GAMES101 作业 01：旋转与投影

作业 01 的实现代码：Assignment01

1. get_model_matrix

Eigen::Matrix4f get_model_matrix(float rotation_angle)
{
    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 radian = rotation_angle * MY_PI / 180.0;
    model <<
        cos(radian), -sin(radian), 0.0, 0.0,
        sin(radian), cos(radian), 0.0, 0.0,
        0.0, 0.0, 1.0, 0.0,
        0.0, 0.0, 0.0, 1.0;

    return model;
}

2. get_projection_matrix

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

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

    // TODO: Implement this function
    // Create the projection matrix for the given parameters.
    // Then return it.

    // 构造透视投影到正交投影矩阵
    Eigen::Matrix4f persp2ortho = Eigen::Matrix4f::Identity();
    persp2ortho <<
        zNear, 0.0, 0.0, 0.0,
        0.0, zNear, 0.0, 0.0,
        0.0, 0.0, zNear+zFar, -1.0 * zNear * zFar,
        0.0, 0.0, 1.0, 0.0;

    // 求出 frustum 的顶、底、左、右
    float top = zNear * tan(eye_fov / 2 * MY_PI / 180.0);
    float botton = -1.0 * top;
    float right = aspect_ratio * top;
    float left = -1.0 * right;

    // 构造缩放 frustum 成为 2 * 2 * 2 的 cuboid 的矩阵
    Eigen::Matrix4f ortho1 = Eigen::Matrix4f::Identity();
    ortho1 <<
        2.0 / (right - left), 0.0, 0.0, 0.0,
        0.0, 2.0 / (top - botton), 0.0, 0.0,
        0.0, 0.0, 2.0 / (zNear - zFar), 0.0,
        0.0, 0.0, 0.0, 1.0;

    // 构造平移 cuboid 的矩阵
    Eigen::Matrix4f ortho2 = Eigen::Matrix4f::Identity();
    ortho2 <<
        1.0, 0.0, 0.0, -1.0 * (left + right) / 2.0,
        0.0, 1.0, 0.0, -1.0 * (top + right) / 2.0,
        0.0, 0.0, 1.0, -1.0 * (zNear + zFar) / 2.0,
        0.0, 0.0, 0.0, 1.0;

    projection = ortho2 * ortho1 * persp2ortho;
    return projection;
}

3. get_rotation

Eigen::Matrix4f get_rotation(Vector3f axis, float angle) {
    float radian = angle * MY_PI / 180.0;
    Eigen::Matrix3f model1 = Eigen::Matrix3f::Identity();
    model1 = cos(radian) * model1;

    Eigen::Matrix3f model2 = Eigen::Matrix3f::Identity();
    model2 = (1 - cos(radian)) * axis * axis.transpose();

    Eigen::Matrix3f model3 = Eigen::Matrix3f::Identity();
    model3 <<
        0.0, -axis[2], axis[1],
        axis[2], 0.0, -axis[0],
        -axis[1], axis[0], 0.0;
    model3 = sin(radian) * model3;

    model3 = model1 + model2 + model3;

    Eigen::Matrix4f model = Eigen::Matrix4f::Identity();
    model <<
        model3(0, 0), model3(0, 1), model3(0, 2), 0.0,
        model3(1, 0), model3(1, 1), model3(1, 2), 0.0,
        model3(2, 0), model3(2, 1), model3(2, 2), 0.0,
        0.0, 0.0, 0.0, 1.0;
    return model;
}

4. 运行结果