1/**************************************************************************/
2/* quaternion.cpp */
3/**************************************************************************/
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30
31#include "quaternion.h"
32
33#include "core/math/basis.h"
34#include "core/string/ustring.h"
35
36real_t Quaternion::angle_to(const Quaternion &p_to) const {
37 real_t d = dot(p_to);
38 // acos does clamping.
39 return Math::acos(d * d * 2 - 1);
40}
41
42Vector3 Quaternion::get_euler(EulerOrder p_order) const {
43#ifdef MATH_CHECKS
44 ERR_FAIL_COND_V_MSG(!is_normalized(), Vector3(0, 0, 0), "The quaternion must be normalized.");
45#endif
46 return Basis(*this).get_euler(p_order);
47}
48
49void Quaternion::operator*=(const Quaternion &p_q) {
50 real_t xx = w * p_q.x + x * p_q.w + y * p_q.z - z * p_q.y;
51 real_t yy = w * p_q.y + y * p_q.w + z * p_q.x - x * p_q.z;
52 real_t zz = w * p_q.z + z * p_q.w + x * p_q.y - y * p_q.x;
53 w = w * p_q.w - x * p_q.x - y * p_q.y - z * p_q.z;
54 x = xx;
55 y = yy;
56 z = zz;
57}
58
59Quaternion Quaternion::operator*(const Quaternion &p_q) const {
60 Quaternion r = *this;
61 r *= p_q;
62 return r;
63}
64
65bool Quaternion::is_equal_approx(const Quaternion &p_quaternion) const {
66 return Math::is_equal_approx(x, p_quaternion.x) && Math::is_equal_approx(y, p_quaternion.y) && Math::is_equal_approx(z, p_quaternion.z) && Math::is_equal_approx(w, p_quaternion.w);
67}
68
69bool Quaternion::is_finite() const {
70 return Math::is_finite(x) && Math::is_finite(y) && Math::is_finite(z) && Math::is_finite(w);
71}
72
73real_t Quaternion::length() const {
74 return Math::sqrt(length_squared());
75}
76
77void Quaternion::normalize() {
78 *this /= length();
79}
80
81Quaternion Quaternion::normalized() const {
82 return *this / length();
83}
84
85bool Quaternion::is_normalized() const {
86 return Math::is_equal_approx(length_squared(), 1, (real_t)UNIT_EPSILON); //use less epsilon
87}
88
89Quaternion Quaternion::inverse() const {
90#ifdef MATH_CHECKS
91 ERR_FAIL_COND_V_MSG(!is_normalized(), Quaternion(), "The quaternion must be normalized.");
92#endif
93 return Quaternion(-x, -y, -z, w);
94}
95
96Quaternion Quaternion::log() const {
97 Quaternion src = *this;
98 Vector3 src_v = src.get_axis() * src.get_angle();
99 return Quaternion(src_v.x, src_v.y, src_v.z, 0);
100}
101
102Quaternion Quaternion::exp() const {
103 Quaternion src = *this;
104 Vector3 src_v = Vector3(src.x, src.y, src.z);
105 real_t theta = src_v.length();
106 src_v = src_v.normalized();
107 if (theta < CMP_EPSILON || !src_v.is_normalized()) {
108 return Quaternion(0, 0, 0, 1);
109 }
110 return Quaternion(src_v, theta);
111}
112
113Quaternion Quaternion::slerp(const Quaternion &p_to, const real_t &p_weight) const {
114#ifdef MATH_CHECKS
115 ERR_FAIL_COND_V_MSG(!is_normalized(), Quaternion(), "The start quaternion must be normalized.");
116 ERR_FAIL_COND_V_MSG(!p_to.is_normalized(), Quaternion(), "The end quaternion must be normalized.");
117#endif
118 Quaternion to1;
119 real_t omega, cosom, sinom, scale0, scale1;
120
121 // calc cosine
122 cosom = dot(p_to);
123
124 // adjust signs (if necessary)
125 if (cosom < 0.0f) {
126 cosom = -cosom;
127 to1 = -p_to;
128 } else {
129 to1 = p_to;
130 }
