void PlanetWidget::mouseReleaseEvent (QMouseEvent*) {
if (!mouseMoving) {
pointSelected(conjugate(rotation_to_default(planetHandler->planet())) * activeRenderer->to_coordinates(vector(mousePosition)));
}
mouseMoving = false;
}
/*!
Rotates \a vector with this quaternion to produce a new vector
in 3D space. The following code:
\code
QVector3D result = q.rotatedVector(vector);
\endcode
is equivalent to the following:
\code
QVector3D result = (q * QQuaternion(0, vector) * q.conjugate()).vector();
\endcode
*/
QVector3D QQuaternion::rotatedVector(const QVector3D& vector) const
{
return (*this * QQuaternion(0, vector) * conjugate()).vector();
}
glm::vec4 quat::operator *(const glm::vec4& other) const
{
auto result = *this * quat(other) * conjugate(*this);
return glm::vec4(result.x, result.y, result.z, 1.0f);
}
// Optimized invert for unit quaternions
void
Quaternion::invertForUnit ()
{
conjugate ();
}
Quaternion Quaternion::inverse() const
{
return conjugate() / length2();
}
static int quaternion_conjugate(lua_State* L)
{
LuaStack stack(L);
stack.push_quaternion(conjugate(stack.get_quaternion(1)));
return 1;
}
void
yypower(void)
{
int n;
p2 = pop();
p1 = pop();
// both base and exponent are rational numbers?
if (isrational(p1) && isrational(p2)) {
push(p1);
push(p2);
qpow();
return;
}
// both base and exponent are either rational or double?
if (isnum(p1) && isnum(p2)) {
push(p1);
push(p2);
dpow();
return;
}
if (istensor(p1)) {
power_tensor();
return;
}
if (p1 == symbol(E) && car(p2) == symbol(LOG)) {
push(cadr(p2));
return;
}
if (p1 == symbol(E) && isdouble(p2)) {
push_double(exp(p2->u.d));
return;
}
// 1 ^ a -> 1
// a ^ 0 -> 1
if (equal(p1, one) || iszero(p2)) {
push(one);
return;
}
// a ^ 1 -> a
if (equal(p2, one)) {
push(p1);
return;
}
// (a * b) ^ c -> (a ^ c) * (b ^ c)
if (car(p1) == symbol(MULTIPLY)) {
p1 = cdr(p1);
push(car(p1));
push(p2);
power();
p1 = cdr(p1);
while (iscons(p1)) {
push(car(p1));
push(p2);
power();
multiply();
p1 = cdr(p1);
}
return;
}
// (a ^ b) ^ c -> a ^ (b * c)
if (car(p1) == symbol(POWER)) {
push(cadr(p1));
push(caddr(p1));
push(p2);
multiply();
power();
return;
}
// (a + b) ^ n -> (a + b) * (a + b) ...
if (expanding && isadd(p1) && isnum(p2)) {
push(p2);
n = pop_integer();
// this && n != 0x80000000 added by DDC
// as it's not always the case that 0x80000000
// is negative
if (n > 1 && n != 0x80000000) {
power_sum(n);
return;
}
}
// sin(x) ^ 2n -> (1 - cos(x) ^ 2) ^ n
if (trigmode == 1 && car(p1) == symbol(SIN) && iseveninteger(p2)) {
push_integer(1);
push(cadr(p1));
cosine();
push_integer(2);
power();
subtract();
push(p2);
push_rational(1, 2);
multiply();
power();
return;
}
// cos(x) ^ 2n -> (1 - sin(x) ^ 2) ^ n
if (trigmode == 2 && car(p1) == symbol(COS) && iseveninteger(p2)) {
push_integer(1);
push(cadr(p1));
sine();
push_integer(2);
power();
subtract();
push(p2);
push_rational(1, 2);
multiply();
power();
return;
}
// complex number? (just number, not expression)
if (iscomplexnumber(p1)) {
// integer power?
