C++如何实现一个简单的物理引擎_基于C++的刚体动力学与碰撞检测入门

struct RigidBody {
    float mass;
    Vec2 position;
    Vec2 velocity;
    Vec2 force;
<pre class='brush:php;toolbar:false;'>void integrate(float dt) {
    Vec2 acceleration = force / mass;
    velocity += acceleration * dt;
    position += velocity * dt;
    force = Vec2(0, 0); // 清除累计力
}

bool checkCollision(const Circle& a, const Circle& b) {
    float dx = a.position.x - b.position.x;
    float dy = a.position.y - b.position.y;
    float distance = sqrt(dx*dx + dy*dy);
    return distance < (a.radius + b.radius);
}

void resolveCollision(RigidBody& a, RigidBody& b) {
    Vec2 normal = (b.position - a.position).normalize();
<pre class='brush:php;toolbar:false;'>// 分离穿透（粗略处理）
float overlap = (a.radius + b.radius) - (b.position - a.position).length();
a.position -= normal * overlap * 0.5;
b.position += normal * overlap * 0.5;

Vec2 varelative = b.velocity - a.velocity;
float velocityAlongNormal = varelative.dot(normal);

if (velocityAlongNormal > 0) return; // 分离中，无需响应

float e = 0.8; // 弹性系数
float j = -(1 + e) * velocityAlongNormal;
j /= (1/a.mass + 1/b.mass);

a.velocity -= normal * j / a.mass;
b.velocity += normal * j / b.mass;

while (running) {
    for (auto& body : bodies) {
        body.force = Vec2(0, gravity * body.mass); // 施加重力
        body.integrate(dt);
    }
<pre class='brush:php;toolbar:false;'>for (size_t i = 0; i < bodies.size(); ++i)
    for (size_t j = i+1; j < bodies.size(); ++j)
        if (checkCollision(bodies[i], bodies[j]))
            resolveCollision(bodies[i], bodies[j]);

render(); // 显示画面
sleep(dt);