OpenVDB: openvdb/math/Ray.h Source File

OpenVDB 10.0.1

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Ray.h
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1// Copyright Contributors to the OpenVDB Project
2// SPDX-License-Identifier: MPL-2.0
3//
4/// @file Ray.h
5///
6/// @author Ken Museth
7///
8/// @brief A Ray class.
9
10#ifndef OPENVDB_MATH_RAY_HAS_BEEN_INCLUDED
11#define OPENVDB_MATH_RAY_HAS_BEEN_INCLUDED
12
13#include "Math.h"
14#include "Vec3.h"
15#include "Transform.h"
16#include <algorithm> // for std::swap()
17#include <iostream> // for std::ostream
18#include <limits> // for std::numeric_limits<Type>::max()
19
20namespace openvdb {
21 OPENVDB_USE_VERSION_NAMESPACE
22namespace OPENVDB_VERSION_NAME {
23namespace math {
24
25template<typename RealT = double>
26 class Ray
27{
28public:
29 static_assert(std::is_floating_point<RealT>::value,
30 "math::Ray requires a floating-point value type");
31
32 using RealType = RealT;
33 using Vec3Type = Vec3<RealT>;
34 using Vec3T = Vec3Type;
35
36 struct TimeSpan {
37 RealT t0, t1;
38 /// @brief Default constructor
39 TimeSpan() {}
40 /// @brief Constructor
41 TimeSpan(RealT _t0, RealT _t1) : t0(_t0), t1(_t1) {}
42 /// @brief Set both times
43 inline void set(RealT _t0, RealT _t1) { t0=_t0; t1=_t1; }
44 /// @brief Get both times
45 inline void get(RealT& _t0, RealT& _t1) const { _t0=t0; _t1=t1; }
46 /// @brief Return @c true if t1 is larger than t0 by at least eps.
47 inline bool valid(RealT eps=math::Delta<RealT>::value()) const { return (t1-t0)>eps; }
48 /// @brief Return the midpoint of the ray.
49 inline RealT mid() const { return 0.5*(t0 + t1); }
50 /// @brief Multiplies both times
51 inline void scale(RealT s) {assert(s>0); t0*=s; t1*=s; }
52 /// @brief Return @c true if time is inclusive
53 inline bool test(RealT t) const { return (t>=t0 && t<=t1); }
54 };
55
56 Ray(const Vec3Type& eye = Vec3Type(0,0,0),
57 const Vec3Type& direction = Vec3Type(1,0,0),
58 RealT t0 = math::Delta<RealT>::value(),
59 RealT t1 = std::numeric_limits<RealT>::max())
60 : mEye(eye), mDir(direction), mInvDir(1/mDir), mTimeSpan(t0, t1)
61 {
62 }
63
64 inline void setEye(const Vec3Type& eye) { mEye = eye; }
65
66 inline void setDir(const Vec3Type& dir)
67 {
68 mDir = dir;
69 mInvDir = 1/mDir;
70 }
71
72 inline void setMinTime(RealT t0) { assert(t0>0); mTimeSpan.t0 = t0; }
73
74 inline void setMaxTime(RealT t1) { assert(t1>0); mTimeSpan.t1 = t1; }
75
76 inline void setTimes(
77 RealT t0 = math::Delta<RealT>::value(),
78 RealT t1 = std::numeric_limits<RealT>::max())
79 {
80 assert(t0>0 && t1>0);
81 mTimeSpan.set(t0, t1);
82 }
83
84 inline void scaleTimes(RealT scale) { mTimeSpan.scale(scale); }
85
86 inline void reset(
87 const Vec3Type& eye,
88 const Vec3Type& direction,
89 RealT t0 = math::Delta<RealT>::value(),
90 RealT t1 = std::numeric_limits<RealT>::max())
91 {
92 this->setEye(eye);
93 this->setDir(direction);
94 this->setTimes(t0, t1);
95 }
96
97 inline const Vec3T& eye() const {return mEye;}
98
99 inline const Vec3T& dir() const {return mDir;}
100
101 inline const Vec3T& invDir() const {return mInvDir;}
102
103 inline RealT t0() const {return mTimeSpan.t0;}
104
105 inline RealT t1() const {return mTimeSpan.t1;}
106
107 /// @brief Return the position along the ray at the specified time.
108 inline Vec3R operator()(RealT time) const { return mEye + mDir * time; }
109
110 /// @brief Return the starting point of the ray.
111 inline Vec3R start() const { return (*this)(mTimeSpan.t0); }
112
113 /// @brief Return the endpoint of the ray.
114 inline Vec3R end() const { return (*this)(mTimeSpan.t1); }
115
116 /// @brief Return the midpoint of the ray.
