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Ray.h
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// Copyright Contributors to the OpenVDB Project
// SPDX-License-Identifier: MPL-2.0
//
/// @file Ray.h
///
/// @author Ken Museth
///
/// @brief A Ray class.
#ifndef OPENVDB_MATH_RAY_HAS_BEEN_INCLUDED
#define OPENVDB_MATH_RAY_HAS_BEEN_INCLUDED
#include "Math.h"
#include "Vec3.h"
#include "Transform.h"
#include <algorithm> // for std::swap()
#include <iostream> // for std::ostream
#include <limits> // for std::numeric_limits<Type>::max()
namespace openvdb {
OPENVDB_USE_VERSION_NAMESPACE
namespace OPENVDB_VERSION_NAME {
namespace math {
template<typename RealT = double>
class Ray
{
public:
static_assert(std::is_floating_point<RealT>::value,
"math::Ray requires a floating-point value type");
using RealType = RealT;
using Vec3Type = Vec3<RealT>;
using Vec3T = Vec3Type;
struct TimeSpan {
RealT t0, t1;
/// @brief Default constructor
TimeSpan() {}
/// @brief Constructor
TimeSpan(RealT _t0, RealT _t1) : t0(_t0), t1(_t1) {}
/// @brief Set both times
inline void set(RealT _t0, RealT _t1) { t0=_t0; t1=_t1; }
/// @brief Get both times
inline void get(RealT& _t0, RealT& _t1) const { _t0=t0; _t1=t1; }
/// @brief Return @c true if t1 is larger than t0 by at least eps.
inline bool valid(RealT eps=math::Delta<RealT>::value()) const { return (t1-t0)>eps; }
/// @brief Return the midpoint of the ray.
inline RealT mid() const { return 0.5*(t0 + t1); }
/// @brief Multiplies both times
inline void scale(RealT s) {assert(s>0); t0*=s; t1*=s; }
/// @brief Return @c true if time is inclusive
inline bool test(RealT t) const { return (t>=t0 && t<=t1); }
};
Ray(const Vec3Type& eye = Vec3Type(0,0,0),
const Vec3Type& direction = Vec3Type(1,0,0),
RealT t0 = math::Delta<RealT>::value(),
RealT t1 = std::numeric_limits<RealT>::max())
: mEye(eye), mDir(direction), mInvDir(1/mDir), mTimeSpan(t0, t1)
{
}
inline void setEye(const Vec3Type& eye) { mEye = eye; }
inline void setDir(const Vec3Type& dir)
{
mDir = dir;
mInvDir = 1/mDir;
}
inline void setMinTime(RealT t0) { assert(t0>0); mTimeSpan.t0 = t0; }
inline void setMaxTime(RealT t1) { assert(t1>0); mTimeSpan.t1 = t1; }
inline void setTimes(
RealT t0 = math::Delta<RealT>::value(),
RealT t1 = std::numeric_limits<RealT>::max())
{
assert(t0>0 && t1>0);
mTimeSpan.set(t0, t1);
}
inline void scaleTimes(RealT scale) { mTimeSpan.scale(scale); }
inline void reset(
const Vec3Type& eye,
const Vec3Type& direction,
RealT t0 = math::Delta<RealT>::value(),
RealT t1 = std::numeric_limits<RealT>::max())
{
this->setEye(eye);
this->setDir(direction);
this->setTimes(t0, t1);
}
inline const Vec3T& eye() const {return mEye;}
inline const Vec3T& dir() const {return mDir;}
inline const Vec3T& invDir() const {return mInvDir;}
inline RealT t0() const {return mTimeSpan.t0;}
inline RealT t1() const {return mTimeSpan.t1;}
/// @brief Return the position along the ray at the specified time.
inline Vec3R operator()(RealT time) const { return mEye + mDir * time; }
/// @brief Return the starting point of the ray.
inline Vec3R start() const { return (*this)(mTimeSpan.t0); }
/// @brief Return the endpoint of the ray.
inline Vec3R end() const { return (*this)(mTimeSpan.t1); }
/// @brief Return the midpoint of the ray.
inline Vec3R mid() const { return (*this)(mTimeSpan.mid()); }
/// @brief Return @c true if t1 is larger than t0 by at least eps.
inline bool valid(RealT eps=math::Delta<float>::value()) const { return mTimeSpan.valid(eps); }
/// @brief Return @c true if @a time is within t0 and t1, both inclusive.
inline bool test(RealT time) const { return mTimeSpan.test(time); }
/// @brief Return a new Ray that is transformed with the specified map.
