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BBox.h
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// Copyright Contributors to the OpenVDB Project
// SPDX-License-Identifier: MPL-2.0
#ifndef OPENVDB_MATH_BBOX_HAS_BEEN_INCLUDED
#define OPENVDB_MATH_BBOX_HAS_BEEN_INCLUDED
#include "Math.h" // for math::isApproxEqual() and math::Tolerance()
#include "Vec3.h"
#include <algorithm> // for std::min(), std::max()
#include <cmath> // for std::abs()
#include <iostream>
#include <limits>
#include <type_traits>
namespace openvdb {
OPENVDB_USE_VERSION_NAMESPACE
namespace OPENVDB_VERSION_NAME {
namespace math {
/// @brief Axis-aligned bounding box
template<typename Vec3T>
class BBox
{
public:
using Vec3Type = Vec3T;
using ValueType = Vec3T;
using VectorType = Vec3T;
using ElementType = typename Vec3Type::ValueType;
/// @brief The default constructor creates an invalid bounding box.
BBox();
/// @brief Construct a bounding box that exactly encloses the given
/// minimum and maximum points.
BBox(const Vec3T& xyzMin, const Vec3T& xyzMax);
/// @brief Construct a bounding box that exactly encloses the given
/// minimum and maximum points.
/// @details If @a sorted is false, sort the points by their
/// @e x, @e y and @e z components.
BBox(const Vec3T& xyzMin, const Vec3T& xyzMax, bool sorted);
/// @brief Contruct a cubical bounding box from a minimum coordinate
/// and an edge length.
/// @note Inclusive for integral <b>ElementType</b>s
BBox(const Vec3T& xyzMin, const ElementType& length);
/// @brief Construct a bounding box that exactly encloses two points,
/// whose coordinates are given by an array of six values,
/// <i>x<sub>1</sub></i>, <i>y<sub>1</sub></i>, <i>z<sub>1</sub></i>,
/// <i>x<sub>2</sub></i>, <i>y<sub>2</sub></i> and <i>z<sub>2</sub></i>.
/// @details If @a sorted is false, sort the points by their
/// @e x, @e y and @e z components.
explicit BBox(const ElementType* xyz, bool sorted = true);
BBox(const BBox&) = default;
BBox& operator=(const BBox&) = default;
/// @brief Sort the mininum and maximum points of this bounding box
/// by their @e x, @e y and @e z components.
void sort();
/// @brief Return a const reference to the minimum point of this bounding box.
const Vec3T& min() const { return mMin; }
/// @brief Return a const reference to the maximum point of this bounding box.
const Vec3T& max() const { return mMax; }
/// @brief Return a non-const reference to the minimum point of this bounding box.
Vec3T& min() { return mMin; }
/// @brief Return a non-const reference to the maximum point of this bounding box.
Vec3T& max() { return mMax; }
/// @brief Return @c true if this bounding box is identical to the given bounding box.
bool operator==(const BBox& rhs) const;
/// @brief Return @c true if this bounding box differs from the given bounding box.
bool operator!=(const BBox& rhs) const { return !(*this == rhs); }
/// @brief Return @c true if this bounding box is empty, i.e., it has no (positive) volume.
bool empty() const;
/// @brief Return @c true if this bounding box has (positive) volume.
bool hasVolume() const { return !this->empty(); }
/// @brief Return @c true if this bounding box has (positive) volume.
operator bool() const { return !this->empty(); }
/// @brief Return @c true if all components of the minimum point are less than
/// or equal to the corresponding components of the maximum point.
/// @details This is equivalent to testing whether this bounding box has nonnegative volume.
/// @note For floating-point <b>ElementType</b>s a tolerance is used for this test.
bool isSorted() const;
/// @brief Return the center point of this bounding box.
Vec3d getCenter() const;
/// @brief Return the extents of this bounding box, i.e., the length along each axis.
