88 Quaternion(
double inI,
double inJ,
double inK,
double inS) noexcept :
89 components_{ inI, inJ, inK, inS }
100 Quaternion(
const std::array<double, 4>& components) noexcept :
101 components_{ components }
115 components_{ 0., 0., 0., 0. }
117 if (inArray.
size() == 3)
120 eulerToQuat(inArray[0], inArray[1], inArray[2]);
122 else if (inArray.
size() == 4)
128 else if (inArray.
size() == 9)
151 const double halfAngle = inAngle / 2.;
152 const double sinHalfAngle =
std::sin(halfAngle);
154 components_[0] = normAxis.
x * sinHalfAngle;
155 components_[1] = normAxis.
y * sinHalfAngle;
156 components_[2] = normAxis.
z * sinHalfAngle;
157 components_[3] =
std::cos(halfAngle);
180 return 2. * std::acos(
s());
202 eyeTimesScalar.
zeros();
203 eyeTimesScalar(0, 0) = inQuat2.
s();
204 eyeTimesScalar(1, 1) = inQuat2.
s();
205 eyeTimesScalar(2, 2) = inQuat2.
s();
207 NdArray<double> epsilonHat = linalg::hat<double>(inQuat2.
i(), inQuat2.
j(), inQuat2.
k());
209 q.
put(
Slice(0, 3),
Slice(0, 3), eyeTimesScalar + epsilonHat);
210 q(3, 0) = -inQuat2.
i();
211 q(3, 1) = -inQuat2.
j();
212 q(3, 2) = -inQuat2.
k();
241 const auto sinHalfAngle =
std::sin(halfAngle);
242 auto axis =
Vec3(
i() / sinHalfAngle,
j() / sinHalfAngle,
k() / sinHalfAngle);
258 return { -
i(), -
j(), -
k(),
s() };
267 double i() const noexcept
269 return components_[0];
301 double j() const noexcept
303 return components_[1];
312 double k() const noexcept
314 return components_[2];
328 if (inPercent < 0. || inPercent > 1.)
342 const double oneMinus = 1. - inPercent;
343 std::array<double, 4> newComponents{};
346 inQuat1.components_.end(),
347 inQuat2.components_.begin(),
348 newComponents.begin(),
349 [inPercent, oneMinus](
double component1,
double component2) ->
double
350 { return oneMinus * component1 + inPercent * component2; });
352 return { newComponents };
365 return nlerp(*
this, inQuat2, inPercent);
376 return std::asin(2 * (
s() *
j() -
k() *
i()));
432 if (inVector.
size() != 3)
437 return *
this * inVector;
449 return *
this * inVec3;
458 double s() const noexcept
460 return components_[3];
474 if (inPercent < 0 || inPercent > 1)
500 constexpr
double DOT_THRESHOLD = 0.9995;
501 if (dotProduct > DOT_THRESHOLD)
505 return nlerp(inQuat1, inQuat2, inPercent);
508 dotProduct =
clip(dotProduct, -1., 1.);
509 const double theta0 = std::acos(dotProduct);
510 const double theta = theta0 * inPercent;
530 return slerp(*
this, inQuat2, inPercent);
557 const double q0 =
i();
558 const double q1 =
j();
559 const double q2 =
k();
560 const double q3 =
s();
567 dcm(0, 0) = q3sqr + q0sqr - q1sqr - q2sqr;
568 dcm(0, 1) = 2. * (q0 * q1 - q3 * q2);
569 dcm(0, 2) = 2. * (q0 * q2 + q3 * q1);
570 dcm(1, 0) = 2. * (q0 * q1 + q3 * q2);
571 dcm(1, 1) = q3sqr + q1sqr - q0sqr - q2sqr;
572 dcm(1, 2) = 2. * (q1 * q2 - q3 * q0);
573 dcm(2, 0) = 2. * (q0 * q2 - q3 * q1);
574 dcm(2, 1) = 2. * (q1 * q2 + q3 * q0);
575 dcm(2, 2) = q3sqr + q2sqr - q0sqr - q1sqr;
588 auto componentsCopy = components_;
601 const Vec3 eulerAxis = { 1., 0., 0. };
611 double yaw() const noexcept
637 const Vec3 eulerAxis = { 0., 1., 0. };
650 const Vec3 eulerAxis = { 0., 0., 1. };
663 const auto comparitor = [](
double value1,
double value2) noexcept ->
bool
668 inRhs.components_.begin(),
681 return !(*
this == inRhs);
695 inRhs.components_.begin(),
697 std::plus<double>());
727 inRhs.components_.begin(),
729 std::minus<double>());
768 double q0 = inRhs.