// n will be negative here, positive n already handled
if (isinteger(p2)) {
// / \ n
// -n | a - ib |
// (a + ib) = | -------- |
// | 2 2 |
// \ a + b /
push(p1);
conjugate();
p3 = pop();
push(p3);
push(p3);
push(p1);
multiply();
divide();
push(p2);
negate();
power();
return;
}
// noninteger or floating power?
if (isnum(p2)) {
#if 1 // use polar form
push(p1);
mag();
push(p2);
power();
push_integer(-1);
push(p1);
arg();
push(p2);
multiply();
push(symbol(PI));
divide();
power();
multiply();
#else // use exponential form
push(p1);
mag();
push(p2);
power();
push(symbol(E));
push(p1);
arg();
push(p2);
multiply();
push(imaginaryunit);
multiply();
power();
multiply();
#endif
return;
}
}
if (simplify_polar())
return;
push_symbol(POWER);
push(p1);
push(p2);
list(3);
}
Vec3<A> rotate( const Vec3<A>& vec, const Quat<A>& quat )
{
auto rotated = conjugate( quat ) * Quat < A > {vec.x, vec.y, vec.z, 1.0f} *quat;
return Vec3 < A > {rotated.x, rotated.y, rotated.z};
};
void quaternion_t::inverse()
{
conjugate();
*this /= norm();
}
quaternion reciprocal(quaternion m)
{
quaternion out;
out = rmult(1/norm2(m),conjugate(m));
return out;
}
// Inverse
Quaternion Quaternion::inverse()
{
return conjugate().scalar(1/norm());
}
real do_ewald(t_inputrec *ir,
rvec x[], rvec f[],
real chargeA[], real chargeB[],
rvec box,
t_commrec *cr, int natoms,
matrix lrvir, real ewaldcoeff,
real lambda, real *dvdlambda,
struct gmx_ewald_tab_t *et)
{
real factor = -1.0/(4*ewaldcoeff*ewaldcoeff);
real scaleRecip = 4.0*M_PI/(box[XX]*box[YY]*box[ZZ])*ONE_4PI_EPS0/ir->epsilon_r; /* 1/(Vol*e0) */
real *charge, energy_AB[2], energy;
rvec lll;
int lowiy, lowiz, ix, iy, iz, n, q;
real tmp, cs, ss, ak, akv, mx, my, mz, m2, scale;
gmx_bool bFreeEnergy;
if (cr != NULL)
{
if (PAR(cr))
{
gmx_fatal(FARGS, "No parallel Ewald. Use PME instead.\n");
}
}
if (!et->eir) /* allocate if we need to */
{
snew(et->eir, et->kmax);
for (n = 0; n < et->kmax; n++)
{
snew(et->eir[n], natoms);
}
snew(et->tab_xy, natoms);
snew(et->tab_qxyz, natoms);
}
bFreeEnergy = (ir->efep != efepNO);
clear_mat(lrvir);
calc_lll(box, lll);
tabulateStructureFactors(natoms, x, et->kmax, et->eir, lll);
for (q = 0; q < (bFreeEnergy ? 2 : 1); q++)
{
if (!bFreeEnergy)
{
charge = chargeA;
scale = 1.0;
}
else if (q == 0)
{
charge = chargeA;
scale = 1.0 - lambda;
}
else
{
charge = chargeB;
scale = lambda;
}
lowiy = 0;
lowiz = 1;
energy_AB[q] = 0;
for (ix = 0; ix < et->nx; ix++)
{
mx = ix*lll[XX];
for (iy = lowiy; iy < et->ny; iy++)
{
my = iy*lll[YY];
if (iy >= 0)
{
for (n = 0; n < natoms; n++)
{
et->tab_xy[n] = cmul(et->eir[ix][n][XX], et->eir[iy][n][YY]);
}
}
else
{
for (n = 0; n < natoms; n++)
{
et->tab_xy[n] = cmul(et->eir[ix][n][XX], conjugate(et->eir[-iy][n][YY]));
}
}
for (iz = lowiz; iz < et->nz; iz++)
{
mz = iz*lll[ZZ];
m2 = mx*mx+my*my+mz*mz;
ak = exp(m2*factor)/m2;
akv = 2.0*ak*(1.0/m2-factor);
if (iz >= 0)
{
for (n = 0; n < natoms; n++)
{
et->tab_qxyz[n] = rcmul(charge[n], cmul(et->tab_xy[n],
et->eir[iz][n][ZZ]));
}
}
else
{
for (n = 0; n < natoms; n++)
{
et->tab_qxyz[n] = rcmul(charge[n], cmul(et->tab_xy[n],
conjugate(et->eir[-iz][n][ZZ])));
}
}
cs = ss = 0;
for (n = 0; n < natoms; n++)
{
cs += et->tab_qxyz[n].re;
ss += et->tab_qxyz[n].im;
}
energy_AB[q] += ak*(cs*cs+ss*ss);