117 inline Vec3R mid() const { return (*this)(mTimeSpan.mid()); }
118
119 /// @brief Return @c true if t1 is larger than t0 by at least eps.
120 inline bool valid(RealT eps=math::Delta<float>::value()) const { return mTimeSpan.valid(eps); }
121
122 /// @brief Return @c true if @a time is within t0 and t1, both inclusive.
123 inline bool test(RealT time) const { return mTimeSpan.test(time); }
124
125 /// @brief Return a new Ray that is transformed with the specified map.
126 /// @param map the map from which to construct the new Ray.
127 /// @warning Assumes a linear map and a normalized direction.
128 /// @details The requirement that the direction is normalized
129 /// follows from the transformation of t0 and t1 - and that fact that
130 /// we want applyMap and applyInverseMap to be inverse operations.
131 template<typename MapType>
132 inline Ray applyMap(const MapType& map) const
133 {
134 assert(map.isLinear());
135 assert(math::isRelOrApproxEqual(mDir.length(), RealT(1),
136 Tolerance<RealT>::value(), Delta<RealT>::value()));
137 const Vec3T eye = map.applyMap(mEye);
138 const Vec3T dir = map.applyJacobian(mDir);
139 const RealT length = dir.length();
140 return Ray(eye, dir/length, length*mTimeSpan.t0, length*mTimeSpan.t1);
141 }
142
143 /// @brief Return a new Ray that is transformed with the inverse of the specified map.
144 /// @param map the map from which to construct the new Ray by inverse mapping.
145 /// @warning Assumes a linear map and a normalized direction.
146 /// @details The requirement that the direction is normalized
147 /// follows from the transformation of t0 and t1 - and that fact that
148 /// we want applyMap and applyInverseMap to be inverse operations.
149 template<typename MapType>
150 inline Ray applyInverseMap(const MapType& map) const
151 {
152 assert(map.isLinear());
153 assert(math::isRelOrApproxEqual(mDir.length(), RealT(1), Tolerance<RealT>::value(), Delta<RealT>::value()));
154 const Vec3T eye = map.applyInverseMap(mEye);
155 const Vec3T dir = map.applyInverseJacobian(mDir);
156 const RealT length = dir.length();
157 return Ray(eye, dir/length, length*mTimeSpan.t0, length*mTimeSpan.t1);
158 }
159
160 /// @brief Return a new ray in world space, assuming the existing
161 /// ray is represented in the index space of the specified grid.
162 template<typename GridType>
163 inline Ray indexToWorld(const GridType& grid) const
164 {
165 return this->applyMap(*(grid.transform().baseMap()));
166 }
167
168 /// @brief Return a new ray in the index space of the specified
169 /// grid, assuming the existing ray is represented in world space.
170 template<typename GridType>
171 inline Ray worldToIndex(const GridType& grid) const
172 {
173 return this->applyInverseMap(*(grid.transform().baseMap()));
174 }
175
176 /// @brief Return true if this ray intersects the specified sphere.
177 /// @param center The center of the sphere in the same space as this ray.
178 /// @param radius The radius of the sphere in the same units as this ray.
179 /// @param t0 The first intersection point if an intersection exists.
180 /// @param t1 The second intersection point if an intersection exists.
181 /// @note If the return value is true, i.e. a hit, and t0 =
182 /// this->t0() or t1 == this->t1() only one true intersection exist.
183 inline bool intersects(const Vec3T& center, RealT radius, RealT& t0, RealT& t1) const
184 {
185 const Vec3T origin = mEye - center;
186 const RealT A = mDir.lengthSqr();
187 const RealT B = 2 * mDir.dot(origin);
188 const RealT C = origin.lengthSqr() - radius * radius;
189 const RealT D = B * B - 4 * A * C;
190
191 if (D < 0) return false;
192
193 const RealT Q = RealT(-0.5)*(B<0 ? (B + Sqrt(D)) : (B - Sqrt(D)));
194
195 t0 = Q / A;
196 t1 = C / Q;
197
198 if (t0 > t1) std::swap(t0, t1);
199 if (t0 < mTimeSpan.t0) t0 = mTimeSpan.t0;
200 if (t1 > mTimeSpan.t1) t1 = mTimeSpan.t1;
201 return t0 <= t1;
202 }
203
204 /// @brief Return true if this ray intersects the specified sphere.
205 /// @param center The center of the sphere in the same space as this ray.
206 /// @param radius The radius of the sphere in the same units as this ray.
207 inline bool intersects(const Vec3T& center, RealT radius) const
208 {
209 RealT t0, t1;
210 return this->intersects(center, radius, t0, t1)>0;
211 }
212
213 /// @brief Return true if this ray intersects the specified sphere.
