OpenVDB 11.0.0

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Coord.h
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1// Copyright Contributors to the OpenVDB Project
2// SPDX-License-Identifier: MPL-2.0
3
4#ifndef OPENVDB_MATH_COORD_HAS_BEEN_INCLUDED
5#define OPENVDB_MATH_COORD_HAS_BEEN_INCLUDED
6
7#include <functional>// for std::hash
8#include <algorithm> // for std::min(), std::max()
9#include <array> // for std::array
10#include <iostream>
11#include <limits>
12#include <openvdb/Platform.h>
13#include "Math.h"
14#include "Vec3.h"
15
16#include <tbb/blocked_range.h> // for tbb::split
17
18 namespace openvdb {
19 OPENVDB_USE_VERSION_NAMESPACE
20 namespace OPENVDB_VERSION_NAME {
21 namespace math {
22
23/// @brief Signed (x, y, z) 32-bit integer coordinates
24 class Coord
25{
26 public:
27 using Int32 = int32_t;
28 using Index32 = uint32_t;
29 using Vec3i = Vec3<Int32>;
30 using Vec3I = Vec3<Index32>;
31
32 using ValueType = Int32;
33 using Limits = std::numeric_limits<ValueType>;
34
35 Coord(): mVec{{0, 0, 0}} {}
36 constexpr explicit Coord(Int32 xyz): mVec{{xyz, xyz, xyz}} {}
37 constexpr Coord(Int32 x, Int32 y, Int32 z): mVec{{x, y, z}} {}
38 explicit Coord(const Vec3i& v): mVec{{v[0], v[1], v[2]}} {}
39 explicit Coord(const Vec3I& v): mVec{{Int32(v[0]), Int32(v[1]), Int32(v[2])}} {}
40 explicit Coord(const Int32* v): mVec{{v[0], v[1], v[2]}} {}
41
42 /// @brief Return the smallest possible coordinate
43 static Coord min() { return Coord(Limits::min()); }
44
45 /// @brief Return the largest possible coordinate
46 static Coord max() { return Coord(Limits::max()); }
47
48 /// @brief Return @a xyz rounded to the closest integer coordinates
49 /// (cell centered conversion).
50 template<typename T> static Coord round(const Vec3<T>& xyz)
51 {
52 return Coord(Int32(Round(xyz[0])), Int32(Round(xyz[1])), Int32(Round(xyz[2])));
53 }
54 /// @brief Return the largest integer coordinates that are not greater
55 /// than @a xyz (node centered conversion).
56 template<typename T> static Coord floor(const Vec3<T>& xyz)
57 {
58 return Coord(Int32(Floor(xyz[0])), Int32(Floor(xyz[1])), Int32(Floor(xyz[2])));
59 }
60
61 /// @brief Return the largest integer coordinates that are not greater
62 /// than @a xyz+1 (node centered conversion).
63 template<typename T> static Coord ceil(const Vec3<T>& xyz)
64 {
65 return Coord(Int32(Ceil(xyz[0])), Int32(Ceil(xyz[1])), Int32(Ceil(xyz[2])));
66 }
67
68 /// @brief Reset all three coordinates with the specified arguments
69 Coord& reset(Int32 x, Int32 y, Int32 z)
70 {
71 mVec[0] = x;
72 mVec[1] = y;
73 mVec[2] = z;
74 return *this;
75 }
76 /// @brief Reset all three coordinates with the same specified argument
77 Coord& reset(Int32 xyz) { return this->reset(xyz, xyz, xyz); }
78
79 Coord& setX(Int32 x) { mVec[0] = x; return *this; }
80 Coord& setY(Int32 y) { mVec[1] = y; return *this; }
81 Coord& setZ(Int32 z) { mVec[2] = z; return *this; }
82
83 Coord& offset(Int32 dx, Int32 dy, Int32 dz)
84 {
85 mVec[0] += dx;
86 mVec[1] += dy;
87 mVec[2] += dz;
88 return *this;
89 }
90 Coord& offset(Int32 n) { return this->offset(n, n, n); }
91 Coord offsetBy(Int32 dx, Int32 dy, Int32 dz) const
92 {
93 return Coord(mVec[0] + dx, mVec[1] + dy, mVec[2] + dz);
94 }
95 Coord offsetBy(Int32 n) const { return offsetBy(n, n, n); }
96
97 Coord& operator+=(const Coord& rhs)
98 {
99 mVec[0] += rhs[0];
100 mVec[1] += rhs[1];
101 mVec[2] += rhs[2];
102 return *this;
103 }
104 Coord& operator-=(const Coord& rhs)
105 {
106 mVec[0] -= rhs[0];
107 mVec[1] -= rhs[1];
108 mVec[2] -= rhs[2];
109 return *this;
110 }
111 Coord operator+(const Coord& rhs) const
112 {
113 return Coord(mVec[0] + rhs[0], mVec[1] + rhs[1], mVec[2] + rhs[2]);
114 }
115 Coord operator-(const Coord& rhs) const
