// @returns the rotation matrix around the vector and point by the specified angle
Matrix4x4 getRotMat (const Vector4 &p, const Vector4 &v, const REAL a) {
REAL theta = atan2(v.z,v.x);
REAL psi=-atan2(v.y,pow(v.x*v.x+v.z*v.z,0.5));
Matrix4x4 m1=getRotYMat(theta);
Matrix4x4 m1i=getRotYMat(-theta);
Matrix4x4 m2=getRotZMat(psi);
Matrix4x4 m2i=getRotZMat(-psi);
Matrix4x4 m3=getRotXMat(a);
Matrix4x4 m0=getTransMat(-p);
Matrix4x4 m0i=getTransMat(p);
Matrix4x4 m=m0i*m1i*m2i*m3*m2*m1*m0;
// @TODO: (CAMTRANS) Fill this in...
return m;
}
// @returns the rotation matrix around the vector and point by the specified angle
//the angle is in degrees
Matrix4x4 getRotMat (const Vector4 &p, const Vector4 &v, const REAL a) {
/* cout<<"point in: "<<p.x<<" "<<p.y<<" "<<p.z<<" "<<p.w<<endl;
cout<<"vec in:"<<v.x<<" "<<v.y<<" "<<v.z<<" "<<v.w<<endl;
cout<<"angle in:"<<a<<endl;*/
Matrix4x4 trans = getTransMat(p);
Matrix4x4 invtrans = getInvTransMat(p);
REAL theta = atan2(v.z,v.x);
REAL phi = -1 * atan2(v.y , sqrt(v.x*v.x + v.z*v.z));
Matrix4x4 M1 = getRotYMat(theta);
Matrix4x4 M2 = getRotZMat(phi);
Matrix4x4 M2Inv = getInvRotZMat(phi);
Matrix4x4 M1Inv = getInvRotYMat(theta);
//Matrix4x4 M3 = getRotXMat(M_PI*a/180);
Matrix4x4 M3 = getRotXMat(a);
Matrix4x4 toReturn = trans * M1Inv * M2Inv * M3 * M2 * M1 * invtrans;
return toReturn;
//return trans * M1 * M2 * M3 * M2Inv * M1Inv * invtrans;
}
// @returns the rotation matrix around the vector and point by the specified angle
Matrix4x4 getRotMat (const Vector4 &p, const Vector4 &v, const REAL a) {
// [CAMTRANS] Fill this in...
REAL theta = atan2(v.z,v.x);
REAL lambda = a;
REAL phi = -atan2(v.y, sqrt(v.x*v.x+v.z*v.z));
Matrix4x4 To = getInvTransMat(p);// translate to origin
Matrix4x4 M1 = getRotYMat(theta);
Matrix4x4 M2 = getRotZMat(phi);
Matrix4x4 M3 = getRotXMat(lambda);
Matrix4x4 M1inv = getInvRotYMat(theta);
Matrix4x4 M2inv = getInvRotZMat(phi);
Matrix4x4 M = M1inv*M2inv*M3*M2*M1;// full rotation matrix
Matrix4x4 ToInv = getTransMat(p);//translate back to point
Matrix4x4 finalmat = ToInv*M*To;//translate to origin, rotate, and then translate back to point
return finalmat;
}
// @returns the rotation matrix around the vector and point by the specified angle
Matrix4x4 getRotMat (const Vector4 &p, const Vector4 &v, const REAL a) {
// @TODO: [CAMTRANS] Fill this in...
const REAL y = atan2(v.z,v.x), z = -atan2(v.y,std::sqrt(SQ(v.x)+SQ(v.z)));
const Matrix4x4 M1 = getRotYMat(y), M1_inv = getInvRotYMat(y),
M2 = getRotZMat(z), M2_inv = getInvRotZMat(z),
M3 = getRotXMat(a);
return getInvTransMat(-p)*M1_inv*M2_inv*M3*M2*M1*getTransMat(-p);
}
void testMatrix::testMatrices()
{
Vector4 testTransV = Vector4(4,5,6,1);
Matrix4x4 testTrans = Matrix4x4(1,0,0,-4,0,1,0,-5,0,0,1,-6,0,0,0,1);
Matrix4x4 testRotZ90 = Matrix4x4(0.f,-1.f,0.f,0.f,1.f,0.f,0.f,0.f,0.f,0.f,1.f,0.f,0.f,0.f,0.f,1.f);
Matrix4x4 testRotY90 = Matrix4x4(0.f,0.f,1.f,0.f,0.f,1.f,0.f,0.f,-1.f,0.f,0.f,0.f,0.f,0.f,0.f,1.f);
Matrix4x4 testRotX90 = Matrix4x4(1.f,0.f,0.f,0.f,0.f,0.f,-1.f,0.f,0.f,1.f,0.f,0.f,0.f,0.f,0.f,1.f);
//y
Matrix4x4 testRot1 = getRotMat(Vector4(0,0,0,1),Vector4(0,1,0,1),90);
//x
Matrix4x4 testRot2 = getRotMat(Vector4(0,0,0,1),Vector4(1,0,0,1), 90);
//z
Matrix4x4 testRot3 = getRotMat(Vector4(0,0,0,1),Vector4(0,0,1,1), 90);
Matrix4x4 trz90 = getRotZMat(M_PI/2);
Matrix4x4 try90 = getRotYMat(M_PI/2);
Matrix4x4 trx90 = getRotXMat(M_PI/2);
Matrix4x4 trans = getTransMat(testTransV);
//Test rotation on z axis
compareMatrices(&testRotZ90,&trz90);
//Z axis as arbitrary rotation
compareMatrices(&testRotZ90,&testRot3);
//inverses are equivalent:
compareMatrices(&getInvRotZMat(M_PI/2),&getInvRotMat(Vector4(0,0,0,1),Vector4(0,0,1,1),90));
//Test rotation on y axis
compareMatrices(&testRotY90,&try90);
//Y axis as arbitrary rotation
compareMatrices(&testRotY90,&testRot1);
//inverses are equivalent:
compareMatrices(&getInvRotYMat(M_PI/2),&getInvRotMat(Vector4(0,0,0,1),Vector4(0,1,0,1),90));
//Test rotation on x axis
compareMatrices(&testRotX90,&trx90);
//X axis as arbitrary rotation
compareMatrices(&testRotX90,&testRot2);
//inverses are equivalent:
compareMatrices(&getInvRotXMat(M_PI/2),&getInvRotMat(Vector4(0,0,0,1),Vector4(1,0,0,1),90));
//test translation
compareMatrices(&testTrans,&trans);
}
// @returns the rotation matrix around the vector and point by the specified angle
Matrix4x4 getRotMat (const Vector4 &p, const Vector4 &v, const REAL a) {
// angles to rotate v to x-axis
REAL th = atan2(v.z,v.x),
ph = -atan2(v.y,sqrt(pow(v.z,2)+pow(v.x,2)));
// all transformations required
// Note: Inverse of Rot mat is just transpose
Matrix4x4 T = getInvTransMat(p),
Tinv = getTransMat(p),
M1 = getRotYMat(th),
M2 = getRotZMat(ph),
M3 = getRotXMat(a);
return Tinv * M1.getTranspose() * M2.getTranspose()
* M3 * M2 * M1 * T;
}
// @returns the inverse rotation matrix around the vector and point by the specified angle
Matrix4x4 getInvRotMat (const Point3 &p, const Vector3 &v, const real_t a) {
const real_t vZ = v[2];
const real_t vX = v[0];
const real_t theta = atan2(vZ, vX);
const real_t phi = -atan2(v[1], sqrt(vX * vX + vZ * vZ));
const Matrix4x4 &transToOrigin = getInvTransMat(Vector3(p[0], p[1], p[2]));
const Matrix4x4 &A = getRotYMat(theta);
const Matrix4x4 &B = getRotZMat(phi);
const Matrix4x4 &C = getRotXMat(a);
const Matrix4x4 &invA = getInvRotYMat(theta);
const Matrix4x4 &invB = getInvRotZMat(phi);
const Matrix4x4 &transBack = getTransMat(Vector3(p[0], p[1], p[2]));
return transBack * (invA * invB * C * B * A).getTranspose() * transToOrigin;
}
// @returns the rotation matrix around the vector and point by the specified angle
Matrix4x4 getRotMat (const Vector4 &p, const Vector4 &v, const REAL a) {
// [PASS]
REAL theta = atan2(v.z, v.x);
REAL phi = -atan2(v.y, sqrt(v.x*v.x + v.z*v.z));
// translate to the origin and back
Matrix4x4 Mt = getTransMat(-p);
Matrix4x4 Mt_1 = getInvTransMat(-p);
Matrix4x4 M1 = getRotYMat(theta);
Matrix4x4 M2 = getRotZMat(phi);
Matrix4x4 M3 = getRotXMat(a);
Matrix4x4 M1_1 = getInvRotYMat(theta);
Matrix4x4 M2_1 = getInvRotZMat(phi);
return Mt_1*M1_1*M2_1*M3*M2*M1*Mt;
}
// @returns the inverse rotation matrix around the vector and
// point by the specified angle
Matrix4x4 getInvRotMat (const Vector4 &h, const Vector4 &a, const REAL lambda) {
// @DONE: [CAMTRANS] Filled in.
double theta = atan2(a.z, a.x);
double phi = -atan2(a.y, sqrt(a.x*a.x + a.z*a.z));
//want to translate by -h to move from h to the origin
Matrix4x4 Th = getTransMat(-h);
Matrix4x4 M1Inv = getInvRotYMat(theta);
Matrix4x4 M2Inv = getInvRotZMat(phi);
Matrix4x4 M3Inv = getInvRotXMat(lambda);
Matrix4x4 M2 = getRotZMat(phi);
Matrix4x4 M1 = getRotYMat(theta);
Matrix4x4 ThInv = getInvTransMat(-h);
Matrix4x4 result = ThInv * M1Inv * M2Inv * M3Inv * M2 * M1 * Th;
return result;
}
// @returns the rotation matrix around the vector and point by the specified angle
Matrix4x4 getRotMat (const Vector4 &p, const Vector4 &v, const REAL a) {
// @TODO: [CAMTRANS] Fill this in...
REAL theta = atan2(v.z, v.x);
REAL otherAngle = -atan2(v.y, sqrt(v.x*v.x+v.z*v.z));
Matrix4x4 trans = Matrix4x4(1,0,0,p.x,
0,1,0, p.y,
0,0,1, p.z,
0,0,0,1);
Matrix4x4 invTrans = Matrix4x4(1,0,0, -p.x,
0,1,0, -p.y,
0,0,1, -p.z,
0,0,0,1);
Matrix4x4 final = trans*getInvRotYMat(theta)*getInvRotZMat(otherAngle)*getRotXMat(a)*getRotZMat(otherAngle)*getRotYMat(theta)*invTrans;
return final;
}
// @returns the inverse rotation matrix about the y axis by the specified angle
Matrix4x4 getInvRotYMat (const REAL radians) {
return getRotYMat(-radians);
// @TODO: (CAMTRANS) Fill this in...
return Matrix4x4::identity();
}
// @returns the inverse rotation matrix about the y axis by the specified angle
Matrix4x4 getInvRotYMat (const REAL radians) {
return getRotYMat(-1*radians);
}
