Eigen/src/Geometry/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)
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#ifndef EIGEN_ALIGNEDBOX_H
#define EIGEN_ALIGNEDBOX_H

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

namespace Eigen {

/** \geometry_module \ingroup Geometry_Module
 *
 *
 * \class AlignedBox
 *
 * \brief An axis aligned box
 *
 * \tparam Scalar_ the type of the scalar coefficients
 * \tparam AmbientDim_ the dimension of the ambient space, can be a compile time value or Dynamic.
 *
 * This class represents an axis aligned box as a pair of the minimal and maximal corners.
 * \warning The result of most methods is undefined when applied to an empty box. You can check for empty boxes using
 * isEmpty(). \sa alignedboxtypedefs
 */
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;  ///< \deprecated since Eigen 3.3
  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;

  /** Define constants to name the corners of a 1D, 2D or 3D axis aligned bounding box */
  enum CornerType {
    /** 1D names @{ */
    Min = 0,
    Max = 1,
    /** @} */

    /** Identifier for 2D corner @{ */
    BottomLeft = 0,
    BottomRight = 1,
    TopLeft = 2,
    TopRight = 3,
    /** @} */

    /** Identifier for 3D corner  @{ */
    BottomLeftFloor = 0,
    BottomRightFloor = 1,
    TopLeftFloor = 2,
    TopRightFloor = 3,
    BottomLeftCeil = 4,
    BottomRightCeil = 5,
    TopLeftCeil = 6,
    TopRightCeil = 7
    /** @} */
  };

  /** Default constructor initializing a null box. */
  EIGEN_DEVICE_FUNC inline AlignedBox() {
    if (EIGEN_CONST_CONDITIONAL(AmbientDimAtCompileTime != Dynamic)) setEmpty();
  }

  /** Constructs a null box with \a _dim the dimension of the ambient space. */
  EIGEN_DEVICE_FUNC inline explicit AlignedBox(Index _dim) : m_min(_dim), m_max(_dim) { setEmpty(); }

  /** Constructs a box with extremities \a _min and \a _max.
   * \warning If either component of \a _min is larger than the same component of \a _max, the constructed box is empty.
   */
  template <typename OtherVectorType1, typename OtherVectorType2>
  EIGEN_DEVICE_FUNC inline AlignedBox(const OtherVectorType1& _min, const OtherVectorType2& _max)
      : m_min(_min), m_max(_max) {}

  /** Constructs a box containing a single point \a p. */
  template <typename Derived>
  EIGEN_DEVICE_FUNC inline explicit AlignedBox(const MatrixBase<Derived>& p) : m_min(p), m_max(m_min) {}

  EIGEN_DEVICE_FUNC ~AlignedBox() {}

  /** \returns the dimension in which the box holds */
  EIGEN_DEVICE_FUNC inline Index dim() const {
    return AmbientDimAtCompileTime == Dynamic ? m_min.size() : Index(AmbientDimAtCompileTime);
  }

  /** \deprecated use isEmpty() */
  EIGEN_DEVICE_FUNC inline bool isNull() const { return isEmpty(); }

  /** \deprecated use setEmpty() */
  EIGEN_DEVICE_FUNC inline void setNull() { setEmpty(); }

  /** \returns true if the box is empty.
   * \sa setEmpty */
  EIGEN_DEVICE_FUNC inline bool isEmpty() const { return (m_min.array() > m_max.array()).any(); }

  /** Makes \c *this an empty box.
   * \sa isEmpty */
  EIGEN_DEVICE_FUNC inline void setEmpty() {
    m_min.setConstant(ScalarTraits::highest());
    m_max.setConstant(ScalarTraits::lowest());
  }

  /** \returns the minimal corner */
  EIGEN_DEVICE_FUNC inline const VectorType&(min)() const { return m_min; }
  /** \returns a non const reference to the minimal corner */
  EIGEN_DEVICE_FUNC inline VectorType&(min)() { return m_min; }
  /** \returns the maximal corner */
  EIGEN_DEVICE_FUNC inline const VectorType&(max)() const { return m_max; }
  /** \returns a non const reference to the maximal corner */
  EIGEN_DEVICE_FUNC inline VectorType&(max)() { return m_max; }

  /** \returns the center of the box */
  EIGEN_DEVICE_FUNC inline const EIGEN_EXPR_BINARYOP_SCALAR_RETURN_TYPE(VectorTypeSum, RealScalar, quotient)
      center() const {
    return (m_min + m_max) / RealScalar(2);
  }

  /** \returns the lengths of the sides of the bounding box.
   * Note that this function does not get the same
   * result for integral or floating scalar types: see
   */
  EIGEN_DEVICE_FUNC inline const CwiseBinaryOp<internal::scalar_difference_op<Scalar, Scalar>, const VectorType,
                                               const VectorType>
  sizes() const {
    return m_max - m_min;
  }

  /** \returns the volume of the bounding box */
  EIGEN_DEVICE_FUNC inline Scalar volume() const { return sizes().prod(); }

  /** \returns an expression for the bounding box diagonal vector
   * if the length of the diagonal is needed: diagonal().norm()
   * will provide it.
   */
  EIGEN_DEVICE_FUNC inline CwiseBinaryOp<internal::scalar_difference_op<Scalar, Scalar>, const VectorType,
                                         const VectorType>
  diagonal() const {
    return sizes();
  }

