13#ifndef ML_QUATERNION_H
14#define ML_QUATERNION_H
91 qx(0), qy(0), qz(0), qw(0) { }
96 qx(0), qy(0), qz(0), qw(d)
104 template <
typename DT2>
107 qx =
static_cast<DT
>(
q2.qx);
108 qy =
static_cast<DT
>(
q2.qy);
109 qz =
static_cast<DT
>(
q2.qz);
110 qw =
static_cast<DT
>(
q2.qw);
152 qx(v[0]), qy(v[1]), qz(v[2]), qw(w)
211 inline void set(
const DT x,
const DT y,
const DT z,
const DT w)
232 printTemplateError(
"TQuaternion::getAsMat4() const, quaternion is not convertible to 4x4 matrix",
234 "Returning Quaterion");
256 const DT
qxqx = qx*qx;
257 const DT
qyqy = qy*qy;
258 const DT
qzqz = qz*qz;
260 const DT
qxqy = qx*qy;
261 const DT
qxqz = qx*qz;
262 const DT
qxqw = qx*qw;
264 const DT
qyqz = qy*qz;
265 const DT
qyqw = qy*qw;
267 const DT
qzqw = qz*qw;
374 qx/=d; qy/=d; qz/=d; qw/=d;
410 b.
qy != 0 ? qy/b.
qy : qy,
411 b.
qz != 0 ? qz/b.
qz : qz,
412 b.
qw != 0 ? qw/b.
qw : qw) :
449 qw*p.
qw - qx*p.
qx - qy*p.
qy - qz*p.
qz); }
478 "Returning unchanged quaternion");
514 inline DT
norm()
const {
return qx*qx + qy*qy + qz*qz + qw*qw; }
519 inline DT
norm2()
const {
return static_cast<DT
>(::sqrt(qx*qx + qy*qy + qz*qz + qw*qw)); }
538 printTemplateError(
"TQuaternion::normalize() const, quaternion can not be normalized",
540 "Returning default quaternion");
573 "Returning default quaternion");
596 const DT
absVal = absoluteValue();
630 "Returning default quaternion");
639 retVal = conjugate().mult(1/
n);
654 const DT
n2 = norm2();
655 const DT
lqv = qv().length();
660 printTemplateError(
"TQuaternion::sqrt() const, sqrt of quaternion cannot be calculated",
662 "Returning default quaternion");
691 const DT
len = qv().length();
707 const DT
n2 = norm2();
708 const DT
qvLen = qv().length();
737 static_cast<DT
>(::cos(qw)) * v /
len *
static_cast<DT
>(::sinh(
len)) :
739 ::sin(qw)*::cosh(
len)
753 static_cast<DT
>(-1)*
static_cast<DT
>(::sin(qw))*qv()/
len*
static_cast<DT
>(::sinh(
len)) :
755 ::cos(qw)*::cosh(
len)
781 static_cast<DT
>(::cosh(qw))*v/
len*
static_cast<DT
>(::sin(
len)) :
783 ::sinh(qw)*::cos(
len)
797 static_cast<DT
>(::sinh(qw))*v/
len*
static_cast<DT
>(::sin(
len)) :
799 ::cosh(qw)*::cos(
len)
807 return sinh().div(cosh(),
isError);
813 return cosh().div(sinh(),
isError);
841 #define _ML_QUATERNION_CALC_CHECKED(FUNC_NAME, CALC_EXPR) \
842 TQuaternion<DT> retVal; \
844 const Tvec3<DT> &v = qv(); \
845 const DT len = v.length(); \
846 if (MLValueIs0WOM(len)){ \
848 if (isError == NULL){ \
850 printTemplateError("TQuaternion::" FUNC_NAME "() const, " FUNC_NAME \
851 " of quaternion cannot be calculated", \
853 "Returning default quaternion"); \
862 if (isError != NULL){ *isError = false; } \
863 retVal = CALC_EXPR; \
871 #define _ML_QUAT_CALC_EXP TQuaternion<DT>(-v/len,0).mult(mult(TQuaternion<DT>(-v/len,0)).arcsinh());
