CG基础学习笔记(Lecture5以及对作业1的理解)

视口变换

作业1 基础版

模型变换：get_model_matrix(float rotation_angle)

//视图转换
Eigen::Matrix4f get_view_matrix(Eigen::Vector3f eye_pos)
{
    // 定义 4 * 4 的单位矩阵
    Eigen::Matrix4f view = Eigen::Matrix4f::Identity();

    Eigen::Matrix4f translate;
    // 初始化视角变换矩阵
    translate << 1, 0, 0, -eye_pos[0], 
                 0, 1, 0, -eye_pos[1], 
                 0, 0, 1,-eye_pos[2], 
                 0, 0, 0, 1;

    view = translate * view;

    return view;
}

透视投影变换矩阵

1 .将视锥压缩成正交投影变换矩阵可处理的形式

2 .正交投影

// 绕 z 轴旋转的变换矩阵
Eigen::Matrix4f get_model_matrix(float rotation_angle)
{
    // 初始化一个单位矩阵model
    Eigen::Matrix4f model = Eigen::Matrix4f::Identity();
    // TODO: Implement this function
    // Create the model matrix for rotating the triangle around the Z axis.
    // Then return it.
    // --------------------
    float r = rotation_angle * MY_PI / 180; //转化为弧度
    Eigen::Matrix4f rotation;

    // 围绕z轴进行旋转
    rotation << cos(rotation_angle), -sin(rotation_angle), 0, 0,
        sin(rotation_angle), cos(rotation_angle), 0, 0,
        0, 0, 1, 0,
        0, 0, 0, 1;

    model *= rotation;

    // --------------------
    return model;
   
}

//eye_fov:纵向视野(度), aspect_ratio:宽高比
Eigen::Matrix4f get_projection_matrix(float eye_fov, float aspect_ratio,
    float zNear, float zFar)
{

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

    // TODO: Implement this function
    // Create the projection matrix for the given parameters.
    // Then return it.
    Eigen::Matrix4f M_perspToOrtho(4, 4);
    Eigen::Matrix4f M_ortho_scale(4, 4);
    Eigen::Matrix4f M_ortho_trans(4, 4);

    float half_angle = eye_fov * MY_PI / 360.0; // 纵向视野的一半,eye_fov*MY_PI/2 / 180.0
    float top = zNear * tan(half_angle);
    float bottom = -top;
    float right = top * aspect_ratio;
    float left = -right;
    
    M_ortho_trans << 1, 0, 0, -(right + left) / 2,
        0, 1, 0, -(top + bottom) / 2,
        0, 0, 1, -(zNear + zFar) / 2,
        0, 0, 0, 1;
    M_ortho_scale << 2 / (right - left), 0, 0, 0,
        0, 2 / (top - bottom), 0, 0,
        0, 0, 2 / (zNear - zFar), 0,
        0, 0, 0, 1;
    M_perspToOrtho << zNear, 0, 0, 0,
        0, zNear, 0, 0,
        0, 0, zNear + zFar, -zNear * zFar,
        0, 0, 1, 0;
                    
    Eigen::Matrix4f M_ortho = M_ortho_scale *M_ortho_trans;

    projection = M_ortho * M_perspToOrtho;

    return projection;
}

效果(测试数据改了改)