# Vector/Matrix/Plane

Vector/Matrix/Plane Test

glmVectorMatrix.zip

void mprint(glm::mat4 Mat)
{
printf(“\n %f %f %f %f
\n %f %f %f %f
\n %f %f %f %f
\n %f %f %f %f\n\n”,

Mat[0][0], Mat[1][0], Mat[2][0], Mat[3][0],
Mat[0][1], Mat[1][1], Mat[2][1], Mat[3][1],
Mat[0][2], Mat[1][2], Mat[2][2], Mat[3][2],
Mat[0][3], Mat[1][3], Mat[2][3], Mat[3][3]);
}

float theta(const glm::vec3 &v1,  const glm::vec3 &v2)
{
float len1 = (float)sqrtf(v1[0]*v1[0] + v1[1]*v1[1] + v1[2]*v1[2]);
float len2 = (float)sqrtf(v2[0]*v2[0] + v2[1]*v2[1] + v2[2]*v2[2]);
return (float)acosf(dot(v1, v2)/len1*len2);
}

glm::vec3 computeNormal(glm::vec3& a, glm::vec3& b, glm::vec3& c)
{
glm::vec3 normal = glm::normalize(glm::cross(c – a, b – a));
return normal;
}

void vec3Test()
{
const float v[3] = { 1.0f, 2.0f, 3.0f };
vec3 a(0.0f, 0.0f, 0.0f), b(1.0f, 2.0f, 3.0f), c(b);
vec3 d = c;
vec3 e = c;
vec3 f = a;
cout << “a = ” << a[0] << ” ” << a[1] << ” ” << a[2] << endl;
cout << “b = ” << b[0] << ” ” << b[1] << ” ” << b[2] << endl;
cout << “c = ” << c[0] << ” ” << c[1] << ” ” << c[2] << endl;
cout << “d = ” << d[0] << ” ” << d[1] << ” ” << d[2] << endl;
cout << “e = ” << e[0] << ” ” << e[1] << ” ” << e[2] << endl;
a[0] = 4;
a[1] = 5;
a[2] = 6;
cout << “after assignments, a (4,5,6) ” << endl;
cout << “a = ” << a[0] << ” ” << a[1] << ” ” << a[2] << endl;
cout << “b = ” << b[0] << ” ” << b[1] << ” ” << b[2] << endl;

cout << “Unary Operation” << endl;
a += b;
cout << “a += b  ” << endl;
cout << “a = ” << a[0] << ” ” << a[1] << ”  ” << a[2] << endl;
a -= b;
cout << “a -= b  ” << endl;
cout << “a = ” << a[0] << ” ” << a[1] << ” ” << a[2] << endl;
a *= 1.5;
cout << “a *= 1.5  ” << endl;
cout << “a = ” << a[0] << ” ” << a[1] << ” ” << a[2] << endl;
a /= 1.5;
cout << “a /= 1.5  ” << endl;
cout << “a = ” << a[0] << ” ” << a[1] << ” ” << a[2] << endl;

cout << “Binary Operation” << endl;
c = a + b;
cout << “c = a + b  ->  c ” << endl;
cout << “c = ” << c[0] << ” ” << c[1] << ” ” << c[2] << endl;
c = a – b;
cout << “c = a – b  ->  c ” << endl;
cout << “c = ” << c[0] << ” ” << c[1] << ” ” << c[2] << endl;

cout << “a == b” << endl;
if (a == b)
cout << ” is true” << endl;
else
cout << ” is false” << endl;

cout << “b == d” << endl;
if (b == d)
cout << ” is true” << endl;
else
cout << ” is false” << endl;

// magnitude
cout << “a = ” << a[0] << ” ” << a[1] << ” ” << a[2] << endl;
cout << “b = ” << b[0] << ” ” << b[1] << ” ” << b[2] << endl;
cout << “a magnitude = ” << (float)sqrt(a[0]*a[0] + a[1]*a[1] + a[2]*a[2]) << endl;

cout << “b magnitude = ” << (float)sqrt(b[0]*b[0] + b[1]*b[1] +
b[2]*b[2]) << endl;

