AlignedBox.h

// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// Copyright (C) 2008 Gael Guennebaud <gael.guennebaud@inria.fr>
//
// 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/.

// Function void Eigen::AlignedBox::transform(const Transform& transform)
// is provided under the following license agreement:
//
// Software License Agreement (BSD License)
//
// Copyright (c) 2011-2014, Willow Garage, Inc.
// Copyright (c) 2014-2015, Open Source Robotics Foundation
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#ifndef EIGEN_ALIGNEDBOX_H
#define EIGEN_ALIGNEDBOX_H

// IWYU pragma: private
#include "./InternalHeaderCheck.h"

namespace Eigen {

template <typename Scalar_, int AmbientDim_>
class AlignedBox {
 public:
  EIGEN_MAKE_ALIGNED_OPERATOR_NEW_IF_VECTORIZABLE_FIXED_SIZE(Scalar_, AmbientDim_)
  enum { AmbientDimAtCompileTime = AmbientDim_ };
  typedef Scalar_ Scalar;
  typedef NumTraits<Scalar> ScalarTraits;
  typedef Eigen::Index Index;  
  typedef typename ScalarTraits::Real RealScalar;
  typedef typename ScalarTraits::NonInteger NonInteger;
  typedef Matrix<Scalar, AmbientDimAtCompileTime, 1> VectorType;
  typedef CwiseBinaryOp<internal::scalar_sum_op<Scalar>, const VectorType, const VectorType> VectorTypeSum;

  enum CornerType {
    Min = 0,
    Max = 1,
    BottomLeft = 0,
    BottomRight = 1,
    TopLeft = 2,
    TopRight = 3,
    BottomLeftFloor = 0,
    BottomRightFloor = 1,
    TopLeftFloor = 2,
    TopRightFloor = 3,
    BottomLeftCeil = 4,
    BottomRightCeil = 5,
    TopLeftCeil = 6,
    TopRightCeil = 7
  };

  EIGEN_DEVICE_FUNC inline AlignedBox() {
    if (EIGEN_CONST_CONDITIONAL(AmbientDimAtCompileTime != Dynamic)) setEmpty();
  }

  EIGEN_DEVICE_FUNC inline explicit AlignedBox(Index _dim) : m_min(_dim), m_max(_dim) { setEmpty(); }

  template <typename OtherVectorType1, typename OtherVectorType2>
  EIGEN_DEVICE_FUNC inline AlignedBox(const OtherVectorType1& _min, const OtherVectorType2& _max)
      : m_min(_min), m_max(_max) {}

  template <typename Derived>
  EIGEN_DEVICE_FUNC inline explicit AlignedBox(const MatrixBase<Derived>& p) : m_min(p), m_max(m_min) {}

  EIGEN_DEVICE_FUNC ~AlignedBox() {}

  EIGEN_DEVICE_FUNC inline Index dim() const {
    return AmbientDimAtCompileTime == Dynamic ? m_min.size() : Index(AmbientDimAtCompileTime);
  }

  EIGEN_DEVICE_FUNC inline bool isNull() const { return isEmpty(); }

  EIGEN_DEVICE_FUNC inline void setNull() { setEmpty(); }

  EIGEN_DEVICE_FUNC inline bool isEmpty() const { return (m_min.array() > m_max.array()).any(); }

  EIGEN_DEVICE_FUNC inline void setEmpty() {
    m_min.setConstant(ScalarTraits::highest());
    m_max.setConstant(ScalarTraits::lowest());
  }

  EIGEN_DEVICE_FUNC inline const VectorType&(min)() const { return m_min; }
  EIGEN_DEVICE_FUNC inline VectorType&(min)() { return m_min; }
  EIGEN_DEVICE_FUNC inline const VectorType&(max)() const { return m_max; }
  EIGEN_DEVICE_FUNC inline VectorType&(max)() { return m_max; }

  EIGEN_DEVICE_FUNC inline const EIGEN_EXPR_BINARYOP_SCALAR_RETURN_TYPE(VectorTypeSum, RealScalar, quotient)
      center() const {
    return (m_min + m_max) / RealScalar(2);
  }

  EIGEN_DEVICE_FUNC inline const CwiseBinaryOp<internal::scalar_difference_op<Scalar, Scalar>, const VectorType,
                                               const VectorType>
  sizes() const {
    return m_max - m_min;
  }

  EIGEN_DEVICE_FUNC inline Scalar volume() const { return isEmpty() ? Scalar(0) : sizes().prod(); }

  EIGEN_DEVICE_FUNC inline CwiseBinaryOp<internal::scalar_difference_op<Scalar, Scalar>, const VectorType,
                                         const VectorType>
  diagonal() const {
    return sizes();
  }