/// @note Inclusive for integral <b>ElementType</b>s
Vec3T extents() const;
/// @brief Return the index (0, 1 or 2) of the longest axis.
size_t maxExtent() const { return MaxIndex(mMax - mMin); }
/// @brief Return the index (0, 1 or 2) of the shortest axis.
size_t minExtent() const { return MinIndex(mMax - mMin); }
/// @brief Return the volume enclosed by this bounding box.
ElementType volume() const { Vec3T e = this->extents(); return e[0] * e[1] * e[2]; }
/// @brief Return @c true if the given point is inside this bounding box.
bool isInside(const Vec3T& xyz) const;
/// @brief Return @c true if the given bounding box is inside this bounding box.
bool isInside(const BBox&) const;
/// @brief Return @c true if the given bounding box overlaps with this bounding box.
bool hasOverlap(const BBox&) const;
/// @brief Return @c true if the given bounding box overlaps with this bounding box.
bool intersects(const BBox& other) const { return hasOverlap(other); }
/// @brief Pad this bounding box.
void expand(ElementType padding);
/// @brief Expand this bounding box to enclose the given point.
void expand(const Vec3T& xyz);
/// @brief Union this bounding box with the given bounding box.
void expand(const BBox&);
/// @brief Union this bounding box with the cubical bounding box with
/// minimum point @a xyzMin and the given edge length.
/// @note Inclusive for integral <b>ElementType</b>s
void expand(const Vec3T& xyzMin, const ElementType& length);
/// @brief Translate this bounding box by
/// (<i>t<sub>x</sub></i>, <i>t<sub>y</sub></i>, <i>t<sub>z</sub></i>).
void translate(const Vec3T& t);
/// @brief Apply a map to this bounding box.
template<typename MapType>
BBox applyMap(const MapType& map) const;
/// @brief Apply the inverse of a map to this bounding box
template<typename MapType>
BBox applyInverseMap(const MapType& map) const;
/// @brief Unserialize this bounding box from the given stream.
void read(std::istream& is) { mMin.read(is); mMax.read(is); }
/// @brief Serialize this bounding box to the given stream.
void write(std::ostream& os) const { mMin.write(os); mMax.write(os); }
private:
Vec3T mMin, mMax;
}; // class BBox
////////////////////////////////////////
template<typename Vec3T>
inline
BBox<Vec3T>::BBox():
mMin( std::numeric_limits<ElementType>::max()),
mMax(-std::numeric_limits<ElementType>::max())
{
}
template<typename Vec3T>
inline
BBox<Vec3T>::BBox(const Vec3T& xyzMin, const Vec3T& xyzMax):
mMin(xyzMin), mMax(xyzMax)
{
}
template<typename Vec3T>
inline
BBox<Vec3T>::BBox(const Vec3T& xyzMin, const Vec3T& xyzMax, bool sorted):
mMin(xyzMin), mMax(xyzMax)
{
if (!sorted) this->sort();
}
template<typename Vec3T>
inline
BBox<Vec3T>::BBox(const Vec3T& xyzMin, const ElementType& length):
mMin(xyzMin), mMax(xyzMin)
{
// min and max are inclusive for integral ElementType
const ElementType size = std::is_integral<ElementType>::value ? length-1 : length;
mMax[0] += size;
mMax[1] += size;
mMax[2] += size;
}
template<typename Vec3T>
inline
