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
|
/*************************************************************************
* 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/>. *
*************************************************************************/
#include "dimension.h"
#include <math.h> /* For sqrt */
/*
* Sphere
*/
/* Sphere object callbacks */
static bool dmnsn_sphere_intersection_fn(const dmnsn_object *sphere,
dmnsn_line line,
dmnsn_intersection *intersection);
static bool dmnsn_sphere_inside_fn(const dmnsn_object *sphere,
dmnsn_vector point);
/* Allocate a new sphere */
dmnsn_object *
dmnsn_new_sphere()
{
dmnsn_object *sphere = dmnsn_new_object();
sphere->intersection_fn = &dmnsn_sphere_intersection_fn;
sphere->inside_fn = &dmnsn_sphere_inside_fn;
sphere->bounding_box.min = dmnsn_new_vector(-1.0, -1.0, -1.0);
sphere->bounding_box.max = dmnsn_new_vector(1.0, 1.0, 1.0);
return sphere;
}
/* Returns the closest intersection of `line' with `sphere' */
static bool
dmnsn_sphere_intersection_fn(const dmnsn_object *sphere, dmnsn_line line,
dmnsn_intersection *intersection)
{
dmnsn_line l = dmnsn_transform_line(sphere->trans_inv, line);
/* Solve (x0 + nx*t)^2 + (y0 + ny*t)^2 + (z0 + nz*t)^2 == 1 */
double a, b, c, t;
a = l.n.x*l.n.x + l.n.y*l.n.y + l.n.z*l.n.z;
b = 2.0*(l.n.x*l.x0.x + l.n.y*l.x0.y + l.n.z*l.x0.z);
c = l.x0.x*l.x0.x + l.x0.y*l.x0.y + l.x0.z*l.x0.z - 1.0;
if (b*b - 4.0*a*c >= 0) {
t = (-b - sqrt(b*b - 4.0*a*c))/(2*a);
if (t < 0.0) {
t = (-b + sqrt(b*b - 4.0*a*c))/(2*a);
}
if (t >= 0.0) {
intersection->ray = line;
intersection->t = t;
intersection->normal = dmnsn_transform_normal(sphere->trans,
dmnsn_line_point(l, t));
intersection->texture = sphere->texture;
intersection->interior = sphere->interior;
return true;
}
}
return false;
}
/* Return whether a point is inside a sphere (x**2 + y**2 + z**2 < 1.0) */
static bool
dmnsn_sphere_inside_fn(const dmnsn_object *sphere, dmnsn_vector point)
{
point = dmnsn_transform_vector(sphere->trans_inv, point);
return point.x*point.x + point.y*point.y + point.z*point.z < 1.0;
}
|