  EIGEN_DEVICE_FUNC inline VectorType corner(CornerType corner) const {
    EIGEN_STATIC_ASSERT(AmbientDim_ <= 3, THIS_METHOD_IS_ONLY_FOR_VECTORS_OF_A_SPECIFIC_SIZE);

    VectorType res;

    Index mult = 1;
    for (Index d = 0; d < dim(); ++d) {
      if (mult & corner)
        res[d] = m_max[d];
      else
        res[d] = m_min[d];
      mult *= 2;
    }
    return res;
  }

  EIGEN_DEVICE_FUNC inline VectorType sample() const {
    VectorType r(dim());
    for (Index d = 0; d < dim(); ++d) {
      if (!ScalarTraits::IsInteger) {
        r[d] = m_min[d] + (m_max[d] - m_min[d]) * internal::random<Scalar>(Scalar(0), Scalar(1));
      } else
        r[d] = internal::random(m_min[d], m_max[d]);
    }
    return r;
  }

  template <typename Derived>
  EIGEN_DEVICE_FUNC inline bool contains(const MatrixBase<Derived>& p) const {
    typename internal::nested_eval<Derived, 2>::type p_n(p.derived());
    return (m_min.array() <= p_n.array()).all() && (p_n.array() <= m_max.array()).all();
  }

  EIGEN_DEVICE_FUNC inline bool contains(const AlignedBox& b) const {
    return (m_min.array() <= (b.min)().array()).all() && ((b.max)().array() <= m_max.array()).all();
  }

  EIGEN_DEVICE_FUNC inline bool intersects(const AlignedBox& b) const {
    return (m_min.array() <= (b.max)().array()).all() && ((b.min)().array() <= m_max.array()).all();
  }

  template <typename Derived>
  EIGEN_DEVICE_FUNC inline AlignedBox& extend(const MatrixBase<Derived>& p) {
    typename internal::nested_eval<Derived, 2>::type p_n(p.derived());
    m_min = m_min.cwiseMin(p_n);
    m_max = m_max.cwiseMax(p_n);
    return *this;
  }

  EIGEN_DEVICE_FUNC inline AlignedBox& extend(const AlignedBox& b) {
    m_min = m_min.cwiseMin(b.m_min);
    m_max = m_max.cwiseMax(b.m_max);
    return *this;
  }

  EIGEN_DEVICE_FUNC inline AlignedBox& clamp(const AlignedBox& b) {
    m_min = m_min.cwiseMax(b.m_min);
    m_max = m_max.cwiseMin(b.m_max);
    return *this;
  }

  EIGEN_DEVICE_FUNC inline AlignedBox intersection(const AlignedBox& b) const {
    return AlignedBox(m_min.cwiseMax(b.m_min), m_max.cwiseMin(b.m_max));
  }

  EIGEN_DEVICE_FUNC inline AlignedBox merged(const AlignedBox& b) const {
    return AlignedBox(m_min.cwiseMin(b.m_min), m_max.cwiseMax(b.m_max));
  }

  template <typename Derived>
  EIGEN_DEVICE_FUNC inline AlignedBox& translate(const MatrixBase<Derived>& a_t) {
    const typename internal::nested_eval<Derived, 2>::type t(a_t.derived());
    m_min += t;
    m_max += t;
    return *this;
  }

  template <typename Derived>
  EIGEN_DEVICE_FUNC inline AlignedBox translated(const MatrixBase<Derived>& a_t) const {
    AlignedBox result(m_min, m_max);
    result.translate(a_t);
    return result;
  }

  template <typename Derived>
  EIGEN_DEVICE_FUNC inline Scalar squaredExteriorDistance(const MatrixBase<Derived>& p) const;

  EIGEN_DEVICE_FUNC inline Scalar squaredExteriorDistance(const AlignedBox& b) const;

  template <typename Derived>
  EIGEN_DEVICE_FUNC inline NonInteger exteriorDistance(const MatrixBase<Derived>& p) const {
    EIGEN_USING_STD(sqrt) return sqrt(NonInteger(squaredExteriorDistance(p)));
  }

  EIGEN_DEVICE_FUNC inline NonInteger exteriorDistance(const AlignedBox& b) const {
    EIGEN_USING_STD(sqrt) return sqrt(NonInteger(squaredExteriorDistance(b)));
  }

  template <int Mode, int Options>
  EIGEN_DEVICE_FUNC inline void transform(
      const typename Transform<Scalar, AmbientDimAtCompileTime, Mode, Options>::TranslationType& translation) {
    this->translate(translation);
  }

  template <int Mode, int Options>
  EIGEN_DEVICE_FUNC inline void transform(const Transform<Scalar, AmbientDimAtCompileTime, Mode, Options>& transform) {
    // Only Affine and Isometry transforms are currently supported.
    EIGEN_STATIC_ASSERT(Mode == Affine || Mode == AffineCompact || Mode == Isometry,
                        THIS_METHOD_IS_ONLY_FOR_SPECIFIC_TRANSFORMATIONS);