BBox<Vec3T>::BBox(const ElementType* xyz, bool sorted):
mMin(xyz[0], xyz[1], xyz[2]),
mMax(xyz[3], xyz[4], xyz[5])
{
if (!sorted) this->sort();
}
////////////////////////////////////////
template<typename Vec3T>
inline bool
BBox<Vec3T>::empty() const
{
if (std::is_integral<ElementType>::value) {
// min and max are inclusive for integral ElementType
return (mMin[0] > mMax[0] || mMin[1] > mMax[1] || mMin[2] > mMax[2]);
}
return mMin[0] >= mMax[0] || mMin[1] >= mMax[1] || mMin[2] >= mMax[2];
}
template<typename Vec3T>
inline bool
BBox<Vec3T>::operator==(const BBox& rhs) const
{
if (std::is_integral<ElementType>::value) {
return mMin == rhs.min() && mMax == rhs.max();
} else {
return math::isApproxEqual(mMin, rhs.min()) && math::isApproxEqual(mMax, rhs.max());
}
}
template<typename Vec3T>
inline void
BBox<Vec3T>::sort()
{
Vec3T tMin(mMin), tMax(mMax);
for (int i = 0; i < 3; ++i) {
mMin[i] = std::min(tMin[i], tMax[i]);
mMax[i] = std::max(tMin[i], tMax[i]);
}
}
template<typename Vec3T>
inline bool
BBox<Vec3T>::isSorted() const
{
if (std::is_integral<ElementType>::value) {
return (mMin[0] <= mMax[0] && mMin[1] <= mMax[1] && mMin[2] <= mMax[2]);
} else {
ElementType t = math::Tolerance<ElementType>::value();
return (mMin[0] < (mMax[0] + t) && mMin[1] < (mMax[1] + t) && mMin[2] < (mMax[2] + t));
}
}
template<typename Vec3T>
inline Vec3d
BBox<Vec3T>::getCenter() const
{
return (Vec3d(mMin.asPointer()) + Vec3d(mMax.asPointer())) * 0.5;
}
template<typename Vec3T>
inline Vec3T
BBox<Vec3T>::extents() const
{
if (std::is_integral<ElementType>::value) {
return (mMax - mMin) + Vec3T(1, 1, 1);
} else {
return (mMax - mMin);
}
}
////////////////////////////////////////
template<typename Vec3T>
inline bool
BBox<Vec3T>::isInside(const Vec3T& xyz) const
{
if (std::is_integral<ElementType>::value) {
return xyz[0] >= mMin[0] && xyz[0] <= mMax[0] &&
xyz[1] >= mMin[1] && xyz[1] <= mMax[1] &&
xyz[2] >= mMin[2] && xyz[2] <= mMax[2];
} else {
ElementType t = math::Tolerance<ElementType>::value();
return xyz[0] > (mMin[0]-t) && xyz[0] < (mMax[0]+t) &&
xyz[1] > (mMin[1]-t) && xyz[1] < (mMax[1]+t) &&
xyz[2] > (mMin[2]-t) && xyz[2] < (mMax[2]+t);
}
}
template<typename Vec3T>
inline bool
BBox<Vec3T>::isInside(const BBox& b) const
{
if (std::is_integral<ElementType>::value) {
return b.min()[0] >= mMin[0] && b.max()[0] <= mMax[0] &&
b.min()[1] >= mMin[1] && b.max()[1] <= mMax[1] &&
b.min()[2] >= mMin[2] && b.max()[2] <= mMax[2];
} else {
ElementType t = math::Tolerance<ElementType>::value();
return (b.min()[0]-t) > mMin[0] && (b.max()[0]+t) < mMax[0] &&
(b.min()[1]-t) > mMin[1] && (b.max()[1]+t) < mMax[1] &&
(b.min()[2]-t) > mMin[2] && (b.max()[2]+t) < mMax[2];
}
}
template<typename Vec3T>
inline bool
BBox<Vec3T>::hasOverlap(const BBox& b) const
{
if (std::is_integral<ElementType>::value) {
return mMax[0] >= b.min()[0] && mMin[0] <= b.max()[0] &&
mMax[1] >= b.min()[1] && mMin[1] <= b.max()[1] &&
mMax[2] >= b.min()[2] && mMin[2] <= b.max()[2];
} else {
ElementType t = math::Tolerance<ElementType>::value();
