1.position - ex1 * w1, -dxx * w2, -dxy * h2, s2.position, ex2 * w2, ey2 * h2, false);
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if (penetration > 0.f) return std::nullopt;
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// box2 vs box1 +y
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side(ey1, s1.position + ey1 * h1, dyx * w2, dyy * h2, s2.position, ex2 * w2, ey2 * h2, false);
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if (penetration > 0.f) return std::nullopt;
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// box2 vs box1 -y
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side(-ey1, s1.position - ey1 * h1, -dyx * w2, -dyy * h2, s2.position, ex2 * w2, ey2 * h2, false);
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if (penetration > 0.f) return std::nullopt;
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// box1 vs box2 +x
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side(ex2, s2.position + ex2 * w2, dxx * w1, dyx * h1, s1.position, ex1 * w1, ey1 * h1, true);
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if (penetration > 0.f) return std::nullopt;
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// box1 vs box2 -x
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side(-ex2, s2.position - ex2 * w2, -dxx * w1, -dyx * h1, s1.position, ex1 * w1, ey1 * h1, true);
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if (penetration > 0.f) return std::nullopt;
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// box1 vs box2 +y
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side(ey2, s2.position + ey2 * h2, dxy * w1, dyy * h1, s1.position, ex1 * w1, ey1 * h1, true);
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if (penetration > 0.f) return std::nullopt;
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// box1 vs box2 -y
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side(-ey2, s2.position - ey2 * h2, -dxy * w1, -dyy * h1, s1.position, ex1 * w1, ey1 * h1, true);
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if (penetration > 0.f) return std::nullopt;
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return collision{point, -normal * penetration};
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}
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}
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struct engine::impl
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{
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util::heterogeneous_container<engine::shape_handle
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, wrapped_shape<ball>
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, wrapped_shape<half_space>
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, wrapped_shape<box>
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// , box
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// , convex_polygon
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> shapes;
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util::flat_list<material, engine::material_handle> materials;
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struct object_info
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{
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engine::shape_handle shape;
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engine::material_handle material;
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float inv_mass;
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float inv_inertia;
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};
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struct group
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{
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std::vector<object_info> infos;
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std::vector<static_state> static_states;
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std::vector<dynamic_state> dynamic_states;
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std::vector<geom::vector<float, 2>> position_change;
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std::vector<geom::vector<float, 2>> velocity_change;
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std::vector<float> angular_velocity_change;
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};
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std::vector<group> groups;
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std::optional<geom::vector<float, 2>> gravity;
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void update(float dt);
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void apply_gravity(float dt);
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void integrate(float dt);
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bool resolve_collisions();
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void log_energy();
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float energy();
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};
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void engine::impl::update(float dt)
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{
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apply_gravity(dt);
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integrate(dt);
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resolve_collisions();
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// log_energy();
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}
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void engine::impl::apply_gravity(float dt)
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{
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if (gravity)
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{
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for (auto & g : groups)
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{
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for (std::size_t i = 0; i < g.infos.size(); ++i)
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{
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if (g.infos[i].inv_mass == 0.f) continue;
