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
230
231
232
233
234
235
|
/*************************************************************************/
/* quaternion.h */
/*************************************************************************/
/* This file is part of: */
/* GODOT ENGINE */
/* https://godotengine.org */
/*************************************************************************/
/* Copyright (c) 2007-2022 Juan Linietsky, Ariel Manzur. */
/* Copyright (c) 2014-2022 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. */
/*************************************************************************/
#ifndef QUATERNION_H
#define QUATERNION_H
#include "core/math/math_funcs.h"
#include "core/math/vector3.h"
class String;
struct _NO_DISCARD_ Quaternion {
union {
struct {
real_t x;
real_t y;
real_t z;
real_t w;
};
real_t components[4] = { 0, 0, 0, 1.0 };
};
_FORCE_INLINE_ real_t &operator[](int idx) {
return components[idx];
}
_FORCE_INLINE_ const real_t &operator[](int idx) const {
return components[idx];
}
_FORCE_INLINE_ real_t length_squared() const;
bool is_equal_approx(const Quaternion &p_quaternion) const;
bool is_finite() const;
real_t length() const;
void normalize();
Quaternion normalized() const;
bool is_normalized() const;
Quaternion inverse() const;
Quaternion log() const;
Quaternion exp() const;
_FORCE_INLINE_ real_t dot(const Quaternion &p_q) const;
real_t angle_to(const Quaternion &p_to) const;
Vector3 get_euler_xyz() const;
Vector3 get_euler_yxz() const;
Vector3 get_euler() const { return get_euler_yxz(); };
static Quaternion from_euler(const Vector3 &p_euler);
Quaternion slerp(const Quaternion &p_to, const real_t &p_weight) const;
Quaternion slerpni(const Quaternion &p_to, const real_t &p_weight) const;
Quaternion spherical_cubic_interpolate(const Quaternion &p_b, const Quaternion &p_pre_a, const Quaternion &p_post_b, const real_t &p_weight) const;
Quaternion spherical_cubic_interpolate_in_time(const Quaternion &p_b, const Quaternion &p_pre_a, const Quaternion &p_post_b, const real_t &p_weight, const real_t &p_b_t, const real_t &p_pre_a_t, const real_t &p_post_b_t) const;
Vector3 get_axis() const;
real_t get_angle() const;
_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 Quaternion &p_q);
Quaternion operator*(const Quaternion &p_q) const;
_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_ Vector3 xform_inv(const Vector3 &v) const {
return inverse().xform(v);
}
_FORCE_INLINE_ void operator+=(const Quaternion &p_q);
_FORCE_INLINE_ void operator-=(const Quaternion &p_q);
_FORCE_INLINE_ void operator*=(const real_t &s);
_FORCE_INLINE_ void operator/=(const real_t &s);
_FORCE_INLINE_ Quaternion operator+(const Quaternion &q2) const;
_FORCE_INLINE_ Quaternion operator-(const Quaternion &q2) const;
_FORCE_INLINE_ Quaternion operator-() const;
_FORCE_INLINE_ Quaternion operator*(const real_t &s) const;
_FORCE_INLINE_ Quaternion operator/(const real_t &s) const;
_FORCE_INLINE_ bool operator==(const Quaternion &p_quaternion) const;
_FORCE_INLINE_ bool operator!=(const Quaternion &p_quaternion) const;
operator String() const;
_FORCE_INLINE_ Quaternion() {}
_FORCE_INLINE_ Quaternion(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) {
}
Quaternion(const Vector3 &p_axis, real_t p_angle);
Quaternion(const Quaternion &p_q) :
x(p_q.x),
y(p_q.y),
z(p_q.z),
w(p_q.w) {
}
void operator=(const Quaternion &p_q) {
x = p_q.x;
y = p_q.y;
z = p_q.z;
w = p_q.w;
}
Quaternion(const Vector3 &v0, const Vector3 &v1) { // Shortest arc.
Vector3 c = v0.cross(v1);
real_t d = v0.dot(v1);
if (d < -1.0f + (real_t)CMP_EPSILON) {
x = 0;
y = 1;
z = 0;
w = 0;
} else {
real_t s = Math::sqrt((1.0f + d) * 2.0f);
real_t rs = 1.0f / s;
x = c.x * rs;
y = c.y * rs;
z = c.z * rs;
w = s * 0.5f;
}
}
};
real_t Quaternion::dot(const Quaternion &p_q) const {
return x * p_q.x + y * p_q.y + z * p_q.z + w * p_q.w;
}
real_t Quaternion::length_squared() const {
return dot(*this);
}
void Quaternion::operator+=(const Quaternion &p_q) {
x += p_q.x;
y += p_q.y;
z += p_q.z;
w += p_q.w;
}
void Quaternion::operator-=(const Quaternion &p_q) {
x -= p_q.x;
y -= p_q.y;
z -= p_q.z;
w -= p_q.w;
}
void Quaternion::operator*=(const real_t &s) {
x *= s;
y *= s;
z *= s;
w *= s;
}
void Quaternion::operator/=(const real_t &s) {
*this *= 1.0f / s;
}
Quaternion Quaternion::operator+(const Quaternion &q2) const {
const Quaternion &q1 = *this;
return Quaternion(q1.x + q2.x, q1.y + q2.y, q1.z + q2.z, q1.w + q2.w);
}
Quaternion Quaternion::operator-(const Quaternion &q2) const {
const Quaternion &q1 = *this;
return Quaternion(q1.x - q2.x, q1.y - q2.y, q1.z - q2.z, q1.w - q2.w);
}
Quaternion Quaternion::operator-() const {
const Quaternion &q2 = *this;
return Quaternion(-q2.x, -q2.y, -q2.z, -q2.w);
}
Quaternion Quaternion::operator*(const real_t &s) const {
return Quaternion(x * s, y * s, z * s, w * s);
}
Quaternion Quaternion::operator/(const real_t &s) const {
return *this * (1.0f / s);
}
bool Quaternion::operator==(const Quaternion &p_quaternion) const {
return x == p_quaternion.x && y == p_quaternion.y && z == p_quaternion.z && w == p_quaternion.w;
}
bool Quaternion::operator!=(const Quaternion &p_quaternion) const {
return x != p_quaternion.x || y != p_quaternion.y || z != p_quaternion.z || w != p_quaternion.w;
}
_FORCE_INLINE_ Quaternion operator*(const real_t &p_real, const Quaternion &p_quaternion) {
return p_quaternion * p_real;
}
#endif // QUATERNION_H
|