s() *
i();
769 q0 += inRhs.i() *
s();
770 q0 -= inRhs.j() *
k();
771 q0 += inRhs.k() *
j();
773 double q1 = inRhs.s() *
j();
774 q1 += inRhs.i() *
k();
775 q1 += inRhs.j() *
s();
776 q1 -= inRhs.k() *
i();
778 double q2 = inRhs.s() *
k();
779 q2 -= inRhs.i() *
j();
780 q2 += inRhs.j() *
i();
781 q2 += inRhs.k() *
s();
783 double q3 = inRhs.s() *
s();
784 q3 -= inRhs.i() *
i();
785 q3 -= inRhs.j() *
j();
786 q3 -= inRhs.k() *
k();
810 [inScalar](
double& component) { component *= inScalar; });
851 if (inVec.
size() != 3)
856 const auto p =
Quaternion(inVec[0], inVec[1], inVec[2], 0.);
857 const auto pPrime = *
this * p * this->
inverse();
910 inOStream << inQuat.
str();
916 std::array<double, 4> components_{ { 0., 0., 0., 1. } };
922 void normalize() noexcept
924 double sumOfSquares = 0.;
927 [&sumOfSquares](
double component) noexcept ->
void
928 { sumOfSquares += utils::sqr(component); });
933 [
norm](
double& component) noexcept ->
void { component /= norm; });
944 void eulerToQuat(
double roll,
double pitch,
double yaw) noexcept
946 const auto halfPhi =
roll / 2.;
947 const auto halfTheta =
pitch / 2.;
948 const auto halfPsi =
yaw / 2.;
950 const auto sinHalfPhi =
std::sin(halfPhi);
951 const auto cosHalfPhi =
std::cos(halfPhi);
953 const auto sinHalfTheta =
std::sin(halfTheta);
954 const auto cosHalfTheta =
std::cos(halfTheta);
956 const auto sinHalfPsi =
std::sin(halfPsi);
957 const auto cosHalfPsi =
std::cos(halfPsi);
959 components_[0] = sinHalfPhi * cosHalfTheta * cosHalfPsi;
960 components_[0] -= cosHalfPhi * sinHalfTheta * sinHalfPsi;
962 components_[1] = cosHalfPhi * sinHalfTheta * cosHalfPsi;
963 components_[1] += sinHalfPhi * cosHalfTheta * sinHalfPsi;
965 components_[2] = cosHalfPhi * cosHalfTheta * sinHalfPsi;
966 components_[2] -= sinHalfPhi * sinHalfTheta * cosHalfPsi;
968 components_[3] = cosHalfPhi * cosHalfTheta * cosHalfPsi;
969 components_[3] += sinHalfPhi * sinHalfTheta * sinHalfPsi;
978 void dcmToQuat(
const NdArray<double>& dcm)
980 const Shape inShape = dcm.shape();
981 if (!(inShape.rows == 3 && inShape.cols == 3))
986 NdArray<double> checks(1, 4);
987 checks[0] = 1 + dcm(0, 0) + dcm(1, 1) + dcm(2, 2);
988 checks[1] = 1 + dcm(0, 0) - dcm(1, 1) - dcm(2, 2);
989 checks[2] = 1 - dcm(0, 0) + dcm(1, 1) - dcm(2, 2);
990 checks[3] = 1 - dcm(0, 0) - dcm(1, 1) + dcm(2, 2);
998 components_[3] = 0.5 *
std::sqrt(1 + dcm(0, 0) + dcm(1, 1) + dcm(2, 2));
999 components_[0] = (dcm(2, 1) - dcm(1, 2)) / (4 * components_[3]);
1000 components_[1] = (dcm(0, 2) - dcm(2, 0)) / (4 * components_[3]);
1001 components_[2] = (dcm(1, 0) - dcm(0, 1)) / (4 * components_[3]);
1007 components_[0] = 0.5 *
std::sqrt(1 + dcm(0, 0) - dcm(1, 1) - dcm(2, 2));
1008 components_[1] = (dcm(1, 0) + dcm(0, 1)) / (4 * components_[0]);
1009 components_[2] = (dcm(2, 0) + dcm(0, 2)) / (4 * components_[0]);
1010 components_[3] = (dcm(2, 1) - dcm(1, 2)) / (4 * components_[0]);
1016 components_[1] = 0.5 *
std::sqrt(1 - dcm(0, 0) + dcm(1, 1) - dcm(2, 2));
1017 components_[0] = (dcm(1, 0) + dcm(0, 1)) / (4 * components_[1]);
1018 components_[2] = (dcm(2, 1) + dcm(1, 2)) / (4 * components_[1]);
1019 components_[3] = (dcm(0, 2) - dcm(2, 0)) / (4 * components_[1]);
1025 components_[2] = 0.5 *
std::sqrt(1 - dcm(0, 0) - dcm(1, 1) + dcm(2, 2));
1026 components_[0] = (dcm(2, 0) + dcm(0, 2)) / (4 * components_[2]);