116 {
117 return Coord(mVec[0] - rhs[0], mVec[1] - rhs[1], mVec[2] - rhs[2]);
118 }
119 Coord operator-() const { return Coord(-mVec[0], -mVec[1], -mVec[2]); }
120
121 Coord operator>> (size_t n) const { return Coord(mVec[0]>>n, mVec[1]>>n, mVec[2]>>n); }
122 Coord operator<< (size_t n) const { return Coord(mVec[0]<<n, mVec[1]<<n, mVec[2]<<n); }
123 Coord& operator<<=(size_t n) { mVec[0]<<=n; mVec[1]<<=n; mVec[2]<<=n; return *this; }
124 Coord& operator>>=(size_t n) { mVec[0]>>=n; mVec[1]>>=n; mVec[2]>>=n; return *this; }
125 Coord operator& (Int32 n) const { return Coord(mVec[0] & n, mVec[1] & n, mVec[2] & n); }
126 Coord operator| (Int32 n) const { return Coord(mVec[0] | n, mVec[1] | n, mVec[2] | n); }
127 Coord& operator&= (Int32 n) { mVec[0]&=n; mVec[1]&=n; mVec[2]&=n; return *this; }
128 Coord& operator|= (Int32 n) { mVec[0]|=n; mVec[1]|=n; mVec[2]|=n; return *this; }
129
130 Int32 x() const { return mVec[0]; }
131 Int32 y() const { return mVec[1]; }
132 Int32 z() const { return mVec[2]; }
133 Int32 operator[](size_t i) const { assert(i < 3); return mVec[i]; }
134 Int32& x() { return mVec[0]; }
135 Int32& y() { return mVec[1]; }
136 Int32& z() { return mVec[2]; }
137 Int32& operator[](size_t i) { assert(i < 3); return mVec[i]; }
138
139 const Int32* data() const { return mVec.data(); }
140 Int32* data() { return mVec.data(); }
141 const Int32* asPointer() const { return mVec.data(); }
142 Int32* asPointer() { return mVec.data(); }
143 Vec3d asVec3d() const { return Vec3d(double(mVec[0]), double(mVec[1]), double(mVec[2])); }
144 Vec3s asVec3s() const { return Vec3s(float(mVec[0]), float(mVec[1]), float(mVec[2])); }
145 Vec3i asVec3i() const { return Vec3i(mVec.data()); }
146 Vec3I asVec3I() const { return Vec3I(Index32(mVec[0]), Index32(mVec[1]), Index32(mVec[2])); }
147 void asXYZ(Int32& x, Int32& y, Int32& z) const { x = mVec[0]; y = mVec[1]; z = mVec[2]; }
148
149 bool operator==(const Coord& rhs) const
150 {
151 return (mVec[0] == rhs.mVec[0] && mVec[1] == rhs.mVec[1] && mVec[2] == rhs.mVec[2]);
152 }
153 bool operator!=(const Coord& rhs) const { return !(*this == rhs); }
154
155 /// Lexicographic less than
156 bool operator<(const Coord& rhs) const
157 {
158 return this->x() < rhs.x() ? true : this->x() > rhs.x() ? false
159 : this->y() < rhs.y() ? true : this->y() > rhs.y() ? false
160 : this->z() < rhs.z() ? true : false;
161 }
162 /// Lexicographic less than or equal to
163 bool operator<=(const Coord& rhs) const
164 {
165 return this->x() < rhs.x() ? true : this->x() > rhs.x() ? false
166 : this->y() < rhs.y() ? true : this->y() > rhs.y() ? false
167 : this->z() <=rhs.z() ? true : false;
168 }
169 /// Lexicographic greater than
170 bool operator>(const Coord& rhs) const { return !(*this <= rhs); }
171 /// Lexicographic greater than or equal to
172 bool operator>=(const Coord& rhs) const { return !(*this < rhs); }
173
174 /// Perform a component-wise minimum with the other Coord.
175 void minComponent(const Coord& other)
176 {
177 mVec[0] = std::min(mVec[0], other.mVec[0]);
178 mVec[1] = std::min(mVec[1], other.mVec[1]);
179 mVec[2] = std::min(mVec[2], other.mVec[2]);
180 }
181
182 /// Perform a component-wise maximum with the other Coord.
183 void maxComponent(const Coord& other)
184 {
185 mVec[0] = std::max(mVec[0], other.mVec[0]);
186 mVec[1] = std::max(mVec[1], other.mVec[1]);
187 mVec[2] = std::max(mVec[2], other.mVec[2]);
188 }
189
190 /// Return the component-wise minimum of the two Coords.
191 static inline Coord minComponent(const Coord& lhs, const Coord& rhs)
192 {
193 return Coord(std::min(lhs.x(), rhs.x()),
194 std::min(lhs.y(), rhs.y()),
195 std::min(lhs.z(), rhs.z()));
196 }
197
198 /// Return the component-wise maximum of the two Coords.
