Modern OpenGL

OpenGL/GLM Transformation (Column-Major Order)

glm::mat4 A(1.0f, 0.0f, 0.0f, 0.0f, // column1
0.0f, 2.0f, 0.0f, 0.0f, // column2
0.0f, 0.0f, 4.0f, 0.0f, // column3
1.0f, 2.0f, 3.0f, 1.0f); // column4
// A =
// 1 0 0 1
// 0 2 0 2
// 0 0 4 3
// 0 0 0 1


glm::mat4 B(1.0f, 0.0f, 0.0f, 0.0f, // column1
0.0f, 1.0f, 0.0f, 0.0f, // column2
0.0f, 0.0f, 1.0f, 0.0f, // column3
2.0f, 2.0f, 2.0f, 1.0f); // column4
// B =
// 1 0 0 2
// 0 1 0 2
// 0 0 1 2
// 0 0 0 1


glm::mat4 C = A*B;
// C = A*B =
// 1 0 0 3
// 0 2 0 6
// 0 0 4 11
// 0 0 0 1


glm::mat4 D = B*A;
// D = B*A =
// 1 0 0 3
// 0 2 0 4
// 0 0 4 5
// 0 0 0 1


glm::mat4 E = glm::inverse(A); // inverse
// E = inverse(A) =
// 1 0 0 -1
// 0 0.5 0 -1
// 0 0 0.25 -0.75
// 0 0 0 1


glm::mat4 I = A * E; // I = A * A-1
// I = A*E =
// 1 0 0 0
// 0 1 0 0
// 0 0 1 0
// 0 0 0 1


// p’ = M * p (OpenGL/GLM uses Column-Major Order)
glm::vec4 p = glm::vec4(1.0f, 0.0f, 0.0f, 1.0f);
// p = (1, 0, 0)

glm::vec4 q = A * p;
// q = A * p = (2, 2, 3)

glm::vec4 r = B * p;
// r = B * p = (3, 2, 2)

glm::vec4 s = C * p;
// s = A * B * p = (4, 6, 11)

glm::vec4 t = D * p;
// t = B * A * p = (4, 4, 5)


glm::mat4 Tx,Ty,Tz;
Tx = glm::translate(glm::mat4(1.0f), glm::vec3(2.0f, 0.0f, 0.0f)); // RHS x+ right
Ty = glm::translate(glm::mat4(1.0f), glm::vec3(0.0f, 2.0f, 0.0f)); // RHS y+ up
Tz = glm::translate(glm::mat4(1.0f), glm::vec3(0.0f, 0.0f, 2.0f)); // RHS z+ front
// Tx =
// 1 0 0 2
// 0 1 0 0
// 0 0 1 0
// 0 0 0 1


glm::mat4 Rx,Ry,Rz,Ra;
Rx = glm::rotate(glm::mat4(1.0f), 30.0f, glm::vec3(1.0f, 0.0f, 0.0f)); // RHS x+ (Y->Z rotation) OpenGL uses DEGREE angle
Ry = glm::rotate(glm::mat4(1.0f), 60.0f, glm::vec3(0.0f, 1.0f, 0.0f)); // RHS y+ (Z->X rotation)
Rz = glm::rotate(glm::mat4(1.0f), 45.0f, glm::vec3(0.0f, 0.0f, 1.0f)); // RHS z+ (X->Y rotation)
Ra = glm::rotate(glm::mat4(1.0f), 45.0f, glm::vec3(1.0f, 1.0f, 1.0f)); // RHS (arbitrary axis)
// Rx =
// 1 0 0 0
// 0 0.999958 -0.0091384 0
// 0 0.0091384 0.999958 0
// 0 0 0 1


// Ry =
// 0.999833 0 0.018276 0
// 0 1 0 0
// -0.018276 0 0.999833 0
// 0 0 0 1


// Rz =
// 0.999906 -0.0137074 0 0
// 0.0137074 0.999906 0 0
// 0 0 1 0
// 0 0 0 1


// Ra =
// 0.999937 -0.00788263 0.00794526 0
// 0.00794526 0.999937 -0.00788263 0
// -0.00788263 0.00794526 0.999937 0
// 0 0 0 1


glm::mat4 Sx,Sy,Sz;
Sx = glm::scale(glm::mat4(1.0f), glm::vec3(2, 1, 1)); // RHS
Sy = glm::scale(glm::mat4(1.0f), glm::vec3(1, 2, 1)); // RHS
Sz = glm::scale(glm::mat4(1.0f), glm::vec3(1, 1, 2)); // RHS
// Sy =
// 1 0 0 0
// 0 2 0 0
// 0 0 1 0
// 0 0 0 1


// p’ = M3 * M2 * M1 * p (OpenGL uses Column-Major Order)
glm::mat4 TR = Tx * Rz; // Rotate Z, and then Translate X
glm::mat4 RT = Rz * Tx; // Translate X, and then Rotate Z
glm::mat4 TRS = Tx * Rz * Sy; // Scale Y, and then Rotate Z, and then Translate X
glm::mat4 SRT = Sy * Rz * Tx; // Translate X, and then Rotate Z, and then Scale Y
// Tx*Rz =
// 0.707107 -0.707107 0 2
// 0.707107 0.707107 0 0
// 0 0 1 0
// 0 0 0 1


// Rz*Tx =
// 0.707107 -0.707107 0 1.41421
// 0.707107 0.707107 0 1.41421
// 0 0 1 0
// 0 0 0 1


// Tx*Rz*Sy =
// 0.707107 -1.41421 0 2
// 0.707107 1.41421 0 0
// 0 0 1 0
// 0 0 0 1


// Sy*Rz*Tx =
// 0.707107 -0.707107 0 1.41421
// 1.41421 1.41421 0 2.82843
// 0 0 1 0
// 0 0 0 1