GAMES101 作业3——三角形光栅化进阶

参考资料：https://zhuanlan.zhihu.com/p/419872527

作业要求：

在这次编程任务中，我们会进一步模拟现代图形技术。我们在代码中添加了 Object Loader(用于加载三维模型), Vertex Shader 与 Fragment Shader，并且支持 了纹理映射。
而在本次实验中，你需要完成的任务是:

1. 修改函数 rasterize_triangle(const Triangle& t) in rasterizer.cpp: 在此 处实现与作业 2 类似的插值算法，实现法向量、颜色、纹理颜色的插值。
2. 修改函数 get_projection_matrix() in main.cpp: 将你自己在之前的实验中 实现的投影矩阵填到此处，此时你可以运行./Rasterizer output.png normal 来观察法向量实现结果。
3. 修改函数 phong_fragment_shader() in main.cpp: 实现 Blinn-Phong 模型计算 Fragment Color.
4. 修改函数 texture_fragment_shader() in main.cpp: 在实现 Blinn-Phong 的基础上，将纹理颜色视为公式中的 kd，实现 Texture Shading Fragment Shader.
5. 修改函数 bump_fragment_shader() in main.cpp: 在实现 Blinn-Phong 的基础上，仔细阅读该函数中的注释，实现 Bump mapping.
6. 修改函数 displacement_fragment_shader() in main.cpp: 在实现 Bump mapping 的基础上，实现 displacement mapping.
7. 双线性纹理插值: 使用双线性插值进行纹理采样, 在 Texture 类中实现一个新方法 Vector3f getColorBilinear(float u, float v) 并 通过 fragment shader 调用它。为了使双线性插值的效果更加明显，你应该 考虑选择更小的纹理图。请同时提交纹理插值与双线性纹理插值的结果，并 进行比较。

1. 修改函数 rasterize_triangle(const Triangle& t) in rasterizer.cpp: 在此处实现与作业 2 类似的插值算法，实现法向量、颜色、纹理颜色的插值。

//Screen space rasterization
void rst::rasterizer::rasterize_triangle(const Triangle &t, const std::array<Eigen::Vector3f, 3> &view_pos) {
    // Inside your rasterization loop:
    //    * v[i].w() is the vertex view space depth value z.
    //    * Z is interpolated view space depth for the current pixel
    //    * zp is depth between zNear and zFar, used for z-buffer

    // Interpolate the attributes:
    // auto interpolated_color
    // auto interpolated_normal
    // auto interpolated_texcoords
    // auto interpolated_shadingcoords

    // Use: fragment_shader_payload payload( interpolated_color, interpolated_normal.normalized(), interpolated_texcoords, texture ? &*texture : nullptr);
    // Use: payload.view_pos = interpolated_shadingcoords;
    // Use: Instead of passing the triangle's color directly to the frame buffer, pass the color to the shaders first to get the final color;
    // Use: auto pixel_color = fragment_shader(payload);

    auto v = t.toVector4();

    // bounding box
    float min_x = std::min(v[0][0], std::min(v[1][0], v[2][0]));
    float max_x = std::max(v[0][0], std::max(v[1][0], v[2][0]));
    float min_y = std::min(v[0][1], std::min(v[1][1], v[2][1]));
    float max_y = std::max(v[0][1], std::max(v[1][1], v[2][1]));

    int x_min = std::floor(min_x);
    int x_max = std::ceil(max_x);
    int y_min = std::floor(min_y);
    int y_max = std::ceil(max_y);

    for (int i = x_min; i <= x_max; ++i) {
        for (int j = y_min; j <= y_max; ++j) {
            if (insideTriangle(i + 0.5, j + 0.5, t.v)) {
                //Depth interpolated
                auto[alpha, beta, gamma] = computeBarycentric2D(i + 0.5, j + 0.5, t.v);

                //直接进行深度插值投影时三角形重心会变，所以要使用透视校正插值
                float Z = 1.0 / (alpha / v[0].w() + beta / v[1].w() + gamma / v[2].w());
                float zp = alpha * v[0].z() / v[0].w() + beta * v[1].z() / v[1].w() + gamma * v[2].z() / v[2].w();
                zp *= Z;

