1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
|
#include <u.h>
#include <libc.h>
#include <ip.h>
#include <draw.h>
#include <geometry.h>
#include "dat.h"
#include "fns.h"
static double G = 6.674e-11;
/*
* Dynamics stepper
*/
static Point2
accelship(Universe *u, Particle *p, double)
{
double g, d;
/* TODO: take thrust into account, based on user input. */
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
eval(Universe *u, Particle *p0, double t, double Δt, Derivative *d, Point2 (*accel)(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 = accel(u, &p, t+Δt);
return res;
}
/*
* Semi-implicit Euler Integrator
*/
static void
euler1(Universe *u, Particle *p, double t, double Δt, Point2 (*accel)(Universe*,Particle*,double))
{
static Derivative ZD = {0};
Derivative d;
d = eval(u, p, t, Δt, &ZD, accel);
p->v = addpt2(p->v, mulpt2(d.dv, Δt));
p->p = addpt2(p->p, mulpt2(p->v, Δt));
}
/*
* RK4 Integrator
*/
static void
rk4(Universe *u, Particle *p, double t, double Δt, Point2 (*accel)(Universe*,Particle*,double))
{
static Derivative ZD = {0};
Derivative a, b, c, d;
Point2 dxdt, dvdt;
a = eval(u, p, t, 0, &ZD, accel);
b = eval(u, p, t, Δt/2, &a, accel);
c = eval(u, p, t, Δt/2, &b, accel);
d = eval(u, p, t, Δt, &c, accel);
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));
}
/*
* The Integrator
*/
void
integrate(Universe *u, double t, double Δt)
{
int i, j;
for(i = 0; i < nelem(u->ships); i++){
rk4(u, &u->ships[i], t, Δt, accelship);
for(j = 0; j < nelem(u->ships[i].rounds); j++)
if(u->ships[i].rounds[j].fired)
euler1(u, &u->ships[i].rounds[j], t, Δt, accelbullet);
}
}
|