return mMax[0] > (b.min()[0]-t) && mMin[0] < (b.max()[0]+t) &&
mMax[1] > (b.min()[1]-t) && mMin[1] < (b.max()[1]+t) &&
mMax[2] > (b.min()[2]-t) && mMin[2] < (b.max()[2]+t);
}
}
////////////////////////////////////////
template<typename Vec3T>
inline void
BBox<Vec3T>::expand(ElementType dx)
{
dx = std::abs(dx);
for (int i = 0; i < 3; ++i) {
mMin[i] -= dx;
mMax[i] += dx;
}
}
template<typename Vec3T>
inline void
BBox<Vec3T>::expand(const Vec3T& xyz)
{
for (int i = 0; i < 3; ++i) {
mMin[i] = std::min(mMin[i], xyz[i]);
mMax[i] = std::max(mMax[i], xyz[i]);
}
}
template<typename Vec3T>
inline void
BBox<Vec3T>::expand(const BBox& b)
{
for (int i = 0; i < 3; ++i) {
mMin[i] = std::min(mMin[i], b.min()[i]);
mMax[i] = std::max(mMax[i], b.max()[i]);
}
}
template<typename Vec3T>
inline void
BBox<Vec3T>::expand(const Vec3T& xyzMin, const ElementType& length)
{
const ElementType size = std::is_integral<ElementType>::value ? length-1 : length;
for (int i = 0; i < 3; ++i) {
mMin[i] = std::min(mMin[i], xyzMin[i]);
mMax[i] = std::max(mMax[i], xyzMin[i] + size);
}
}
template<typename Vec3T>
inline void
BBox<Vec3T>::translate(const Vec3T& dx)
{
mMin += dx;
mMax += dx;
}
template<typename Vec3T>
template<typename MapType>
inline BBox<Vec3T>
BBox<Vec3T>::applyMap(const MapType& map) const
{
using Vec3R = Vec3<double>;
BBox<Vec3T> bbox;
bbox.expand(map.applyMap(Vec3R(mMin[0], mMin[1], mMin[2])));
bbox.expand(map.applyMap(Vec3R(mMin[0], mMin[1], mMax[2])));
bbox.expand(map.applyMap(Vec3R(mMin[0], mMax[1], mMin[2])));
bbox.expand(map.applyMap(Vec3R(mMax[0], mMin[1], mMin[2])));
bbox.expand(map.applyMap(Vec3R(mMax[0], mMax[1], mMin[2])));
bbox.expand(map.applyMap(Vec3R(mMax[0], mMin[1], mMax[2])));
bbox.expand(map.applyMap(Vec3R(mMin[0], mMax[1], mMax[2])));
bbox.expand(map.applyMap(Vec3R(mMax[0], mMax[1], mMax[2])));
return bbox;
}
template<typename Vec3T>
template<typename MapType>
inline BBox<Vec3T>
BBox<Vec3T>::applyInverseMap(const MapType& map) const
{
using Vec3R = Vec3<double>;
BBox<Vec3T> bbox;
bbox.expand(map.applyInverseMap(Vec3R(mMin[0], mMin[1], mMin[2])));
bbox.expand(map.applyInverseMap(Vec3R(mMin[0], mMin[1], mMax[2])));
bbox.expand(map.applyInverseMap(Vec3R(mMin[0], mMax[1], mMin[2])));
bbox.expand(map.applyInverseMap(Vec3R(mMax[0], mMin[1], mMin[2])));
bbox.expand(map.applyInverseMap(Vec3R(mMax[0], mMax[1], mMin[2])));
bbox.expand(map.applyInverseMap(Vec3R(mMax[0], mMin[1], mMax[2])));
bbox.expand(map.applyInverseMap(Vec3R(mMin[0], mMax[1], mMax[2])));
bbox.expand(map.applyInverseMap(Vec3R(mMax[0], mMax[1], mMax[2])));
return bbox;
}
////////////////////////////////////////
template<typename Vec3T>
inline std::ostream&
operator<<(std::ostream& os, const BBox<Vec3T>& b)
{
os << b.min() << " -> " << b.max();
return os;
}
} // namespace math
} // namespace OPENVDB_VERSION_NAME
} // namespace openvdb
#endif // OPENVDB_MATH_BBOX_HAS_BEEN_INCLUDED
Math.h
General-purpose arithmetic and comparison routines, most of which accept arbitrary value types (or at...