                if (zp < depth_buf[get_index(i, j)]) {
                    // color
                    auto interpolated_color = interpolate(alpha, beta, gamma, t.color[0], t.color[1], t.color[2], 1);
                    // normal
                    auto interpolated_normal = interpolate(alpha, beta, gamma, t.normal[0], t.normal[1], t.normal[2],
                                                           1).normalized();
                    // texture
                    auto interpolated_texcoords = interpolate(alpha, beta, gamma, t.tex_coords[0], t.tex_coords[1],
                                                              t.tex_coords[2], 1);
                    // shadingcoords
                    //view_pos[] 是三角形顶点在view space中的坐标，插值是为了还原在camera space 中的坐标
                    //详见http://games-cn.org/forums/topic/zuoye3-interpolated_shadingcoords/
                    auto interpolated_shadingcoords = interpolate(alpha, beta, gamma, view_pos[0], view_pos[1],
                                                                  view_pos[2], 1);
                    // 用来传递插值结果的结构体
                    fragment_shader_payload payload(interpolated_color, interpolated_normal, interpolated_texcoords,
                                                    texture ? &*texture : nullptr);
                    payload.view_pos = interpolated_shadingcoords;
                    auto pixel_color = fragment_shader(payload);
                    // 设置深度
                    depth_buf[get_index(i, j)] = zp;
                    // 设置颜色
                    set_pixel(Eigen::Vector2i(i, j), pixel_color);
                }
            }
        }
    }
}

2. 修改函数 get_projection_matrix() in main.cpp: 将你自己在之前的实验中实现的投影矩阵填到此处，此时你可以运行 ./Rasterizer output.png normal 来观察法向量实现结果

详见作业2.

此时可看到基本结果：

3. 修改函数 phong_fragment_shader() in main.cpp: 实现 Blinn-Phong 模型计算 Fragment Color

Eigen::Vector3f phong_fragment_shader(const fragment_shader_payload& payload)
{
    Eigen::Vector3f ka = Eigen::Vector3f(0.005, 0.005, 0.005); //环境光系数
    Eigen::Vector3f kd = payload.color; //漫反射系数
    Eigen::Vector3f ks = Eigen::Vector3f(0.7937, 0.7937, 0.7937); //高光系数

    auto l1 = light{{20, 20, 20}, {500, 500, 500}};
    auto l2 = light{{-20, 20, 0}, {500, 500, 500}};

    std::vector<light> lights = {l1, l2};
    Eigen::Vector3f amb_light_intensity{10, 10, 10};
    Eigen::Vector3f eye_pos{0, 0, 10};

    float p = 150;

    Eigen::Vector3f color = payload.color;
    Eigen::Vector3f point = payload.view_pos;
    Eigen::Vector3f normal = payload.normal;

    Eigen::Vector3f result_color = {0, 0, 0};
    for (auto& light : lights)
    {
        // For each light source in the code, calculate what the *ambient*, *diffuse*, and *specular*
        // components are. Then, accumulate that result on the *result_color* object.
        Eigen::Vector3f light_dir = (light.position - point).normalized();
        Eigen::Vector3f view_dir = (eye_pos - point).normalized();
        Eigen::Vector3f half_vector = (light_dir + view_dir).normalized();

        //距离衰减
        float r2 = (light.position - point).dot(light.position - point);

        //漫反射
        Eigen::Vector3f Ld = kd.cwiseProduct(light.intensity / r2);
        Ld *= std::max(0.0f, normal.normalized().dot(light_dir));

        //环境光
        Eigen::Vector3f La = ka.cwiseProduct(amb_light_intensity);

        //高光
        Eigen::Vector3f Ls = ks.cwiseProduct(light.intensity / r2);
        Ls *= std::pow(std::max(0.0f, normal.normalized().dot(half_vector)), p);

        result_color += (La + Ld + Ls);
    }

    return result_color * 255.f;
}

4. 修改函数 texture_fragment_shader() in main.cpp: 在实现 Blinn-Phong 的基础上，将纹理颜色视为公式中的 kd，实现 Texture Shading Fragment Shader.

Eigen::Vector3f texture_fragment_shader(const fragment_shader_payload& payload)
{
    Eigen::Vector3f return_color = {0, 0, 0};
    if (payload.texture)
    {
        // Get the texture value at the texture coordinates of the current fragment
        return_color = payload.texture->getColor(payload.tex_coords.x(), payload.tex_coords.y());
    }

    Eigen::Vector3f texture_color;
    texture_color << return_color.x(), return_color.y(), return_color.z();

