Orthographic Projection

Vector/Matrix/Plane Test3789522709.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]);
}

// p’ = M3 * M2 * M1 * p (OpenGL uses Column-Major Order)
// p’= R T p (red) => translate, and then rotate
// p’= T R p (green) => rotate, and then translate
// p’= T R S p (blue) => scale, and then rotate, and then translate

OpenGL 1.x or 2.x
http://dis.dankook.ac.kr/lectures/cg10/entry/Transform

OpenGL 3.x or 4.x using GLM
http://dis.dankook.ac.kr/lectures/cg13/entry/OpenGLGLM-Transformation-Column-Major-Order