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g.dynamic_states[i].velocity += *gravity * dt;
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}
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}
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}
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}
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void engine::impl::integrate(float dt)
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{
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for (auto & g : groups)
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{
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for (std::size_t i = 0; i < g.infos.size(); ++i)
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{
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g.static_states[i].position += dt * g.dynamic_states[i].velocity;
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g.static_states[i].rotation += dt * g.dynamic_states[i].angular_velocity;
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}
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}
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}
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bool engine::impl::resolve_collisions()
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{
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bool had_collision = false;
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for (std::size_t gi = 0; gi < groups.size(); ++gi)
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{
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for (std::size_t gj = gi; gj < groups.size(); ++gj)
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{
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for (std::size_t i = 0; i < groups[gi].infos.size(); ++i)
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{
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for (std::size_t j = (gi == gj) ? i + 1 : 0; j < groups[gj].infos.size(); ++j)
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{
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auto shi = groups[gi].infos[i].shape;
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auto shj = groups[gj].infos[j].shape;
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auto & sti = groups[gi].static_states[i];
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auto & stj = groups[gj].static_states[j];
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auto c = shapes.visit([&](auto const & si, auto const & sj){
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return shape_collision(si.shape, sti, sj.shape, stj);
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}, shi, shj);
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if (!c) continue;
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if (c->penetration == geom::vector<float, 2>::zero()) continue;
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// TODO: handle inv_mass == 0
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auto const n = geom::normalized(c->penetration);
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auto const & infoi = groups[gi].infos[i];
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auto const & infoj = groups[gj].infos[j];
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auto ri = c->position - sti.position;
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auto rj = c->position - stj.position;
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auto & dsi = groups[gi].dynamic_states[i];
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auto & dsj = groups[gj].dynamic_states[j];
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auto ui = dsi.velocity + geom::ort(ri) * dsi.angular_velocity;
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auto uj = dsj.velocity + geom::ort(rj) * dsj.angular_velocity;
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auto const u = uj - ui;
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if (geom::dot(u, n) > 0.f) continue;
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had_collision = true;
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auto const & mati = materials[infoi.material];
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auto const & matj = materials[infoj.material];
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geom::matrix<float, 2, 2> K;
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K[0][0] = infoi.inv_mass + infoj.inv_mass;
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K[1][1] = K[0][0];
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K[0][1] = 0.f;
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K[1][0] = 0.f;
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K[0][0] += ri[1] * ri[1] * infoi.inv_inertia;
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K[1][1] += ri[0] * ri[0] * infoi.inv_inertia;
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K[0][1] -= ri[0] * ri[1] * infoi.inv_inertia;
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K[0][0] += rj[1] * rj[1] * infoj.inv_inertia;
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K[1][1] += rj[0] * rj[0] * infoj.inv_inertia;
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K[0][1] -= rj[0] * rj[1] * infoj.inv_inertia;
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K[1][0] = K[0][1];
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// Plastic sliding impulse
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// Normal relative velocity -> 0
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// Tangential relative velocity -> unchanged
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auto const J1 = - n * geom::dot(n, u) / geom::dot(n, K * n);
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// Plastic sticking impulse
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// Normal relative velocity -> 0
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// Tangential relative velocity -> 0
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auto const J2 = - *geom::solve(K, u);
