I am following the tutorials at LearnOpenGL.com and I am confused about the order of Matrices.
The Transformations chapter tells:
Matrix multiplication is not commutative, which means their order is important. When multiplying matrices the right-most matrix is first multiplied with the vector so you should read the multiplications from right to left. It is advised to first do scaling operations, then rotations and lastly translations when combining matrices otherwise they might (negatively) affect each other. For example, if you would first do a translation and then scale, the translation vector would also scale!
So If I am not wrong, the order is Translate * Rotate * Scale * vector_to_transform.
But immediately in the next Chapter, when calculating the LookAt matrix, the multiplication order is flipped. Here is the code snippet from the website:
// Custom implementation of the LookAt function
glm::mat4 calculate_lookAt_matrix(glm::vec3 position, glm::vec3 target, glm::vec3 worldUp)
{
// 1. Position = known
// 2. Calculate cameraDirection
glm::vec3 zaxis = glm::normalize(position - target);
// 3. Get positive right axis vector
glm::vec3 xaxis = glm::normalize(glm::cross(glm::normalize(worldUp), zaxis));
// 4. Calculate camera up vector
glm::vec3 yaxis = glm::cross(zaxis, xaxis);
// Create translation and rotation matrix
// In glm we access elements as mat[col][row] due to column-major layout
glm::mat4 translation = glm::mat4(1.0f); // Identity matrix by default
translation[3][0] = -position.x; // Third column, first row
translation[3][1] = -position.y;
translation[3][2] = -position.z;
glm::mat4 rotation = glm::mat4(1.0f);
rotation[0][0] = xaxis.x; // First column, first row
rotation[1][0] = xaxis.y;
rotation[2][0] = xaxis.z;
rotation[0][1] = yaxis.x; // First column, second row
rotation[1][1] = yaxis.y;
rotation[2][1] = yaxis.z;
rotation[0][2] = zaxis.x; // First column, third row
rotation[1][2] = zaxis.y;
rotation[2][2] = zaxis.z;
// Return lookAt matrix as combination of translation and rotation matrix
return rotation * translation; // Remember to read from right to left (first translation then rotation)
}
At the end of the code snippet, the matrix is calculated as rotation * translation, even though the matrix is going to be multiplied as,
gl_position = projection * lookAt * model * vec4(vertexPosition, 1.0);
as Column-major matrices must be pre-multiplied to the vector.
Please help me understand this.
rotation * translation. But it always depends on how you derive the formula. You can also usetranslation * rotationif you calculate the translation a bit differently. - Nico SchertlerCombining Matricessection of Transformations chapter. - Vignesh Gunasekaran