131
132 // calculate coefficients
133
134 if ((1.0f - cosom) > (real_t)CMP_EPSILON) {
135 // standard case (slerp)
136 omega = Math::acos(cosom);
137 sinom = Math::sin(omega);
138 scale0 = Math::sin((1.0 - p_weight) * omega) / sinom;
139 scale1 = Math::sin(p_weight * omega) / sinom;
140 } else {
141 // "from" and "to" quaternions are very close
142 // ... so we can do a linear interpolation
143 scale0 = 1.0f - p_weight;
144 scale1 = p_weight;
145 }
146 // calculate final values
147 return Quaternion(
148 scale0 * x + scale1 * to1.x,
149 scale0 * y + scale1 * to1.y,
150 scale0 * z + scale1 * to1.z,
151 scale0 * w + scale1 * to1.w);
152}
153
154Quaternion Quaternion::slerpni(const Quaternion &p_to, const real_t &p_weight) const {
155#ifdef MATH_CHECKS
156 ERR_FAIL_COND_V_MSG(!is_normalized(), Quaternion(), "The start quaternion must be normalized.");
157 ERR_FAIL_COND_V_MSG(!p_to.is_normalized(), Quaternion(), "The end quaternion must be normalized.");
158#endif
159 const Quaternion &from = *this;
160
161 real_t dot = from.dot(p_to);
162
163 if (Math::absf(dot) > 0.9999f) {
164 return from;
165 }
166
167 real_t theta = Math::acos(dot),
168 sinT = 1.0f / Math::sin(theta),
169 newFactor = Math::sin(p_weight * theta) * sinT,
170 invFactor = Math::sin((1.0f - p_weight) * theta) * sinT;
171
172 return Quaternion(invFactor * from.x + newFactor * p_to.x,
173 invFactor * from.y + newFactor * p_to.y,
174 invFactor * from.z + newFactor * p_to.z,
175 invFactor * from.w + newFactor * p_to.w);
176}
177
178Quaternion Quaternion::spherical_cubic_interpolate(const Quaternion &p_b, const Quaternion &p_pre_a, const Quaternion &p_post_b, const real_t &p_weight) const {
179#ifdef MATH_CHECKS
180 ERR_FAIL_COND_V_MSG(!is_normalized(), Quaternion(), "The start quaternion must be normalized.");
181 ERR_FAIL_COND_V_MSG(!p_b.is_normalized(), Quaternion(), "The end quaternion must be normalized.");
182#endif
183 Quaternion from_q = *this;
184 Quaternion pre_q = p_pre_a;
185 Quaternion to_q = p_b;
186 Quaternion post_q = p_post_b;
187
188 // Align flip phases.
189 from_q = Basis(from_q).get_rotation_quaternion();
190 pre_q = Basis(pre_q).get_rotation_quaternion();
191 to_q = Basis(to_q).get_rotation_quaternion();
192 post_q = Basis(post_q).get_rotation_quaternion();
193
194 // Flip quaternions to shortest path if necessary.
195 bool flip1 = signbit(from_q.dot(pre_q));
196 pre_q = flip1 ? -pre_q : pre_q;
197 bool flip2 = signbit(from_q.dot(to_q));
198 to_q = flip2 ? -to_q : to_q;
199 bool flip3 = flip2 ? to_q.dot(post_q) <= 0 : signbit(to_q.dot(post_q));
200 post_q = flip3 ? -post_q : post_q;
201
202 // Calc by Expmap in from_q space.
203 Quaternion ln_from = Quaternion(0, 0, 0, 0);
204 Quaternion ln_to = (from_q.inverse() * to_q).log();
205 Quaternion ln_pre = (from_q.inverse() * pre_q).log();
206 Quaternion ln_post = (from_q.inverse() * post_q).log();
207 Quaternion ln = Quaternion(0, 0, 0, 0);
208 ln.x = Math::cubic_interpolate(ln_from.x, ln_to.x, ln_pre.x, ln_post.x, p_weight);
209 ln.y = Math::cubic_interpolate(ln_from.y, ln_to.y, ln_pre.y, ln_post.y, p_weight);
210 ln.z = Math::cubic_interpolate(ln_from.z, ln_to.z, ln_pre.z, ln_post.z, p_weight);
211 Quaternion q1 = from_q * ln.exp();
212
213 // Calc by Expmap in to_q space.
