OpenVDB 5.1.0

Ray.h
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3 // Copyright (c) 2012-2018 DreamWorks Animation LLC
4 //
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36
37 #ifndef OPENVDB_MATH_RAY_HAS_BEEN_INCLUDED
38 #define OPENVDB_MATH_RAY_HAS_BEEN_INCLUDED
39
40 #include "Math.h"
41 #include "Vec3.h"
42 #include "Transform.h"
43 #include <algorithm> // for std::swap()
44 #include <iostream> // for std::ostream
45 #include <limits> // for std::numeric_limits<Type>::max()
46
47 namespace openvdb {
48 OPENVDB_USE_VERSION_NAMESPACE
49 namespace OPENVDB_VERSION_NAME {
50 namespace math {
51
52 template<typename RealT = double>
53 class Ray
54 {
55 public:
56 static_assert(std::is_floating_point<RealT>::value,
57 "math::Ray requires a floating-point value type");
58
59 using RealType = RealT;
60 using Vec3Type = Vec3<RealT>;
61 using Vec3T = Vec3Type;
62
63 struct TimeSpan {
64 RealT t0, t1;
66 TimeSpan() {}
68 TimeSpan(RealT _t0, RealT _t1) : t0(_t0), t1(_t1) {}
70 inline void set(RealT _t0, RealT _t1) { t0=_t0; t1=_t1; }
72 inline void get(RealT& _t0, RealT& _t1) const { _t0=t0; _t1=t1; }
74 inline bool valid(RealT eps=math::Delta<RealT>::value()) const { return (t1-t0)>eps; }
76 inline RealT mid() const { return 0.5*(t0 + t1); }
78 inline void scale(RealT s) {assert(s>0); t0*=s; t1*=s; }
80 inline bool test(RealT t) const { return (t>=t0 && t<=t1); }
81 };
82
83 Ray(const Vec3Type& eye = Vec3Type(0,0,0),
84 const Vec3Type& direction = Vec3Type(1,0,0),
85 RealT t0 = math::Delta<RealT>::value(),
86 RealT t1 = std::numeric_limits<RealT>::max())
87 : mEye(eye), mDir(direction), mInvDir(1/mDir), mTimeSpan(t0, t1)
88 {
89 }
90
91 inline void setEye(const Vec3Type& eye) { mEye = eye; }
92
93 inline void setDir(const Vec3Type& dir)
94 {
95 mDir = dir;
96 mInvDir = 1/mDir;
97 }
98
99 inline void setMinTime(RealT t0) { assert(t0>0); mTimeSpan.t0 = t0; }
100
101 inline void setMaxTime(RealT t1) { assert(t1>0); mTimeSpan.t1 = t1; }
102
103 inline void setTimes(
104 RealT t0 = math::Delta<RealT>::value(),
105 RealT t1 = std::numeric_limits<RealT>::max())
106 {
107 assert(t0>0 && t1>0);
108 mTimeSpan.set(t0, t1);
109 }
110
111 inline void scaleTimes(RealT scale) { mTimeSpan.scale(scale); }
112
113 inline void reset(
114 const Vec3Type& eye,
115 const Vec3Type& direction,
116 RealT t0 = math::Delta<RealT>::value(),
117 RealT t1 = std::numeric_limits<RealT>::max())
118 {
119 this->setEye(eye);
120 this->setDir(direction);
121 this->setTimes(t0, t1);
122 }
123
124 inline const Vec3T& eye() const {return mEye;}
125
126 inline const Vec3T& dir() const {return mDir;}
127
128 inline const Vec3T& invDir() const {return mInvDir;}
129
130 inline RealT t0() const {return mTimeSpan.t0;}
131
132 inline RealT t1() const {return mTimeSpan.t1;}
133
135 inline Vec3R operator()(RealT time) const { return mEye + mDir * time; }
136
138 inline Vec3R start() const { return (*this)(mTimeSpan.t0); }
139
141 inline Vec3R end() const { return (*this)(mTimeSpan.t1); }
142
144 inline Vec3R mid() const { return (*this)(mTimeSpan.mid()); }
145