// normalize
c = normalize(a);
cout << “c = normalize(a) = ” << c[0] << ” ” << c[1] << ” ” << c[2] << endl;
cout << “c magnitude = ” << (float)sqrt(c[0]*c[0] + c[1]*c[1] + c[2]*c[2]) << endl;
d = normalize(b);
cout << “d = normalize(b) = ” << d[0] << ” ” << d[1] << ” ” << d[2] << endl;
cout << “d magnitude = ” << (float)sqrt(d[0]*d[0] + d[1]*d[1] + d[2]*d[2]) << endl;

// dot product, theta, cross product, compute normal
cout << “dot(a, b) = ” << dot(a, b) << endl;
cout << “a,b angle = ” << degrees(theta(a, b)) << endl;
e = cross(a, b);
cout << “e = cross(a, b) = ” << e[0] << ” ” << e[1] << ” ” << e[2] << endl;
f = cross(vec3(1.0f, 3.0f, -4.0f), vec3(2.0f, -5.0f, 8.0f));
cout << “(1, 3, -4) x (2, -5, 8) = ” << f[0] << ” ” << f[1] << ” ” << f[2] << endl;

glm::vec3 g = computeNormal(glm::vec3(1.0f, 0.0f, 0.0f),
glm::vec3(1.0f, 1.0f, 0.0f), glm::vec3(1.0f, 2.0f, 3.0f));
cout << “g = ” << g[0] << ” ” << g[1] << ” ” << g[2] << endl;
}

void mat4Test()
{
// matrix test
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
cout << “A = ”   << endl;
mprint(A);

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
cout << “B = ”               << endl;
mprint(B);

glm::mat4 C = A * B; // multiplication
cout << “C = A*B = ”         << endl;
mprint(C);

glm::mat4 D = B * A; // multiplication
cout << “D = B*A = ”         << endl;
mprint(D);

glm::mat4 E = glm::inverse(A);
// inverse
cout << “E = inverse(A) = ”  << endl;
mprint(E);

glm::mat4 I = A * E;   // multiplication
cout << “I = A*E = ”         << endl;
mprint(I);

glm::vec4 p = glm::vec4(1.0f, 0.0f, 0.0f, 1.0f);
glm::vec4 q = A * p;
glm::vec4 r = B * p;
glm::vec4 s = C * p;
glm::vec4 t = D * p;
cout << “q = A*p = ”   << endl;
printf(“(1, 0, 0, 1) => (%f, %f, %f, %f)\n”, q[0], q[1], q[2], q[3]);
cout << “r = B*p = ”   << endl;
printf(“(1, 0, 0, 1) => (%f, %f, %f, %f)\n”, r[0], r[1], r[2], r[3]);
cout << “s = A*B*p = ”  << endl;
printf(“(1, 0, 0, 1) => (%f, %f, %f, %f)\n”, s[0], s[1], s[2], s[3]);
cout << “t = B*A*p = ”         << endl;
printf(“(1, 0, 0, 1) => (%f, %f, %f, %f)\n”, t[0], t[1], t[2], t[3]);

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
printf(“Tx\n”);
mprint(Tx);

glm::vec4 Position = glm::vec4(1.0f, 0.0f, 0.0f, 1.0f);
glm::vec4 tV = Tx * Position;
printf(“(1, 0, 0, 1) => (%f, %f, %f, %f)\n”, tV[0], tV[1], tV[2], tV[3]);

glm::mat4 Rx, Ry, Rz, Ra;
Rx = glm::rotate(glm::mat4(1.0f), 30.0f, glm::vec3(1.0f, 0.0f, 0.0f));
Ry = glm::rotate(glm::mat4(1.0f), 60.0f, glm::vec3(0.0f, 1.0f, 0.0f));
Rz = glm::rotate(glm::mat4(1.0f), 45.0f, glm::vec3(0.0f, 0.0f, 1.0f));
Ra = glm::rotate(glm::mat4(1.0f), 45.0f, glm::vec3(1.0f, 1.0f, 1.0f));
printf(“R\n”);
mprint(Rx);
mprint(Ry);
mprint(Rz);
mprint(Ra);