1027 components_[1] = (dcm(2, 1) + dcm(1, 2)) / (4 * components_[2]);
1028 components_[3] = (dcm(1, 0) - dcm(0, 1)) / (4 * components_[2]);
#define THROW_INVALID_ARGUMENT_ERROR(msg)
Definition: Error.hpp:36
NdArray< dtype > & put(int32 inIndex, value_type inValue)
Definition: NdArrayCore.hpp:3479
size_type size() const noexcept
Definition: NdArrayCore.hpp:4105
const_iterator cbegin() const noexcept
Definition: NdArrayCore.hpp:1221
NdArray< dtype > transpose() const
Definition: NdArrayCore.hpp:4457
const_iterator cend() const noexcept
Definition: NdArrayCore.hpp:1529
value_type item() const
Definition: NdArrayCore.hpp:2809
NdArray< dtype > & zeros() noexcept
Definition: NdArrayCore.hpp:4475
NdArray< dtype > dot(const NdArray< dtype > &inOtherArray) const
Definition: NdArrayCore.hpp:2520
A Class for slicing into NdArrays.
Definition: Slice.hpp:44
Holds a 3D vector.
Definition: Vec3.hpp:50
double z
Definition: Vec3.hpp:55
NdArray< double > toNdArray() const
Definition: Vec3.hpp:324
Vec3 normalize() const noexcept
Definition: Vec3.hpp:276
double x
Definition: Vec3.hpp:53
double y
Definition: Vec3.hpp:54
Holds a unit quaternion.
Definition: Quaternion.hpp:58
double s() const noexcept
Definition: Quaternion.hpp:458
std::string str() const
Definition: Quaternion.hpp:539
NdArray< double > operator*(const NdArray< double > &inVec) const
Definition: Quaternion.hpp:849
NdArray< double > angularVelocity(const Quaternion &inQuat2, double inTime) const
Definition: Quaternion.hpp:227
Quaternion & operator*=(double inScalar) noexcept
Definition: Quaternion.hpp:806
double angleOfRotation() const noexcept
Definition: Quaternion.hpp:178
double roll() const noexcept
Definition: Quaternion.hpp:406
NdArray< double > rotate(const NdArray< double > &inVector) const
Definition: Quaternion.hpp:430
static Quaternion xRotation(double inAngle) noexcept
Definition: Quaternion.hpp:599
static Quaternion nlerp(const Quaternion &inQuat1, const Quaternion &inQuat2, double inPercent)
Definition: Quaternion.hpp:326
static Quaternion rollRotation(double inAngle) noexcept
Definition: Quaternion.hpp:418
Vec3 rotate(const Vec3 &inVec3) const
Definition: Quaternion.hpp:447
Quaternion(double inI, double inJ, double inK, double inS) noexcept
Definition: Quaternion.hpp:88
Quaternion operator-() const noexcept
Definition: Quaternion.hpp:754
NdArray< double > toNdArray() const
Definition: Quaternion.hpp:586
Quaternion(const std::array< double, 4 > &components) noexcept
Definition: Quaternion.hpp:100
Quaternion operator+(const Quaternion &inRhs) const noexcept
Definition: Quaternion.hpp:711
double i() const noexcept
Definition: Quaternion.hpp:267
double yaw() const noexcept
Definition: Quaternion.hpp:611
double pitch() const noexcept
Definition: Quaternion.hpp:374
Quaternion & operator-=(const Quaternion &inRhs) noexcept
Definition: Quaternion.hpp:723
Quaternion slerp(const Quaternion &inQuat2, double inPercent) const
Definition: Quaternion.hpp:528
friend std::ostream & operator<<(std::ostream &inOStream, const Quaternion &inQuat)
Definition: Quaternion.hpp:908
static Quaternion slerp(const Quaternion &inQuat1, const Quaternion &inQuat2, double inPercent)
Definition: Quaternion.hpp:472
static Quaternion yawRotation(double inAngle) noexcept
Definition: Quaternion.hpp:623
static NdArray< double > angularVelocity(const Quaternion &inQuat1, const Quaternion &inQuat2, double inTime)