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// float const e = (mati.elasticity + matj.elasticity) / 2.f;
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float const e = std::sqrt(mati.elasticity * matj.elasticity);
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// float const f = (mati.friction + matj.friction) / 2.f;
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float const f = std::sqrt(mati.friction * matj.friction);
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float const mu = f;
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auto J = (1.f + e) * J1 + f * (J2 - J1);
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// Test for friction cone
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float q = geom::length(J - n * geom::dot(J, n));
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if (q > mu * geom::dot(J, n))
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{
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float k = (mu * (1.f + e) * geom::dot(J1, n)) / (geom::length(J2 - n * geom::dot(J2, n)) - mu * geom::dot(n, J2 - J1));
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J = (1.f + e) * J1 + k * (J2 - J1);
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}
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groups[gi].dynamic_states[i].velocity -= J * infoi.inv_mass;
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groups[gj].dynamic_states[j].velocity += J * infoj.inv_mass;
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groups[gi].dynamic_states[i].angular_velocity -= geom::det(ri, J) * infoi.inv_inertia;
|
|
groups[gj].dynamic_states[j].angular_velocity += geom::det(rj, J) * infoj.inv_inertia;
|
|
|
|
groups[gi].static_states[i].position -= c->penetration * infoi.inv_mass / (infoi.inv_mass + infoj.inv_mass);
|
|
groups[gj].static_states[j].position += c->penetration * infoj.inv_mass / (infoi.inv_mass + infoj.inv_mass);
|
|
}
|
|
}
|
|
}
|
|
}
|
|
|
|
return !had_collision;
|
|
}
|
|
|
|
float engine::impl::energy()
|
|
{
|
|
float Eg = 0.f;
|
|
float Er = 0.f;
|
|
float Ek = 0.f;
|
|
|
|
for (auto & g : groups)
|
|
{
|
|
for (std::size_t i = 0; i < g.infos.size(); ++i)
|
|
{
|
|
if (g.infos[i].inv_mass == 0.f) continue;
|
|
|
|
if (gravity)
|
|
Eg -= geom::dot(*gravity, g.static_states[i].position - geom::point<float, 2>::zero()) / g.infos[i].inv_mass;
|
|
|
|
Ek += geom::length_sqr(g.dynamic_states[i].velocity) / g.infos[i].inv_mass / 2.f;
|
|
Er += geom::sqr(g.dynamic_states[i].angular_velocity) / g.infos[i].inv_inertia / 2.f;
|
|
}
|
|
}
|
|
|
|
return Eg + Ek + Er;
|
|
}
|
|
|
|
void engine::impl::log_energy()
|
|
{
|
|
float Eg = 0.f;
|
|
float Er = 0.f;
|
|
float Ek = 0.f;
|
|
|
|
for (auto & g : groups)
|
|
{
|
|
for (std::size_t i = 0; i < g.infos.size(); ++i)
|
|
{
|
|
if (g.infos[i].inv_mass == 0.f) continue;
|
|
|
|
if (gravity)
|
|
Eg -= geom::dot(*gravity, g.static_states[i].position - geom::point<float, 2>::zero()) / g.infos[i].inv_mass;
|
|
|
|
Ek += geom::length_sqr(g.dynamic_states[i].velocity) / g.infos[i].inv_mass / 2.f;
|
|
Er += geom::sqr(g.dynamic_states[i].angular_velocity) / g.infos[i].inv_inertia / 2.f;
|
|
}
|
|
}
|
|
|
|
log::info() << "G " << Eg << " K " << Ek << " R " << Er;
|
|
}
|
|
|
|
engine::engine()
|
|
: pimpl_{std::make_unique<struct impl>()}
|
|
{}
|
|
|
|
engine::~engine() = default;
|
|
|
|
engine::shape_handle engine::add_shape(ball const & b)
|
|
{
|
|
return impl().shapes.insert(wrap(b));
|
|
}
|
|
|
|
engine::shape_handle engine::add_shape(half_space const & s)
|
|
{
|
|
return impl().shapes.insert(wrap(s));
|
|
}
|
|
|
|
engine::shape_handle engine::add_shape(box const & b)
|
|
{
|
|
return impl().shapes.insert(wrap(b));
|
|
}
|
|
|
|
void engine::remove_shape(shape_handle handle)
|
|
{
|
|
impl().shapes.erase(handle);
|
|
}
|
|
|
|
engine::material_handle engine::add_material(material const & m)
|
|
{
|
|
return impl().materials.insert(m);
|
|
}
|
|
|
|
void engine::remove_material(material_handle handle)
|
|
{
|
|
impl().materials.erase(handle);
|
|
}
|
|
|
|
engine::group_handle engine::create_group()
|
|
{
|
|
auto h = static_cast<group_handle>(impl().groups.size());
|
|
impl().groups.emplace_back();
|
|
return h;
|
|
}
|
|
|
|
void engine::remove_group(group_handle handle)
|
|
{
|
|
auto & g = impl().groups[handle];
|
|
g.infos.clear();
|
|
g.static_states.clear();
|
|
g.dynamic_states.clear();
|
|
}
|
|
|
|
std::size_t engine::group_size(group_handle handle) const
|
|
{
|
|
return impl().groups[handle].infos.size();
|
|
}
|
|
|
|
static_state const * engine::group_static_state(group_handle handle) const
|
|
{
|
|
return impl().groups[handle].static_states.data();
|
|
}
|
|
|
|
dynamic_state const * engine::group_dynamic_state(group_handle handle) const
|
|
{
|
|
return impl().groups[handle].dynamic_states.data();
|
|
}
|
|
|
|
static_state * engine::group_static_state(group_handle handle)
|
|
{
|
|
return impl().groups[handle].static_states.data();
|
|
}
|
|
|
|
dynamic_state * engine::group_dynamic_state(group_handle handle)
|
|
{
|
|
return impl().groups[handle].dynamic_states.data();
|
|
}
|
|
|
|
void engine::add_object(group_handle group, shape_handle shape, material_handle material, static_state const & ss, dynamic_state const & ds)
|
|
{
|
|
float const density = impl().materials[material].density;
|
|
float const area = impl().shapes.visit([](auto const & s){ return s.area; }, shape);
|
|
float const inertia = impl().shapes.visit([](auto const & s){ return s.inertia; }, shape);
|
|
|
|
auto & g = impl().groups[group];
|
|
g.infos.push_back({shape, material, 1.f / (area * density), 1.f / (inertia * density)});
|
|
g.static_states.push_back(ss);
|
|
g.dynamic_states.push_back(ds);
|
|
}
|
|
|
|
void engine::remove_object(group_handle group, std::size_t index)
|
|
{
|
|
auto & g = impl().groups[group];
|
|
g.infos.erase(g.infos.begin() + index);
|
|
g.static_states.erase(g.static_states.begin() + index);
|
|
g.dynamic_states.erase(g.dynamic_states.begin() + index);
|
|
}
|
|
|
|
void engine::set_gravity(geom::vector<float, 2> const & g)
|
|
{
|
|
impl().gravity = g;
|
|
}
|
|
|
|
void engine::update(float dt)
|
|
{
|
|
impl().update(dt);
|
|
}
|
|
|
|
}
|