    Eigen::Vector3f ka = Eigen::Vector3f(0.005, 0.005, 0.005);
    Eigen::Vector3f kd = texture_color / 255.f;
    Eigen::Vector3f ks = Eigen::Vector3f(0.7937, 0.7937, 0.7937);

    auto l1 = light{{20, 20, 20}, {500, 500, 500}};
    auto l2 = light{{-20, 20, 0}, {500, 500, 500}};

    std::vector<light> lights = {l1, l2};
    Eigen::Vector3f amb_light_intensity{10, 10, 10};
    Eigen::Vector3f eye_pos{0, 0, 10};

    float p = 150;

    Eigen::Vector3f color = texture_color;
    Eigen::Vector3f point = payload.view_pos;
    Eigen::Vector3f normal = payload.normal;

    Eigen::Vector3f result_color = {0, 0, 0};

    for (auto& light : lights)
    {
        // For each light source in the code, calculate what the *ambient*, *diffuse*, and *specular*
        // components are. Then, accumulate that result on the *result_color* object.
        Eigen::Vector3f light_dir = (light.position - point).normalized();
        Eigen::Vector3f view_dir = (eye_pos - point).normalized();
        Eigen::Vector3f half_vector = (light_dir + view_dir).normalized();

        //距离衰减
        float r2 = (light.position - point).dot(light.position - point);

        //漫反射
        Eigen::Vector3f Ld = kd.cwiseProduct(light.intensity / r2);
        Ld *= std::max(0.0f, normal.normalized().dot(light_dir));

        //环境光
        Eigen::Vector3f La = ka.cwiseProduct(amb_light_intensity);

        //高光
        Eigen::Vector3f Ls = ks.cwiseProduct(light.intensity / r2);
        Ls *= std::pow(std::max(0.0f, normal.normalized().dot(half_vector)), p);

        result_color += (La + Ld + Ls);

    }

    return result_color * 255.f;
}

注意：实现下面的代码前需要先对getColor方法进行修改,要限定UV坐标，qu’zhi范围在0~1之间，否则代码会报Process finished with exit code -1073741819 (0xC0000005)错误。

Eigen::Vector3f getColor(float u, float v)
    {
        // 坐标限定
        if (u < 0) u = 0;
        if (u > 1) u = 1;
        if (v < 0) v = 0;
        if (v > 1) v = 1;

        auto u_img = u * width;
        auto v_img = (1 - v) * height;
        auto color = image_data.at<cv::Vec3b>(v_img, u_img);
        return Eigen::Vector3f(color[0], color[1], color[2]);
    }

5. 修改函数 bump_fragment_shader() in main.cpp: 在实现 Blinn-Phong 的基础上，实现 Bump mapping

Eigen::Vector3f bump_fragment_shader(const fragment_shader_payload &payload) {

    Eigen::Vector3f ka = Eigen::Vector3f(0.005, 0.005, 0.005);
    Eigen::Vector3f kd = payload.color;
    Eigen::Vector3f ks = Eigen::Vector3f(0.7937, 0.7937, 0.7937);

    auto l1 = light{{20,  20,  20},
                    {500, 500, 500}};
    auto l2 = light{{-20, 20,  0},
                    {500, 500, 500}};

    std::vector<light> lights = {l1, l2};
    Eigen::Vector3f amb_light_intensity{10, 10, 10};
    Eigen::Vector3f eye_pos{0, 0, 10};

    float p = 150;

    Eigen::Vector3f color = payload.color;
    Eigen::Vector3f point = payload.view_pos;
    Eigen::Vector3f normal = payload.normal;


    float kh = 0.2, kn = 0.1;

    // Implement bump mapping here
    // Let n = normal = (x, y, z)
    // Vector t = (x*y/sqrt(x*x+z*z),sqrt(x*x+z*z),z*y/sqrt(x*x+z*z))
    // Vector b = n cross product t
    // Matrix TBN = [t b n]
    // dU = kh * kn * (h(u+1/w,v)-h(u,v))
    // dV = kh * kn * (h(u,v+1/h)-h(u,v))
    // Vector ln = (-dU, -dV, 1)
    // Normal n = normalize(TBN * ln)
    float x = normal.x();
    float y = normal.y();
    float z = normal.z();

    Eigen::Vector3f t = Eigen::Vector3f(x * y / std::sqrt(x * x + z * z), std::sqrt(x * x + z * z), z * y / std::sqrt(x * x + z * z));
    Eigen::Vector3f b = normal.cross(t);

