games101_Homework3

在Raster部分实现数值插值，然后实现四种不同的像素着色器

作业描述：

作业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。

在rasterize_triangle函数中重复上次的包围盒进行点采样，在深度测试通过之后分别对法向量、颜色、纹理颜色、视图空间坐标做插值，然后通过shader计算出像素颜色后设定其值。

//Screen space rasterization
void rst::rasterizer::rasterize_triangle(const Triangle& t, const std::array<Eigen::Vector3f, 3>& view_pos)     //t为经mvp变换后的顶点坐标，view_pos为mv变换后顶点在视图空间中的位置
{
    // TODO: From your Homework3, get the triangle rasterization code.  
    auto v = t.toVector4();    // t.to is array<Vector4f, 3>，为三角形三个顶点坐标的齐次坐标表达

    // Find out the bounding box of current triangle.
    float min_x, max_x, min_y, max_y;
    min_x = std::min(v[0].x(), std::min(v[1].x(), v[2].x()));
    max_x = std::max(v[0].x(), std::max(v[1].x(), v[2].x()));
    min_y = std::min(v[0].y(), std::min(v[1].y(), v[2].y()));
    max_y = std::max(v[0].y(), std::max(v[1].y(), v[2].y()));

    // iterate through the pixel and find if the current pixel is inside the triangle
    for(int x = min_x; x < max_x; ++x){
        for(int y = min_y; y < max_y; ++y){
            if(insideTriangle((float)x + 0.5, (float)y + 0.5, t.v)){
                // If so, use the following code to get the interpolated z value.
                // TODO: 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 
                auto[alpha, beta, gamma] = computeBarycentric2D(x, y, t.v);                 //计算(x,y)点的重心坐标
                float Z = 1.0 / (alpha / v[0].w() + beta / v[1].w() + gamma / v[2].w());    //Z是当前像素的视图空间深度(插值)，v[i].w()是顶点的视图空间深度值
                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;    //zp是nf之间的深度

                if(zp < depth_buf[get_index(x, y)]){
                    // set the z_buffer
                    depth_buf[get_index(x, y)] = zp;

                    // TODO: Interpolate the attributes:
                    // auto interpolated_color
                    // auto interpolated_normal
                    // auto interpolated_texcoords
                    // auto interpolated_shadingcoords  //着色点在
                    
                    // 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);
                    // 调用准备好的interpolate()函数获取这些属性的插值
                    auto interpolated_color = interpolate(alpha, beta, gamma, t.color[0], t.color[1], t.color[2], 1);                           //颜色
                    auto interpolated_normal = interpolate(alpha, beta, gamma, t.normal[0], t.normal[1], t.normal[2], 1);                       //法向量
                    auto interpolated_texcoords = interpolate(alpha, beta, gamma, t.tex_coords[0], t.tex_coords[1], t.tex_coords[2], 1);        //纹理坐标
                    auto interpolated_shadingcoords = interpolate(alpha, beta, gamma, view_pos[0], view_pos[1], view_pos[2], 1);                //着色点在mv变换后可视空间的真实坐标
                    fragment_shader_payload payload(interpolated_color, interpolated_normal.normalized(), interpolated_texcoords, texture ? &*texture : nullptr);
                    payload.view_pos = interpolated_shadingcoords;
                    auto pixel_color = fragment_shader(payload);    //调用我们设置的fragment_shader进行点的像素的着色

                    set_pixel(Vector2i(x, y), pixel_color);     //调用写好的set_pixel函数写入framebuffer
                }
            }
        }
    }
}

注：本次作业的insideTriangle依然需要修改传入接口为 static bool insideTriangle(float x, float y, const Vector4f* _v)

作业2：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);
    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;

    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.
        
        // L = (Ka * Ia) + (Kd * I/r^2 * max(0, n·l)) + (Ks * (I / r^2) * max(0, n · h)^p)
        // 光照方向
        Eigen::Vector3f light_direc = (light.position - point).normalized();
        // 视线方向
        Eigen::Vector3f eye_direc = (eye_pos - point).normalized();
        // 半程向量
        Eigen::Vector3f half_vector = (light_direc + eye_direc).normalized();
        // 距离的平方
        float R2 = (light.position - point).squaredNorm();

        // 环境光
        auto ambient = ka.cwiseProduct(amb_light_intensity);
        // 漫反射
        auto diffuse = kd.cwiseProduct(light.intensity / R2) * std::max(0.0f, normal.dot(light_direc)) ;
        // 高光
        auto specular = ks.cwiseProduct(light.intensity / R2) * std::pow(std::max(0.0f, normal.dot(half_vector)), p);

        result_color += (ambient + diffuse + specular);
    }

    return result_color * 255.f;
}

作业3：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)
    {
        // TODO: Get the texture value at the texture coordinates of the current fragment
        return_color = payload.texture->getColor(payload.tex_coords[0], payload.tex_coords[1]);
    }
    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)
    {
        // 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.
        
