ParametrizedLine.h

// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// Copyright (C) 2008 Gael Guennebaud <gael.guennebaud@inria.fr>
// Copyright (C) 2008 Benoit Jacob <jacob.benoit.1@gmail.com>
//
// This Source Code Form is subject to the terms of the Mozilla
// Public License v. 2.0. If a copy of the MPL was not distributed
// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
// SPDX-License-Identifier: MPL-2.0
 
#ifndef EIGEN_PARAMETRIZEDLINE_H
#define EIGEN_PARAMETRIZEDLINE_H
 
// IWYU pragma: private
#include "./InternalHeaderCheck.h"
 
namespace Eigen {

template <typename Scalar_, int AmbientDim_, int Options_>
class ParametrizedLine {
 public:
  EIGEN_MAKE_ALIGNED_OPERATOR_NEW_IF_VECTORIZABLE_FIXED_SIZE(Scalar_, AmbientDim_)
  enum { AmbientDimAtCompileTime = AmbientDim_, Options = Options_ };
  using Scalar = Scalar_;
  using RealScalar = typename NumTraits<Scalar>::Real;
  using Index = Eigen::Index;  
  using VectorType = Matrix<Scalar, AmbientDimAtCompileTime, 1, Options>;

  EIGEN_DEVICE_FUNC inline ParametrizedLine() {}
 
  template <int OtherOptions>
  EIGEN_DEVICE_FUNC ParametrizedLine(const ParametrizedLine<Scalar, AmbientDimAtCompileTime, OtherOptions>& other)
      : m_origin(other.origin()), m_direction(other.direction()) {}

  EIGEN_DEVICE_FUNC inline explicit ParametrizedLine(Index _dim) : m_origin(_dim), m_direction(_dim) {}

  EIGEN_DEVICE_FUNC ParametrizedLine(const VectorType& origin, const VectorType& direction)
      : m_origin(origin), m_direction(direction) {}
 
  template <int OtherOptions>
  EIGEN_DEVICE_FUNC explicit ParametrizedLine(const Hyperplane<Scalar_, AmbientDim_, OtherOptions>& hyperplane);

  EIGEN_DEVICE_FUNC static inline ParametrizedLine Through(const VectorType& p0, const VectorType& p1) {
    return ParametrizedLine(p0, (p1 - p0).normalized());
  }

  EIGEN_DEVICE_FUNC inline Index dim() const { return m_direction.size(); }
 
  EIGEN_DEVICE_FUNC const VectorType& origin() const { return m_origin; }
  EIGEN_DEVICE_FUNC VectorType& origin() { return m_origin; }
 
  EIGEN_DEVICE_FUNC const VectorType& direction() const { return m_direction; }
  EIGEN_DEVICE_FUNC VectorType& direction() { return m_direction; }

  EIGEN_DEVICE_FUNC RealScalar squaredDistance(const VectorType& p) const {
    VectorType diff = p - origin();
    return (diff - direction().dot(diff) * direction()).squaredNorm();
  }

  EIGEN_DEVICE_FUNC RealScalar distance(const VectorType& p) const {
    EIGEN_USING_STD(sqrt) return sqrt(squaredDistance(p));
  }

  EIGEN_DEVICE_FUNC VectorType projection(const VectorType& p) const {
    return origin() + direction().dot(p - origin()) * direction();
  }
 
  EIGEN_DEVICE_FUNC VectorType pointAt(const Scalar& t) const;
 
  template <int OtherOptions>
  EIGEN_DEVICE_FUNC Scalar
  intersectionParameter(const Hyperplane<Scalar_, AmbientDim_, OtherOptions>& hyperplane) const;
 
  template <int OtherOptions>
  EIGEN_DEVICE_FUNC Scalar intersection(const Hyperplane<Scalar_, AmbientDim_, OtherOptions>& hyperplane) const;
 
  template <int OtherOptions>
  EIGEN_DEVICE_FUNC VectorType
  intersectionPoint(const Hyperplane<Scalar_, AmbientDim_, OtherOptions>& hyperplane) const;

