GAMES101 HW8

这里回顾GAMES101 HW8，这次作业的内容是质点弹簧系统。

课程主页：

• https://sites.cs.ucsb.edu/~lingqi/teaching/games101.html

课程作业：

• http://games-cn.org/forums/topic/allhw/

课程视频：

• https://www.bilibili.com/video/BV1X7411F744?spm_id_from=333.337.search-card.all.click

参考资料：

• https://blog.csdn.net/triste_who/article/details/103298548
• https://games-cn.org/forums/topic/guanyuzuoye8deyixiewentijieda/
• https://blog.csdn.net/weixin_44491423/article/details/127522750

一些问题

配置环境时不能复制pdf的命令，有全角半角的问题，命令如下：

sudo apt install libglu1-mesa-dev freeglut3-dev mesa-common-dev
sudo apt install xorg-dev

本次作业在WSL2下无法运行，最后使用Ubuntu系统完成了此次作业。

rope

Rope::Rope(Vector2D start, Vector2D end, int num_nodes, float node_mass, float k, vector<int> pinned_nodes)
{
    // TODO (Part 1): Create a rope starting at `start`, ending at `end`, and containing `num_nodes` nodes.
    // node_mass: 质点质量; k: 弹簧系数
    Vector2D delta = (end - start) / (num_nodes - 1);
    // 质点
    for (int i = 0; i < num_nodes; i++) {
        Vector2D position = start + i * delta;
        // 终点位置
        Mass *e = new Mass(position, node_mass, false);
        // 弹簧
        if (i > 0) {
            // 起始位置
            Mass *s = masses.back();
            Spring *spring = new Spring(s, e, k);
            springs.push_back(spring);
        }
        masses.push_back(e);
    }
    for (auto &i : pinned_nodes) {
        masses[i]->pinned = true;
    }
}

simulateEuler

void Rope::simulateEuler(float delta_t, Vector2D gravity)
{
    for (auto &s : springs)
    {
        // TODO (Part 2): Use Hooke's law to calculate the force on a node
        float l1 = s->rest_length;
        // a: m1; b: m2
        Vector2D ab = ((s->m2)->position - (s->m1)->position);
        float l2 = ab.norm();
        // a收到的力
        Vector2D f = s->k * ab / l2 * (l2 - l1);
        (s->m1)->forces += f;
        (s->m2)->forces += -f;
    }
    // int cnt = 0;
    for (auto &m : masses)
    {
        if (!m->pinned)
        {
            // TODO (Part 2): Add the force due to gravity, then compute the new velocity and position
            // 考虑重力
            m->forces += gravity * m->mass;
            // TODO (Part 2): Add global damping
            m->forces -= kd_euler * m->velocity;
            Vector2D a = m->forces / m->mass;
            // 显式欧拉
            // m->position += m->velocity * delta_t;
            // m->velocity += a * delta_t;
            // 隐式欧拉
            m->velocity += a * delta_t;
            m->position += m->velocity * delta_t;
        }
        
        // Reset all forces on each mass
        m->forces = Vector2D(0, 0);
    }
}

simulateVerlet

void Rope::simulateVerlet(float delta_t, Vector2D gravity)
{
    for (auto &s : springs)
    {
        // TODO (Part 3): Simulate one timestep of the rope using explicit Verlet （solving constraints)
        float l1 = s->rest_length;
        // a: m1; b: m2
        Vector2D ab = ((s->m2)->position - (s->m1)->position);
        float l2 = ab.norm();
        // a收到的力
        Vector2D f = s->k * ab / l2 * (l2 - l1);
        (s->m1)->forces += f;
        (s->m2)->forces += -f;
    }

    for (auto &m : masses)
    {
        if (!m->pinned)
        {
            Vector2D temp_position = m->position;
            // TODO (Part 3.1): Set the new position of the rope mass
            // 考虑重力
            m->forces += gravity * m->mass;
            Vector2D a = m->forces / m->mass;
            // TODO (Part 4): Add global Verlet damping
            Vector2D pos = m->position + (1 - kd_verlet) * (m->position - m->last_position) + a * delta_t * delta_t;
            m->last_position = m->position;
            m->position = pos;
        }
        // Reset all forces on each mass
        m->forces = Vector2D(0, 0);
    }
}