Vec3.h
openvdb::v11_0::math::BBox
Axis-aligned bounding box.
Definition BBox.h:24
openvdb::v11_0::math::BBox::BBox
BBox(const Vec3T &xyzMin, const ElementType &length)
Contruct a cubical bounding box from a minimum coordinate and an edge length.
Definition BBox.h:171
openvdb::v11_0::math::BBox::isInside
bool isInside(const Vec3T &xyz) const
Return true if the given point is inside this bounding box.
Definition BBox.h:267
openvdb::v11_0::math::BBox::BBox
BBox(const Vec3T &xyzMin, const Vec3T &xyzMax)
Construct a bounding box that exactly encloses the given minimum and maximum points.
Definition BBox.h:156
openvdb::v11_0::math::BBox::BBox
BBox()
The default constructor creates an invalid bounding box.
Definition BBox.h:148
openvdb::v11_0::math::BBox::minExtent
size_t minExtent() const
Return the index (0, 1 or 2) of the shortest axis.
Definition BBox.h:97
openvdb::v11_0::math::BBox::max
const Vec3T & max() const
Return a const reference to the maximum point of this bounding box.
Definition BBox.h:64
openvdb::v11_0::math::BBox::write
void write(std::ostream &os) const
Serialize this bounding box to the given stream.
Definition BBox.h:136
openvdb::v11_0::math::BBox::hasOverlap
bool hasOverlap(const BBox &) const
Return true if the given bounding box overlaps with this bounding box.
Definition BBox.h:301
openvdb::v11_0::math::BBox::expand
void expand(const Vec3T &xyz)
Expand this bounding box to enclose the given point.
Definition BBox.h:333
openvdb::v11_0::math::BBox::expand
void expand(const Vec3T &xyzMin, const ElementType &length)
Union this bounding box with the cubical bounding box with minimum point xyzMin and the given edge le...
Definition BBox.h:354
openvdb::v11_0::math::BBox::sort
void sort()
Sort the mininum and maximum points of this bounding box by their x, y and z components.
Definition BBox.h:220
openvdb::v11_0::math::BBox::volume
ElementType volume() const
Return the volume enclosed by this bounding box.
Definition BBox.h:100
openvdb::v11_0::math::BBox::hasVolume
bool hasVolume() const
Return true if this bounding box has (positive) volume.
Definition BBox.h:78
openvdb::v11_0::math::BBox::getCenter
Vec3d getCenter() const
Return the center point of this bounding box.
Definition BBox.h:245
openvdb::v11_0::math::BBox::BBox
BBox(const Vec3T &xyzMin, const Vec3T &xyzMax, bool sorted)
Construct a bounding box that exactly encloses the given minimum and maximum points.
Definition BBox.h:163
openvdb::v11_0::math::BBox::isSorted
bool isSorted() const
Return true if all components of the minimum point are less than or equal to the corresponding compon...
Definition BBox.h:232
openvdb::v11_0::math::BBox::empty
bool empty() const
Return true if this bounding box is empty, i.e., it has no (positive) volume.
Definition BBox.h:196
openvdb::v11_0::math::BBox::expand
void expand(ElementType padding)
Pad this bounding box.
Definition BBox.h:321
openvdb::v11_0::math::BBox::translate
void translate(const Vec3T &t)
Translate this bounding box by (tx, ty, tz).
Definition BBox.h:366
openvdb::v11_0::math::BBox::expand
void expand(const BBox &)
Union this bounding box with the given bounding box.
Definition BBox.h:344
openvdb::v11_0::math::BBox::maxExtent
size_t maxExtent() const
Return the index (0, 1 or 2) of the longest axis.
Definition BBox.h:95
openvdb::v11_0::math::BBox::operator==
bool operator==(const BBox &rhs) const
Return true if this bounding box is identical to the given bounding box.
Definition BBox.h:208
openvdb::v11_0::math::BBox::isInside
bool isInside(const BBox &) const
Return true if the given bounding box is inside this bounding box.