glm::vec4 tV1 = Ra * Position;
printf(“Ra * Position(1, 0, 0, 1) => (%f, %f, %f, %f)\n”, tV1[0], tV1[1], tV1[2], tV1[3]);

glm::mat4 Sx, Sy, Sz;
Sx = glm::scale(glm::mat4(1.0f), glm::vec3(2, 1, 1));
Sy = glm::scale(glm::mat4(1.0f), glm::vec3(1, 2, 1));
Sz = glm::scale(glm::mat4(1.0f), glm::vec3(1, 1, 2));
printf(“Sy\n”);
mprint(Sy);

glm::vec4 tV2 = Sy * Position;
printf(“(1, 0, 0, 1) => (%f, %f, %f, %f)\n”, tV2[0], tV2[1], tV2[2], tV2[3]);

glm::mat4 TR = Tx * Rz; // Rotate Z and then Translate X
printf(“TR\n”);
mprint(TR);

glm::vec4 tV3 = TR * Position;
printf(“(1, 0, 0, 1) => (%f, %f, %f, %f)\n”, tV3[0], tV3[1], tV3[2], tV3[3]);

mat4 RT = Rz * Tx; // Translate X and then Rotate Z
printf(“RT\n”);
mprint(RT);

glm::vec4 tV4 = RT * Position;
printf(“(1, 0, 0, 1) => (%f, %f, %f, %f)\n”, tV4[0], tV4[1], tV4[2], tV4[3]);
}

# Lab5

CatmullRom Animation 도형을 그려본다.
(n-key를 누를 시, “사”-도형이 아지랑이 피어오르듯이 올라간다)

Sa::Sa(glm::vec3 p_) : GeometryPositionColor()
{
p = p_;
for (int i=0; i<4; i++) pipe[i] = Parallelpiped();

std::vector<KeyFrame> keyframes;
keyframes.push_back(KeyFrame(glm::vec3(0, 0, 0), 0)); // Posotion & Time
keyframes.push_back(KeyFrame(glm::vec3(1, 1, 0), 2000));
// Posotion & Time
keyframes.push_back(KeyFrame(glm::vec3(-1, 2, 0),
4000
));
// Posotion & Time
keyframes.push_back(KeyFrame(glm::vec3(2, 3, 0), 6000)); // Posotion & Time
curve = new CatmullRomCurveAnimation(keyframes, false);
// loop을 원하면 true

init();
}

void Sa::init() // “사”
{
glm::vec3 p0 = p;
pipe[0].set(p0, glm::vec3(0.3f, 0.0f, 0.0f), glm::vec3(0.0f, 0.0f, 0.3f), glm::vec3(0.7f, 1.0f, 0.0f));
glm::vec3 p1 = p + glm::vec3(1.4f, 0.0f, 0.0f);
pipe[1].set(p1, glm::vec3(0.3f, 0.0f, 0.0f),
glm::vec3(0.0f, 0.0f, 0.3f), glm::vec3(-0.7f, 1.0f, 0.0f));
glm::vec3 p2 = p + glm::vec3(2.0f, 0.0f, 0.0f);
pipe[2].set(p2, glm::vec3(0.3f, 0.0f, 0.0f), glm::vec3(0.0f, 0.0f, 0.3f), glm::vec3(0.0f, 1.0f,
0.0f));
glm::vec3 p3 = p + glm::vec3(2.3f, 0.35f, 0.0f);
pipe[3].set(p3, glm::vec3(0.5f, 0.0f, 0.0f), glm::vec3(0.0f, 0.0f, 0.3f), glm::vec3(0.0f, 0.3f, 0.0f));
}

void Sa::draw(bool wireframe)
{
for (int i=0; i<4; i++) pipe[i].draw();
}

// GeometryPositionColor 의 update을 override
bool Sa::update(float elapsedTime)
{
if (active)
{
if (curve)
{
curve->updatePosition(elapsedTime);
p = curve->getPosition();

