itkVersor.h

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/*=========================================================================
 *
 *  Copyright NumFOCUS
 *
 *  Licensed under the Apache License, Version 2.0 (the "License");
 *  you may not use this file except in compliance with the License.
 *  You may obtain a copy of the License at
 *
 *         https://www.apache.org/licenses/LICENSE-2.0.txt
 *
 *  Unless required by applicable law or agreed to in writing, software
 *  distributed under the License is distributed on an "AS IS" BASIS,
 *  WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
 *  See the License for the specific language governing permissions and
 *  limitations under the License.
 *
 *=========================================================================*/
#ifndef itkVersor_h
#define itkVersor_h
 
#include "itkMatrix.h"
#include "vnl/vnl_quaternion.h"
#include "vnl/vnl_vector_fixed.h"
 
namespace itk
{
template <typename T>
class ITK_TEMPLATE_EXPORT Versor
{
public:
  using Self = Versor;

  using ValueType = T;

  using RealType = typename NumericTraits<ValueType>::RealType;

  using VectorType = Vector<T, 3>;

  using PointType = Point<T, 3>;

  using CovariantVectorType = CovariantVector<T, 3>;

  using VnlVectorType = vnl_vector_fixed<T, 3>;

  using VnlQuaternionType = vnl_quaternion<T>;

  using MatrixType = Matrix<T, 3, 3>;

  vnl_quaternion<T>
  GetVnlQuaternion() const;

  void
  Set(const VnlQuaternionType &);

  void
  Set(T x, T y, T z, T w);

  const Self &
  operator*=(const Self & v);

  const Self &
  operator/=(const Self & v);

  ValueType
  GetTensor() const;

  void
  Normalize();

  Self
  GetConjugate() const;

  Self
  GetReciprocal() const;

  Self
  operator*(const Self & v) const;

  Self
  operator/(const Self & v) const;

  bool
  operator==(const Self & v) const;
 
  ITK_UNEQUAL_OPERATOR_MEMBER_FUNCTION(Self);

  ValueType
  GetScalar() const;

  ValueType
  GetX() const
  {
    return m_X;
  }

  ValueType
  GetY() const
  {
    return m_Y;
  }

  ValueType
  GetZ() const
  {
    return m_Z;
  }

  ValueType
  GetW() const
  {
    return m_W;
  }

  ValueType
  GetAngle() const;

  VectorType
  GetAxis() const;

  VectorType
  GetRight() const;

  void
  Set(const VectorType & axis, ValueType angle);

  void
  Set(const MatrixType & mat);

  void
  Set(const VectorType & axis);

  void
  SetRotationAroundX(ValueType angle);

  void
  SetRotationAroundY(ValueType angle);

  void
  SetRotationAroundZ(ValueType angle);

  void
  SetIdentity();

  VectorType
  Transform(const VectorType & v) const;

  CovariantVectorType
  Transform(const CovariantVectorType & v) const;

  PointType
  Transform(const PointType & v) const;

  VnlVectorType
  Transform(const VnlVectorType & v) const;

  MatrixType
  GetMatrix() const;

  Self
  SquareRoot() const;

  Self
  Exponential(ValueType exponent) const;
 
private:
  static inline ValueType
  Epsilon(double *)
  {
    return 1e-10;
  }
  static inline ValueType
  Epsilon(float *)
  {
    return 1e-7;
  }
  static inline ValueType
  Epsilon()
  {
    return Epsilon((ValueType *)nullptr);
  }


  ValueType m_X{};

  ValueType m_Y{};

  ValueType m_Z{};

  ValueType m_W{ NumericTraits<T>::OneValue() };
};
 
template <typename T>
std::ostream &
operator<<(std::ostream & os, const Versor<T> & v)
{
  os << "[ ";
  os << v.GetX() << ", " << v.GetY() << ", ";
  os << v.GetZ() << ", " << v.GetW() << " ]";
  return os;
}
 
template <typename T>
std::istream &
operator>>(std::istream & is, Versor<T> & v);
} // end namespace itk
 
#ifndef ITK_MANUAL_INSTANTIATION
#  include "itkVersor.hxx"
#endif
 
#endif