tmp = scale*akv*(cs*cs+ss*ss);
lrvir[XX][XX] -= tmp*mx*mx;
lrvir[XX][YY] -= tmp*mx*my;
lrvir[XX][ZZ] -= tmp*mx*mz;
lrvir[YY][YY] -= tmp*my*my;
lrvir[YY][ZZ] -= tmp*my*mz;
lrvir[ZZ][ZZ] -= tmp*mz*mz;
for (n = 0; n < natoms; n++)
{
/*tmp=scale*ak*(cs*tab_qxyz[n].im-ss*tab_qxyz[n].re);*/
tmp = scale*ak*(cs*et->tab_qxyz[n].im-ss*et->tab_qxyz[n].re);
f[n][XX] += tmp*mx*2*scaleRecip;
f[n][YY] += tmp*my*2*scaleRecip;
f[n][ZZ] += tmp*mz*2*scaleRecip;
#if 0
f[n][XX] += tmp*mx;
f[n][YY] += tmp*my;
f[n][ZZ] += tmp*mz;
#endif
}
lowiz = 1-et->nz;
}
lowiy = 1-et->ny;
}
}
}
if (!bFreeEnergy)
{
energy = energy_AB[0];
}
else
{
energy = (1.0 - lambda)*energy_AB[0] + lambda*energy_AB[1];
*dvdlambda += scaleRecip*(energy_AB[1] - energy_AB[0]);
}
lrvir[XX][XX] = -0.5*scaleRecip*(lrvir[XX][XX]+energy);
lrvir[XX][YY] = -0.5*scaleRecip*(lrvir[XX][YY]);
lrvir[XX][ZZ] = -0.5*scaleRecip*(lrvir[XX][ZZ]);
lrvir[YY][YY] = -0.5*scaleRecip*(lrvir[YY][YY]+energy);
lrvir[YY][ZZ] = -0.5*scaleRecip*(lrvir[YY][ZZ]);
lrvir[ZZ][ZZ] = -0.5*scaleRecip*(lrvir[ZZ][ZZ]+energy);
lrvir[YY][XX] = lrvir[XX][YY];
lrvir[ZZ][XX] = lrvir[XX][ZZ];
lrvir[ZZ][YY] = lrvir[YY][ZZ];
energy *= scaleRecip;
return energy;
}
//
// Find the complex roots of a complex polynomial Poly
// The order is Maxpow
// The result will be in the array Root
//
void HighPrecisionComplexPolynom::Polyrootc(cln::cl_N* Poly, int Maxpow, cln::cl_N* Root) {
int ord, pow, fnd, pov, maxp;
cln::cl_N poly[1+Maxpow], polc[1+Maxpow], coef[1+Maxpow], coen[1+Maxpow];
// Put coefficients in an array
for(pow = 0; pow < Maxpow+1; pow++) {
poly[pow] = As(cln::cl_N)(Poly[pow]);
coef[pow] = As(cln::cl_N)(Poly[pow]);
}
for(pow = 0; pow < Maxpow+1; pow++) {
polc[pow] = As(cln::cl_N)(complex(ZERO,ZERO));
}
polc[0] = As(cln::cl_N)(complex(ONE,ZERO));
fnd = -1;
// Loop for finding all roots
for(ord = 0; ord < Maxpow; ord++) {
fnd++;
pov = Maxpow-fnd;
if(fnd < Maxpow) {
if(LogLevel>4) {
printf(" root number: %d\n",fnd+1);
}
if((ord%2 == 1) && (Maxpow%2 == 0) && (false)) {
Root[fnd] = As(cln::cl_N)(conjugate(Root[fnd-1]));
cln::cl_N val0 = EvalPoly(poly, Maxpow, Root[fnd]);
if(LogLevel>3) {
printf("root = %f +i*%f\n", double_approx(realpart(Root[fnd])), double_approx(imagpart(Root[fnd])));
printf("value at root: %f +i*%f\n", double_approx(realpart(val0)), double_approx(imagpart(val0)));
}
}
else {
Root[fnd] = Lasolv(poly,pov, complex(ONE,ONE), 150);
}
for(pow = Maxpow; pow > 0; pow--) {
polc[pow] = polc[pow-1]-Root[fnd]*polc[pow];
}
polc[0] = -Root[fnd]*polc[pow];
// Divide the polynomial by the root
maxp = Maxpow-fnd-1;
coen[maxp] = coef[maxp+1];
for(pow = maxp-1; pow > -1; pow--) {
coen[pow] = coef[pow+1]+Root[fnd]*coen[pow+1];
}
for(pow = 0; pow < maxp+1; pow++) {
coef[pow] = coen[pow];
poly[pow] = coef[pow];
}
}
else {
break;
}
}
// Compare input with product of root factors
for(pow = 0; pow < Maxpow+1; pow++) {
polc[pow] = Poly[pow]-poly[0]*polc[pow];
}
if(LogLevel>4) {
printf("control polynomial should be close to zero:\n");
for(pow = 0; pow < Maxpow+1; pow++) {
printf(" x^{%d}\n",pow);
printf("%1.15f +i*%1.15f\n",double_approx(realpart(polc[pow])), double_approx(imagpart(polc[pow])));
}
}
}
//
// Find a root of a complex polynomial by Laguerre iteration.