881 #undef _ML_QUAT_CALC_EXP
886 #define _ML_QUAT_CALC_EXP TQuaternion<DT>(-v/len,0).mult(arccosh());
892 #undef _ML_QUAT_CALC_EXP
897 #define _ML_QUAT_CALC_EXP TQuaternion<DT>(-v/len,0).mult(mult(TQuaternion<DT>(-v/len,0)).arctanh());
903 #undef _ML_QUAT_CALC_EXP
907 #undef _ML_QUATERNION_CALC_CHECKED
942#ifdef _ML_IMPLEMENT_GLOBAL_QUATERNION_OPERATORS
943#ifndef _ML_IMPLEMENT_GLOBAL_QUATERNION_FUNCS_AND_OPS_IN_GLOBAL_NAMESPACE
951template <
typename DT>
952inline ML_LA_NAMESPACE::TQuaternion<DT> operator+(DT d,
const ML_LA_NAMESPACE::TQuaternion<DT> &
q){
953 return ML_LA_NAMESPACE::TQuaternion<DT>(
q.qx,
q.qy,
q.qz,
q.qw+d);
957template <
typename DT>
958inline ML_LA_NAMESPACE::TQuaternion<DT> operator+(
const ML_LA_NAMESPACE::TQuaternion<DT> &
q, DT d){
959 return ML_LA_NAMESPACE::TQuaternion<DT>(
q.qx,
q.qy,
q.qz,
q.qw+d);
963template <
typename DT>
964inline ML_LA_NAMESPACE::TQuaternion<DT>
operator+(
const ML_LA_NAMESPACE::TQuaternion<DT> &
qa,
965 const ML_LA_NAMESPACE::TQuaternion<DT> &
qb){
966 return qa.operator+(
qb);
975template <
typename DT>
976inline ML_LA_NAMESPACE::TQuaternion<DT>
operator-(DT d,
const ML_LA_NAMESPACE::TQuaternion<DT> &
q){
977 return ML_LA_NAMESPACE::TQuaternion<DT>(-
q.qx, -
q.qy, -
q.qz, d-
q.qw);
981template <
typename DT>
982inline ML_LA_NAMESPACE::TQuaternion<DT>
operator-(
const ML_LA_NAMESPACE::TQuaternion<DT> &
q, DT d){
983 return ML_LA_NAMESPACE::TQuaternion<DT>(
q.qx,
q.qy,
q.qz,
q.qw-d);
987template <
typename DT>
988inline ML_LA_NAMESPACE::TQuaternion<DT>
operator-(
const ML_LA_NAMESPACE::TQuaternion<DT> &
qa,
989 const ML_LA_NAMESPACE::TQuaternion<DT> &
qb){
990 return qa.operator-(
qb);
995template <
typename DT>
996inline ML_LA_NAMESPACE::TQuaternion<DT>
operator*(DT d,
const ML_LA_NAMESPACE::TQuaternion<DT> &
q){
1001template <
typename DT>
1002inline ML_LA_NAMESPACE::TQuaternion<DT>
operator*(
const ML_LA_NAMESPACE::TQuaternion<DT> &
q, DT d){
1007template <
typename DT>
1008inline ML_LA_NAMESPACE::TQuaternion<DT>
operator*(
const ML_LA_NAMESPACE::TQuaternion<DT> &
qa,
1009 const ML_LA_NAMESPACE::TQuaternion<DT> &
qb){
1010 return qa.operator*(
qb);
1014#ifndef _ML_IMPLEMENT_GLOBAL_QUATERNION_FUNCS_AND_OPS_IN_GLOBAL_NAMESPACE
1030#ifdef _ML_IMPLEMENT_GLOBAL_QUATERNION_FUNCTIONS
1031#ifndef _ML_IMPLEMENT_GLOBAL_QUATERNION_FUNCS_AND_OPS_IN_GLOBAL_NAMESPACE
1037#ifdef _ML_IMPLEMENT_QUATERNION_SQRT
1038template <
typename DT>
1039inline ML_LA_NAMESPACE::TQuaternion<DT> sqrt (
const ML_LA_NAMESPACE::TQuaternion<DT> &
q) {
return q.sqrt(); }
1043template <
typename DT>
1044inline ML_LA_NAMESPACE::TQuaternion<DT> exp (
const ML_LA_NAMESPACE::TQuaternion<DT> &
q) {
return q.exp(); }
1047template <