214 ln_from = (to_q.inverse() * from_q).log();
215 ln_to = Quaternion(0, 0, 0, 0);
216 ln_pre = (to_q.inverse() * pre_q).log();
217 ln_post = (to_q.inverse() * post_q).log();
218 ln = Quaternion(0, 0, 0, 0);
219 ln.x = Math::cubic_interpolate(ln_from.x, ln_to.x, ln_pre.x, ln_post.x, p_weight);
220 ln.y = Math::cubic_interpolate(ln_from.y, ln_to.y, ln_pre.y, ln_post.y, p_weight);
221 ln.z = Math::cubic_interpolate(ln_from.z, ln_to.z, ln_pre.z, ln_post.z, p_weight);
222 Quaternion q2 = to_q * ln.exp();
223
224 // To cancel error made by Expmap ambiguity, do blending.
225 return q1.slerp(q2, p_weight);
226}
227
228Quaternion 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,
229 const real_t &p_b_t, const real_t &p_pre_a_t, const real_t &p_post_b_t) const {
230#ifdef MATH_CHECKS
231 ERR_FAIL_COND_V_MSG(!is_normalized(), Quaternion(), "The start quaternion must be normalized.");
232 ERR_FAIL_COND_V_MSG(!p_b.is_normalized(), Quaternion(), "The end quaternion must be normalized.");
233#endif
234 Quaternion from_q = *this;
235 Quaternion pre_q = p_pre_a;
236 Quaternion to_q = p_b;
237 Quaternion post_q = p_post_b;
238
239 // Align flip phases.
240 from_q = Basis(from_q).get_rotation_quaternion();
241 pre_q = Basis(pre_q).get_rotation_quaternion();
242 to_q = Basis(to_q).get_rotation_quaternion();
243 post_q = Basis(post_q).get_rotation_quaternion();
244
245 // Flip quaternions to shortest path if necessary.
246 bool flip1 = signbit(from_q.dot(pre_q));
247 pre_q = flip1 ? -pre_q : pre_q;
248 bool flip2 = signbit(from_q.dot(to_q));
249 to_q = flip2 ? -to_q : to_q;
250 bool flip3 = flip2 ? to_q.dot(post_q) <= 0 : signbit(to_q.dot(post_q));
251 post_q = flip3 ? -post_q : post_q;
252
253 // Calc by Expmap in from_q space.
254 Quaternion ln_from = Quaternion(0, 0, 0, 0);
255 Quaternion ln_to = (from_q.inverse() * to_q).log();
256 Quaternion ln_pre = (from_q.inverse() * pre_q).log();
257 Quaternion ln_post = (from_q.inverse() * post_q).log();
258 Quaternion ln = Quaternion(0, 0, 0, 0);
259 ln.x = Math::cubic_interpolate_in_time(ln_from.x, ln_to.x, ln_pre.x, ln_post.x, p_weight, p_b_t, p_pre_a_t, p_post_b_t);
260 ln.y = Math::cubic_interpolate_in_time(ln_from.y, ln_to.y, ln_pre.y, ln_post.y, p_weight, p_b_t, p_pre_a_t, p_post_b_t);
261 ln.z = Math::cubic_interpolate_in_time(ln_from.z, ln_to.z, ln_pre.z, ln_post.z, p_weight, p_b_t, p_pre_a_t, p_post_b_t);
262 Quaternion q1 = from_q * ln.exp();
263
264 // Calc by Expmap in to_q space.
