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#include <u.h>
#include <libc.h>
#include <draw.h>
#include "libgeometry/geometry.h"
#include "dat.h"
#include "fns.h"
static double G = 6.674e-11;
/*
* Dynamics stepper
*/
static Point2
accel(GameState *s, double)
{
static double k = 15, b = 0.1;
return Vec2(0, -k*s->p.y - b*s->v.y);
}
static Derivative
eval(GameState *s0, double t, double Δt, Derivative *d)
{
GameState s;
Derivative res;
s.p = addpt2(s0->p, mulpt2(d->dx, Δt));
s.v = addpt2(s0->v, mulpt2(d->dv, Δt));
res.dx = s.v;
res.dv = accel(&s, t+Δt);
return res;
}
/*
* Explicit Euler Integrator
*/
static void
euler0(GameState *s, double t, double Δt)
{
static Derivative ZD = {0};
Derivative d;
d = eval(s, t, Δt, &ZD);
s->p = addpt2(s->p, mulpt2(d.dx, Δt));
s->v = addpt2(s->v, mulpt2(d.dv, Δt));
}
/*
* Semi-implicit Euler Integrator
*/
static void
euler1(GameState *s, double t, double Δt)
{
static Derivative ZD = {0};
Derivative d;
d = eval(s, t, Δt, &ZD);
s->v = addpt2(s->v, mulpt2(d.dv, Δt));
s->p = addpt2(s->p, mulpt2(s->v, Δt));
}
/*
* RK4 Integrator
*/
static void
rk4(GameState *s, double t, double Δt)
{
static Derivative ZD = {0};
Derivative a, b, c, d;
Point2 dxdt, dvdt;
a = eval(s, t, 0, &ZD);
b = eval(s, t, Δt/2, &a);
c = eval(s, t, Δt/2, &b);
d = eval(s, t, Δt, &c);
dxdt = divpt2(addpt2(addpt2(a.dx, mulpt2(addpt2(b.dx, c.dx), 2)), d.dx), 6);
dvdt = divpt2(addpt2(addpt2(a.dv, mulpt2(addpt2(b.dv, c.dv), 2)), d.dv), 6);
s->p = addpt2(s->p, mulpt2(dxdt, Δt));
s->v = addpt2(s->v, mulpt2(dvdt, Δt));
}
/*
* The Integrator
*/
void
integrate(GameState *s, double t, double Δt)
{
//euler0(s, t, Δt);
//euler1(s, t, Δt);
rk4(s, t, Δt);
}
/*
*
* UNIVERSE MIGRATION. KEEP CALM AND FASTEN YOUR SEAT BELTS.
*
*/
/*
* XXX: remember to take thrust into account, based on user input.
*/
static Point2
accelship(Universe *u, Particle *p, double)
{
double g, d;
d = vec2len(subpt2(u->star.p, p->p));
d *= 1e5; /* scale to the 100km/px range */
g = G*u->star.mass/(d*d);
return mulpt2(normvec2(subpt2(u->star.p, p->p)), g);
}
static Point2
accelbullet(Universe *, Particle *, double)
{
return Vec2(0,0);
}
static Derivative
evalu(Universe *u, Particle *p0, double t, double Δt, Derivative *d, Point2 (*a)(Universe*,Particle*,double))
{
Particle p;
Derivative res;
p.p = addpt2(p0->p, mulpt2(d->dx, Δt));
p.v = addpt2(p0->v, mulpt2(d->dv, Δt));
res.dx = p.v;
res.dv = a(u, &p, t+Δt);
return res;
}
static void
rk4u(Universe *u, Particle *p, double t, double Δt, Point2 (*acc)(Universe*,Particle*,double))
{
static Derivative ZD = {0};
Derivative a, b, c, d;
Point2 dxdt, dvdt;
a = evalu(u, p, t, 0, &ZD, acc);
b = evalu(u, p, t, Δt/2, &a, acc);
c = evalu(u, p, t, Δt/2, &b, acc);
d = evalu(u, p, t, Δt, &c, acc);
dxdt = divpt2(addpt2(addpt2(a.dx, mulpt2(addpt2(b.dx, c.dx), 2)), d.dx), 6);
dvdt = divpt2(addpt2(addpt2(a.dv, mulpt2(addpt2(b.dv, c.dv), 2)), d.dv), 6);
p->p = addpt2(p->p, mulpt2(dxdt, Δt));
p->v = addpt2(p->v, mulpt2(dvdt, Δt));
}
void
integrateu(Universe *u, double t, double Δt)
{
int i, j;
for(i = 0; i < nelem(u->ships); i++){
rk4u(u, &u->ships[i], t, Δt, accelship);
for(j = 0; j < nelem(u->ships[i].rounds); j++)
if(u->ships[i].rounds[j].fired)
rk4u(u, &u->ships[i].rounds[j], t, Δt, accelbullet);
}
}
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