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-rw-r--r--core/math/quaternion.cpp151
1 files changed, 97 insertions, 54 deletions
diff --git a/core/math/quaternion.cpp b/core/math/quaternion.cpp
index c681c60694..34e212a5b6 100644
--- a/core/math/quaternion.cpp
+++ b/core/math/quaternion.cpp
@@ -1,62 +1,48 @@
-/*************************************************************************/
-/* quaternion.cpp */
-/*************************************************************************/
-/* 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. */
-/*************************************************************************/
+/**************************************************************************/
+/* quaternion.cpp */
+/**************************************************************************/
+/* This file is part of: */
+/* GODOT ENGINE */
+/* https://godotengine.org */
+/**************************************************************************/
+/* Copyright (c) 2014-present Godot Engine contributors (see AUTHORS.md). */
+/* Copyright (c) 2007-2014 Juan Linietsky, Ariel Manzur. */
+/* */
+/* 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. */
+/**************************************************************************/
#include "quaternion.h"
#include "core/math/basis.h"
-#include "core/string/print_string.h"
+#include "core/string/ustring.h"
real_t Quaternion::angle_to(const Quaternion &p_to) const {
real_t d = dot(p_to);
return Math::acos(CLAMP(d * d * 2 - 1, -1, 1));
}
-// get_euler_xyz returns a vector containing the Euler angles in the format
-// (ax,ay,az), where ax is the angle of rotation around x axis,
-// and similar for other axes.
-// This implementation uses XYZ convention (Z is the first rotation).
-Vector3 Quaternion::get_euler_xyz() const {
- Basis m(*this);
- return m.get_euler(Basis::EULER_ORDER_XYZ);
-}
-
-// get_euler_yxz returns a vector containing the Euler angles in the format
-// (ax,ay,az), where ax is the angle of rotation around x axis,
-// and similar for other axes.
-// This implementation uses YXZ convention (Z is the first rotation).
-Vector3 Quaternion::get_euler_yxz() const {
+Vector3 Quaternion::get_euler(EulerOrder p_order) const {
#ifdef MATH_CHECKS
ERR_FAIL_COND_V_MSG(!is_normalized(), Vector3(0, 0, 0), "The quaternion must be normalized.");
#endif
- Basis m(*this);
- return m.get_euler(Basis::EULER_ORDER_YXZ);
+ return Basis(*this).get_euler(p_order);
}
void Quaternion::operator*=(const Quaternion &p_q) {
@@ -79,6 +65,10 @@ bool Quaternion::is_equal_approx(const Quaternion &p_quaternion) const {
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);
}
+bool Quaternion::is_finite() const {
+ return Math::is_finite(x) && Math::is_finite(y) && Math::is_finite(z) && Math::is_finite(w);
+}
+
real_t Quaternion::length() const {
return Math::sqrt(length_squared());
}
@@ -112,10 +102,11 @@ Quaternion Quaternion::exp() const {
Quaternion src = *this;
Vector3 src_v = Vector3(src.x, src.y, src.z);
real_t theta = src_v.length();
- if (theta < CMP_EPSILON) {
+ src_v = src_v.normalized();
+ if (theta < CMP_EPSILON || !src_v.is_normalized()) {
return Quaternion(0, 0, 0, 1);
}
- return Quaternion(src_v.normalized(), theta);
+ return Quaternion(src_v, theta);
}
Quaternion Quaternion::slerp(const Quaternion &p_to, const real_t &p_weight) const {
@@ -229,7 +220,58 @@ Quaternion Quaternion::spherical_cubic_interpolate(const Quaternion &p_b, const
ln.z = Math::cubic_interpolate(ln_from.z, ln_to.z, ln_pre.z, ln_post.z, p_weight);
Quaternion q2 = to_q * ln.exp();
- // To cancel error made by Expmap ambiguity, do blends.
+ // To cancel error made by Expmap ambiguity, do blending.