        // L = (Ka * Ia) + (Kd * I/r^2 * max(0, n·l)) + (Ks * (I / r^2) * max(0, n · h)^p)
        // 光照方向
        Eigen::Vector3f light_direc = (light.position - point).normalized();
        // 视线方向
        Eigen::Vector3f eye_direc = (eye_pos - point).normalized();
        // 半程向量
        Eigen::Vector3f half_vector = (light_direc + eye_direc).normalized();
        // 距离的平方
        float R2 = (light.position - point).squaredNorm();

        // 环境光
        auto ambient = ka.cwiseProduct(amb_light_intensity);
        // 漫反射
        auto diffuse = kd.cwiseProduct(light.intensity / R2) * std::max(0.0f, normal.dot(light_direc)) ;
        // 高光
        auto specular = ks.cwiseProduct(light.intensity / R2) * std::pow(std::max(0.0f, normal.dot(half_vector)), p);

        result_color += (ambient + diffuse + specular);
    }

    return result_color * 255.f;
}

作业4：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，将新的法线设置为颜色值。

Eigen::Vector3f bump_fragment_shader(const fragment_shader_payload& payload)    //凹凸贴图
{
    
    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 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     //叉积
    // 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)
    
    auto n = normal;
    auto x = n.x();
    auto y = n.y();
    auto z = n.z();
    Vector3f t(x*y/sqrt(x*x+z*z),sqrt(x*x+z*z),z*y/sqrt(x*x+z*z));
    Vector3f b = n.cross(t);
    auto u = payload.tex_coords.x();        //在切线空间中的x坐标
    auto v = payload.tex_coords.y();        //在切线空间中的y坐标

    Matrix3f TBN;
    TBN << t.x(), t.y(), t.z(),
           b.x(), b.y(), b.z(),
           n.x(), n.y(), n.z();
    // 纹理实际宽度
    auto w = payload.texture->width;
    // 纹理实际高度
    auto h = payload.texture->height;
    // U、V方向的切线(导数)
    auto dU = kh * kn * (payload.texture->getColor(u + 1.0f / w, v).norm() - payload.texture->getColor(u,v).norm());
    auto dV = kh * kn * (payload.texture->getColor(u, v + 1.0f / h).norm() - payload.texture->getColor(u,v).norm());
    // 当前点的法向量
    Vector3f ln(-dU, -dV, 1);

    //使用tbn矩阵将法线变换到世界空间中
    normal = (TBN * ln).normalized();   //

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

    return result_color * 255.f;
}

作业5：修改函数 displacement_fragment_shader() in main.cpp: 在实现 Bump mapping 的基础上，实现 displacement mapping.。将实际改变点的位置。

Eigen::Vector3f displacement_fragment_shader(const fragment_shader_payload& payload)    //位移贴图像素着色
{
    
    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)

    auto n = normal;
    auto x = n.x();
    auto y = n.y();
    auto z = n.z();
    Vector3f t(x*y/sqrt(x*x+z*z),sqrt(x*x+z*z),z*y/sqrt(x*x+z*z));
    Vector3f b = n.cross(t);
    auto u = payload.tex_coords.x();        //在切线空间中的x坐标
    auto v = payload.tex_coords.y();        //在切线空间中的y坐标
    Matrix3f TBN;
    TBN << t.x(), t.y(), t.z(),
           b.x(), b.y(), b.z(),
           n.x(), n.y(), n.z();
    auto w = payload.texture->width;
    auto h = payload.texture->height;
    auto dU = kh * kn * (payload.texture->getColor(u + 1.0f / w, v).norm() - payload.texture->getColor(u,v).norm());
    auto dV = kh * kn * (payload.texture->getColor(u, v + 1.0f / h).norm() - payload.texture->getColor(u,v).norm());
    Vector3f ln(-dU, -dV, 1);

    // 计算当前点新的位置,产生位移
    point += (kn * normal * payload.texture->getColor(u, v).norm());
    // 计算新的法线
    normal = (TBN * ln).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.
        
        // L = (Ka * Ia) + (Kd * I/r^2 * max(0, n·l)) + (Ks * (I / r^2) * max(0, n · h)^p)
        // 光照方向
        Eigen::Vector3f light_direc = (light.position - point).normalized();
        // 视线方向
        Eigen::Vector3f eye_direc = (eye_pos - point).normalized();
        // 半程向量
        Eigen::Vector3f half_vector = (light_direc + eye_direc).normalized();
        // 距离的平方
        float R2 = (light.position - point).squaredNorm();

        // 环境光
        auto ambient = ka.cwiseProduct(amb_light_intensity);
        // 漫反射
        auto diffuse = kd.cwiseProduct(light.intensity / R2) * std::max(0.0f, normal.dot(light_direc)) ;
        // 高光
        auto specular = ks.cwiseProduct(light.intensity / R2) * std::pow(std::max(0.0f, normal.dot(half_vector)), p);

        result_color += (ambient + diffuse + specular);
    }

    return result_color * 255.f;
}