  template <typename XprType>
  EIGEN_DEVICE_FUNC inline ParametrizedLine& transform(const MatrixBase<XprType>& mat,
                                                       TransformTraits traits = Affine) {
    if (traits == Affine)
      direction() = (mat * direction()).normalized();
    else if (traits == Isometry)
      direction() = mat * direction();
    else {
      eigen_assert(0 && "invalid traits value in ParametrizedLine::transform()");
    }
    origin() = mat * origin();
    return *this;
  }

  template <int TrOptions>
  EIGEN_DEVICE_FUNC inline ParametrizedLine& transform(
      const Transform<Scalar, AmbientDimAtCompileTime, Affine, TrOptions>& t, TransformTraits traits = Affine) {
    transform(t.linear(), traits);
    origin() += t.translation();
    return *this;
  }

  template <typename NewScalarType>
  EIGEN_DEVICE_FUNC inline
      typename internal::cast_return_type<ParametrizedLine,
                                          ParametrizedLine<NewScalarType, AmbientDimAtCompileTime, Options> >::type
      cast() const {
    return typename internal::cast_return_type<
        ParametrizedLine, ParametrizedLine<NewScalarType, AmbientDimAtCompileTime, Options> >::type(*this);
  }

  template <typename OtherScalarType, int OtherOptions>
  EIGEN_DEVICE_FUNC inline explicit ParametrizedLine(
      const ParametrizedLine<OtherScalarType, AmbientDimAtCompileTime, OtherOptions>& other) {
    m_origin = other.origin().template cast<Scalar>();
    m_direction = other.direction().template cast<Scalar>();
  }

  EIGEN_DEVICE_FUNC bool isApprox(const ParametrizedLine& other, const typename NumTraits<Scalar>::Real& prec =
                                                                     NumTraits<Scalar>::dummy_precision()) const {
    return m_origin.isApprox(other.m_origin, prec) && m_direction.isApprox(other.m_direction, prec);
  }
 
 protected:
  VectorType m_origin, m_direction;
};

template <typename Scalar_, int AmbientDim_, int Options_>
template <int OtherOptions>
EIGEN_DEVICE_FUNC inline ParametrizedLine<Scalar_, AmbientDim_, Options_>::ParametrizedLine(
    const Hyperplane<Scalar_, AmbientDim_, OtherOptions>& hyperplane) {
  EIGEN_STATIC_ASSERT_VECTOR_SPECIFIC_SIZE(VectorType, 2)
  direction() = hyperplane.normal().unitOrthogonal();
  origin() = -hyperplane.normal() * hyperplane.offset();
}

template <typename Scalar_, int AmbientDim_, int Options_>
EIGEN_DEVICE_FUNC inline typename ParametrizedLine<Scalar_, AmbientDim_, Options_>::VectorType
ParametrizedLine<Scalar_, AmbientDim_, Options_>::pointAt(const Scalar_& t) const {
  return origin() + direction() * t;
}

template <typename Scalar_, int AmbientDim_, int Options_>
template <int OtherOptions>
EIGEN_DEVICE_FUNC inline Scalar_ ParametrizedLine<Scalar_, AmbientDim_, Options_>::intersectionParameter(
    const Hyperplane<Scalar_, AmbientDim_, OtherOptions>& hyperplane) const {
  return -(hyperplane.offset() + hyperplane.normal().dot(origin())) / hyperplane.normal().dot(direction());
}

template <typename Scalar_, int AmbientDim_, int Options_>
template <int OtherOptions>
EIGEN_DEVICE_FUNC inline Scalar_ ParametrizedLine<Scalar_, AmbientDim_, Options_>::intersection(
    const Hyperplane<Scalar_, AmbientDim_, OtherOptions>& hyperplane) const {
  return intersectionParameter(hyperplane);
}

template <typename Scalar_, int AmbientDim_, int Options_>
template <int OtherOptions>
EIGEN_DEVICE_FUNC inline typename ParametrizedLine<Scalar_, AmbientDim_, Options_>::VectorType
ParametrizedLine<Scalar_, AmbientDim_, Options_>::intersectionPoint(
    const Hyperplane<Scalar_, AmbientDim_, OtherOptions>& hyperplane) const {
  return pointAt(intersectionParameter(hyperplane));
}
 
}  // end namespace Eigen
 
#endif  // EIGEN_PARAMETRIZEDLINE_H