147 inline bool valid(RealT eps=math::Delta<float>::value()) const { return mTimeSpan.valid(eps); }
148
150 inline bool test(RealT time) const { return mTimeSpan.test(time); }
151
158 template<typename MapType>
159 inline Ray applyMap(const MapType& map) const
160 {
161 assert(map.isLinear());
162 assert(math::isRelOrApproxEqual(mDir.length(), RealT(1),
163 Tolerance<RealT>::value(), Delta<RealT>::value()));
164 const Vec3T eye = map.applyMap(mEye);
165 const Vec3T dir = map.applyJacobian(mDir);
166 const RealT length = dir.length();
167 return Ray(eye, dir/length, length*mTimeSpan.t0, length*mTimeSpan.t1);
168 }
169
176 template<typename MapType>
177 inline Ray applyInverseMap(const MapType& map) const
178 {
179 assert(map.isLinear());
180 assert(math::isRelOrApproxEqual(mDir.length(), RealT(1), Tolerance<RealT>::value(), Delta<RealT>::value()));
181 const Vec3T eye = map.applyInverseMap(mEye);
182 const Vec3T dir = map.applyInverseJacobian(mDir);
183 const RealT length = dir.length();
184 return Ray(eye, dir/length, length*mTimeSpan.t0, length*mTimeSpan.t1);
185 }
186
189 template<typename GridType>
190 inline Ray indexToWorld(const GridType& grid) const
191 {
192 return this->applyMap(*(grid.transform().baseMap()));
193 }
194
197 template<typename GridType>
198 inline Ray worldToIndex(const GridType& grid) const
199 {
200 return this->applyInverseMap(*(grid.transform().baseMap()));
201 }
202
210 inline bool intersects(const Vec3T& center, RealT radius, RealT& t0, RealT& t1) const
211 {
212 const Vec3T origin = mEye - center;
213 const RealT A = mDir.lengthSqr();
214 const RealT B = 2 * mDir.dot(origin);
215 const RealT C = origin.lengthSqr() - radius * radius;
216 const RealT D = B * B - 4 * A * C;
217
218 if (D < 0) return false;
219
220 const RealT Q = RealT(-0.5)*(B<0 ? (B + Sqrt(D)) : (B - Sqrt(D)));
221
222 t0 = Q / A;
223 t1 = C / Q;
224
225 if (t0 > t1) std::swap(t0, t1);
226 if (t0 < mTimeSpan.t0) t0 = mTimeSpan.t0;
227 if (t1 > mTimeSpan.t1) t1 = mTimeSpan.t1;
228 return t0 <= t1;
229 }
230
234 inline bool intersects(const Vec3T& center, RealT radius) const
235 {
236 RealT t0, t1;
237 return this->intersects(center, radius, t0, t1)>0;
238 }
239
244 inline bool clip(const Vec3T& center, RealT radius)
245 {
246 RealT t0, t1;
247 const bool hit = this->intersects(center, radius, t0, t1);
248 if (hit) mTimeSpan.set(t0, t1);
249 return hit;
250 }
251
259 template<typename BBoxT>
260 inline bool intersects(const BBoxT& bbox, RealT& t0, RealT& t1) const
261 {
262 mTimeSpan.get(t0, t1);
263 for (int i = 0; i < 3; ++i) {
264 RealT a = (bbox.min()[i] - mEye[i]) * mInvDir[i];
265 RealT b = (bbox.max()[i] - mEye[i]) * mInvDir[i];
266 if (a > b) std::swap(a, b);
267 if (a > t0) t0 = a;
268 if (b < t1) t1 = b;
269 if (t0 > t1) return false;
270 }
271 return true;
272 }
273
276 template<typename BBoxT>
277 inline bool intersects(const BBoxT& bbox) const
278 {
279 RealT t0, t1;
280 return this->intersects(bbox, t0, t1);
281 }
282
286 template<typename BBoxT>
287 inline bool clip(const BBoxT& bbox)
288 {
289 RealT t0, t1;
290 const bool hit = this->intersects(bbox, t0, t1);
