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#include <u.h>
#include <libc.h>
#include <draw.h>
#include "dat.h"
#include "fns.h"
Quaternion
Quat(double r, double i, double j, double k)
{
return (Quaternion){r, i, j, k};
}
Quaternion
Quatvec(double s, Vector3 v)
{
return (Quaternion){s, v.x, v.y, v.z};
}
Quaternion
addq(Quaternion a, Quaternion b)
{
return Quat(a.r+b.r, a.i+b.i, a.j+b.j, a.k+b.k);
}
Quaternion
subq(Quaternion a, Quaternion b)
{
return Quat(a.r-b.r, a.i-b.i, a.j-b.j, a.k-b.k);
}
Quaternion
mulq(Quaternion q, Quaternion r)
{
Vector3 qv, rv, tmp;
qv = Vec3(q.i, q.j, q.k);
rv = Vec3(r.i, r.j, r.k);
tmp = addvec3(addvec3(mulvec3(rv, q.r), mulvec3(qv, r.r)), crossvec(qv, rv));
return Quatvec(q.r*r.r - dotvec3(qv, rv), tmp);
}
Quaternion
smulq(Quaternion q, double s)
{
return Quat(q.r*s, q.i*s, q.j*s, q.k*s);
}
Quaternion
sdivq(Quaternion q, double s)
{
return Quat(q.r/s, q.i/s, q.j/s, q.k/s);
}
double
dotq(Quaternion q, Quaternion r)
{
return q.r*r.r + q.i*r.i + q.j*r.j + q.k*r.k;
}
Quaternion
invq(Quaternion q)
{
double len²;
len² = dotq(q, q);
if(len² == 0)
return Quat(0,0,0,0);
return Quat(q.r/len², -q.i/len², -q.j/len², -q.k/len²);
}
double
qlen(Quaternion q)
{
return sqrt(dotq(q, q));
}
Quaternion
normq(Quaternion q)
{
return sdivq(q, qlen(q));
}
Vector3
qrotate(Vector3 p, Vector3 axis, double θ)
{
Quaternion qaxis, qr;
θ /= 2;
qaxis = Quatvec(cos(θ), mulvec3(axis, sin(θ)));
qr = mulq(mulq(qaxis, Quatvec(0, p)), invq(qaxis)); /* qpq⁻¹ */
return Vec3(qr.i, qr.j, qr.k);
}
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