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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);
}
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