// if time is greater than duration, then set time to duration and set active to false
if (!curve->getLoop() && elapsedTime >=  curve->getDuration())
{
done = true;
active = false;
}
}
init();
}
return true;
}

# Sa class

class Parallelpiped : public
GeometryPositionColor
{
public:
Parallelpiped(glm::vec3 p_=glm::vec3(0, 0, 0), glm::vec3 u=glm::vec3(1, 0, 0), glm::vec3 v=glm::vec3(0, 0, 1), glm::vec3 w=glm::vec3(0, 1, 0));
void set(glm::vec3 p_, glm::vec3 u_, glm::vec3 v_, glm::vec3 w_);
void init();
void draw(bool wireframe=false);

private:
//glm::vec3 p; // BL position
glm::vec3 u;
glm::vec3 v;
glm::vec3 w;
};

class Sa : public GeometryPositionColor
{
public:
Sa(glm::vec3 p=glm::vec3(0, 0, 0));
void init();
void draw(bool wireframe=false);

private:
//glm::vec3 p; // BL position
Parallelpiped pipe[4];
};

Parallelpiped::Parallelpiped(glm::vec3 p_, glm::vec3 u_, glm::vec3 v_,
glm::vec3 w_) : GeometryPositionColor()
{
set(p_, u_, v_, w_);
}

void Parallelpiped::set(glm::vec3 p_, glm::vec3 u_, glm::vec3 v_, glm::vec3 w_)
{
p = p_;
u = u_;
v = v_;
w = w_;
init();
}

void Parallelpiped::init()
{
glm::vec3 pu = p + u;
glm::vec3 pv = p + v;
glm::vec3 pw = p + w;
glm::vec3 puv = p + u + v;
glm::vec3 pvw = p + v + w;
glm::vec3 puw = p + u + w;
glm::vec3 puvw = p + u + v + w;

glm::vec3 frontNormal = glm::cross(u, w);
glm::vec3 backNormal = glm::cross(w, u);
glm::vec3 rightNormal = glm::cross(v, w);
glm::vec3 leftNormal = glm::cross(w, v);
glm::vec3 topNormal = glm::cross(u, v);
glm::vec3 bottomNormal = glm::cross(v, u);

// Front face
vbo.addData(&p[0],
sizeof(glm::vec3));
vbo.addData(&color[0], sizeof(glm::vec3)); //
vertex color
vbo.addData(&pu[0],
sizeof(glm::vec3));
vbo.addData(&color[0], sizeof(glm::vec3)); //
vertex color
vbo.addData(&puw[0],
sizeof(glm::vec3));
vbo.addData(&color[0], sizeof(glm::vec3)); //
vertex color
vbo.addData(&p[0],
sizeof(glm::vec3));
vbo.addData(&color[0], sizeof(glm::vec3)); //
vertex color
vbo.addData(&puw[0],
sizeof(glm::vec3));
vbo.addData(&color[0], sizeof(glm::vec3)); //
vertex color
vbo.addData(&pw[0],
sizeof(glm::vec3));
vbo.addData(&color[0], sizeof(glm::vec3)); //
vertex color

// Back face
vbo.addData(&puv[0],
sizeof(glm::vec3));
vbo.addData(&color[0], sizeof(glm::vec3)); //
vertex color
vbo.addData(&pv[0],
sizeof(glm::vec3));
vbo.addData(&color[0], sizeof(glm::vec3)); //
vertex color
vbo.addData(&pvw[0],
sizeof(glm::vec3));
vbo.addData(&color[0], sizeof(glm::vec3)); //
vertex color
vbo.addData(&puv[0],
sizeof(glm::vec3));
vbo.addData(&color[0], sizeof(glm::vec3)); //
vertex color
vbo.addData(&pvw[0],
sizeof(glm::vec3));
vbo.addData(&color[0], sizeof(glm::vec3)); //
vertex color
vbo.addData(&puvw[0],
sizeof(glm::vec3));
vbo.addData(&color[0], sizeof(glm::vec3)); //
vertex color