  /** \returns the vertex of the bounding box at the corner defined by
   * the corner-id corner. It works only for a 1D, 2D or 3D bounding box.
   * For 1D bounding boxes corners are named by 2 enum constants:
   * BottomLeft and BottomRight.
   * For 2D bounding boxes, corners are named by 4 enum constants:
   * BottomLeft, BottomRight, TopLeft, TopRight.
   * For 3D bounding boxes, the following names are added:
   * BottomLeftCeil, BottomRightCeil, TopLeftCeil, TopRightCeil.
   */
  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;
  }

  /** \returns a random point inside the bounding box sampled with
   * a uniform distribution */
  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;
  }

  /** \returns true if the point \a p is inside the box \c *this. */
  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();
  }

  /** \returns true if the box \a b is entirely inside the box \c *this. */
  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();
  }

  /** \returns true if the box \a b is intersecting the box \c *this.
   * \sa intersection, clamp */
  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();
  }

  /** Extends \c *this such that it contains the point \a p and returns a reference to \c *this.
   * \sa extend(const AlignedBox&) */
  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;
  }

  /** Extends \c *this such that it contains the box \a b and returns a reference to \c *this.
   * \sa merged, extend(const MatrixBase&) */
  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;
  }

  /** Clamps \c *this by the box \a b and returns a reference to \c *this.
   * \note If the boxes don't intersect, the resulting box is empty.
   * \sa intersection(), intersects() */
  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;
  }

  /** Returns an AlignedBox that is the intersection of \a b and \c *this
   * \note If the boxes don't intersect, the resulting box is empty.
   * \sa intersects(), clamp, contains()  */
  EIGEN_DEVICE_FUNC inline AlignedBox intersection(const AlignedBox& b) const {
    return AlignedBox(m_min.cwiseMax(b.m_min), m_max.cwiseMin(b.m_max));
  }

  /** Returns an AlignedBox that is the union of \a b and \c *this.
   * \note Merging with an empty box may result in a box bigger than \c *this.
   * \sa extend(const AlignedBox&) */
  EIGEN_DEVICE_FUNC inline AlignedBox merged(const AlignedBox& b) const {
    return AlignedBox(m_min.cwiseMin(b.m_min), m_max.cwiseMax(b.m_max));
  }

  /** Translate \c *this by the vector \a t and returns a reference to \c *this. */
  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;
  }

  /** \returns a copy of \c *this translated by the vector \a t. */
  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;
  }

  /** \returns the squared distance between the point \a p and the box \c *this,
   * and zero if \a p is inside the box.
   * \sa exteriorDistance(const MatrixBase&), squaredExteriorDistance(const AlignedBox&)
   */
  template <typename Derived>
  EIGEN_DEVICE_FUNC inline Scalar squaredExteriorDistance(const MatrixBase<Derived>& p) const;

  /** \returns the squared distance between the boxes \a b and \c *this,
   * and zero if the boxes intersect.
   * \sa exteriorDistance(const AlignedBox&), squaredExteriorDistance(const MatrixBase&)
   */
  EIGEN_DEVICE_FUNC inline Scalar squaredExteriorDistance(const AlignedBox& b) const;

  /** \returns the distance between the point \a p and the box \c *this,
   * and zero if \a p is inside the box.
   * \sa squaredExteriorDistance(const MatrixBase&), exteriorDistance(const AlignedBox&)
   */
  template <typename Derived>
  EIGEN_DEVICE_FUNC inline NonInteger exteriorDistance(const MatrixBase<Derived>& p) const {
    EIGEN_USING_STD(sqrt) return sqrt(NonInteger(squaredExteriorDistance(p)));
  }

  /** \returns the distance between the boxes \a b and \c *this,
   * and zero if the boxes intersect.
   * \sa squaredExteriorDistance(const AlignedBox&), exteriorDistance(const MatrixBase&)
   */
  EIGEN_DEVICE_FUNC inline NonInteger exteriorDistance(const AlignedBox& b) const {
    EIGEN_USING_STD(sqrt) return sqrt(NonInteger(squaredExteriorDistance(b)));
  }

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

  /**
   * Transforms this box by \a transform and recomputes it to
   * still be an axis-aligned box.
   *
   * \note This method is provided under BSD license (see the top of this file).
   */
  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);
  }

  /**
   * \returns a copy of \c *this transformed by \a transform and recomputed to
   * still be an axis-aligned box.
   */
  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;
  }

  /** \returns \c *this with scalar type casted to \a NewScalarType
   *
   * Note that if \a NewScalarType is equal to the current scalar type of \c *this
   * then this function smartly returns a const reference to \c *this.
   */
  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);
  }

  /** Copy constructor with scalar type conversion */
  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>();
  }

  /** \returns \c true if \c *this is approximately equal to \a other, within the precision
   * determined by \a prec.
   *
   * \sa MatrixBase::isApprox() */
  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;
}

/** \defgroup alignedboxtypedefs Global aligned box typedefs
 *
 * \ingroup Geometry_Module
 *
 * Eigen defines several typedef shortcuts for most common aligned box types.
 *
 * The general patterns are the following:
 *
 * \c AlignedBoxSizeType where \c Size can be \c 1, \c 2,\c 3,\c 4 for fixed size boxes or \c X for dynamic size,
 * and where \c Type can be \c i for integer, \c f for float, \c d for double.
 *
 * For example, \c AlignedBox3d is a fixed-size 3x3 aligned box type of doubles, and \c AlignedBoxXf is a dynamic-size
 * aligned box of floats.
 *
 * \sa class AlignedBox
 */

#define EIGEN_MAKE_TYPEDEFS(Type, TypeSuffix, Size, SizeSuffix) \
  /** \ingroup alignedboxtypedefs */                            \
  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