+ return q1.slerp(q2, p_weight);
+}
+
+Quaternion 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 {
+#ifdef MATH_CHECKS
+ ERR_FAIL_COND_V_MSG(!is_normalized(), Quaternion(), "The start quaternion must be normalized.");
+ ERR_FAIL_COND_V_MSG(!p_b.is_normalized(), Quaternion(), "The end quaternion must be normalized.");
+#endif
+ Quaternion from_q = *this;
+ Quaternion pre_q = p_pre_a;
+ Quaternion to_q = p_b;
+ Quaternion post_q = p_post_b;
+
+ // Align flip phases.
+ from_q = Basis(from_q).get_rotation_quaternion();
+ pre_q = Basis(pre_q).get_rotation_quaternion();
+ to_q = Basis(to_q).get_rotation_quaternion();
+ post_q = Basis(post_q).get_rotation_quaternion();
+
+ // Flip quaternions to shortest path if necessary.
+ bool flip1 = signbit(from_q.dot(pre_q));
+ pre_q = flip1 ? -pre_q : pre_q;
+ bool flip2 = signbit(from_q.dot(to_q));
+ to_q = flip2 ? -to_q : to_q;
+ bool flip3 = flip2 ? to_q.dot(post_q) <= 0 : signbit(to_q.dot(post_q));
+ post_q = flip3 ? -post_q : post_q;
+
+ // Calc by Expmap in from_q space.
+ Quaternion ln_from = Quaternion(0, 0, 0, 0);
+ Quaternion ln_to = (from_q.inverse() * to_q).log();
+ Quaternion ln_pre = (from_q.inverse() * pre_q).log();
+ Quaternion ln_post = (from_q.inverse() * post_q).log();
+ Quaternion ln = Quaternion(0, 0, 0, 0);
+ 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);
+ 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);
+ 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);
+ Quaternion q1 = from_q * ln.exp();
+
+ // Calc by Expmap in to_q space.
+ ln_from = (to_q.inverse() * from_q).log();
+ ln_to = Quaternion(0, 0, 0, 0);
+ ln_pre = (to_q.inverse() * pre_q).log();
+ ln_post = (to_q.inverse() * post_q).log();
+ ln = Quaternion(0, 0, 0, 0);
+ 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);
+ 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);
+ 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);
+ Quaternion q2 = to_q * ln.exp();
+
+ // To cancel error made by Expmap ambiguity, do blending.
return q1.slerp(q2, p_weight);
}
@@ -274,7 +316,7 @@ Quaternion::Quaternion(const Vector3 &p_axis, real_t p_angle) {
// (ax, ay, az), where ax is the angle of rotation around x axis,
// and similar for other axes.
// This implementation uses YXZ convention (Z is the first rotation).
-Quaternion::Quaternion(const Vector3 &p_euler) {
+Quaternion Quaternion::from_euler(const Vector3 &p_euler) {
real_t half_a1 = p_euler.y * 0.5f;
real_t half_a2 = p_euler.x * 0.5f;
real_t half_a3 = p_euler.z * 0.5f;
@@ -290,8 +332,9 @@ Quaternion::Quaternion(const Vector3 &p_euler) {
real_t cos_a3 = Math::cos(half_a3);
real_t sin_a3 = Math::sin(half_a3);
- x = sin_a1 * cos_a2 * sin_a3 + cos_a1 * sin_a2 * cos_a3;
- y = sin_a1 * cos_a2 * cos_a3 - cos_a1 * sin_a2 * sin_a3;
- z = -sin_a1 * sin_a2 * cos_a3 + cos_a1 * cos_a2 * sin_a3;
- w = sin_a1 * sin_a2 * sin_a3 + cos_a1 * cos_a2 * cos_a3;
+ return Quaternion(
+ sin_a1 * cos_a2 * sin_a3 + cos_a1 * sin_a2 * cos_a3,
+ sin_a1 * cos_a2 * cos_a3 - cos_a1 * sin_a2 * sin_a3,
+ -sin_a1 * sin_a2 * cos_a3 + cos_a1 * cos_a2 * sin_a3,
+ sin_a1 * sin_a2 * sin_a3 + cos_a1 * cos_a2 * cos_a3);
}
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