214 /// @note For intersection this ray is clipped to the two intersection points.
215 /// @param center The center of the sphere in the same space as this ray.
216 /// @param radius The radius of the sphere in the same units as this ray.
217 inline bool clip(const Vec3T& center, RealT radius)
218 {
219 RealT t0, t1;
220 const bool hit = this->intersects(center, radius, t0, t1);
221 if (hit) mTimeSpan.set(t0, t1);
222 return hit;
223 }
224
225 /// @brief Return true if the Ray intersects the specified
226 /// axisaligned bounding box.
227 /// @param bbox Axis-aligned bounding box in the same space as the Ray.
228 /// @param t0 If an intersection is detected this is assigned
229 /// the time for the first intersection point.
230 /// @param t1 If an intersection is detected this is assigned
231 /// the time for the second intersection point.
232 template<typename BBoxT>
233 inline bool intersects(const BBoxT& bbox, RealT& t0, RealT& t1) const
234 {
235 mTimeSpan.get(t0, t1);
236 for (int i = 0; i < 3; ++i) {
237 RealT a = (bbox.min()[i] - mEye[i]) * mInvDir[i];
238 RealT b = (bbox.max()[i] - mEye[i]) * mInvDir[i];
239 if (a > b) std::swap(a, b);
240 if (a > t0) t0 = a;
241 if (b < t1) t1 = b;
242 if (t0 > t1) return false;
243 }
244 return true;
245 }
246
247 /// @brief Return true if this ray intersects the specified bounding box.
248 /// @param bbox Axis-aligned bounding box in the same space as this ray.
249 template<typename BBoxT>
250 inline bool intersects(const BBoxT& bbox) const
251 {
252 RealT t0, t1;
253 return this->intersects(bbox, t0, t1);
254 }
255
256 /// @brief Return true if this ray intersects the specified bounding box.
257 /// @note For intersection this ray is clipped to the two intersection points.
258 /// @param bbox Axis-aligned bounding box in the same space as this ray.
259 template<typename BBoxT>
260 inline bool clip(const BBoxT& bbox)
261 {
262 RealT t0, t1;
263 const bool hit = this->intersects(bbox, t0, t1);
264 if (hit) mTimeSpan.set(t0, t1);
265 return hit;
266 }
267
268 /// @brief Return true if the Ray intersects the plane specified
269 /// by a normal and distance from the origin.
270 /// @param normal Normal of the plane.
271 /// @param distance Distance of the plane to the origin.
272 /// @param t Time of intersection, if one exists.
273 inline bool intersects(const Vec3T& normal, RealT distance, RealT& t) const
274 {
275 const RealT cosAngle = mDir.dot(normal);
276 if (math::isApproxZero(cosAngle)) return false;//parallel
277 t = (distance - mEye.dot(normal))/cosAngle;
278 return this->test(t);
279 }
280
281 /// @brief Return true if the Ray intersects the plane specified
282 /// by a normal and point.
283 /// @param normal Normal of the plane.
284 /// @param point Point in the plane.
285 /// @param t Time of intersection, if one exists.
286 inline bool intersects(const Vec3T& normal, const Vec3T& point, RealT& t) const
287 {
288 return this->intersects(normal, point.dot(normal), t);
289 }
290
291private:
292 Vec3T mEye, mDir, mInvDir;
293 TimeSpan mTimeSpan;
294}; // end of Ray class
295
296
297/// @brief Output streaming of the Ray class.
298/// @note Primarily intended for debugging.
299template<typename RealT>
300 inline std::ostream& operator<<(std::ostream& os, const Ray<RealT>& r)
301{
302 os << "eye=" << r.eye() << " dir=" << r.dir() << " 1/dir="<<r.invDir()
303 << " t0=" << r.t0() << " t1=" << r.t1();
304 return os;
305}
306
307} // namespace math
308} // namespace OPENVDB_VERSION_NAME
309} // namespace openvdb
310
311#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::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::setEye
void setEye(const Vec3Type &eye)
Definition Ray.h:64
openvdb::v10_0::math::Ray::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::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::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::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::length
T length() const
Length of the vector.
Definition Vec3.h:200
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::Sqrt
float Sqrt(float x)
Return the square root of a floating-point value.
Definition Math.h:761
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::operator<<
std::ostream & operator<<(std::ostream &ostr, const Metadata &metadata)
Write a Metadata to an output stream.
Definition Metadata.h:351
openvdb
Definition Exceptions.h:13
openvdb::v10_0::math::Delta
Delta for small floating-point offsets.
Definition Math.h:155
openvdb::v10_0::math::Ray::TimeSpan
Definition Ray.h:36
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::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
Tolerance for floating-point comparison.
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