Quaternion

Quaternion is the static container storing 4-component quaternion representing rotations in 3D space. It is used to store orientations and rotations due to deformation or other effects.

Constructors

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Quaternion();
Default constructor. Initializes current quaternion to represent zero rotation ({1, 0, 0, 0}).

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Quaternion(const Quaternion& rhS);
Copy constructor. Initializes current quaterion with the copy of rhs.

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Quaternion(std::array<double,4> vecinit);
Constructs quaternion using array of four values.

Access operators

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double& operator[](const size_t index);
double const& operator[](const size_t index) const;

Return (const) reference to the element index.

Arithmetic and vector operations

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Quaternion operator+(const Quaternion rhS) const;
Returns sum of two quaternions.

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Quaternion operator-(const Quaternion rhS) const;
Returns difference of two quaternions.

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Quaternion operator*(const Quaternion rhS) const;
Returns a product of two quaternions.

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Quaternion operator*(const double scalar) const;
Returns copy of the current quaternion with all elements multiplied by the factor scalar.

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Quaternion operator/(const double divisor) const;
Returns copy of the current quaternion with all elements divided by the factor `divisor`.

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Quaternion& operator+=(const Quaternion rhS);
Adds rhS to the current quaternion.

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Quaternion& operator-=(const Quaternion rhS);
Subtracts rhS from the current quaternion.

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Quaternion& operator*=(const Quaternion rhS);
Multiplies current quaternion by the rhS.

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Quaternion& operator*=(const double scalar);
Multiplies current quaternion by the factor scalar.

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Quaternion& operator/=(const double divisor);
Divides current quaternion by the factor scalar.

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Quaternion& operator=(const Quaternion rhS);
Assigns the content of the rhS to the current container.

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double length() const;
Returns length of the quaternion.

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Quaternion& normalize();
Normalizes quaternion.

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Quaternion normalized() const;
Returns normalized copy of the current quaternion.

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Quaternion& conjugate();
Conjugates quaternion (reverse rotation).

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Quaternion conjugated() const;
Returns conjugated copy of the current quaternion (reverse rotation).

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Quaternion& invert();
Inverts current quaternion (reverse rotation if quaternion is normalized).

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Quaternion inverted() const;
Returns inverted copy of the current quaternion (reverse rotation if quaternion is normalized).

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void setRotationMatrix(void);
Sets internally stored rotation matrix representing the same rotation at the current quaternion.

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dMatrix3x3 getRotationMatrix(const bool Active = true);
Returns rotation matrix representing the same rotation at the current quaternion (default: active rotation). Allows switching between active and passive rotation.

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static Quaternion lerp(const Quaternion& rhSQ1, const Quaternion& rhSQ2, const double t);
Returns linear interpolation between two quaternions, where 0.0 < t < 1.0.

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static Quaternion slerp(const Quaternion& a, const Quaternion& b, const double t);
Returns spherical linear interpolation between two quaternions, where 0.0 < t < 1.0.

Data manipulation methods

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void set(const double sIn, const double x, const double y, const double z);

Sets quaternion using individual entries.

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void set(const double sIn, const dVector3 vIn);
Sets quaternion using first entry and imaginary part vector.

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void set(const dMatrix3x3& RotMatrix);
Sets quaternion from rotation matrix RotMatrix.

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void set_entry(const int idx, const double val);

Sets individual entry.

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void set(dVector3 Axis, const double Angle);
Sets quaternion from rotation axis and angle.

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void set_to_zero();
Sets zero rotation quaternion ({1, 0, 0, 0}).

Container properties

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constexpr size_t size(void) const;
Returns the size of the quaternion.

MPI communication methods

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void pack(std::vector<double>& buffer);
Packs the content of the current object into the MPI communication buffer.

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void unpack(std::vector<double>& buffer, size_t& it);
Unpacks (reads) the content of the current object from the MPI communication buffer. The existing data in the container is overwritten.

Read/write methods

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std::string print(void) const;
Returns formatted string of the quaternion values ready to print to the terminal.

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void read_ASCII(std::istream& inp);
Reads quaternion content from the input stream.

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void write_ASCII(std::ostream& outp, const int precision = 16, const char sep = ' ') const;
Writes quaternion content in ASCII format with the specified precision using sep as entry separator into the output stream.

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std::string get_output_string(const int precision = 16, const char sep = ' ') const;
Returns output string with quaternion content in ASCII format with the specified precision using sep as entry separator.

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std::vector<double> get_vector() const;
Returns std::vector containing current quaternion components.

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std::vector<float> get_vector_float() const;
Returns std::vector<float> containing current quaternion components rounded to float precision.

Quaternion ​

Constructors ​

Access operators ​

Arithmetic and vector operations ​

Data manipulation methods ​

Container properties ​

MPI communication methods ​

Read/write methods ​