镜之国的爱丽丝
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06 - 光栅化与深度缓冲hwk

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1. 作业要求

栅格化一个三角形并且实现深度缓冲。

1.1 实现流程

  1. 创建三角形的 2 维 bounding box。
  2. 遍历此 bounding box 内的所有像素（使用其整数索引）。然后，使用像素中
    心的屏幕空间坐标来检查中心点是否在三角形内。
  3. 如果在内部，则将其位置处的插值深度值 (interpolated depth value) 与深度
    缓冲区 (depth buffer) 中的相应值进行比较。
  4. 如果当前点更靠近相机，请设置像素颜色并更新深度缓冲区 (depth buffer)。

2. 源代码

2.1 insideTriangle()

测试点是否在三角形内。

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static bool insideTriangle(int x, int y, const Vector3f* _v)
{   
    Vector3f P(x+0.5f,y+0.5f,1.0f);

    const Vector3f& A = _v[0];
    const Vector3f& B = _v[1];
    const Vector3f& C = _v[2];

    Vector3f AB =  B - A;
    Vector3f BC =  C - B;
    Vector3f CA =  A - C;

    Vector3f AP = P - A;
    Vector3f BP = P - B;
    Vector3f CP = P - C;

    float z1 = AB.cross(AP).z();
    float z2 = BC.cross(BP).z();
    float z3 = CA.cross(CP).z();

    return (z1 > 0 && z2 >0 && z3 > 0) ||  (z1 < 0 && z2 <0 && z3 < 0);
}

2.2 rasterize_triangle()

2.2.1 未抗锯齿

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void rst::rasterizer::rasterize_triangle(const Triangle& t) {
    auto v = t.toVector4();
    
    // TODO : Find out the bounding box of current triangle.
    // iterate through the pixel and find if the current pixel is inside the triangle
    
    // check triangle coordinates
    // for(auto idx : {0, 1, 2})
    // {
    //     std::clog << "pt" << idx << " | " << v[idx].x() 
    //                              << " | " << v[idx].y() 
    //                              << " | " << v[idx].z() 
    //                              << " | " << v[idx].w() << std::endl;
    // }
    
    // get bounding box
    auto ext_pt_x = std::minmax_element(v.begin(), v.end(),
                                       [](const Eigen::Vector4f& lhs, const Eigen::Vector4f & rhs){
                                            return lhs.x() < rhs.x();
                                       });
    auto ext_pt_y = std::minmax_element(v.begin(), v.end(),
                                       [](const Eigen::Vector4f& lhs, const Eigen::Vector4f & rhs){
                                            return lhs.y() < rhs.y();
                                       });
    // std::clog << "ext_pt_x: " << ext_pt_x.first->x() << " | " << ext_pt_x.second->x() << std::endl;
    // std::clog << "ext_pt_y: " << ext_pt_y.first->y() << " | " << ext_pt_y.second->y() << std::endl;

    int min_x = floor(ext_pt_x.first->x());
    int max_x = ceil(ext_pt_x.second->x());
    int min_y = floor(ext_pt_y.first->y());
    int max_y = ceil(ext_pt_y.second->y());

    Eigen::Vector3f v3f[3];
    for (int idx : {0, 1, 2})
    {
        v3f[idx] << v[idx].x(), v[idx].y(), 1.0f;
    }
    // std::transform(std::begin(v), std::end(v), v3f.begin(), [](auto& vec) { return Eigen::Vector3f(vec.x(), vec.y(), vec.z()); });
    
    // If so, use the following code to get the interpolated z value.
    //auto[alpha, beta, gamma] = computeBarycentric2D(x, y, t.v);
    //float w_reciprocal = 1.0/(alpha / v[0].w() + beta / v[1].w() + gamma / v[2].w());
    //float z_interpolated = alpha * v[0].z() / v[0].w() + beta * v[1].z() / v[1].w() + gamma * v[2].z() / v[2].w();
    //z_interpolated *= w_reciprocal;

    // loop [min_x, max_x] x [min_y, max_y]
    for (int x=min_x;x<=max_x;++x)
    {
        for (int y=min_y;y<=max_y;++y)
        {
            // no msaa
            float x_pos = (float)x + 0.5;
            float y_pos = (float)y + 0.5;
            auto[alpha, beta, gamma] = computeBarycentric2D(x_pos, y_pos, t.v);
            float w_reciprocal = 1.0/(alpha / v[0].w() + beta / v[1].w() + gamma / v[2].w());
            float z_interpolated = alpha * v[0].z() / v[0].w() + beta * v[1].z() / v[1].w() + gamma * v[2].z() / v[2].w();
            z_interpolated *= w_reciprocal;
            int buff_ind = x + y*width;
            if (insideTriangle(x_pos, y_pos, v3f) && (-z_interpolated<depth_buf[buff_ind]))
            {
                set_pixel(Eigen::Vector3f(x, y, 1.0f), t.getColor());
                depth_buf[buff_ind] = -z_interpolated;
            }
        }
    }
}

