Template Class Quaternion¶
Defined in File Quaternion.hxx
Class Documentation¶
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template<typename T>
class Utils::Quaternion¶
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Quaternion class
A quaternion is a quadruplet (A,B,C,D) of real numbers, which may be written as
\[ Q = A + B \mathbf{i} + C\mathbf{j} + D\mathbf{k} \]Reference:
| James Foley, Andries van Dam, Steven Feiner, John Hughes, | Computer Graphics, Principles and Practice, Second Edition, | Addison Wesley, 1990.
Public Functions
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inline Quaternion()¶
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Build null quaternion.
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inline Quaternion(real_type A, real_type B, real_type C, real_type D)¶
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Build quaternion \( A + B \mathbf{i} + C \mathbf{j} + D \mathbf{k} \).
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inline void setup(real_type A, real_type B, real_type C, real_type D)¶
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Build quaternion \( A + B \mathbf{i} + C \mathbf{j} + D \mathbf{k} \).
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inline void print(ostream &os) const¶
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Print a quaternion to stream.
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inline void conj()¶
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Conjugates a quaternion
\[ Q = A + B \mathbf{i} + C \mathbf{j} + D \mathbf{k} \]The conjugate of \( Q \) is
\[ \overline{Q} = A - B \mathbf{i} - C \mathbf{j} - D \mathbf{k} \]
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inline void invert()¶
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Invert a quaternion \( Q = A + B \mathbf{i} + C \mathbf{j} + D \mathbf{k} \). The inverse of of \( Q \) is
\[ Q^{-1} = \dfrac{ A - B \mathbf{i} - C \mathbf{j} - D \mathbf{k}} { A^2 + B^2 + C^2 + D^2 } \]
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inline real_type norm() const¶
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Computes the norm of a quaternion. The norm of \( Q \) is \( \sqrt{A^2+B^2+C^2+D^2} \).
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inline void rotate(real_type const v[3], real_type w[3]) const¶
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Applies a quaternion rotation to a vector in 3D.
If \( Q \) is a unit quaternion that encodes a rotation of ANGLE radians about the vector AXIS, then for an arbitrary real vector \( V \), the result \( W \) of the rotation on \( V \) can be written as:
\( W = Q * V * Conj(Q) \)
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inline real_type to_axis(real_type axis[3]) const¶
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Converts a rotation from quaternion to axis format in 3D.
A rotation quaternion Q has the form:
\[ Q = A + B \mathbf{i} + C \mathbf{j} + D \mathbf{k} \]where A, B, C and D are real numbers, and \( \mathbf{i} \), \( \mathbf{j} \), and \( \mathbf{k} \) are to be regarded as symbolic constant basis vectors, similar to the role of the “\f$ \mathbf{i} \f$” in the representation of imaginary numbers.
A is the cosine of half of the angle of rotation. (B,C,D) is a vector pointing in the direction of the axis of rotation. Rotation multiplication and inversion can be carried out using this format and the usual rules for quaternion multiplication and inversion.