265 ln_from = (to_q.inverse() * from_q).log();
266 ln_to = Quaternion(0, 0, 0, 0);
267 ln_pre = (to_q.inverse() * pre_q).log();
268 ln_post = (to_q.inverse() * post_q).log();
269 ln = Quaternion(0, 0, 0, 0);
270 ln.x = Math::cubic_interpolate_in_time(ln_from.x, ln_to.x, ln_pre.x, ln_post.x, p_weight, p_b_t, p_pre_a_t, p_post_b_t);
271 ln.y = Math::cubic_interpolate_in_time(ln_from.y, ln_to.y, ln_pre.y, ln_post.y, p_weight, p_b_t, p_pre_a_t, p_post_b_t);
272 ln.z = Math::cubic_interpolate_in_time(ln_from.z, ln_to.z, ln_pre.z, ln_post.z, p_weight, p_b_t, p_pre_a_t, p_post_b_t);
273 Quaternion q2 = to_q * ln.exp();
274
275 // To cancel error made by Expmap ambiguity, do blending.
276 return q1.slerp(q2, p_weight);
277}
278
279Quaternion::operator String() const {
280 return "(" + String::num_real(x, false) + ", " + String::num_real(y, false) + ", " + String::num_real(z, false) + ", " + String::num_real(w, false) + ")";
281}
282
283Vector3 Quaternion::get_axis() const {
284 if (Math::abs(w) > 1 - CMP_EPSILON) {
285 return Vector3(x, y, z);
286 }
287 real_t r = ((real_t)1) / Math::sqrt(1 - w * w);
288 return Vector3(x * r, y * r, z * r);
289}
290
291real_t Quaternion::get_angle() const {
292 return 2 * Math::acos(w);
293}
294
295Quaternion::Quaternion(const Vector3 &p_axis, real_t p_angle) {
296#ifdef MATH_CHECKS
297 ERR_FAIL_COND_MSG(!p_axis.is_normalized(), "The axis Vector3 must be normalized.");
298#endif
299 real_t d = p_axis.length();
300 if (d == 0) {
301 x = 0;
302 y = 0;
303 z = 0;
304 w = 0;
305 } else {
306 real_t sin_angle = Math::sin(p_angle * 0.5f);
307 real_t cos_angle = Math::cos(p_angle * 0.5f);
308 real_t s = sin_angle / d;
309 x = p_axis.x * s;
310 y = p_axis.y * s;
311 z = p_axis.z * s;
312 w = cos_angle;
313 }
314}
315
316// Euler constructor expects a vector containing the Euler angles in the format
317// (ax, ay, az), where ax is the angle of rotation around x axis,
318// and similar for other axes.
319// This implementation uses YXZ convention (Z is the first rotation).
320Quaternion Quaternion::from_euler(const Vector3 &p_euler) {
321 real_t half_a1 = p_euler.y * 0.5f;
322 real_t half_a2 = p_euler.x * 0.5f;
323 real_t half_a3 = p_euler.z * 0.5f;
324
325 // R = Y(a1).X(a2).Z(a3) convention for Euler angles.
326 // Conversion to quaternion as listed in https://ntrs.nasa.gov/archive/nasa/casi.ntrs.nasa.gov/19770024290.pdf (page A-6)
327 // a3 is the angle of the first rotation, following the notation in this reference.
328
329 real_t cos_a1 = Math::cos(half_a1);
330 real_t sin_a1 = Math::sin(half_a1);
331 real_t cos_a2 = Math::cos(half_a2);
332 real_t sin_a2 = Math::sin(half_a2);
333 real_t cos_a3 = Math::cos(half_a3);
334 real_t sin_a3 = Math::sin(half_a3);
335
336 return Quaternion(
337 sin_a1 * cos_a2 * sin_a3 + cos_a1 * sin_a2 * cos_a3,
338 sin_a1 * cos_a2 * cos_a3 - cos_a1 * sin_a2 * sin_a3,
339 -sin_a1 * sin_a2 * cos_a3 + cos_a1 * cos_a2 * sin_a3,
340 sin_a1 * sin_a2 * sin_a3 + cos_a1 * cos_a2 * cos_a3);
341}
342