Month: October 2020

lab4-Vector Matrix Plane using glm

lab4-glmVectorMatrixPlaneQuaternion-src

 

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 M(1.0f, 2.0f, 3.0f, 4.0f, // column1
5.0f, 6.0f, 7.0f, 8.0f, // column2
9.0f, 10.0f, 11.0f, 12.0f, // column3
13.0f, 14.0f, 15.0f, 16.0f); // column4
cout << “M = ” << endl;
mprint(M);

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]);
}

void matrix4x4Test()
{
// matrix test
matrix4x4 A(1.0f, 0.0f, 0.0f, 1.0f,
0.0f, 2.0f, 0.0f, 2.0f,
0.0f, 0.0f, 4.0f, 3.0f,
0.0f, 0.0f, 0.0f, 1.0f);

matrix4x4 B(1.0f, 0.0f, 0.0f, 2.0f,
0.0f, 1.0f, 0.0f, 2.0f,
0.0f, 0.0f, 1.0f, 2.0f,
0.0f, 0.0f, 0.0f, 1.0f);

matrix4x4 C = A * B; // multiplication
matrix4x4 D = B * A; // multiplication
float det = A.determinant(); // determinant
matrix4x4 E = A.inverse(); // inverse
matrix4x4 F = A * E; // multiplication

vector3 p(1.0f, 0.0f, 0.0f);
vector3 q = A * p;
vector3 r = B * p;
vector3 s = C * p;
vector3 t = D * p;

cout << “A = ” << endl << A << endl;
cout << “B = ” << endl << B << endl;
cout << “C = A*B = ” << endl << C << endl;
cout << “D = B*A = ” << endl << D << endl;
cout << “E = inverse(A) = ” << endl << E << endl;
cout << “det = determinant(A) = ” << endl << det << endl;
cout << “F = A*E = ” << endl << F << endl;
cout << “p = ” << p << endl;
cout << “q = A * p = ” << q << endl;
cout << “r = B * p = ” << r << endl;
cout << “s = A * B * p = ” << s << endl;
cout << “t = B * A * p = ” << t << endl;

matrix4x4 Tx, Ty, Tz;
Tx.translate(2.0f, 0.0f, 0.0f); // RHS x+ right
Ty.translate(0.0f, 2.0f, 0.0f); // RHS y+ up
Tz.translate(0.0f, 0.0f, 2.0f); // RHS z+ front

vector3 Position(1.0f, 0.0f, 0.0f);
vector3 tV = Tx * Position;
printf(“Tx*P = (1, 0, 0, 1) => (%f, %f, %f)\n”, tV[0], tV[1], tV[2]);

matrix4x4 Rx, Ry, Rz, Ra;
Rx.rotate(30.0f, ‘x’);
Ry.rotate(60.0f, ‘y’);
Rz.rotate(45.0f, ‘z’);
Ra.rotate(45.0f, 1.0f, 1.0f, 1.0f);

matrix4x4 Sx, Sy, Sz;
Sx.scale(2, 1, 1);
Sy.scale(1, 2, 1);
Sz.scale(1, 1, 2);

cout << “Tx = ” << endl << Tx << endl;
cout << “Rx = ” << endl << Rx << endl;
cout << “Ry = ” << endl << Ry << endl;
cout << “Rz = ” << endl << Rz << endl;
cout << “Ra = ” << endl << Ra << endl;
cout << “Sy = ” << endl << Sy << endl;
cout << “Tx*Rz = ” << endl << Tx*Rz << endl; // Rotate Z, and then Translate X
cout << “Rz*Tx = ” << endl << Rz*Tx << endl; // Translate X, and then Rotate Z
cout << “Tx*Rz*Sy = ” << endl << Tx*Rz*Sy << endl; // Scale Y, and then Rotate Z, and then Translate X
cout << “Sy*Rz*Tx = ” << endl << Sy*Rz*Tx << endl; // Translate X, and then Rotate Z, and then Scale Y
vector3 tV1 = Ra * Position;
printf(“Ra*P = (1, 0, 0, 1) => (%f, %f, %f)\n”, tV1[0], tV1[1], tV1[2]);
}
typedef struct _RAY {
vector3 p; // start point
vector3 u; // direction
} RAY;

bool RayPlaneIntersection(oglclass::plane p, RAY l, vector3& out)
{
float denom = plane::dotNormal(p, l.u); // dotNormal = a.x + b*y + c*z
//cout << “denom = ” << denom << endl;
if (denom == 0)
return false;

float t = -plane::dotCoord(p, l.p)/denom; // dotCoord = a*x + b*y + c*z + d*1
//cout << “t = ” << t << endl; // [0, -1, 0]
if (t < 0)
return false;

out = l.p + t*(l.u); // return vector

return true;
}

void planeTest()
{
// RAY-plane intersection test
plane plane0(1, 0, 0, 1);
cout << “plane0 = ” << plane0 << endl;

vector3 Q(2, 1, -1), P(-1, 1, 0);
int ret = plane::isPointInsideOutside(plane0, Q);
cout << “ret = ” << ret << endl; // ret = 1 (outside the plane)
ret = plane::isPointInsideOutside(plane0, P);
cout << “ret = ” << ret << endl; // ret = 0 (on the plane)
P = plane::closestPointOnPlane(plane0, Q);
cout << “P = ” << P << endl; // P = (-1, 1, -1)

RAY ray1, ray2, ray3;
ray1.p = vector3(1, 0, 0);
ray1.u = vector3(-1, -1, 0);
ray2.p = vector3(1, 0, -2);
ray2.u = vector3(1, 1, 1);
ray3.p = vector3(1, 1, 0);
ray3.u = vector3(1, 1, 1);
vector3 out1, out2, out3;
if (RayPlaneIntersection(plane0, ray1, out1))
cout << “out1 = ” << out1 << endl; // out1=(-1, -2, 0)
if (RayPlaneIntersection(plane0, ray2, out2))
cout << “out2 = ” << out2 << endl; // nothing
if (RayPlaneIntersection(plane0, ray3, out3))
cout << “out3 = ” << out3 << endl; // nothing
}

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));
// (1.0, 0.0, 0.0, 1.0)
// (0.0, 1.0, 0.0, 2.0)
// (0.0, 0.0, 1.0, 3.0)
// (0.0, 0.0, 0.0, 1.0)

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; // P’ (1, 2, 3) = Model * P (0, 0, 0) (OpenGL uses Column-Major Order) RHS
…
return 0;
}

Affine Space (아핀공간) – 벡터공간에 점을 추가한 공간
http://mathworld.wolfram.com/AffineSpace.html

벡터와 벡터 간의 덧셈/뺄셈 -> 벡터 생성
스칼라와 벡터의 곱셈/나눗셈 -> 벡터 생성
벡터와 점의 덧셈/뺄셈 -> 점 생성
점과 점 간의 뺄셈 -> 벡터 생성
점과 점 간의 덧셈은 허용되지 않는다.
아핀공간에서 점의 덧셈은 각 점들 앞의 계수의 합이 1일 때에만 허용되고 이처럼 계수의 합이 1이 되는 경우를 Affine Sum(아핀합)이라 한다.

Homogeneous Coordinate (동차좌표) – 어떤 목적을 위해 한 차원의 좌표(n)을 추가한 좌표 (n+1)로 표현을 하는 것
http://mathworld.wolfram.com/HomogeneousCoordinates.html

4차원 동차 좌표 (x,y,z,w) => 3차원 좌표 (x/w , y/w , z/w)
만약 w == 1, (x,y,z,1)은 position이다.
만약 w == 0, (x,y,z,0)은 vector이다.