typename DT>
1048inline ML_LA_NAMESPACE::TQuaternion<DT> ln (
const ML_LA_NAMESPACE::TQuaternion<DT> &
q) {
return q.ln(); }
1051template <
typename DT>
1052inline ML_LA_NAMESPACE::TQuaternion<DT> sin (
const ML_LA_NAMESPACE::TQuaternion<DT> &
q) {
return q.sin(); }
1055template <
typename DT>
1056inline ML_LA_NAMESPACE::TQuaternion<DT> cos (
const ML_LA_NAMESPACE::TQuaternion<DT> &
q) {
return q.cos(); }
1059template <
typename DT>
1060inline ML_LA_NAMESPACE::TQuaternion<DT> tan (
const ML_LA_NAMESPACE::TQuaternion<DT> &
q) {
return q.tan(); }
1063template <
typename DT>
1064inline ML_LA_NAMESPACE::TQuaternion<DT> cotan (
const ML_LA_NAMESPACE::TQuaternion<DT> &
q) {
return q.cotan(); }
1067template <
typename DT>
1068inline ML_LA_NAMESPACE::TQuaternion<DT> sinh (
const ML_LA_NAMESPACE::TQuaternion<DT> &
q) {
return q.sinh(); }
1071template <
typename DT>
1072inline ML_LA_NAMESPACE::TQuaternion<DT> cosh (
const ML_LA_NAMESPACE::TQuaternion<DT> &
q) {
return q.cosh(); }
1075template <
typename DT>
1076inline ML_LA_NAMESPACE::TQuaternion<DT> tanh (
const ML_LA_NAMESPACE::TQuaternion<DT> &
q) {
return q.tanh(); }
1079template <
typename DT>
1080inline ML_LA_NAMESPACE::TQuaternion<DT> cotanh (
const ML_LA_NAMESPACE::TQuaternion<DT> &
q) {
return q.cotanh(); }
1083template <
typename DT>
1084inline ML_LA_NAMESPACE::TQuaternion<DT> arcsinh(
const ML_LA_NAMESPACE::TQuaternion<DT> &
q) {
return q.arcsinh(); }
1087template <
typename DT>
1088inline ML_LA_NAMESPACE::TQuaternion<DT> arccosh(
const ML_LA_NAMESPACE::TQuaternion<DT> &
q) {
return q.arccosh(); }
1091template <
typename DT>
1092inline ML_LA_NAMESPACE::TQuaternion<DT> arctanh(
const ML_LA_NAMESPACE::TQuaternion<DT> &
q) {
return q.arctanh(); }
1095template <
typename DT>
1096inline ML_LA_NAMESPACE::TQuaternion<DT> arcsin (
const ML_LA_NAMESPACE::TQuaternion<DT> &
q) {
return q.arcsin(); }
1099template <
typename DT>
1100inline ML_LA_NAMESPACE::TQuaternion<DT> arccos (
const ML_LA_NAMESPACE::TQuaternion<DT> &
q) {
return q.arccos(); }
1103template <
typename DT>
1104inline ML_LA_NAMESPACE::TQuaternion<DT> arctan (
const ML_LA_NAMESPACE::TQuaternion<DT> &
q) {
return q.arctan(); }
1107#ifndef _ML_IMPLEMENT_GLOBAL_QUATERNION_FUNCS_AND_OPS_IN_GLOBAL_NAMESPACE
1121 template <
typename DT>
1122 inline ostream&
operator<<(ostream& s,
const ML_NAMESPACE::TQuaternion<DT> &v){
1123 return s <<
"(" << v.qx <<
"," << v.qy <<
"," << v.qz <<
"," << v.qw <<
")";
Template class for vector arithmetic with floating point datatypes.
T length() const
Returns the length of the vector, i.e., norm2().
Declaration of complex type traits.
TQuaternion< DT > arctan(bool *isError=nullptr) const
Inverse tangent; for error handling see _ML_QUATERNION_CALC_CHECKED.
