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
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
|
/*************************************************************************/
/* quat.h */
/*************************************************************************/
/* This file is part of: */
/* GODOT ENGINE */
/* https://godotengine.org */
/*************************************************************************/
/* Copyright (c) 2007-2020 Juan Linietsky, Ariel Manzur. */
/* Copyright (c) 2014-2020 Godot Engine contributors (cf. AUTHORS.md). */
/* */
/* Permission is hereby granted, free of charge, to any person obtaining */
/* a copy of this software and associated documentation files (the */
/* "Software"), to deal in the Software without restriction, including */
/* without limitation the rights to use, copy, modify, merge, publish, */
/* distribute, sublicense, and/or sell copies of the Software, and to */
/* permit persons to whom the Software is furnished to do so, subject to */
/* the following conditions: */
/* */
/* The above copyright notice and this permission notice shall be */
/* included in all copies or substantial portions of the Software. */
/* */
/* THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, */
/* EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF */
/* MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT.*/
/* IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY */
/* CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, */
/* TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE */
/* SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE. */
/*************************************************************************/
// Circular dependency between Vector3 and Basis :/
#include "core/math/vector3.h"
#ifndef QUAT_H
#define QUAT_H
#include "core/math/math_defs.h"
#include "core/math/math_funcs.h"
#include "core/ustring.h"
class Quat {
public:
real_t x = 0, y = 0, z = 0, w = 1;
_FORCE_INLINE_ real_t length_squared() const;
bool is_equal_approx(const Quat &p_quat) const;
real_t length() const;
void normalize();
Quat normalized() const;
bool is_normalized() const;
Quat inverse() const;
_FORCE_INLINE_ real_t dot(const Quat &q) const;
void set_euler_xyz(const Vector3 &p_euler);
Vector3 get_euler_xyz() const;
void set_euler_yxz(const Vector3 &p_euler);
Vector3 get_euler_yxz() const;
void set_euler(const Vector3 &p_euler) { set_euler_yxz(p_euler); };
Vector3 get_euler() const { return get_euler_yxz(); };
Quat slerp(const Quat &q, const real_t &t) const;
Quat slerpni(const Quat &q, const real_t &t) const;
Quat cubic_slerp(const Quat &q, const Quat &prep, const Quat &postq, const real_t &t) const;
void set_axis_angle(const Vector3 &axis, const real_t &angle);
_FORCE_INLINE_ void get_axis_angle(Vector3 &r_axis, real_t &r_angle) const {
r_angle = 2 * Math::acos(w);
real_t r = ((real_t)1) / Math::sqrt(1 - w * w);
r_axis.x = x * r;
r_axis.y = y * r;
r_axis.z = z * r;
}
void operator*=(const Quat &q);
Quat operator*(const Quat &q) const;
Quat operator*(const Vector3 &v) const {
return Quat(w * v.x + y * v.z - z * v.y,
w * v.y + z * v.x - x * v.z,
w * v.z + x * v.y - y * v.x,
-x * v.x - y * v.y - z * v.z);
}
_FORCE_INLINE_ Vector3 xform(const Vector3 &v) const {
#ifdef MATH_CHECKS
ERR_FAIL_COND_V_MSG(!is_normalized(), v, "The quaternion must be normalized.");
#endif
Vector3 u(x, y, z);
Vector3 uv = u.cross(v);
return v + ((uv * w) + u.cross(uv)) * ((real_t)2);
}
_FORCE_INLINE_ void operator+=(const Quat &q);
_FORCE_INLINE_ void operator-=(const Quat &q);
_FORCE_INLINE_ void operator*=(const real_t &s);
_FORCE_INLINE_ void operator/=(const real_t &s);
_FORCE_INLINE_ Quat operator+(const Quat &q2) const;
_FORCE_INLINE_ Quat operator-(const Quat &q2) const;
_FORCE_INLINE_ Quat operator-() const;
_FORCE_INLINE_ Quat operator*(const real_t &s) const;
_FORCE_INLINE_ Quat operator/(const real_t &s) const;
_FORCE_INLINE_ bool operator==(const Quat &p_quat) const;
_FORCE_INLINE_ bool operator!=(const Quat &p_quat) const;
operator String() const;
inline void set(real_t p_x, real_t p_y, real_t p_z, real_t p_w) {
x = p_x;
y = p_y;
z = p_z;
w = p_w;
}
_FORCE_INLINE_ Quat() {}
_FORCE_INLINE_ Quat(real_t p_x, real_t p_y, real_t p_z, real_t p_w) :
x(p_x),
y(p_y),
z(p_z),
w(p_w) {
}
Quat(const Vector3 &axis, const real_t &angle) { set_axis_angle(axis, angle); }
Quat(const Vector3 &euler) { set_euler(euler); }
Quat(const Quat &q) :
x(q.x),
y(q.y),
z(q.z),
w(q.w) {
}
Quat operator=(const Quat &q) {
x = q.x;
y = q.y;
z = q.z;
w = q.w;
return *this;
}
Quat(const Vector3 &v0, const Vector3 &v1) // shortest arc
{
Vector3 c = v0.cross(v1);
real_t d = v0.dot(v1);
if (d < -1.0 + CMP_EPSILON) {
x = 0;
y = 1;
z = 0;
w = 0;
} else {
real_t s = Math::sqrt((1.0 + d) * 2.0);
real_t rs = 1.0 / s;
x = c.x * rs;
y = c.y * rs;
z = c.z * rs;
w = s * 0.5;
}
}
};
real_t Quat::dot(const Quat &q) const {
return x * q.x + y * q.y + z * q.z + w * q.w;
}
real_t Quat::length_squared() const {
return dot(*this);
}
void Quat::operator+=(const Quat &q) {
x += q.x;
y += q.y;
z += q.z;
w += q.w;
}
void Quat::operator-=(const Quat &q) {
x -= q.x;
y -= q.y;
z -= q.z;
w -= q.w;
}
void Quat::operator*=(const real_t &s) {
x *= s;
y *= s;
z *= s;
w *= s;
}
void Quat::operator/=(const real_t &s) {
*this *= 1.0 / s;
}
Quat Quat::operator+(const Quat &q2) const {
const Quat &q1 = *this;
return Quat(q1.x + q2.x, q1.y + q2.y, q1.z + q2.z, q1.w + q2.w);
}
Quat Quat::operator-(const Quat &q2) const {
const Quat &q1 = *this;
return Quat(q1.x - q2.x, q1.y - q2.y, q1.z - q2.z, q1.w - q2.w);
}
Quat Quat::operator-() const {
const Quat &q2 = *this;
return Quat(-q2.x, -q2.y, -q2.z, -q2.w);
}
Quat Quat::operator*(const real_t &s) const {
return Quat(x * s, y * s, z * s, w * s);
}
Quat Quat::operator/(const real_t &s) const {
return *this * (1.0 / s);
}
bool Quat::operator==(const Quat &p_quat) const {
return x == p_quat.x && y == p_quat.y && z == p_quat.z && w == p_quat.w;
}
bool Quat::operator!=(const Quat &p_quat) const {
return x != p_quat.x || y != p_quat.y || z != p_quat.z || w != p_quat.w;
}
#endif // QUAT_H
|