/// @param map the map from which to construct the new Ray.
/// @warning Assumes a linear map and a normalized direction.
/// @details The requirement that the direction is normalized
/// follows from the transformation of t0 and t1 - and that fact that
/// we want applyMap and applyInverseMap to be inverse operations.
template<typename MapType>
inline Ray applyMap(const MapType& map) const
{
assert(map.isLinear());
assert(math::isRelOrApproxEqual(mDir.length(), RealT(1),
Tolerance<RealT>::value(), Delta<RealT>::value()));
const Vec3T eye = map.applyMap(mEye);
const Vec3T dir = map.applyJacobian(mDir);
const RealT length = dir.length();
return Ray(eye, dir/length, length*mTimeSpan.t0, length*mTimeSpan.t1);
}
/// @brief Return a new Ray that is transformed with the inverse of the specified map.
/// @param map the map from which to construct the new Ray by inverse mapping.
/// @warning Assumes a linear map and a normalized direction.
/// @details The requirement that the direction is normalized
/// follows from the transformation of t0 and t1 - and that fact that
/// we want applyMap and applyInverseMap to be inverse operations.
template<typename MapType>
inline Ray applyInverseMap(const MapType& map) const
{
assert(map.isLinear());
assert(math::isRelOrApproxEqual(mDir.length(), RealT(1), Tolerance<RealT>::value(), Delta<RealT>::value()));
const Vec3T eye = map.applyInverseMap(mEye);
const Vec3T dir = map.applyInverseJacobian(mDir);
const RealT length = dir.length();
return Ray(eye, dir/length, length*mTimeSpan.t0, length*mTimeSpan.t1);
}
/// @brief Return a new ray in world space, assuming the existing
/// ray is represented in the index space of the specified grid.
template<typename GridType>
inline Ray indexToWorld(const GridType& grid) const
{
return this->applyMap(*(grid.transform().baseMap()));
}
/// @brief Return a new ray in the index space of the specified
/// grid, assuming the existing ray is represented in world space.
template<typename GridType>
inline Ray worldToIndex(const GridType& grid) const
{
return this->applyInverseMap(*(grid.transform().baseMap()));
}
/// @brief Return true if this ray intersects the specified sphere.
/// @param center The center of the sphere in the same space as this ray.
/// @param radius The radius of the sphere in the same units as this ray.
/// @param t0 The first intersection point if an intersection exists.
/// @param t1 The second intersection point if an intersection exists.
/// @note If the return value is true, i.e. a hit, and t0 =
/// this->t0() or t1 == this->t1() only one true intersection exist.
inline bool intersects(const Vec3T& center, RealT radius, RealT& t0, RealT& t1) const
{
const Vec3T origin = mEye - center;
const RealT A = mDir.lengthSqr();
const RealT B = 2 * mDir.dot(origin);
const RealT C = origin.lengthSqr() - radius * radius;
const RealT D = B * B - 4 * A * C;
if (D < 0) return false;
const RealT Q = RealT(-0.5)*(B<0 ? (B + Sqrt(D)) : (B - Sqrt(D)));
t0 = Q / A;
t1 = C / Q;
if (t0 > t1) std::swap(t0, t1);
if (t0 < mTimeSpan.t0) t0 = mTimeSpan.t0;
if (t1 > mTimeSpan.t1) t1 = mTimeSpan.t1;
return t0 <= t1;
}
/// @brief Return true if this ray intersects the specified sphere.
/// @param center The center of the sphere in the same space as this ray.
/// @param radius The radius of the sphere in the same units as this ray.
inline bool intersects(const Vec3T& center, RealT radius) const
{
RealT t0, t1;
return this->intersects(center, radius, t0, t1)>0;
}
/// @brief Return true if this ray intersects the specified sphere.
