summaryrefslogtreecommitdiffstats
path: root/libdimension/torus.c
blob: 244f174dab5066ef5c964616b5de59a1f02a7674 (plain)
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
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
/*************************************************************************
 * Copyright (C) 2009-2010 Tavian Barnes <tavianator@gmail.com>          *
 *                                                                       *
 * This file is part of The Dimension Library.                           *
 *                                                                       *
 * The Dimension Library is free software; you can redistribute it and/  *
 * or modify it under the terms of the GNU Lesser General Public License *
 * as published by the Free Software Foundation; either version 3 of the *
 * License, or (at your option) any later version.                       *
 *                                                                       *
 * The Dimension Library is distributed in the hope that it will be      *
 * useful, but WITHOUT ANY WARRANTY; without even the implied warranty   *
 * of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU  *
 * Lesser General Public License for more details.                       *
 *                                                                       *
 * You should have received a copy of the GNU Lesser General Public      *
 * License along with this program.  If not, see                         *
 * <http://www.gnu.org/licenses/>.                                       *
 *************************************************************************/

/**
 * @file
 * Torii.  A special case of a quartic.
 */

#include "dimension.h"

/** Torus payload type. */
typedef struct dmnsn_torus_payload {
  double major, minor;
} dmnsn_torus_payload;

/** Bound the torus in a cylindrical shell. */
static inline bool
dmnsn_torus_bound_intersection(const dmnsn_torus_payload *payload, dmnsn_line l)
{
  double R = payload->major, r = payload->minor;
  double rmax = R + r, rmin = R - r;
  double rmax2 = rmax*rmax, rmin2 = rmin*rmin;

  /* Try the caps first */
  double tlower = (-r - l.x0.y)/l.n.y;
  double tupper = (+r - l.x0.y)/l.n.y;
  dmnsn_vector lower = dmnsn_line_point(l, tlower);
  dmnsn_vector upper = dmnsn_line_point(l, tupper);
  double ldist2 = lower.x*lower.x + lower.z*lower.z;
  double udist2 = upper.x*upper.x + upper.z*upper.z;
  if ((ldist2 < rmin2 || ldist2 > rmax2) && (udist2 < rmin2 || udist2 > rmax2))
  {
    /* No valid intersection with the caps, try the cylinder walls */
    double dist2 = l.x0.x*l.x0.x + l.x0.z*l.x0.z;
    double bigcyl[3], smallcyl[3];
    bigcyl[2]   = smallcyl[2] = l.n.x*l.n.x + l.n.z*l.n.z;
    bigcyl[1]   = smallcyl[1] = 2.0*(l.n.x*l.x0.x + l.n.z*l.x0.z);
    bigcyl[0]   = dist2 - rmax2;
    smallcyl[0] = dist2 - rmin2;

    double x[4];
    size_t n = dmnsn_solve_polynomial(bigcyl, 2, x);
    n += dmnsn_solve_polynomial(smallcyl, 2, x + n);

    size_t i;
    for (i = 0; i < n; ++i) {
      dmnsn_vector p = dmnsn_line_point(l, x[i]);
      if (p.y >= -r && p.y <= r)
        break;
    }

    if (i == n) {
      /* No valid intersection found */
      return false;
    }
  }

  return true;
}

/** Torus intersection callback. */
static bool
dmnsn_torus_intersection_fn(const dmnsn_object *torus, dmnsn_line l,
                            dmnsn_intersection *intersection)
{
  const dmnsn_torus_payload *payload = torus->ptr;
  double R = payload->major, r = payload->minor;
  double R2 = R*R, r2 = r*r;

  if (!dmnsn_torus_bound_intersection(payload, l))
    return false;

  /* This bit of algebra here is correct */
  dmnsn_vector x0mod = dmnsn_new_vector(l.x0.x, -l.x0.y, l.x0.z);
  dmnsn_vector nmod  = dmnsn_new_vector(l.n.x,  -l.n.y,  l.n.z);
  double nn      = dmnsn_vector_dot(l.n, l.n);
  double nx0     = dmnsn_vector_dot(l.n, l.x0);
  double x0x0    = dmnsn_vector_dot(l.x0, l.x0);
  double x0x0mod = dmnsn_vector_dot(l.x0, x0mod);
  double nx0mod  = dmnsn_vector_dot(l.n, x0mod);
  double nnmod   = dmnsn_vector_dot(l.n, nmod);

  double poly[5];
  poly[4] = nn*nn;
  poly[3] = 4*nn*nx0;
  poly[2] = 2.0*(nn*(x0x0 - r2) + 2.0*nx0*nx0 - R2*nnmod);
  poly[1] = 4.0*(nx0*(x0x0 - r2) - R2*nx0mod);
  poly[0] = x0x0*x0x0 + R2*(R2 - 2.0*x0x0mod) - r2*(2.0*(R2 + x0x0) - r2);

  double x[4];
  size_t n = dmnsn_solve_polynomial(poly, 4, x);
  if (n == 0)
    return false;

  double t = x[0];
  for (size_t i = 1; i < n; ++i) {
    t = dmnsn_min(t, x[i]);
  }

  if (t < 0.0)
    return false;

  dmnsn_vector p = dmnsn_line_point(l, t);
  dmnsn_vector center = dmnsn_vector_mul(
    payload->major,
    dmnsn_vector_normalize(dmnsn_new_vector(p.x, 0.0, p.z))
  );
  dmnsn_vector normal = dmnsn_vector_normalize(dmnsn_vector_sub(p, center));
  intersection->ray      = l;
  intersection->t        = t;
  intersection->normal   = normal;
  intersection->texture  = torus->texture;
  intersection->interior = torus->interior;
  return true;
}

/** Torus inside callback. */
static bool
dmnsn_torus_inside_fn(const dmnsn_object *torus, dmnsn_vector point)
{
  const dmnsn_torus_payload *payload = torus->ptr;
  double dmajor = payload->major - sqrt(point.x*point.x + point.z*point.z);
  return dmajor*dmajor + point.y*point.y < payload->minor*payload->minor;
}

/* Allocate a new torus */
dmnsn_object *
dmnsn_new_torus(double major, double minor)
{
  dmnsn_object *torus = dmnsn_new_object();
  torus->intersection_fn  = &dmnsn_torus_intersection_fn;
  torus->inside_fn        = &dmnsn_torus_inside_fn;
  torus->bounding_box.min = dmnsn_new_vector(-(major + minor),
                                             -minor,
                                             -(major + minor));
  torus->bounding_box.max = dmnsn_new_vector(major + minor,
                                             minor,
                                             major + minor);

  dmnsn_torus_payload *payload = dmnsn_malloc(sizeof(dmnsn_torus_payload));
  payload->major = major;
  payload->minor = minor;
  torus->ptr     = payload;
  torus->free_fn = &dmnsn_free;
  return torus;
}