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-rw-r--r--core/math/quaternion.cpp126
1 files changed, 107 insertions, 19 deletions
diff --git a/core/math/quaternion.cpp b/core/math/quaternion.cpp
index 11bfcc1a6f..6a5f29f3d8 100644
--- a/core/math/quaternion.cpp
+++ b/core/math/quaternion.cpp
@@ -31,7 +31,7 @@
#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);
@@ -79,6 +79,10 @@ 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());
}
@@ -111,11 +115,12 @@ Quaternion Quaternion::log() const {
Quaternion Quaternion::exp() const {
Quaternion src = *this;
Vector3 src_v = Vector3(src.x, src.y, src.z);
- float theta = src_v.length();
- if (theta < CMP_EPSILON) {
+ real_t theta = src_v.length();
+ 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 {
@@ -132,15 +137,9 @@ Quaternion Quaternion::slerp(const Quaternion &p_to, const real_t &p_weight) con
// adjust signs (if necessary)
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
@@ -189,16 +188,105 @@ 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
+ 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 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
- //the only way to do slerp :|
- real_t t2 = (1.0f - 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_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 blends.
+ return q1.slerp(q2, p_weight);
}
Quaternion::operator String() const {
@@ -213,7 +301,7 @@ Vector3 Quaternion::get_axis() const {
return Vector3(x * r, y * r, z * r);
}
-float Quaternion::get_angle() const {
+real_t Quaternion::get_angle() const {
return 2 * Math::acos(w);
}
generated by cgit v1.2.3 (git 2.25.1) at 2025-04-08 01:42:51 +0000