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-rw-r--r--core/math/quaternion.cpp118
1 files changed, 89 insertions, 29 deletions
diff --git a/core/math/quaternion.cpp b/core/math/quaternion.cpp
index 3f1d2c58e5..c681c60694 100644
--- a/core/math/quaternion.cpp
+++ b/core/math/quaternion.cpp
@@ -5,8 +5,8 @@
/* GODOT ENGINE */
/* https://godotengine.org */
/*************************************************************************/
-/* Copyright (c) 2007-2021 Juan Linietsky, Ariel Manzur. */
-/* Copyright (c) 2014-2021 Godot Engine contributors (cf. AUTHORS.md). */
+/* 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 */
@@ -44,7 +44,7 @@ real_t Quaternion::angle_to(const Quaternion &p_to) const {
// This implementation uses XYZ convention (Z is the first rotation).
Vector3 Quaternion::get_euler_xyz() const {
Basis m(*this);
- return m.get_euler_xyz();
+ return m.get_euler(Basis::EULER_ORDER_XYZ);
}
// get_euler_yxz returns a vector containing the Euler angles in the format
@@ -56,7 +56,7 @@ Vector3 Quaternion::get_euler_yxz() const {
ERR_FAIL_COND_V_MSG(!is_normalized(), Vector3(0, 0, 0), "The quaternion must be normalized.");
#endif
Basis m(*this);
- return m.get_euler_yxz();
+ return m.get_euler(Basis::EULER_ORDER_YXZ);
}
void Quaternion::operator*=(const Quaternion &p_q) {
@@ -102,6 +102,22 @@ Quaternion Quaternion::inverse() const {
return Quaternion(-x, -y, -z, w);
}
+Quaternion Quaternion::log() const {
+ Quaternion src = *this;
+ Vector3 src_v = src.get_axis() * src.get_angle();
+ return Quaternion(src_v.x, src_v.y, src_v.z, 0);
+}
+
+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) {
+ return Quaternion(0, 0, 0, 1);
+ }
+ return Quaternion(src_v.normalized(), theta);
+}
+
Quaternion Quaternion::slerp(const Quaternion &p_to, const real_t &p_weight) const {
#ifdef MATH_CHECKS
ERR_FAIL_COND_V_MSG(!is_normalized(), Quaternion(), "The start quaternion must be normalized.");
@@ -114,22 +130,16 @@ Quaternion Quaternion::slerp(const Quaternion &p_to, const real_t &p_weight) con
cosom = dot(p_to);
// adjust signs (if necessary)
- if (cosom < 0.0) {
+ if (cosom < 0.0f) {
cosom = -cosom;
- to1.x = -p_to.x;
- to1.y = -p_to.y;
- to1.z = -p_to.z;
- to1.w = -p_to.w;
+ to1 = -p_to;
} else {
- to1.x = p_to.x;
- to1.y = p_to.y;
- to1.z = p_to.z;
- to1.w = p_to.w;
+ to1 = p_to;
}
// calculate coefficients
- if ((1.0 - cosom) > CMP_EPSILON) {
+ if ((1.0f - cosom) > (real_t)CMP_EPSILON) {
// standard case (slerp)
omega = Math::acos(cosom);
sinom = Math::sin(omega);
@@ -138,7 +148,7 @@ Quaternion Quaternion::slerp(const Quaternion &p_to, const real_t &p_weight) con
} else {
// "from" and "to" quaternions are very close
// ... so we can do a linear interpolation
- scale0 = 1.0 - p_weight;
+ scale0 = 1.0f - p_weight;
scale1 = p_weight;
}
// calculate final values
@@ -158,14 +168,14 @@ Quaternion Quaternion::slerpni(const Quaternion &p_to, const real_t &p_weight) c
real_t dot = from.dot(p_to);
- if (Math::absf(dot) > 0.9999) {
+ if (Math::absf(dot) > 0.9999f) {
return from;
}
real_t theta = Math::acos(dot),
- sinT = 1.0 / Math::sin(theta),
+ sinT = 1.0f / Math::sin(theta),
newFactor = Math::sin(p_weight * theta) * sinT,