Definition: Quaternion.hpp:193
void print() const
Definition: Quaternion.hpp:395
Quaternion(const NdArray< double > &inAxis, double inAngle)
Definition: Quaternion.hpp:167
bool operator==(const Quaternion &inRhs) const noexcept
Definition: Quaternion.hpp:661
Quaternion & operator/=(const Quaternion &inRhs) noexcept
Definition: Quaternion.hpp:883
Quaternion(double roll, double pitch, double yaw) noexcept
Definition: Quaternion.hpp:74
Vec3 operator*(const Vec3 &inVec3) const
Definition: Quaternion.hpp:871
Quaternion inverse() const noexcept
Definition: Quaternion.hpp:289
double k() const noexcept
Definition: Quaternion.hpp:312
NdArray< double > toDCM() const
Definition: Quaternion.hpp:553
Quaternion & operator*=(const Quaternion &inRhs) noexcept
Definition: Quaternion.hpp:766
static Quaternion zRotation(double inAngle) noexcept
Definition: Quaternion.hpp:648
Quaternion operator/(const Quaternion &inRhs) const noexcept
Definition: Quaternion.hpp:895
Quaternion nlerp(const Quaternion &inQuat2, double inPercent) const
Definition: Quaternion.hpp:363
static Quaternion yRotation(double inAngle) noexcept
Definition: Quaternion.hpp:635
Quaternion(const Vec3 &inAxis, double inAngle) noexcept
Definition: Quaternion.hpp:146
double j() const noexcept
Definition: Quaternion.hpp:301
Quaternion operator*(double inScalar) const noexcept
Definition: Quaternion.hpp:837
Quaternion operator-(const Quaternion &inRhs) const noexcept
Definition: Quaternion.hpp:743
Quaternion operator*(const Quaternion &inRhs) const noexcept
Definition: Quaternion.hpp:824
bool operator!=(const Quaternion &inRhs) const noexcept
Definition: Quaternion.hpp:679
Quaternion(const NdArray< double > &inArray)
Definition: Quaternion.hpp:114
Quaternion conjugate() const noexcept
Definition: Quaternion.hpp:256
static Quaternion identity() noexcept
Definition: Quaternion.hpp:278
Vec3 axisOfRotation() const noexcept
Definition: Quaternion.hpp:238
Quaternion & operator+=(const Quaternion &inRhs) noexcept
Definition: Quaternion.hpp:691
static Quaternion pitchRotation(double inAngle) noexcept
Definition: Quaternion.hpp:386
OutputIt transform(InputIt first, InputIt last, OutputIt destination, UnaryOperation unaryFunction)
Definition: StlAlgorithms.hpp:784
void for_each(InputIt first, InputIt last, UnaryFunction f)
Definition: StlAlgorithms.hpp:227
bool equal(InputIt1 first1, InputIt1 last1, InputIt2 first2) noexcept
Definition: StlAlgorithms.hpp:142
OutputIt copy(InputIt first, InputIt last, OutputIt destination) noexcept
Definition: StlAlgorithms.hpp:99
std::string num2str(dtype inNumber)
Definition: num2str.hpp:46
bool essentiallyEqual(dtype inValue1, dtype inValue2) noexcept
Definition: essentiallyEqual.hpp:51
constexpr dtype sqr(dtype inValue) noexcept
Definition: sqr.hpp:44
Definition: Coordinate.hpp:45
NdArray< uint32 > argmax(const NdArray< dtype > &inArray, Axis inAxis=Axis::NONE)
Definition: argmax.hpp:46
auto sin(dtype inValue) noexcept
Definition: sin.hpp:49
dtype clip(dtype inValue, dtype inMinValue, dtype inMaxValue)
Definition: clip.hpp:50
auto cos(dtype inValue) noexcept
Definition: cos.hpp:49
auto sqrt(dtype inValue) noexcept
Definition: sqrt.hpp:48
NdArray< double > norm(const NdArray< dtype > &inArray, Axis inAxis=Axis::NONE)
Definition: norm.hpp:51
std::uint32_t uint32
Definition: Types.hpp:40