运行结果 ：

screenShot.png

2.2.2 使用MSAA抗锯齿

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void rst::rasterizer::rasterize_triangle(const Triangle& t) {
    auto v = t.toVector4();
    
    // TODO : Find out the bounding box of current triangle.
    // iterate through the pixel and find if the current pixel is inside the triangle
    
    // check triangle coordinates
    // for(auto idx : {0, 1, 2})
    // {
    //     std::clog << "pt" << idx << " | " << v[idx].x() 
    //                              << " | " << v[idx].y() 
    //                              << " | " << v[idx].z() 
    //                              << " | " << v[idx].w() << std::endl;
    // }
    
    // get bounding box
    auto ext_pt_x = std::minmax_element(v.begin(), v.end(),
                                       [](const Eigen::Vector4f& lhs, const Eigen::Vector4f & rhs){
                                            return lhs.x() < rhs.x();
                                       });
    auto ext_pt_y = std::minmax_element(v.begin(), v.end(),
                                       [](const Eigen::Vector4f& lhs, const Eigen::Vector4f & rhs){
                                            return lhs.y() < rhs.y();
                                       });
    // std::clog << "ext_pt_x: " << ext_pt_x.first->x() << " | " << ext_pt_x.second->x() << std::endl;
    // std::clog << "ext_pt_y: " << ext_pt_y.first->y() << " | " << ext_pt_y.second->y() << std::endl;

    int min_x = floor(ext_pt_x.first->x());
    int max_x = ceil(ext_pt_x.second->x());
    int min_y = floor(ext_pt_y.first->y());
    int max_y = ceil(ext_pt_y.second->y());

    Eigen::Vector3f v3f[3];
    for (int idx : {0, 1, 2})
    {
        v3f[idx] << v[idx].x(), v[idx].y(), 1.0f;
    }
    // std::transform(std::begin(v), std::end(v), v3f.begin(), [](auto& vec) { return Eigen::Vector3f(vec.x(), vec.y(), vec.z()); });
    
    // If so, use the following code to get the interpolated z value.
    //auto[alpha, beta, gamma] = computeBarycentric2D(x, y, t.v);
    //float w_reciprocal = 1.0/(alpha / v[0].w() + beta / v[1].w() + gamma / v[2].w());
    //float z_interpolated = alpha * v[0].z() / v[0].w() + beta * v[1].z() / v[1].w() + gamma * v[2].z() / v[2].w();
    //z_interpolated *= w_reciprocal;

    // loop [min_x, max_x] x [min_y, max_y]
    for (int x=min_x;x<=max_x;++x)
    {
        for (int y=min_y;y<=max_y;++y)
        {
            // // apply msaa
            int sup_px_cnt = 0;
            for (int x_sup: {0, 1})
            {
                for (int y_sup: {0, 1})
                {
                    float x_pos = (float)x + 0.25 + x_sup*0.5;
                    float y_pos = (float)y + 0.25 + y_sup*0.5;

                    auto[alpha, beta, gamma] = computeBarycentric2D(x_pos, y_pos, t.v);
                    float w_reciprocal = 1.0/(alpha / v[0].w() + beta / v[1].w() + gamma / v[2].w());
                    float z_interpolated = alpha * v[0].z() / v[0].w() + beta * v[1].z() / v[1].w() + gamma * v[2].z() / v[2].w();
                    z_interpolated *= w_reciprocal;

                    int buff_ind = (x*2 + x_sup) + (y*2 + y_sup)*width*2;
                    if (insideTriangle(x_pos, y_pos, v3f))
                    {
                        if ((-z_interpolated<depth_buf_msaa2x2[buff_ind]))
                        {
                            depth_buf_msaa2x2[buff_ind] = -z_interpolated;
                            ++sup_px_cnt;
                        }
                    }
                }
            }
            if ((sup_px_cnt>0))
            {
                float intensity = (float)sup_px_cnt / 4.0f;
                mix_pixel(Eigen::Vector3f(x, y, 1.0f), t.getColor()*intensity);
            }
        }

    }
}

运行结果 ：

screenShot.png

3. 运行结果

Assignment2hwk.png