/// @note For intersection this ray is clipped to the two intersection points.
/// @param center The center of the sphere in the same space as this ray.
/// @param radius The radius of the sphere in the same units as this ray.
inline bool clip(const Vec3T& center, RealT radius)
{
RealT t0, t1;
const bool hit = this->intersects(center, radius, t0, t1);
if (hit) mTimeSpan.set(t0, t1);
return hit;
}
/// @brief Return true if the Ray intersects the specified
/// axisaligned bounding box.
/// @param bbox Axis-aligned bounding box in the same space as the Ray.
/// @param t0 If an intersection is detected this is assigned
/// the time for the first intersection point.
/// @param t1 If an intersection is detected this is assigned
/// the time for the second intersection point.
template<typename BBoxT>
inline bool intersects(const BBoxT& bbox, RealT& t0, RealT& t1) const
{
mTimeSpan.get(t0, t1);
for (int i = 0; i < 3; ++i) {
RealT a = (bbox.min()[i] - mEye[i]) * mInvDir[i];
RealT b = (bbox.max()[i] - mEye[i]) * mInvDir[i];
if (a > b) std::swap(a, b);
if (a > t0) t0 = a;
if (b < t1) t1 = b;
if (t0 > t1) return false;
}
return true;
}
/// @brief Return true if this ray intersects the specified bounding box.
/// @param bbox Axis-aligned bounding box in the same space as this ray.
template<typename BBoxT>
inline bool intersects(const BBoxT& bbox) const
{
RealT t0, t1;
return this->intersects(bbox, t0, t1);
}
/// @brief Return true if this ray intersects the specified bounding box.
/// @note For intersection this ray is clipped to the two intersection points.
/// @param bbox Axis-aligned bounding box in the same space as this ray.
template<typename BBoxT>
inline bool clip(const BBoxT& bbox)
{
RealT t0, t1;
const bool hit = this->intersects(bbox, t0, t1);
if (hit) mTimeSpan.set(t0, t1);
return hit;
}
/// @brief Return true if the Ray intersects the plane specified
/// by a normal and distance from the origin.
/// @param normal Normal of the plane.
/// @param distance Distance of the plane to the origin.
/// @param t Time of intersection, if one exists.
inline bool intersects(const Vec3T& normal, RealT distance, RealT& t) const
{
const RealT cosAngle = mDir.dot(normal);
if (math::isApproxZero(cosAngle)) return false;//parallel
t = (distance - mEye.dot(normal))/cosAngle;
return this->test(t);
}
/// @brief Return true if the Ray intersects the plane specified
/// by a normal and point.
/// @param normal Normal of the plane.
/// @param point Point in the plane.
/// @param t Time of intersection, if one exists.
inline bool intersects(const Vec3T& normal, const Vec3T& point, RealT& t) const
{
return this->intersects(normal, point.dot(normal), t);
}
private:
Vec3T mEye, mDir, mInvDir;
TimeSpan mTimeSpan;
}; // end of Ray class
/// @brief Output streaming of the Ray class.
/// @note Primarily intended for debugging.
template<typename RealT>
inline std::ostream& operator<<(std::ostream& os, const Ray<RealT>& r)
{
os << "eye=" << r.eye() << " dir=" << r.dir() << " 1/dir="<<r.invDir()
<< " t0=" << r.t0() << " t1=" << r.t1();
return os;
}
} // namespace math
} // namespace OPENVDB_VERSION_NAME
} // namespace openvdb
#endif // OPENVDB_MATH_RAY_HAS_BEEN_INCLUDED
Math.h
General-purpose arithmetic and comparison routines, most of which accept arbitrary value types (or at...
Transform.h
Vec3.h
openvdb::v10_0::math::Ray
Definition Ray.h:27
openvdb::v10_0::math::Ray::test
bool test(RealT time) const
Return true if time is within t0 and t1, both inclusive.