//
// The polynomial is Poly
// The order is Maxpow
//
// The precision: Digit
cln::cl_N HighPrecisionComplexPolynom::Lasolv(cln::cl_N* Poly, int Maxpow, cln::cl_N root, int itemax) {
int pow, ite;
root = complex(ZERO,ZERO);
cln::cl_F angl, small = As(cln::cl_F)(expt(cln::cl_float(0.1,clnDIGIT),DIGIT/2));
cln::cl_N dif1[Maxpow], dif2[Maxpow-1];
cln::cl_N val0, val, val1, val2, denp, denm, las1, las2, sqrv;
// cln::cl_N root;
for(pow = 0; pow < Maxpow; pow++)
dif1[pow] = (pow+1)*Poly[pow+1];
for(pow = 0; pow < Maxpow-1; pow++)
dif2[pow] = (pow+1)*dif1[pow+1];
// The maximal allowed number of iterations is set here;
// this can be chosen larger, but 100 usually suffices
// root = As(cln::cl_N)(complex(ZERO,ZERO));
val0 = EvalPoly(Poly,Maxpow,root);
// Iteration
for(ite = 0; ite < itemax; ite++)
{
val = val0;
val1 = EvalPoly(dif1,Maxpow-1,root);
val2 = EvalPoly(dif2,Maxpow-2,root);
sqrv = (Maxpow-1)*((Maxpow-1)*val1*val1-Maxpow*val0*val2);
angl = HALF*cln::cl_float(phase(sqrv),clnDIGIT);
sqrv = sqrt(abs(sqrv))*complex(cos(angl),sin(angl));
denp = val1+sqrv;
denm = val1-sqrv;
if(denp == complex(ZERO,ZERO))
root = root-Maxpow*val0/denm;
else
{ if(denm == complex(ZERO,ZERO))
root = root-Maxpow*val0/denp;
else
{ las1 = -Maxpow*val0/denp;
las2 = -Maxpow*val0/denm;
if(realpart(las1*conjugate(las1)) <
realpart(las2*conjugate(las2)))
root = root+las1;
else
root = root+las2; } }
// Look whether the root is good enough
val0 = EvalPoly(Poly,Maxpow,root);
if(abs(val0) == ZERO || (abs(val0) < small) && abs(val0/val) > 0.7) {
if(LogLevel>4) {
printf("Laguerre iterations: %d\n", ite);
printf("root = %f +i* %f\n", double_approx(realpart(root)), double_approx(imagpart(root)));
printf("value at root: %f +i* %f\n", double_approx(realpart(val0)), double_approx(imagpart(val0)));
}
break;
}
}
if(ite >= itemax) {
printf("Laguerre iteration did not converge\n");
exit(5);
}
return root;
}
t4 = magE*t2; t3 = tan(t4); t5 = t3*t3; t6 = t5+1.0; t7 = 1.0/(magN*magN); t8 = OP_l_18_c_18_r_*t2*t6; t15 = OP_l_17_c_18_r_*magE*t6*t7; t9 = t8-t15; t10 = t2*t6*t9; t11 = OP_l_18_c_17_r_*t2*t6; t16 = OP_l_17_c_17_r_*magE*t6*t7; t12 = t11-t16; t17 = magE*t6*t7*t12; t13 = R_DECL+t10-t17; t14 = 1.0/t13; t18 = conjugate(magE); t19 = conjugate(magN); t21 = 1.0/t19; t22 = t18*t21; t20 = tan(t22); t23 = t20*t20; t24 = t23+1.0; Kfusion[0] = t14*(OP_l_1_c_18_r_*t2*t6-OP_l_1_c_17_r_*magE*t6*t7); Kfusion[1] = t14*(OP_l_2_c_18_r_*t2*t6-OP_l_2_c_17_r_*magE*t6*t7); Kfusion[2] = t14*(OP_l_3_c_18_r_*t2*t6-OP_l_3_c_17_r_*magE*t6*t7); Kfusion[3] = t14*(OP_l_4_c_18_r_*t2*t6-OP_l_4_c_17_r_*magE*t6*t7); Kfusion[4] = t14*(OP_l_5_c_18_r_*t2*t6-OP_l_5_c_17_r_*magE*t6*t7); Kfusion[5] = t14*(OP_l_6_c_18_r_*t2*t6-OP_l_6_c_17_r_*magE*t6*t7); Kfusion[6] = t14*(OP_l_7_c_18_r_*t2*t6-OP_l_7_c_17_r_*magE*t6*t7); Kfusion[7] = t14*(OP_l_8_c_18_r_*t2*t6-OP_l_8_c_17_r_*magE*t6*t7); Kfusion[8] = t14*(OP_l_9_c_18_r_*t2*t6-OP_l_9_c_17_r_*magE*t6*t7);
/// Computes the inverse orientation represented by this quaternion in place
QUAT& QUAT::invert()
{
conjugate();
return *this;
}
Quaternion<T> quat_conjugate(const Quaternion<T>& q)
{
return conjugate(q);
}
/// Computes the inverse orientation of a quaternion
QUAT QUAT::invert(const QUAT& q)
{
return conjugate(q);
}
t2 = magE*magE; t3 = magN*magN; t4 = t2+t3; t5 = P[16][16]*t2; t6 = P[17][17]*t3; t7 = t2*t2; t8 = R_DECL*t7; t9 = t3*t3; t10 = R_DECL*t9; t11 = R_DECL*t2*t3*2.0; t14 = P[16][17]*magE*magN; t15 = P[17][16]*magE*magN; t12 = t5+t6+t8+t10+t11-t14-t15; t13 = 1.0/t12; t16 = conjugate(magE); t17 = conjugate(magN); t18 = t16*t16; t19 = t17*t17; t20 = t18+t19; t21 = 1.0/t20; A0[0][0] = -t4*t13*(P[0][16]*magE-P[0][17]*magN); A0[1][0] = -t4*t13*(P[1][16]*magE-P[1][17]*magN); A0[2][0] = -t4*t13*(P[2][16]*magE-P[2][17]*magN); A0[3][0] = -t4*t13*(P[3][16]*magE-P[3][17]*magN); A0[4][0] = -t4*t13*(P[4][16]*magE-P[4][17]*magN); A0[5][0] = -t4*t13*(P[5][16]*magE-P[5][17]*magN); A0[6][0] = -t4*t13*(P[6][16]*magE-P[6][17]*magN); A0[7][0] = -t4*t13*(P[7][16]*magE-P[7][17]*magN); A0[8][0] = -t4*t13*(P[8][16]*magE-P[8][17]*magN); A0[9][0] = -t4*t13*(P[9][16]*magE-P[9][17]*magN); A0[10][0] = -t4*t13*(P[10][16]*magE-P[10][17]*magN);
/// Multiplies inv(q) by <b>this</b> and returns the result
QUAT QUAT::operator/(const QUAT& q) const
{
return conjugate(q) * (*this);
}
inline vec3 rotate(const Quaternion& q, const vec3& v) {
return vec3((q * Quaternion(vec4(v)) * conjugate(q)).val);
}
/// Negates the value of each of the x, y, and z coordinates in place
void QUAT::conjugate()
{
*this = conjugate(*this);
}
Vector3f Quaternion::operator*(const Vector3f &vec) const
{
Vector3f v = vec.normal();
Quaternion quat = *this * (Quaternion(v.getX(), v.getY(), v.getZ(), 0.0) * conjugate());
return Vector3f(quat.x, quat.y, quat.z);
}
AABB3d TransformSequence::compute_motion_segment_bbox(
const AABB3d& bbox,
const Transformd& from,
const Transformd& to) const
{
//
// Reference:
//
// http://gruenschloss.org/motion-blur/motion-blur.pdf page 11.
