void leap_frog(const data* dat, output_function output)
{
int i;
double dt = dat->eta * delta_t_factor;
vector *a = (vector*) malloc((dat->N)*sizeof(vector)),
*a_1 = (vector*) malloc((dat->N)*sizeof(vector)),
*r_p = (vector*) malloc((dat->N)*sizeof(vector)), // r_(n+1/2), not initialized
*r = init_r(dat), // r_(n+1)
*r_n = (vector*) malloc((dat->N)*sizeof(vector)), // r_(n+3/2), not initialized
*v = init_v(dat); // v_(n+1)
double time = 0;
output(time, dt, dat, r, v);
// initial step
for (i = 0; i < dat->N; i++)
// set r_(1/2)
r_n[i] = vector_add(r[i], scalar_mult(0.5 * dt, v[i]));
// regular timesteps
while (time < dat->t_max)
{
// a_(n+1/2)
accelerations(dat, r_n, a);
adots(dat, r_n, v, a_1);
for (i = 0; i < dat->N; i++)
{
// store previous values as r_(n+1/2)
r_p[i] = r_n[i];
// v_(n+1)
vector_add_to(&v[i], scalar_mult(dt, a[i]));
// r_(n+3/2)
vector_add_to(&r_n[i], scalar_mult(dt, v[i]));
// build r_(n+1)
r[i] = scalar_mult(0.5, vector_add(r_p[i], r_n[i]));
}
dt = delta_t(dat, a, a_1);
time += dt;
output(time, dt, dat, r, v);
}
free(a); free(r_p); free(r); free(r_n); free(v);
}
static void update_shape(jigglystruct *js)
{
vertex *vtx = js->shape->vertices;
edge *e = js->shape->edges;
vector zero;
vector_init(zero, 0, 0, 0);
/* sum all the vertex-vertex forces */
while(e) {
vector f;
coord mag;
vector_sub(e->left->vtx->v, e->right->vtx->v, f);
mag = js->stable_distance - magnitude(f);
vector_scale(f, mag);
vector_add_to(e->left->vtx->f, f);
vector_sub(zero, f, f);
vector_add_to(e->right->vtx->f, f);
e = e->next;
}
/* scale back the v-v force and add the spherical force
* then add the result to the vertex velocity, damping
* if necessary. Finally, move the vertex */
while(vtx) {
coord mag;
vector to_sphere;
vector_scale(vtx->f, js->hold_strength);
vector_copy(to_sphere, vtx->v);
mag = 1 - magnitude(to_sphere);
vector_scale(to_sphere, mag * js->spherify_strength);
vector_add_to(vtx->f, to_sphere);
vector_add_to(vtx->vel, vtx->f);
vector_init(vtx->f, 0, 0, 0);
mag = magnitude2(vtx->vel);
if(mag > js->damping_velocity)
vector_scale(vtx->vel, js->damping_factor);
vector_add_to(vtx->v, vtx->vel);
vtx = vtx->next;
}
}
static inline void vertex_calcnormal(vertex *vtx, jigglystruct *js)
{
hedge *start = vtx->h, *h=start;
vector_init(vtx->n, 0, 0, 0);
do {
vector u, v, norm;
vector_sub(h->prev->vtx->v, vtx->v, u);
vector_sub(h->next->vtx->v, vtx->v, v);
cross(u, v, norm);
vector_add_to(vtx->n, norm);
h = partner(h)->next;
} while(h != start);
if(!js->spooky)
normalize(vtx->n);
else
vector_scale(vtx->n, js->spooky);
}
void runge_kutta(const data* dat, output_function output)
{
int i;
double dt = dat->eta * delta_t_factor;
vector *r = init_r(dat),
*v = init_v(dat),
*a = (vector*) malloc((dat->N)*sizeof(vector)),
*a_1 = (vector*) malloc((dat->N)*sizeof(vector));
// temporary r vector for acceleration calculations
vector *rt = (vector*) malloc((dat->N)*sizeof(vector));
vector *a1 = (vector*) malloc((dat->N)*sizeof(vector)),
*a2 = (vector*) malloc((dat->N)*sizeof(vector)),
*a3 = (vector*) malloc((dat->N)*sizeof(vector)),
*a4 = (vector*) malloc((dat->N)*sizeof(vector));
vector *r1 = (vector*) malloc((dat->N)*sizeof(vector)),
*r2 = (vector*) malloc((dat->N)*sizeof(vector)),
*r3 = (vector*) malloc((dat->N)*sizeof(vector)),
*r4 = (vector*) malloc((dat->N)*sizeof(vector));
vector *v1 = (vector*) malloc((dat->N)*sizeof(vector)),
*v2 = (vector*) malloc((dat->N)*sizeof(vector)),
*v3 = (vector*) malloc((dat->N)*sizeof(vector)),
*v4 = (vector*) malloc((dat->N)*sizeof(vector));
double time = 0;
while (time < dat->t_max)
{
accelerations(dat, r, a1);
for (i = 0; i < dat->N; i++)
{
v1[i] = scalar_mult(dt, a1[i]);
r1[i] = scalar_mult(dt, v[i]);
// temp r for a2
rt[i] = vector_add(r[i], scalar_mult(0.5, r1[i]));
}
accelerations(dat, rt, a2);
for (i = 0; i < dat->N; i++)
{
v2[i] = scalar_mult(dt, a2[i]);
r2[i] = scalar_mult(dt, vector_add(v[i], scalar_mult(0.5, v1[i])));
// temp r for a3
rt[i] = vector_add(r[i], scalar_mult(0.5, r2[i]));
}
accelerations(dat, rt, a3);
for (i = 0; i < dat->N; i++)
{
v3[i] = scalar_mult(dt, a3[i]);
r3[i] = scalar_mult(dt, vector_add(v[i], scalar_mult(0.5, v2[i])));
// temp r for a3
rt[i] = vector_add(r[i], scalar_mult(0.5, r3[i]));
}
accelerations(dat, rt, a4);
for (i = 0; i < dat->N; i++)
{
v4[i] = scalar_mult(dt, a4[i]);
r4[i] = scalar_mult(dt, vector_add(v[i], v3[i]));
// calculate v_(n+1) and r_(n+1)
vector_add_to(&v[i], vector_add(scalar_mult(1.0/6.0, v1[i]),
vector_add(scalar_mult(1.0/3.0, v2[i]),
vector_add(scalar_mult(1.0/3.0, v3[i]),
scalar_mult(1.0/6.0, v4[i])))));
vector_add_to(&r[i], vector_add(scalar_mult(1.0/6.0, r1[i]),
vector_add(scalar_mult(1.0/3.0, r2[i]),
vector_add(scalar_mult(1.0/3.0, r3[i]),
scalar_mult(1.0/6.0, r4[i])))));
}
// increase time
adots(dat, r, v, a_1);
dt = delta_t(dat, a1, a_1); // a1 = a(t_n), a_1 = a'(t_n)
time += dt;
output(time, dt, dat, r, v);
}
free(r); free(v); free(a); free(a_1);
free(rt);
free(r1); free(r2); free(r3); free(r4);
free(v1); free(v2); free(v3); free(v4);
free(a1); free(a2); free(a3); free(a4);
}