Definition Ray.h:123
openvdb::v10_0::math::Ray::Ray
Ray(const Vec3Type &eye=Vec3Type(0, 0, 0), const Vec3Type &direction=Vec3Type(1, 0, 0), RealT t0=math::Delta< RealT >::value(), RealT t1=std::numeric_limits< RealT >::max())
Definition Ray.h:56
openvdb::v10_0::math::Ray::intersects
bool intersects(const Vec3T &normal, RealT distance, RealT &t) const
Return true if the Ray intersects the plane specified by a normal and distance from the origin.
Definition Ray.h:273
openvdb::v10_0::math::Ray::applyInverseMap
Ray applyInverseMap(const MapType &map) const
Return a new Ray that is transformed with the inverse of the specified map.
Definition Ray.h:150
openvdb::v10_0::math::Ray< RealT >::dir
const Vec3T & dir() const
Definition Ray.h:99
openvdb::v10_0::math::Ray::clip
bool clip(const BBoxT &bbox)
Return true if this ray intersects the specified bounding box.
Definition Ray.h:260
openvdb::v10_0::math::Ray::Vec3Type
Vec3< RealT > Vec3Type
Definition Ray.h:33
openvdb::v10_0::math::Ray::setEye
void setEye(const Vec3Type &eye)
Definition Ray.h:64
openvdb::v10_0::math::Ray< RealT >::eye
const Vec3T & eye() const
Definition Ray.h:97
openvdb::v10_0::math::Ray::intersects
bool intersects(const BBoxT &bbox) const
Return true if this ray intersects the specified bounding box.
Definition Ray.h:250
openvdb::v10_0::math::Ray::applyMap
Ray applyMap(const MapType &map) const
Return a new Ray that is transformed with the specified map.
Definition Ray.h:132
openvdb::v10_0::math::Ray::RealType
RealT RealType
Definition Ray.h:32
openvdb::v10_0::math::Ray::operator()
Vec3R operator()(RealT time) const
Return the position along the ray at the specified time.
Definition Ray.h:108
openvdb::v10_0::math::Ray::setDir
void setDir(const Vec3Type &dir)
Definition Ray.h:66
openvdb::v10_0::math::Ray::intersects
bool intersects(const Vec3T &center, RealT radius) const
Return true if this ray intersects the specified sphere.
Definition Ray.h:207
openvdb::v10_0::math::Ray::valid
bool valid(RealT eps=math::Delta< float >::value()) const
Return true if t1 is larger than t0 by at least eps.
Definition Ray.h:120
openvdb::v10_0::math::Ray::scaleTimes
void scaleTimes(RealT scale)
Definition Ray.h:84
openvdb::v10_0::math::Ray::worldToIndex
Ray worldToIndex(const GridType &grid) const
Return a new ray in the index space of the specified grid, assuming the existing ray is represented i...
Definition Ray.h:171
openvdb::v10_0::math::Ray::setTimes
void setTimes(RealT t0=math::Delta< RealT >::value(), RealT t1=std::numeric_limits< RealT >::max())
Definition Ray.h:76
openvdb::v10_0::math::Ray::start
Vec3R start() const
Return the starting point of the ray.
Definition Ray.h:111
openvdb::v10_0::math::Ray::invDir
const Vec3T & invDir() const
Definition Ray.h:101
openvdb::v10_0::math::Ray::setMaxTime
void setMaxTime(RealT t1)
Definition Ray.h:74
openvdb::v10_0::math::Ray::Vec3T
Vec3Type Vec3T
Definition Ray.h:34
openvdb::v10_0::math::Ray::clip
bool clip(const Vec3T &center, RealT radius)
Return true if this ray intersects the specified sphere.
Definition Ray.h:217
openvdb::v10_0::math::Ray::intersects
bool intersects(const BBoxT &bbox, RealT &t0, RealT &t1) const
Return true if the Ray intersects the specified axisaligned bounding box.
Definition Ray.h:233
openvdb::v10_0::math::Ray::intersects
bool intersects(const Vec3T &normal, const Vec3T &point, RealT &t) const
Return true if the Ray intersects the plane specified by a normal and point.