//
// Parameters.
const double MinLength = Pi / 2.0;
const double RootEps = 1.0e-6;
const double GrowEps = 1.0e-4;
const size_t MaxIterations = 100;
// Start with the bounding box at 'from'.
const AABB3d from_bbox = from.to_parent(bbox);
AABB3d motion_bbox = from_bbox;
// Setup an interpolator between 'from' and 'to'.
TransformInterpolatord interpolator;
if (!interpolator.set_transforms(from, to))
return motion_bbox;
// Compute the scalings at 'from' and 'to'.
const Vector3d s0 = interpolator.get_s0();
const Vector3d s1 = interpolator.get_s1();
// Compute the relative rotation between 'from' and 'to'.
const Quaterniond q =
interpolator.get_q1() * conjugate(interpolator.get_q0());
// Transform the relative rotation to the axis-angle representation.
Vector3d axis;
double angle;
q.extract_axis_angle(axis, angle);
if (axis.z < 0.0)
angle = -angle;
// The following code only makes sense if there is a rotation component.
if (angle == 0.0)
return motion_bbox;
// Compute the rotation required to align the rotation axis with the Z axis.
const Vector3d Z(0.0, 0.0, 1.0);
const Vector3d perp = cross(Z, axis);
const double perp_norm = norm(perp);
Transformd axis_to_z;
if (perp_norm == 0.0)
axis_to_z = Transformd::identity();
else
{
const Vector3d v = perp / perp_norm;
const double sin_a = clamp(perp_norm, -1.0, 1.0);
const double cos_a = sqrt(1.0 - sin_a * sin_a);
axis_to_z.set_local_to_parent(Matrix4d::make_rotation(v, cos_a, +sin_a));
axis_to_z.set_parent_to_local(Matrix4d::make_rotation(v, cos_a, -sin_a));
}
// Build the linear scaling functions Sx(theta), Sy(theta) and Sz(theta).
const LinearFunction sx(1.0, s1.x / s0.x, angle);
const LinearFunction sy(1.0, s1.y / s0.y, angle);
const LinearFunction sz(1.0, s1.z / s0.z, angle);
// Consider each corner of the bounding box. Notice an important trick here:
// we take advantage of the way AABB::compute_corner() works to only iterate
// over the four corners at Z=min instead of over all eight corners since we
// anyway transform the rotation to be aligned with the Z axis.
for (size_t c = 0; c < 4; ++c)
{
// Compute the position of this corner at 'from'.
const Vector3d corner = axis_to_z.point_to_local(from_bbox.compute_corner(c));
const Vector2d corner2d(corner.x, corner.y);
// Build the trajectory functions x(theta) and y(theta).
const TrajectoryX tx(sx, sy, corner2d);
const TrajectoryY ty(sx, sy, corner2d);
// Find all the rotation angles at which this corner is an extremum and update the motion bounding box.
RootHandler root_handler(tx, ty, sz, axis_to_z, corner, motion_bbox);
find_multiple_roots_newton(
Bind<TrajectoryX>(tx, &TrajectoryX::d),
Bind<TrajectoryX>(tx, &TrajectoryX::dd),
0.0, angle,
MinLength,
RootEps,
MaxIterations,
root_handler);
find_multiple_roots_newton(
Bind<TrajectoryY>(ty, &TrajectoryY::d),
Bind<TrajectoryY>(ty, &TrajectoryY::dd),
0.0, angle,
MinLength,
RootEps,
MaxIterations,
root_handler);
}
motion_bbox.robust_grow(GrowEps);
return motion_bbox;
}
quat inverse(quat q) {
return conjugate(q) / norm(q);
}
static quat invert(quat &q) {
return conjugate(q) / lengthSqr(q);
}
glm::vec3 quat::operator *(const glm::vec3& other) const
{
auto result = *this * quat(other) * conjugate(*this);
return glm::vec3(result.x, result.y, result.z);
}
Quaternion Quaternion::inverse()
{
return conjugate().divideByFloat(norm()); // conjugate() / norm();
}
inline Vector3 transform(const Transform& transform, const Vector3& point)
{
return (conjugate(transform.orientation) * (transform.position - point)) / transform.scale;
}
// negate
inline quat operator-(const quat &q) {
return conjugate(q);
}