// Left face
vbo.addData(&pv[0],
sizeof(glm::vec3));
vbo.addData(&color[0], sizeof(glm::vec3)); //
vertex color
vbo.addData(&p[0],
sizeof(glm::vec3));
vbo.addData(&color[0], sizeof(glm::vec3)); //
vertex color
vbo.addData(&pw[0],
sizeof(glm::vec3));
vbo.addData(&color[0], sizeof(glm::vec3)); //
vertex color
vbo.addData(&pv[0],
sizeof(glm::vec3));
vbo.addData(&color[0], sizeof(glm::vec3)); //
vertex color
vbo.addData(&pw[0],
sizeof(glm::vec3));
vbo.addData(&color[0], sizeof(glm::vec3)); //
vertex color
vbo.addData(&pvw[0],
sizeof(glm::vec3));
vbo.addData(&color[0], sizeof(glm::vec3)); //
vertex color

// Right face
vbo.addData(&pu[0],
sizeof(glm::vec3));
vbo.addData(&color[0], sizeof(glm::vec3)); //
vertex color
vbo.addData(&puv[0],
sizeof(glm::vec3));
vbo.addData(&color[0], sizeof(glm::vec3)); //
vertex color
vbo.addData(&puvw[0],
sizeof(glm::vec3));
vbo.addData(&color[0], sizeof(glm::vec3)); //
vertex color
vbo.addData(&pu[0],
sizeof(glm::vec3));
vbo.addData(&color[0], sizeof(glm::vec3)); //
vertex color
vbo.addData(&puvw[0],
sizeof(glm::vec3));
vbo.addData(&color[0], sizeof(glm::vec3)); //
vertex color
vbo.addData(&puw[0],
sizeof(glm::vec3));
vbo.addData(&color[0], sizeof(glm::vec3)); //
vertex color

// Top face
vbo.addData(&pw[0],
sizeof(glm::vec3));
vbo.addData(&color[0], sizeof(glm::vec3)); //
vertex color
vbo.addData(&puw[0],
sizeof(glm::vec3));
vbo.addData(&color[0], sizeof(glm::vec3)); //
vertex color
vbo.addData(&puvw[0],
sizeof(glm::vec3));
vbo.addData(&color[0], sizeof(glm::vec3)); //
vertex color
vbo.addData(&pw[0],
sizeof(glm::vec3));
vbo.addData(&color[0], sizeof(glm::vec3)); //
vertex color
vbo.addData(&puvw[0],
sizeof(glm::vec3));
vbo.addData(&color[0], sizeof(glm::vec3)); //
vertex color
vbo.addData(&pvw[0],
sizeof(glm::vec3));
vbo.addData(&color[0], sizeof(glm::vec3)); //
vertex color

// Bottom face
vbo.addData(&pv[0],
sizeof(glm::vec3));
vbo.addData(&color[0], sizeof(glm::vec3)); //
vertex color
vbo.addData(&puv[0],
sizeof(glm::vec3));
vbo.addData(&color[0], sizeof(glm::vec3)); //
vertex color
vbo.addData(&pu[0],
sizeof(glm::vec3));
vbo.addData(&color[0], sizeof(glm::vec3)); //
vertex color
vbo.addData(&pv[0],
sizeof(glm::vec3));
vbo.addData(&color[0], sizeof(glm::vec3)); //
vertex color
vbo.addData(&pu[0],
sizeof(glm::vec3));
vbo.addData(&color[0], sizeof(glm::vec3)); //
vertex color
vbo.addData(&p[0],
sizeof(glm::vec3));
vbo.addData(&color[0], sizeof(glm::vec3)); //
vertex color

numVertices = 36;