Definition Ray.h:286
openvdb::v10_0::math::Ray< RealT >::t0
RealT t0() const
Definition Ray.h:103
openvdb::v10_0::math::Ray::reset
void reset(const Vec3Type &eye, const Vec3Type &direction, RealT t0=math::Delta< RealT >::value(), RealT t1=std::numeric_limits< RealT >::max())
Definition Ray.h:86
openvdb::v10_0::math::Ray::indexToWorld
Ray indexToWorld(const GridType &grid) const
Return a new ray in world space, assuming the existing ray is represented in the index space of the s...
Definition Ray.h:163
openvdb::v10_0::math::Ray< RealT >::t1
RealT t1() const
Definition Ray.h:105
openvdb::v10_0::math::Ray::end
Vec3R end() const
Return the endpoint of the ray.
Definition Ray.h:114
openvdb::v10_0::math::Ray::intersects
bool intersects(const Vec3T &center, RealT radius, RealT &t0, RealT &t1) const
Return true if this ray intersects the specified sphere.
Definition Ray.h:183
openvdb::v10_0::math::Ray::mid
Vec3R mid() const
Return the midpoint of the ray.
Definition Ray.h:117
openvdb::v10_0::math::Ray::setMinTime
void setMinTime(RealT t0)
Definition Ray.h:72
openvdb::v10_0::math::Vec3
Definition Vec3.h:24
openvdb::v10_0::math::Vec3::dot
T dot(const Vec3< T > &v) const
Dot product.
Definition Vec3.h:191
openvdb::v10_0::math::Vec3::lengthSqr
T lengthSqr() const
Definition Vec3.h:211
openvdb::v10_0::math::isApproxZero
bool isApproxZero(const Type &x)
Return true if x is equal to zero to within the default floating-point comparison tolerance.
Definition Math.h:349
openvdb::v10_0::math::operator<<
std::ostream & operator<<(std::ostream &os, const BBox< Vec3T > &b)
Definition BBox.h:413
openvdb::v10_0::math::Sqrt
float Sqrt(float x)
Return the square root of a floating-point value.
Definition Math.h:761
openvdb::v10_0::math::isRelOrApproxEqual
bool isRelOrApproxEqual(const Type &a, const Type &b, const Type &absTol, const Type &relTol)
Definition Math.h:453
openvdb::v10_0::math::scale
MatType scale(const Vec3< typename MatType::value_type > &s)
Return a matrix that scales by s.
Definition Mat.h:615
openvdb::v10_0::Vec3R
math::Vec3< Real > Vec3R
Definition Types.h:72
openvdb
Definition Exceptions.h:13
openvdb::v10_0::math::Delta::value
static T value()
Definition Math.h:155
openvdb::v10_0::math::Ray::TimeSpan::TimeSpan
TimeSpan(RealT _t0, RealT _t1)
Constructor.
Definition Ray.h:41
openvdb::v10_0::math::Ray::TimeSpan::mid
RealT mid() const
Return the midpoint of the ray.
Definition Ray.h:49
openvdb::v10_0::math::Ray::TimeSpan::TimeSpan
TimeSpan()
Default constructor.
Definition Ray.h:39
openvdb::v10_0::math::Ray::TimeSpan::test
bool test(RealT t) const
Return true if time is inclusive.
Definition Ray.h:53
openvdb::v10_0::math::Ray::TimeSpan::scale
void scale(RealT s)
Multiplies both times.
Definition Ray.h:51
openvdb::v10_0::math::Ray::TimeSpan::t1
RealT t1
Definition Ray.h:37
openvdb::v10_0::math::Ray::TimeSpan::valid
bool valid(RealT eps=math::Delta< RealT >::value()) const
Return true if t1 is larger than t0 by at least eps.
Definition Ray.h:47
openvdb::v10_0::math::Ray::TimeSpan::t0
RealT t0
Definition Ray.h:37
openvdb::v10_0::math::Ray::TimeSpan::set
void set(RealT _t0, RealT _t1)
Set both times.
Definition Ray.h:43
openvdb::v10_0::math::Ray::TimeSpan::get
void get(RealT &_t0, RealT &_t1) const
Get both times.
Definition Ray.h:45
openvdb::v10_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