    Eigen::Matrix3f TBN;
    TBN <<
        t.x(), b.x(), normal.x(),
            t.y(), b.y(), normal.y(),
            t.z(), b.z(), normal.z();

    float u = payload.tex_coords.x();
    float v = payload.tex_coords.y();
    float w = payload.texture->width;
    float h = payload.texture->height;

    float dU = kh * kn * (payload.texture->getColor(u + 1.0f / w, v).norm() - payload.texture->getColor(u, v).norm());
    float dV = kh * kn * (payload.texture->getColor(u, v + 1.0f / h).norm() - payload.texture->getColor(u, v).norm());

    Eigen::Vector3f ln = Eigen::Vector3f(-dU, -dV, 1.0f);
    normal = TBN * ln;

    Eigen::Vector3f result_color = normal.normalized();

    return result_color * 255.f;
}

6. 修改函数 displacement_fragment_shader() in main.cpp: 在实现 Bump mapping 的基础上，实现 displacement mapping

bump只是将法向量和它的梯度作为模型的颜色可视化了出来，而displacement在此基础上考虑了光照因素

Eigen::Vector3f displacement_fragment_shader(const fragment_shader_payload &payload) {

    Eigen::Vector3f ka = Eigen::Vector3f(0.005, 0.005, 0.005);
    Eigen::Vector3f kd = payload.color;
    Eigen::Vector3f ks = Eigen::Vector3f(0.7937, 0.7937, 0.7937);

    auto l1 = light{{20,  20,  20},
                    {500, 500, 500}};
    auto l2 = light{{-20, 20,  0},
                    {500, 500, 500}};

    std::vector<light> lights = {l1, l2};
    Eigen::Vector3f amb_light_intensity{10, 10, 10};
    Eigen::Vector3f eye_pos{0, 0, 10};

    float p = 150;

    Eigen::Vector3f color = payload.color;
    Eigen::Vector3f point = payload.view_pos;
    Eigen::Vector3f normal = payload.normal;

    float kh = 0.2, kn = 0.1;

    // TODO: Implement displacement mapping here
    // Let n = normal = (x, y, z)
    // Vector t = (x*y/sqrt(x*x+z*z),sqrt(x*x+z*z),z*y/sqrt(x*x+z*z))
    // Vector b = n cross product t
    // Matrix TBN = [t b n]
    // dU = kh * kn * (h(u+1/w,v)-h(u,v))
    // dV = kh * kn * (h(u,v+1/h)-h(u,v))
    // Vector ln = (-dU, -dV, 1)
    // Position p = p + kn * n * h(u,v)
    // Normal n = normalize(TBN * ln)


    float x = normal.x();
    float y = normal.y();
    float z = normal.z();
    Eigen::Vector3f t{ x*y / std::sqrt(x*x + z * z), std::sqrt(x*x + z * z), z*y / std::sqrt(x*x + z * z) };
    Eigen::Vector3f b = normal.cross(t);
    Eigen::Matrix3f TBN;
    TBN << t.x(), b.x(), normal.x(),
            t.y(), b.y(), normal.y(),
            t.z(), b.z(), normal.z();

    float u = payload.tex_coords.x();
    float v = payload.tex_coords.y();
    float w = payload.texture->width;
    float h = payload.texture->height;


    float dU = kh * kn * (payload.texture->getColor(u + 1.0f / w, v).norm() - payload.texture->getColor(u , v).norm());
    float dV = kh * kn * (payload.texture->getColor(u, v + 1.0f / h).norm() - payload.texture->getColor(u , v).norm());

    Eigen::Vector3f ln{ -dU,-dV,1.0f };

    point += (kn * normal * payload.texture->getColor(u , v).norm());

    normal = TBN * ln;
    normal = normal.normalized();

    Eigen::Vector3f result_color = {0, 0, 0};

    for (auto& light : lights)
    {
        // TODO: For each light source in the code, calculate what the *ambient*, *diffuse*, and *specular*
        // components are. Then, accumulate that result on the *result_color* object.
        Eigen::Vector3f light_dir = light.position - point;
        Eigen::Vector3f view_dir = eye_pos - point;
        float r = light_dir.dot(light_dir);

        // ambient
        Eigen::Vector3f La = ka.cwiseProduct(amb_light_intensity);
        // diffuse
        Eigen::Vector3f Ld = kd.cwiseProduct(light.intensity / r);
        Ld *= std::max(0.0f, normal.dot(light_dir.normalized()));
        // specular
        Eigen::Vector3f h = (light_dir + view_dir).normalized();
        Eigen::Vector3f Ls = ks.cwiseProduct(light.intensity / r);
        Ls *= std::pow(std::max(0.0f, normal.dot(h)), p);

        result_color += (La + Ld + Ls);

    }

    return result_color * 255.f;
}