/*
* given a triangle a,b,c, create 4 triangles:
*
* a
* / \
* / \
* d-------e
* /\ /\
* / \ / \
* / \ / \
* / \ \
* b-------f-------c
*
* a,d,e, e,d,f, d,b,f, and e,f,c
*
*/
static void subdivide_triangle(struct mesh *m, int tri)
{
struct vertex d, e, f, *pa, *pb, *pc, *pd, *pe, *pf;
union vec3 vd, ve, vf;
int shared, t;
pa = m->t[tri].v[0];
pb = m->t[tri].v[1];
pc = m->t[tri].v[2];
vd.v.x = (pa->x + pb->x) / 2.0;
vd.v.y = (pa->y + pb->y) / 2.0;
vd.v.z = (pa->z + pb->z) / 2.0;
ve.v.x = (pa->x + pc->x) / 2.0;
ve.v.y = (pa->y + pc->y) / 2.0;
ve.v.z = (pa->z + pc->z) / 2.0;
vf.v.x = (pb->x + pc->x) / 2.0;
vf.v.y = (pb->y + pc->y) / 2.0;
vf.v.z = (pb->z + pc->z) / 2.0;
vec3_normalize_self(&vd);
vec3_normalize_self(&ve);
vec3_normalize_self(&vf);
d.x = vd.v.x;
d.y = vd.v.y;
d.z = vd.v.z;
e.x = ve.v.x;
e.y = ve.v.y;
e.z = ve.v.z;
f.x = vf.v.x;
f.y = vf.v.y;
f.z = vf.v.z;
pd = lookup_maybe_add_vertex(m, &d, &shared);
pe = lookup_maybe_add_vertex(m, &e, &shared);
pf = lookup_maybe_add_vertex(m, &f, &shared);
/* replace initial triangle with central triangle, e,d,f */
m->t[tri].v[0] = pe;
m->t[tri].v[1] = pd;
m->t[tri].v[2] = pf;
/* add 3 surrounding triangles a,d,e, d,b,f, and e,f,c */
t = m->ntriangles;
m->t[t].v[0] = pa;
m->t[t].v[1] = pd;
m->t[t].v[2] = pe;
t++;
m->t[t].v[0] = pd;
m->t[t].v[1] = pb;
m->t[t].v[2] = pf;
t++;
m->t[t].v[0] = pe;
m->t[t].v[1] = pf;
m->t[t].v[2] = pc;
t++;
m->ntriangles = t;
}
/* For the +z face of a cubemapped unit sphere, returns tangent and bitangent vectors
* See: http://www.iquilezles.org/www/articles/patchedsphere/patchedsphere.htm
*/
void cubemapped_sphere_tangent_and_bitangent(float x, float y, union vec3 *u, union vec3 *v)
{
u->v.x = -(1.0f + y * y);
u->v.y = x * y;
u->v.z = x;
vec3_normalize_self(u);
v->v.x = x * y;
v->v.y = -(1 + x * x);
v->v.z = y;
vec3_normalize_self(v);
}
/* for a plane defined by n=normal, return a u and v vector that is on that plane and perpendictular */
void plane_vector_u_and_v_from_normal(union vec3 *u, union vec3 *v, const union vec3 *n)
{
union vec3 basis = { { 1, 0, 0 } };
/* find a vector we can use for our basis to define v */
float dot = vec3_dot(n, &basis);
if (fabs(dot) >= 1.0 - ZERO_TOLERANCE) {
/* if forward is parallel, we can use up */
vec3_init(&basis, 0, 1, 0);
}
/* find the right vector from our basis and the normal */
vec3_cross(v, &basis, n);
vec3_normalize_self(v);
/* now the final forward vector is perpendicular n and v */
vec3_cross(u, n, v);
vec3_normalize_self(u);
}
static void normalize_sphere(struct mesh *m)
{
int i;
for (i = 0; i < m->nvertices; i++) {
union vec3 v = { { m->v[i].x, m->v[i].y, m->v[i].z } };
vec3_normalize_self(&v);
m->v[i].x = v.v.x;
m->v[i].y = v.v.y;
m->v[i].y = v.v.y;
}
m->radius = 1.0;
}
static void recursive_add_bump(union vec3 pos, float r, float h,
float shrink, float rlimit)
{
float hoffset;
add_bump(pos, r, h);
if (r * shrink < rlimit)
return;
for (int i = 0; i < nbumps; i++) {
union vec3 d;
d.v.x = snis_random_float() * r * scatterfactor;
d.v.y = snis_random_float() * r * scatterfactor;
d.v.z = snis_random_float() * r * scatterfactor;
vec3_add_self(&d, &pos);
vec3_normalize_self(&d);
hoffset = snis_random_float() * h * shrink * 0.5;
recursive_add_bump(d, r * shrink, h * (shrink + 0.5 * (1.0 - shrink)) + hoffset, shrink, rlimit);
}
}
void mesh_set_spherical_vertex_normals(struct mesh *m)
{
int i, j;
for (i = 0; i < m->ntriangles; i++) {
union vec3 normal;
normal = compute_triangle_normal(&m->t[i]);
m->t[i].n.x = normal.v.x;
m->t[i].n.y = normal.v.y;
m->t[i].n.z = normal.v.z;
for (j = 0; j < 3; j++) {
union vec3 normal = { { m->t[i].v[j]->x, m->t[i].v[j]->y, m->t[i].v[j]->z } };