TQuaternion(DT d)
Builds a quaternion from a scalar by setting all elements to 0 and qw to the scalar; use explicitly t...
TQuaternion< DT > arccos(bool *isError=nullptr) const
Inverse cosine; for error handling see _ML_QUATERNION_CALC_CHECKED.
TQuaternion< DT > euclideanMult(const TQuaternion< DT > &q) const
Euclidean product of this quaternion with another one (which is non-commutative).
DT dot(const TQuaternion< DT > &p) const
Dot product, equivalent to four component vector dot product.
TQuaternion< DT > arg(bool *isError=nullptr) const
Computes the quaternion argument.
TQuaternion< DT > ln() const
Computes the natural logarithm.
TQuaternion(DT x, DT y, DT z, DT w)
Creates a new TQuaternion with the DT values given.
TQuaternion< DT > arccosh() const
Computes the inverse hyperbolic cosine.
DT qx
First element of imaginary part.
TQuaternion< DT > sinh() const
Hyperbolic functions: Hyperbolic sine, hyperbolic cosine, hyperbolic tangent https://en....
DT absoluteValue() const
Returns the absolute value of a quaternion, which is the scalar quantity that determines the length o...
TQuaternion< DT > tan(bool *isError=nullptr) const
Computes the tangent; for error handling see _ML_QUATERNION_CALC_CHECKED.
TQuaternion< DT > add(const TQuaternion< DT > &b) const
Adds another quaternion b to this one and returns the sum.
TQuaternion< DT > tanh(bool *isError=nullptr) const
Computes the hyperbolic tangent; for error handling see _ML_QUATERNION_CALC_CHECKED.
FloatingPointVector< DT, 3, Vector3DataContainer< DT > > getImaginaryPart() const
Returns a copy of the quaternion's imaginary part.
TQuaternion< DT > sqrt(bool *isError=nullptr) const
Computes the square root of a quaternion.
void set(const FloatingPointVector< DT, 3, Vector3DataContainer< DT > > &v, const DT w)
Sets all quaternion elements from a vector and DT parameter.
TQuaternion< DT > div(const TQuaternion< DT > &d, bool *isError=nullptr) const
Divides a quaternion by another quaternion.
TQuaternion< DT > sgn(bool *isError=nullptr) const
Returns the sign of the quaternion.
const FloatingPointVector< DT, 3, Vector3DataContainer< DT > > & qv() const
Returns a constant reference to the quaternion's imaginary part as vector object.
TQuaternion< DT > cotan(bool *isError=nullptr) const
Computes the cotangent; for error handling see _ML_QUATERNION_CALC_CHECKED.
FloatingPointVector< DT, 3, Vector3DataContainer< DT > > & qv()
Returns a modifiable reference to the quaternion's imaginary part as vector object,...
TQuaternion< DT > sin() const
Trigonometric functions: sine, cosine, tangent, cotangent.
TQuaternion< DT > cosh() const
Computes the hyperbolic cosine.
TQuaternion< DT > arcsin(bool *isError=nullptr) const
Inverse trigonometric functions: Inverse sine, inverse cosine, inverse tangent.
TQuaternion< DT > exp() const
Exponential and logarithmic functions: natural exponential, natural logarithm, power.
TQuaternion< DT > negate() const
Computes the negation.
DT norm() const
Computes the d-norm.
TQuaternion< DT > arctanh() const
Computes the inverse hyperbolic tangent.
TQuaternion< DT > arcsinh() const
Inverse hyperbolic function: arcsinh, arccosh, arctanh.
TQuaternion< DT > mult(const TQuaternion< DT > &q) const
Multiplies this quaternion with another one (which is non-commutative). It is also called Grassman pr...
TQuaternion< DT > compDiv(const TQuaternion< DT > &b, bool *isError=nullptr) const
Divides each component by its corresponding component from b.
TQuaternion()
Standard constructor that is setting all elements to 0.
TQuaternion< DT > inverse(bool *isInvertible=nullptr) const
Computes and returns the inverse.
DT value_type
Scalar type used for qx, qy, qz, and qw.
DT & operator[](const size_t i)
Indexing operator.