Definition BBox.h:284
openvdb::v11_0::math::BBox::operator!=
bool operator!=(const BBox &rhs) const
Return true if this bounding box differs from the given bounding box.
Definition BBox.h:73
openvdb::v11_0::math::BBox< Vec3d >::ValueType
Vec3d ValueType
Definition BBox.h:27
openvdb::v11_0::math::BBox::extents
Vec3T extents() const
Return the extents of this bounding box, i.e., the length along each axis.
Definition BBox.h:253
openvdb::v11_0::math::BBox< Vec3d >::Vec3Type
Vec3d Vec3Type
Definition BBox.h:26
openvdb::v11_0::math::BBox::min
const Vec3T & min() const
Return a const reference to the minimum point of this bounding box.
Definition BBox.h:62
openvdb::v11_0::math::BBox::BBox
BBox(const ElementType *xyz, bool sorted=true)
Construct a bounding box that exactly encloses two points, whose coordinates are given by an array of...
Definition BBox.h:183
openvdb::v11_0::math::BBox::min
Vec3T & min()
Return a non-const reference to the minimum point of this bounding box.
Definition BBox.h:66
openvdb::v11_0::math::BBox::BBox
BBox(const BBox &)=default
openvdb::v11_0::math::BBox::intersects
bool intersects(const BBox &other) const
Return true if the given bounding box overlaps with this bounding box.
Definition BBox.h:109
openvdb::v11_0::math::BBox::max
Vec3T & max()
Return a non-const reference to the maximum point of this bounding box.
Definition BBox.h:68
openvdb::v11_0::math::BBox< Vec3d >::ElementType
typename Vec3Type::ValueType ElementType
Definition BBox.h:29
openvdb::v11_0::math::BBox< Vec3d >::VectorType
Vec3d VectorType
Definition BBox.h:28
openvdb::v11_0::math::BBox::operator=
BBox & operator=(const BBox &)=default
openvdb::v11_0::math::BBox::applyInverseMap
BBox applyInverseMap(const MapType &map) const
Apply the inverse of a map to this bounding box.
openvdb::v11_0::math::BBox::applyMap
BBox applyMap(const MapType &map) const
Apply a map to this bounding box.
openvdb::v11_0::math::BBox::read
void read(std::istream &is)
Unserialize this bounding box from the given stream.
Definition BBox.h:134
openvdb::v11_0::math::Vec3
Definition Vec3.h:24
openvdb::v11_0::math::Vec3< double >::ValueType
double ValueType
Definition Vec3.h:27
openvdb::v11_0::math::MaxIndex
size_t MaxIndex(const Vec3T &v)
Return the index [0,1,2] of the largest value in a 3D vector.
Definition Math.h:947
openvdb::v11_0::math::operator<<
std::ostream & operator<<(std::ostream &os, const BBox< Vec3T > &b)
Definition BBox.h:413
openvdb::v11_0::math::isApproxEqual
bool isApproxEqual(const Type &a, const Type &b, const Type &tolerance)
Return true if a is equal to b to within the given tolerance.
Definition Math.h:406
openvdb::v11_0::math::MinIndex
size_t MinIndex(const Vec3T &v)
Return the index [0,1,2] of the smallest value in a 3D vector.
Definition Math.h:931
openvdb::v11_0::math::Vec3d
Vec3< double > Vec3d
Definition Vec3.h:664
openvdb::v11_0::Vec3R
math::Vec3< Real > Vec3R
Definition Types.h:72
openvdb
Definition Exceptions.h:13
std
Definition Coord.h:589
openvdb::v11_0::math::Tolerance::value
static T value()
Definition Math.h:148
OPENVDB_VERSION_NAME
#define OPENVDB_VERSION_NAME
The version namespace name for this library version.
Definition version.h.in:121
OPENVDB_USE_VERSION_NAMESPACE
#define OPENVDB_USE_VERSION_NAMESPACE
Definition version.h.in:212