    // Method adapted from FCL src/shape/geometric_shapes_utility.cpp#computeBV<AABB, Box>(...)
    // https://github.com/flexible-collision-library/fcl/blob/fcl-0.4/src/shape/geometric_shapes_utility.cpp#L292
    //
    // Here's a nice explanation why it works: https://zeuxcg.org/2010/10/17/aabb-from-obb-with-component-wise-abs/

    // two times rotated extent
    const VectorType rotated_extent_2 = transform.linear().cwiseAbs() * sizes();
    // two times new center
    const VectorType rotated_center_2 =
        transform.linear() * (this->m_max + this->m_min) + Scalar(2) * transform.translation();

    this->m_max = (rotated_center_2 + rotated_extent_2) / Scalar(2);
    this->m_min = (rotated_center_2 - rotated_extent_2) / Scalar(2);
  }

  template <int Mode, int Options>
  EIGEN_DEVICE_FUNC AlignedBox
  transformed(const Transform<Scalar, AmbientDimAtCompileTime, Mode, Options>& transform) const {
    AlignedBox result(m_min, m_max);
    result.transform(transform);
    return result;
  }

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

  template <typename OtherScalarType>
  EIGEN_DEVICE_FUNC inline explicit AlignedBox(const AlignedBox<OtherScalarType, AmbientDimAtCompileTime>& other) {
    m_min = (other.min)().template cast<Scalar>();
    m_max = (other.max)().template cast<Scalar>();
  }

  EIGEN_DEVICE_FUNC bool isApprox(const AlignedBox& other,
                                  const RealScalar& prec = ScalarTraits::dummy_precision()) const {
    return m_min.isApprox(other.m_min, prec) && m_max.isApprox(other.m_max, prec);
  }

 protected:
  VectorType m_min, m_max;
};

template <typename Scalar, int AmbientDim>
template <typename Derived>
EIGEN_DEVICE_FUNC inline Scalar AlignedBox<Scalar, AmbientDim>::squaredExteriorDistance(
    const MatrixBase<Derived>& a_p) const {
  typename internal::nested_eval<Derived, 2 * AmbientDim>::type p(a_p.derived());
  Scalar dist2(0);
  Scalar aux;
  for (Index k = 0; k < dim(); ++k) {
    if (m_min[k] > p[k]) {
      aux = m_min[k] - p[k];
      dist2 += aux * aux;
    } else if (p[k] > m_max[k]) {
      aux = p[k] - m_max[k];
      dist2 += aux * aux;
    }
  }
  return dist2;
}

template <typename Scalar, int AmbientDim>
EIGEN_DEVICE_FUNC inline Scalar AlignedBox<Scalar, AmbientDim>::squaredExteriorDistance(const AlignedBox& b) const {
  Scalar dist2(0);
  Scalar aux;
  for (Index k = 0; k < dim(); ++k) {
    if (m_min[k] > b.m_max[k]) {
      aux = m_min[k] - b.m_max[k];
      dist2 += aux * aux;
    } else if (b.m_min[k] > m_max[k]) {
      aux = b.m_min[k] - m_max[k];
      dist2 += aux * aux;
    }
  }
  return dist2;
}

#define EIGEN_MAKE_TYPEDEFS(Type, TypeSuffix, Size, SizeSuffix) \
                            \
  typedef AlignedBox<Type, Size> AlignedBox##SizeSuffix##TypeSuffix;

#define EIGEN_MAKE_TYPEDEFS_ALL_SIZES(Type, TypeSuffix) \
  EIGEN_MAKE_TYPEDEFS(Type, TypeSuffix, 1, 1)           \
  EIGEN_MAKE_TYPEDEFS(Type, TypeSuffix, 2, 2)           \
  EIGEN_MAKE_TYPEDEFS(Type, TypeSuffix, 3, 3)           \
  EIGEN_MAKE_TYPEDEFS(Type, TypeSuffix, 4, 4)           \
  EIGEN_MAKE_TYPEDEFS(Type, TypeSuffix, Dynamic, X)

EIGEN_MAKE_TYPEDEFS_ALL_SIZES(int, i)
EIGEN_MAKE_TYPEDEFS_ALL_SIZES(float, f)
EIGEN_MAKE_TYPEDEFS_ALL_SIZES(double, d)

#undef EIGEN_MAKE_TYPEDEFS_ALL_SIZES
#undef EIGEN_MAKE_TYPEDEFS

}  // end namespace Eigen

#endif  // EIGEN_ALIGNEDBOX_H