291 if (hit) mTimeSpan.set(t0, t1);
292 return hit;
293 }
294
300 inline bool intersects(const Vec3T& normal, RealT distance, RealT& t) const
301 {
302 const RealT cosAngle = mDir.dot(normal);
303 if (math::isApproxZero(cosAngle)) return false;//parallel
304 t = (distance - mEye.dot(normal))/cosAngle;
305 return this->test(t);
306 }
307
313 inline bool intersects(const Vec3T& normal, const Vec3T& point, RealT& t) const
314 {
315 return this->intersects(normal, point.dot(normal), t);
316 }
317
318 private:
319 Vec3T mEye, mDir, mInvDir;
320 TimeSpan mTimeSpan;
321 }; // end of Ray class
322
323
326 template<typename RealT>
327 inline std::ostream& operator<<(std::ostream& os, const Ray<RealT>& r)
328 {
329 os << "eye=" << r.eye() << " dir=" << r.dir() << " 1/dir="<<r.invDir()
330 << " t0=" << r.t0() << " t1=" << r.t1();
331 return os;
332 }
333
334 } // namespace math
335 } // namespace OPENVDB_VERSION_NAME
336 } // namespace openvdb
337
338 #endif // OPENVDB_MATH_RAY_HAS_BEEN_INCLUDED
339
340 // Copyright (c) 2012-2018 DreamWorks Animation LLC
341 // All rights reserved. This software is distributed under the
342 // Mozilla Public License 2.0 ( http://www.mozilla.org/MPL/2.0/ )
openvdb::v5_1::math::Ray
Definition: Ray.h:53
openvdb::v5_1::math::Ray::invDir
const Vec3T & invDir() const
Definition: Ray.h:128
openvdb::v5_1::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:83
Vec3.h
Math.h
General-purpose arithmetic and comparison routines, most of which accept arbitrary value types (or at...
openvdb::v5_1::math::Ray::dir
const Vec3T & dir() const
Definition: Ray.h:126
openvdb::v5_1::math::Ray::setEye
void setEye(const Vec3Type &eye)
Definition: Ray.h:91
openvdb::v5_1::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:313
openvdb::v5_1::math::Ray::TimeSpan::TimeSpan
TimeSpan(RealT _t0, RealT _t1)
Constructor.
Definition: Ray.h:68
openvdb::v5_1::math::Vec3::length
T length() const
Length of the vector.
Definition: Vec3.h:225
openvdb::v5_1::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:147
openvdb::v5_1::math::Ray::clip
bool clip(const Vec3T &center, RealT radius)
Return true if this ray intersects the specified sphere.
Definition: Ray.h:244
openvdb::v5_1::math::Vec3< double >
openvdb::v5_1::math::scale
MatType scale(const Vec3< typename MatType::value_type > &s)
Return a matrix that scales by s.
Definition: Mat.h:645
openvdb::v5_1::math::Tolerance
Tolerance for floating-point comparison.
Definition: Math.h:117
Transform.h
openvdb::v5_1::math::Ray::scaleTimes
void scaleTimes(RealT scale)
Definition: Ray.h:111
openvdb::v5_1::math::Ray::setTimes
void setTimes(RealT t0=math::Delta< RealT >::value(), RealT t1=std::numeric_limits< RealT >::max())
Definition: Ray.h:103
openvdb::v5_1::math::Ray< double >::RealType
double RealType
Definition: Ray.h:59
openvdb::v5_1::math::Ray::setMinTime
void setMinTime(RealT t0)
Definition: Ray.h:99
openvdb::v5_1::math::Ray::start
Vec3R start() const
Return the starting point of the ray.
Definition: Ray.h:138
OPENVDB_VERSION_NAME
#define OPENVDB_VERSION_NAME
The version namespace name for this library version.