// VAO &
VBOs
vbo.createVBO();
vbo.bindVBO();
vbo.uploadDataToGPU(GL_STATIC_DRAW);

glGenVertexArrays(1, &vao);
glBindVertexArray(vao);

int iDataStride = 2 * sizeof(glm::vec3); // vertex &
color
int iDataOffset =
0;
glEnableVertexAttribArray(0);
glVertexAttribPointer(0, 3,
GL_FLOAT, GL_FALSE, iDataStride, (void*)iDataOffset);
iDataOffset +=
sizeof(glm::vec3);
glEnableVertexAttribArray(1);
glVertexAttribPointer(1,
3, GL_FLOAT, GL_FALSE, iDataStride, (void*)iDataOffset);

isLoaded = true;
}

void Parallelpiped::draw(bool wireframe)
{
if (!isLoaded)
return;
glBindVertexArray(vao);
glDrawArrays(GL_TRIANGLES, 0,
numVertices);
}

Sa::Sa(glm::vec3 p_) : GeometryPositionColor()
{
p = p_;
for (int i = 0; i < 4; i++)
pipe[i] = Parallelpiped();
init();

}

void Sa::init() // “사”
{
glm::vec3 p0 = p;
pipe[0].set(p0, glm::vec3(0.3f, 0.0f, 0.0f), glm::vec3(0.0f, 0.0f, 0.3f), glm::vec3(0.7f, 1.0f, 0.0f));
glm::vec3 p1 = p + glm::vec3(1.4f, 0.0f, 0.0f);
pipe[1].set(p1, glm::vec3(0.3f, 0.0f, 0.0f), glm::vec3(0.0f, 0.0f, 0.3f), glm::vec3(-0.7f, 1.0f, 0.0f));
glm::vec3 p2 = p + glm::vec3(2.0f, 0.0f, 0.0f);
pipe[2].set(p2, glm::vec3(0.3f, 0.0f, 0.0f), glm::vec3(0.0f, 0.0f, 0.3f), glm::vec3(0.0f, 1.0f,
0.0f));
glm::vec3 p3 = p + glm::vec3(2.3f, 0.35f, 0.0f);
pipe[3].set(p3, glm::vec3(0.5f, 0.0f, 0.0f), glm::vec3(0.0f, 0.0f, 0.3f), glm::vec3(0.0f, 0.3f, 0.0f));
}

void Sa::draw(bool wireframe)
{
for (int i = 0; i < 4; i++)
pipe[i].draw();
}

# main update animation

// each geometry update
geoList[g_geometrymode]->update(elapsedTime);
if (geoList[g_geometrymode]->IsAnimationDone())
{
g_geometrymode++;
if (g_geometrymode == 8)
{
g_geometrymode = 0;
for (int i = 0; i < 8; i++)
geoList[i]->reset();
}
geoList[g_geometrymode]->activate();
startTime = glutGet(GLUT_ELAPSED_TIME);
printf(“geoList[%d] animation is activate\n”, g_geometrymode);
}

# 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

# GLM Matrix (Column-major order)

int foo()
{
glm::vec4 Position = glm::vec4(glm:: vec3(0.0f), 1.0f);
glm::mat4 Model = glm::translate(glm::mat4(1.0f), glm::vec3(1.0f, 2.0f, 3.0f));
printf(“%f %f %f %f\n”, Model[0][0], Model[1][0], Model[2][0], Model[3][0]);
printf(“%f %f %f %f\n”, Model[0][1], Model[1][1], Model[2][1], Model[3][1]);
printf(“%f %f %f %f\n”, Model[0][2], Model[1][2], Model[2][2], Model[3][2]);
printf(“%f %f %f %f\n”, Model[0][3], Model[1][3], Model[2][3], Model[3][3]);

glm::vec4 Transformed = Model * Position;

return 0;
}