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-rw-r--r--src/variant/quaternion.cpp204
1 files changed, 162 insertions, 42 deletions
diff --git a/src/variant/quaternion.cpp b/src/variant/quaternion.cpp
index 7a06cda..6b1ff14 100644
--- a/src/variant/quaternion.cpp
+++ b/src/variant/quaternion.cpp
@@ -35,13 +35,18 @@
namespace godot {
+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_xyz();
+ return m.get_euler(Basis::EULER_ORDER_XYZ);
}
// get_euler_yxz returns a vector containing the Euler angles in the format
@@ -50,17 +55,20 @@ Vector3 Quaternion::get_euler_xyz() const {
// This implementation uses YXZ convention (Z is the first rotation).
Vector3 Quaternion::get_euler_yxz() const {
#ifdef MATH_CHECKS
- ERR_FAIL_COND_V(!is_normalized(), Vector3(0, 0, 0));
+ 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) {
- x = w * p_q.x + x * p_q.w + y * p_q.z - z * p_q.y;
- y = w * p_q.y + y * p_q.w + z * p_q.x - x * p_q.z;
- z = w * p_q.z + z * p_q.w + x * p_q.y - y * p_q.x;
+ real_t xx = w * p_q.x + x * p_q.w + y * p_q.z - z * p_q.y;
+ real_t yy = w * p_q.y + y * p_q.w + z * p_q.x - x * p_q.z;
+ real_t zz = w * p_q.z + z * p_q.w + x * p_q.y - y * p_q.x;
w = w * p_q.w - x * p_q.x - y * p_q.y - z * p_q.z;
+ x = xx;
+ y = yy;
+ z = zz;
}
Quaternion Quaternion::operator*(const Quaternion &p_q) const {
@@ -69,8 +77,8 @@ Quaternion Quaternion::operator*(const Quaternion &p_q) const {
return r;
}
-bool Quaternion::is_equal_approx(const Quaternion &p_quat) const {
- return Math::is_equal_approx(x, p_quat.x) && Math::is_equal_approx(y, p_quat.y) && Math::is_equal_approx(z, p_quat.z) && Math::is_equal_approx(w, p_quat.w);
+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);
}
real_t Quaternion::length() const {
@@ -91,15 +99,32 @@ bool Quaternion::is_normalized() const {
Quaternion Quaternion::inverse() const {
#ifdef MATH_CHECKS
- ERR_FAIL_COND_V(!is_normalized(), Quaternion());
+ ERR_FAIL_COND_V_MSG(!is_normalized(), Quaternion(), "The quaternion must be normalized.");
#endif
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();
+ src_v = src_v.normalized();
+ if (theta < CMP_EPSILON || !src_v.is_normalized()) {
+ return Quaternion(0, 0, 0, 1);
+ }
+ return Quaternion(src_v, theta);
+}
+
Quaternion Quaternion::slerp(const Quaternion &p_to, const real_t &p_weight) const {
#ifdef MATH_CHECKS
- ERR_FAIL_COND_V(!is_normalized(), Quaternion());
- ERR_FAIL_COND_V(!p_to.is_normalized(), Quaternion());
+ ERR_FAIL_COND_V_MSG(!is_normalized(), Quaternion(), "The start quaternion must be normalized.");
+ ERR_FAIL_COND_V_MSG(!p_to.is_normalized(), Quaternion(), "The end quaternion must be normalized.");
#endif
Quaternion to1;
real_t omega, cosom, sinom, scale0, scale1;
@@ -108,22 +133,16 @@ 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);
@@ -132,7 +151,7 @@ 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
@@ -145,21 +164,21 @@ Quaternion Quaternion::slerp(const Quaternion &p_to, const real_t &p_weight) con
Quaternion Quaternion::slerpni(const Quaternion &p_to, const real_t &p_weight) const {
#ifdef MATH_CHECKS
- ERR_FAIL_COND_V(!is_normalized(), Quaternion());
- ERR_FAIL_COND_V(!p_to.is_normalized(), Quaternion());
+ ERR_FAIL_COND_V_MSG(!is_normalized(), Quaternion(), "The start quaternion must be normalized.");
+ ERR_FAIL_COND_V_MSG(!p_to.is_normalized(), Quaternion(), "The end quaternion must be normalized.");
#endif
const Quaternion &from = *this;
real_t dot = from.dot(p_to);
- if (Math::abs(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,
@@ -167,25 +186,126 @@ 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 = Math::sign(from_q.dot(pre_q));
+ pre_q = flip1 ? -pre_q : pre_q;
+ bool flip2 = Math::sign(from_q.dot(to_q));
+ to_q = flip2 ? -to_q : to_q;
+ bool flip3 = flip2 ? to_q.dot(post_q) <= 0 : Math::sign(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(!is_normalized(), Quaternion());
- ERR_FAIL_COND_V(!p_b.is_normalized(), Quaternion());
+ 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 = Math::sign(from_q.dot(pre_q));
+ pre_q = flip1 ? -pre_q : pre_q;
+ bool flip2 = Math::sign(from_q.dot(to_q));
+ to_q = flip2 ? -to_q : to_q;
+ bool flip3 = flip2 ? to_q.dot(post_q) <= 0 : Math::sign(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 {
- return String::num(x, 5) + ", " + String::num(y, 5) + ", " + String::num(z, 5) + ", " + String::num(w, 5);
+ 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(!p_axis.is_normalized());
+ ERR_FAIL_COND_MSG(!p_axis.is_normalized(), "The axis Vector3 must be normalized.");
#endif
real_t d = p_axis.length();
if (d == 0) {
@@ -194,8 +314,8 @@ 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;
@@ -209,9 +329,9 @@ 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)