Definition: version.h:136
openvdb::v5_1::math::Vec3::dot
T dot(const Vec3< T > &v) const
Dot product.
Definition: Vec3.h:216
openvdb::v5_1::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:190
openvdb::v5_1::math::Ray::mid
Vec3R mid() const
Return the midpoint of the ray.
Definition: Ray.h:144
openvdb
Definition: Exceptions.h:40
openvdb::v5_1::math::Delta
Delta for small floating-point offsets.
Definition: Math.h:124
openvdb::v5_1::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:210
openvdb::v5_1::math::Ray::t1
RealT t1() const
Definition: Ray.h:132
openvdb::v5_1::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:177
openvdb::v5_1::math::Ray::TimeSpan::mid
RealT mid() const
Return the midpoint of the ray.
Definition: Ray.h:76
openvdb::v5_1::math::Ray::test
bool test(RealT time) const
Return true if time is within t0 and t1, both inclusive.
Definition: Ray.h:150
openvdb::v5_1::math::Ray::TimeSpan::TimeSpan
TimeSpan()
Default constructor.
Definition: Ray.h:66
openvdb::v5_1::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:300
openvdb::v5_1::math::Sqrt
float Sqrt(float x)
Return the square root of a floating-point value.
Definition: Math.h:715
openvdb::v5_1::math::Ray::t0
RealT t0() const
Definition: Ray.h:130
openvdb::v5_1::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:320
openvdb::v5_1::math::isRelOrApproxEqual
bool isRelOrApproxEqual(const Type &a, const Type &b, const Type &absTol, const Type &relTol)
Definition: Math.h:405
openvdb::v5_1::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:260
openvdb::v5_1::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:198
openvdb::v5_1::math::Ray::eye
const Vec3T & eye() const
Definition: Ray.h:124
openvdb::v5_1::math::Ray::TimeSpan::scale
void scale(RealT s)
Multiplies both times.
Definition: Ray.h:78
openvdb::v5_1::math::Ray::setMaxTime
void setMaxTime(RealT t1)
Definition: Ray.h:101
openvdb::v5_1::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:113
openvdb::v5_1::math::Ray::operator()
Vec3R operator()(RealT time) const
Return the position along the ray at the specified time.
Definition: Ray.h:135
OPENVDB_USE_VERSION_NAMESPACE
#define OPENVDB_USE_VERSION_NAMESPACE
Definition: version.h:188
openvdb::v5_1::math::Ray::TimeSpan::t1
RealT t1
Definition: Ray.h:64
openvdb::v5_1::math::Vec3::lengthSqr
T lengthSqr() const
Definition: Vec3.h:236
openvdb::v5_1::math::Ray::end
Vec3R end() const
Return the endpoint of the ray.
Definition: Ray.h:141
openvdb::v5_1::tools::composite::max
const std::enable_if<!VecTraits< T >::IsVec, T >::type & max(const T &a, const T &b)
Definition: Composite.h:133
openvdb::v5_1::math::Ray::TimeSpan::test
bool test(RealT t) const
Return true if time is inclusive.
Definition: Ray.h:80
openvdb::v5_1::math::Ray::clip
bool clip(const BBoxT &bbox)
Return true if this ray intersects the specified bounding box.
Definition: Ray.h:287
openvdb::v5_1::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:74
openvdb::v5_1::math::Ray::setDir
void setDir(const Vec3Type &dir)
Definition: Ray.h:93
openvdb::v5_1::math::Ray::TimeSpan
Definition: Ray.h:63
openvdb::v5_1::math::Ray::applyMap
Ray applyMap(const MapType &map) const
Return a new Ray that is transformed with the specified map.
Definition: Ray.h:159
openvdb::v5_1::math::Ray::intersects
bool intersects(const Vec3T &center, RealT radius) const
Return true if this ray intersects the specified sphere.
Definition: Ray.h:234
openvdb::v5_1::math::Ray::intersects
bool intersects(const BBoxT &bbox) const
Return true if this ray intersects the specified bounding box.
Definition: Ray.h:277