- invFactor = Math::sin((1.0 - p_weight) * theta) * sinT;
+ invFactor = Math::sin((1.0f - p_weight) * theta) * sinT;
return Quaternion(invFactor * from.x + newFactor * p_to.x,
invFactor * from.y + newFactor * p_to.y,
@@ -173,22 +183,72 @@ Quaternion Quaternion::slerpni(const Quaternion &p_to, const real_t &p_weight) c
invFactor * from.w + newFactor * p_to.w);
}
-Quaternion Quaternion::cubic_slerp(const Quaternion &p_b, const Quaternion &p_pre_a, const Quaternion &p_post_b, const real_t &p_weight) const {
+Quaternion Quaternion::spherical_cubic_interpolate(const Quaternion &p_b, const Quaternion &p_pre_a, const Quaternion &p_post_b, const real_t &p_weight) 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
- //the only way to do slerp :|
- real_t t2 = (1.0 - p_weight) * p_weight * 2;
- Quaternion sp = this->slerp(p_b, p_weight);
- Quaternion sq = p_pre_a.slerpni(p_post_b, p_weight);
- return sp.slerpni(sq, t2);
+ 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(ln_from.x, ln_to.x, ln_pre.x, ln_post.x, p_weight);
+ ln.y = Math::cubic_interpolate(ln_from.y, ln_to.y, ln_pre.y, ln_post.y, p_weight);
+ ln.z = Math::cubic_interpolate(ln_from.z, ln_to.z, ln_pre.z, ln_post.z, p_weight);
+ 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(ln_from.x, ln_to.x, ln_pre.x, ln_post.x, p_weight);
+ ln.y = Math::cubic_interpolate(ln_from.y, ln_to.y, ln_pre.y, ln_post.y, p_weight);
+ 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.
+ return q1.slerp(q2, p_weight);
}
Quaternion::operator String() const {
return "(" + String::num_real(x, false) + ", " + String::num_real(y, false) + ", " + String::num_real(z, false) + ", " + String::num_real(w, false) + ")";
}
+Vector3 Quaternion::get_axis() const {
+ if (Math::abs(w) > 1 - CMP_EPSILON) {
+ return Vector3(x, y, z);
+ }
+ real_t r = ((real_t)1) / Math::sqrt(1 - w * w);
+ return Vector3(x * r, y * r, z * r);
+}
+
+real_t Quaternion::get_angle() const {
+ return 2 * Math::acos(w);
+}
+
Quaternion::Quaternion(const Vector3 &p_axis, real_t p_angle) {
#ifdef MATH_CHECKS
ERR_FAIL_COND_MSG(!p_axis.is_normalized(), "The axis Vector3 must be normalized.");
@@ -200,8 +260,8 @@ Quaternion::Quaternion(const Vector3 &p_axis, real_t p_angle) {
z = 0;
w = 0;
} else {
- real_t sin_angle = Math::sin(p_angle * 0.5);
- real_t cos_angle = Math::cos(p_angle * 0.5);
+ real_t sin_angle = Math::sin(p_angle * 0.5f);
+ real_t cos_angle = Math::cos(p_angle * 0.5f);
real_t s = sin_angle / d;
x = p_axis.x * s;
y = p_axis.y * s;
@@ -215,9 +275,9 @@ Quaternion::Quaternion(const Vector3 &p_axis, real_t p_angle) {
// and similar for other axes.
// This implementation uses YXZ convention (Z is the first rotation).
Quaternion::Quaternion(const Vector3 &p_euler) {
- real_t half_a1 = p_euler.y * 0.5;
- real_t half_a2 = p_euler.x * 0.5;
- real_t half_a3 = p_euler.z * 0.5;
+ 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;
// R = Y(a1).X(a2).Z(a3) convention for Euler angles.
// Conversion to quaternion as listed in https://ntrs.nasa.gov/archive/nasa/casi.ntrs.nasa.gov/19770024290.pdf (page A-6)
generated by cgit v1.2.3 (git 2.25.1) at 2025-04-07 16:51:48 +0000