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#include "config.h"
#include "point.h"
#include "vector.h"
#include "eval.h"
#include "object.h"
#include "surface.h"
/* Sphere:
x = sqrt(1 - y^2) sin(360u)
y = 2v - 1
z = sqrt(1 - y^2) cos(360u)
hence v = (y+1)/2
and u = atan2_turns(x, z) (atan2 in "number of turns")
*/
#define INV2PI (1.0 / (2.0 * M_PI))
static inline flt atan2_turns(flt x, flt z)
{
flt r = atan2(x, z) * INV2PI;
if (r < 0.0) r += 1.0;
return r;
}
static inline void sphere_coords(flt x, flt y, flt z,
int * face, flt * u, flt * v)
{
*face = 0;
*u = atan2_turns(x, z);
*v = (y + 1.0) * 0.5;
}
/* Cube:
(x, y, 0) -> (0, x, y)
(x, y, 1) -> (1, x, y)
(0, y, z) -> (2, z, y)
(1, y, z) -> (3, z, y)
(x, 1, z) -> (4, x, z)
(x, 0, z) -> (5, x, z)
Watch out for rounding errors when determining which coordinate is 0 or 1;
see which one is closest to 0 or 1 */
static inline void cube_coords(flt x, flt y, flt z,
int * face, flt * u, flt * v)
{
flt dists[6] =
{ fabs(z), fabs(1 - z), fabs(x), fabs(1 - x), fabs(y), fabs(1 - y) };
flt min;
int f, i;
f = 0; min = dists[0];
for (i = 1; i < 6; i++)
if (dists[i] < min) { min = dists[i]; f = i; }
*face = f;
switch (f) {
case 0: case 1:
*u = x; *v = y; break;
case 2: case 3:
*u = z; *v = y; break;
case 4: case 5:
*u = x; *v = z; break;
}
}
/* Cylinder:
(x, 0, z) -> (2, u, v) where x = 2u-1 and z = 2v-1 hence
(x, 1, z) -> (1, x, z) u = (x+1)/2 and v = (z+1)/2
(x, y, z) -> (0, u, v) where x = sin(360u) v = y z = cos(360u)
hence u = atan2_turns(x, z) and v = y
*/
static inline void cylinder_coords(flt x, flt y, flt z,
int * face, flt * u, flt * v)
{
flt min, d;
int f;
min = y * y; f = 0;
d = (1 - y) * (1 - y);
if (d < min) { min = d; f = 1; }
d = fabs(x * x + z * z - 1);
if (d < min) { min = d; f = 2; }
*face = 2 - f;
if (f < 2) {
*u = (x + 1) * 0.5;
*v = (z + 1) * 0.5;
} else {
*u = atan2_turns(x, z);
*v = y;
}
}
/* Cone:
(x, y, z) -> (0, u, v) where x = v sin 360u
y = v
z = v cos 360u
hence u = atan2_turns(x, z) and v = y
(x, 1, z) -> (1, u, v) where x = 2u-1 and z = 2v-1
hence u = (x+1)/2 and v = (z+1)/2
*/
static inline void cone_coords(flt x, flt y, flt z,
int * face, flt * u, flt * v)
{
if ((1 - y) * (1 - y) < fabs(x * x + z * z - y * y)) {
*face = 1;
*u = (x + 1) * 0.5;
*v = (z + 1) * 0.5;
} else {
*face = 0;
*u = atan2_turns(x, z);
*v = y;
}
}
/* Plane */
static inline void plane_coords(flt x, flt y, flt z,
int * face, flt * u, flt * v)
{
*face = 0;
*u = x;
*v = z;
}
/* All together */
void surface_coords(struct object * obj, struct point * p,
/*out*/ int * face,
/*out*/ flt * u,
/*out*/ flt * v)
{
switch (obj->kind) {
case Cone:
cone_coords(p->x, p->y, p->z, face, u, v); break;
case Cube:
cube_coords(p->x, p->y, p->z, face, u, v); break;
case Cylinder:
cylinder_coords(p->x, p->y, p->z, face, u, v); break;
case Plane:
plane_coords(p->x, p->y, p->z, face, u, v); break;
case Sphere:
sphere_coords(p->x, p->y, p->z, face, u, v); break;
default:
assert(0);
}
}
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