diff options
Diffstat (limited to 'core/math/quaternion.cpp')
| -rw-r--r-- | core/math/quaternion.cpp | 91 |
1 files changed, 67 insertions, 24 deletions
diff --git a/core/math/quaternion.cpp b/core/math/quaternion.cpp index c681c60694..942a0b766e 100644 --- a/core/math/quaternion.cpp +++ b/core/math/quaternion.cpp @@ -31,32 +31,18 @@ #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 { @@ -233,6 +224,57 @@ Quaternion Quaternion::spherical_cubic_interpolate(const Quaternion &p_b, const 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 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) + ")"; } @@ -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); } |