Course Knowledge

• Review Materials
  Lecture4, Lecture5
• MVP Transformation
  Model, View, Projection
  M: Positioning, like where a person stands when taking a photo
  V: Camera angle selection
  P: Capture operation
• Homework Key Points
  Mpersp = Mortho · Mpersp→ortho
  Perspective projection matrix = Orthographic projection matrix multiplied by Perspective-to-Orthographic matrix
  Timestamp: Lecture4 1:14:00
• FOV (field of view)
  Field of view angle, using aspect ratio = r/t and tan(fov/2) = t/|n|, along with near and far plane values to calculate other parameters
  Timestamp: Lecture5 12:00
• Additional Topics
  Lecture4: Rotation around an axis (10:20)

Experiences and Insights

• Attempted to configure the Windows development environment, referenced (Zhihu) GAMES101 course enviroment setup (Win10 + VSCode)
  (CSDN) games101 [Homework 0] Environment Configuration - Windows Environment Setup
  Bilibili (GAMES101 - Windows Homework Environment Configuration VSCode + CMake + MinGW)
  Nearly succeeded but encountered issues with Eigen header file paths. After spending too much time debugging, decided to abandon this approach.
• Resolved the missing compiler issue when configuring CMake on Windows. After clicking configuration, selected the native option, set C compiler to mingw64/bin/gcc.exe, C++ compiler to mingw64/bin/g++.exe, left Fortran unselected. After errors apeared, clicked Add entry and selected the corresponding files. For details, search on Baidu.
• Minor issues during homework implemantation such as extra or missing matrix elements, incorrect matrix memory, and missing the provided MY_PI condition consumed significant time. The final result generated a rotating triangle, but it didn't meet the requirements in the assignment documentation regarding the make -r 20 command. The exact reason remains unclear.

Eigen::Matrix4f get_model_matrix(float rotation_angle)
{
    Eigen::Matrix4f transformation = Eigen::Matrix4f::Identity();

    // TODO: Implement this function
    // Create the model matrix for rotating the triangle around the Z axis.
    // Then return it.

    //my code start
    float rad = rotation_angle / 180.0f * MY_PI;
    transformation << cos(rad), -sin(rad), 0, 0,  // Z-axis rotation formula
                     sin(rad),  cos(rad), 0, 0,
                     0,        0,       1, 0,
                     0,        0,       0, 1;
    //end   
    
    return transformation;
}

Eigen::Matrix4f get_projection_matrix(float eye_fov, float aspect_ratio,
                                      float z_near, float z_far)
{
    // Students will implement this function

    Eigen::Matrix4f proj = Eigen::Matrix4f::Identity();

    // TODO: Implement this function
    // Create the projection matrix for the given parameters.
    // Then return it.
    
    //my code
    Eigen::Matrix4f translate_mat = Eigen::Matrix4f::Identity();  // translation matrix
    Eigen::Matrix4f scale_mat = Eigen::Matrix4f::Identity();      // scaling matrix
    Eigen::Matrix4f ortho_mat = Eigen::Matrix4f::Identity();      // orthographic projection
    Eigen::Matrix4f persp_to_ortho = Eigen::Matrix4f::Identity(); // perspective to orthographic
    
    float right, left, top, bottom;  // right, left, top, bottom bounds
    float half_rad = eye_fov / 2.0f / 180.0f * MY_PI;  // half field of view in radians
    top = std::tan(half_rad) * z_near;
    right = aspect_ratio * top;
    left = -right;
    bottom = -top;
    
    translate_mat << 1, 0, 0, -(right + left) / 2,
                     0, 1, 0, -(top + bottom) / 2,
                     0, 0, 1, -(z_near + z_far) / 2,
                     0, 0, 0, 1;  // translation to origin
    
    scale_mat << 2 / (right - left), 0, 0, 0,
                 0, 2 / (top - bottom), 0, 0,
                 0, 0, 2 / (z_near - z_far), 0,
                 0, 0, 0, 1;    // uniform scaling
    
    ortho_mat = scale_mat * translate_mat;        
    persp_to_ortho << z_near, 0, 0, 0,
                      0, z_near, 0, 0,
                      0, 0, z_near + z_far, -z_near * z_far,
                      0, 0, 1, 0;
    proj = ortho_mat * persp_to_ortho;
    //end
    return proj;
}