Tmat4< DT > getAsMat4(bool *isConvertible=nullptr) const
Converts this quaternion to a 4x4 matrix.
TQuaternion< DT > & operator=(const TQuaternion< DT > &q)
Assignment operator.
TQuaternion< DT > add(DT s) const
Adds a scalar s to the quaternion and returns the sum. It is equivalent to a 'scalar add' of s to the...
void set(const DT x, const DT y, const DT z, const DT w)
Sets all quaternion elements qx, qy, qz, and qw from parameters x, y, z, and w, respectively.
DT norm2() const
Computes the magnitude of the quaternion.
TQuaternion< DT > odd(const TQuaternion< DT > &p) const
Odd product, also known as cross-product or Grassman outer product.
TQuaternion< DT > normalize(bool *isError=nullptr) const
Returns the normalization of the quaternion.
TQuaternion(const TQuaternion< DT2 > &q2)
Copy constructor from another TQuaternion of same or different type.
TQuaternion< DT > conjugate() const
Computes the conjugate.
DT qz
Third element of imaginary part.
TQuaternion< DT > mult(DT s) const
Multiplies this quaternion with a scalar factor s.
TQuaternion(const FloatingPointVector< DT, 4 > &v)
Creates a new TQuaternion from the four-dimensional parameter vector.
TQuaternion< DT > cos() const
Computes the cosine.
DT operator[](const size_t i) const
Constant indexing operator.
TQuaternion< DT > cotanh(bool *isError=nullptr) const
Computes the hyperbolic cotangent; for error handling see _ML_QUATERNION_CALC_CHECKED.
TQuaternion< DT > pow(const TQuaternion< DT > &quat) const
Computes the power of a quaternion.
TQuaternion(const FloatingPointVector< DT, 3, Vector3DataContainer< DT > > &v, DT w)
Constructor with a vector and DT parameter.
TQuaternion(const TQuaternion &q2)=default
Explicitly generating the default constructor to avoid a warning message with gcc9.
DT getRealPart() const
Returns a copy of the quaternion's real part, also called scalar() of a quaternion.
DT qy
Second element of imaginary part.
TQuaternion< DT > even(const TQuaternion< DT > &p) const
Even product, also known as Grassman inner product.
TQuaternion< DT > outer(const TQuaternion< DT > &q) const
Euclidean outer product of this quaternion with another one.
A 4x4 matrix class consisting of four row vectors.
Forward declarations to resolve header file dependencies.
Specialized base class for the FloatingPointVectorDataContainerBase.
bool MLValueIs0WOM(MLint8 a)
Returns true if value is 0; otherwise, it returns false.
bool MLValuesAreEqualWOM(MLint8 a, MLint8 b)
Returns true if values a and b are equal; otherwise, it returns false.
#define ML_BAD_PARAMETER
A bad/invalid parameter (or even an inappropriate image) has been passed to a module or an algorithm,...
#define ML_CHECK_FLOAT(x)
#define _ML_QUAT_CALC_EXP
Internal helper macro - do not use.
#define _ML_QUATERNION_CALC_CHECKED(FUNC_NAME, CALC_EXPR)
Defines a code fragment that checks and handles operations for safe expression calculations.
Target mlrange_cast(Source arg)
Generic version of checked ML casts.
ScopeGuard< Functor > operator+(ScopeGuardOnExit, Functor &&fn)
void ML_UTILS_EXPORT printTemplateError(const char *location, MLErrorCode reason, const std::string_view &handling)
bool operator==(const Tmat2< DT > &a, const Tmat2< DT > &b)
a == b ? Returns true if yes.
T operator*(const FloatingPointVector< T, size, DataContainer > &a, const FloatingPointVector< T, size, DataContainer > &b)
Dot product, returns a.dot(b).
FloatingPointVector< T, size, DataContainer > operator-(FloatingPointVector< T, size, DataContainer > lhs, const FloatingPointVector< T, size, DataContainer > &rhs)
Return value is the component-wise subtraction of rhs from lhs.
MLEXPORT std::ostream & operator<<(std::ostream &s, const ml::Field &v)
Overloads the operator '<<' for stream output of Field objects.