vec3_normalize_self(&normal);
m->t[i].vnormal[j].x = normal.v.x;
m->t[i].vnormal[j].y = normal.v.y;
m->t[i].vnormal[j].z = normal.v.z;
}
}
}
static union vec3 compute_triangle_normal(struct triangle *t)
{
union vec3 v1, v2, cross;
v1.v.x = t->v[1]->x - t->v[0]->x;
v1.v.y = t->v[1]->y - t->v[0]->y;
v1.v.z = t->v[1]->z - t->v[0]->z;
v2.v.x = t->v[2]->x - t->v[1]->x;
v2.v.y = t->v[2]->y - t->v[1]->y;
v2.v.z = t->v[2]->z - t->v[1]->z;
vec3_cross(&cross, &v1, &v2);
vec3_normalize_self(&cross);
/* make sure we always have a valid normal */
if (isnan(cross.v.x) || isnan(cross.v.y) || isnan(cross.v.z))
vec3_init(&cross, 0, 1, 0);
return cross;
}
/* convert from cubemap coords to cartesian coords on surface of sphere */
static union vec3 fij_to_xyz(int f, int i, int j, const int dim)
{
union vec3 answer;
switch (f) {
case 0:
answer.v.x = (float) (i - dim / 2) / (float) dim;
answer.v.y = -(float) (j - dim / 2) / (float) dim;
answer.v.z = 0.5;
break;
case 1:
answer.v.x = 0.5;
answer.v.y = -(float) (j - dim / 2) / (float) dim;
answer.v.z = -(float) (i - dim / 2) / (float) dim;
break;
case 2:
answer.v.x = -(float) (i - dim / 2) / (float) dim;
answer.v.y = -(float) (j - dim / 2) / (float) dim;
answer.v.z = -0.5;
break;
case 3:
answer.v.x = -0.5;
answer.v.y = -(float) (j - dim / 2) / (float) dim;
answer.v.z = (float) (i - dim / 2) / (float) dim;
break;
case 4:
answer.v.x = (float) (i - dim / 2) / (float) dim;
answer.v.y = 0.5;
answer.v.z = (float) (j - dim / 2) / (float) dim;
break;
case 5:
answer.v.x = (float) (i - dim / 2) / (float) dim;
answer.v.y = -0.5;
answer.v.z = -(float) (j - dim / 2) / (float) dim;
break;
}
vec3_normalize_self(&answer);
return answer;
}
/* fabricate a tube of length h, radius r, with nfaces, parallel to x axis */
struct mesh *mesh_tube(float h, float r, float nfaces)
{
struct mesh *m;
int ntris = nfaces * 2;
int nvertices = nfaces * 2;
int i, j;
float angle, da;
float l = h / 2.0;
m = allocate_mesh_for_copy(ntris, nvertices, 0, 1);
if (!m)
return m;
m->geometry_mode = MESH_GEOMETRY_TRIANGLES;
da = 2 * M_PI / (float) nfaces;
angle = 0.0;
for (i = 0; i < nvertices; i += 2) {
m->v[i].x = -l;
m->v[i].y = r * cos(angle);
m->v[i].z = r * -sin(angle);
m->v[i + 1].x = l;
m->v[i + 1].y = m->v[i].y;
m->v[i + 1].z = m->v[i].z;
angle += da;
}
m->nvertices = nvertices;
for (i = 0; i < ntris; i += 2) {
m->t[i].v[2] = &m->v[i % nvertices];
m->t[i].v[1] = &m->v[(i + 1) % nvertices];
m->t[i].v[0] = &m->v[(i + 2) % nvertices];
m->t[i + 1].v[2] = &m->v[(i + 2) % nvertices];
m->t[i + 1].v[1] = &m->v[(i + 1) % nvertices];
m->t[i + 1].v[0] = &m->v[(i + 3) % nvertices];
}
m->ntriangles = ntris;
for (i = 0; i < ntris; i++) {
union vec3 normal;
normal = compute_triangle_normal(&m->t[i]);
m->t[i].n.x = normal.v.x;
m->t[i].n.y = normal.v.y;
m->t[i].n.z = normal.v.z;
for (j = 0; j < 3; j++) {
union vec3 normal = { { 0, -m->t[i].v[j]->y, -m->t[i].v[j]->z } };
vec3_normalize_self(&normal);
m->t[i].vnormal[j].x = normal.v.x;
m->t[i].vnormal[j].y = normal.v.y;
m->t[i].vnormal[j].z = normal.v.z;
}
}
mesh_set_flat_shading_vertex_normals(m);
for (i = 0; i < ntris; i += 2) {
mesh_set_triangle_texture_coords(m, i,
0.0, (float) ((int) ((i + 2) / 2)) * 1.0 / (float) nfaces,
1.0, (float) ((int) (i / 2)) / (float) nfaces,
0.0, (float) ((int) (i / 2)) / (float) nfaces);
mesh_set_triangle_texture_coords(m, i + 1,
1.0, (float) ((int) ((i + 2) / 2)) / (float) nfaces,
1.0, (float) ((int) (i / 2)) / (float) nfaces,
0.0, (float) ((int) ((i + 2) / 2)) / (float) nfaces);
}
m->nlines = 0;
m->radius = mesh_compute_radius(m);
mesh_graph_dev_init(m);
return m;
}