199 static inline Coord maxComponent(const Coord& lhs, const Coord& rhs)
200 {
201 return Coord(std::max(lhs.x(), rhs.x()),
202 std::max(lhs.y(), rhs.y()),
203 std::max(lhs.z(), rhs.z()));
204 }
205
206 /// Return true if any of the components of @a a are smaller than the
207 /// corresponding components of @a b.
208 static inline bool lessThan(const Coord& a, const Coord& b)
209 {
210 return (a[0] < b[0] || a[1] < b[1] || a[2] < b[2]);
211 }
212
213 /// @brief Return the index (0, 1 or 2) with the smallest value.
214 size_t minIndex() const { return MinIndex(mVec); }
215
216 /// @brief Return the index (0, 1 or 2) with the largest value.
217 size_t maxIndex() const { return MaxIndex(mVec); }
218
219 void read(std::istream& is) { is.read(reinterpret_cast<char*>(mVec.data()), sizeof(mVec)); }
220 void write(std::ostream& os) const
221 {
222 os.write(reinterpret_cast<const char*>(mVec.data()), sizeof(mVec));
223 }
224
225 /// @brief Return a hash value for this coordinate
226 /// @note Log2N is the binary logarithm of the hash table size.
227 /// @details The hash function is originally taken from the SIGGRAPH paper:
228 /// "VDB: High-resolution sparse volumes with dynamic topology"
229 /// and the prime numbers are modified based on the ACM Transactions on Graphics paper:
230 /// "Real-time 3D reconstruction at scale using voxel hashing"
231 template<int Log2N = 20>
232 size_t hash() const
233 {
234 const uint32_t* vec = reinterpret_cast<const uint32_t*>(mVec.data());
235 return ((1<<Log2N)-1) & (vec[0]*73856093 ^ vec[1]*19349669 ^ vec[2]*83492791);
236 }
237
238 private:
239 std::array<Int32, 3> mVec;
240}; // class Coord
241
242
243////////////////////////////////////////
244
245
246/// @brief Axis-aligned bounding box of signed integer coordinates
247/// @note The range of the integer coordinates, [min, max], is inclusive.
248/// Thus, a bounding box with min = max is not empty but rather encloses
249/// a single coordinate.
250 class CoordBBox
251{
252 public:
253 using Index64 = uint64_t;
254 using ValueType = Coord::ValueType;
255
256 /// @brief Iterator over the Coord domain covered by a CoordBBox
257 /// @note If ZYXOrder is @c true, @e z is the fastest-moving coordinate,
258 /// otherwise the traversal is in XYZ order (i.e., @e x is fastest-moving).
259 template<bool ZYXOrder>
260 class Iterator
261 {
262 public:
263 /// @brief C-tor from a bounding box
264 Iterator(const CoordBBox& b): mPos(b.min()), mMin(b.min()), mMax(b.max()) {}
265 /// @brief Increment the iterator to point to the next coordinate.
266 /// @details Iteration stops one past the maximum coordinate
267 /// along the axis determined by the template parameter.
268 Iterator& operator++() { ZYXOrder ? next<2,1,0>() : next<0,1,2>(); return *this; }
269 /// @brief Return @c true if the iterator still points to a valid coordinate.
270 operator bool() const { return ZYXOrder ? (mPos[0] <= mMax[0]) : (mPos[2] <= mMax[2]); }
271 /// @brief Return a const reference to the coordinate currently pointed to.
272 const Coord& operator*() const { return mPos; }
273 /// Return @c true if this iterator and the given iterator point to the same coordinate.
274 bool operator==(const Iterator& other) const
275 {
276 return ((mPos == other.mPos) && (mMin == other.mMin) && (mMax == other.mMax));
277 }
278 /// Return @c true if this iterator and the given iterator point to different coordinates.
279 bool operator!=(const Iterator& other) const { return !(*this == other); }
280 private:
281 template<size_t a, size_t b, size_t c>
282 void next()
283 {
284 if (mPos[a] < mMax[a]) { ++mPos[a]; } // this is the most common case
285 else if (mPos[b] < mMax[b]) { mPos[a] = mMin[a]; ++mPos[b]; }
286 else if (mPos[c] <= mMax[c]) { mPos[a] = mMin[a]; mPos[b] = mMin[b]; ++mPos[c]; }
287 }
288 Coord mPos, mMin, mMax;
289 friend class CoordBBox; // for CoordBBox::end()
290 };// CoordBBox::Iterator
291
292 using ZYXIterator = Iterator</*ZYX=*/true>;
293 using XYZIterator = Iterator</*ZYX=*/false>;
294
295 /// @brief The default constructor produces an empty bounding box.
296 CoordBBox(): mMin(Coord::max()), mMax(Coord::min()) {}
297 /// @brief Construct a bounding box with the given @a min and @a max bounds.
298 CoordBBox(const Coord& min, const Coord& max): mMin(min), mMax(max) {}
299 /// @brief Construct from individual components of the min and max bounds.
300 CoordBBox(ValueType xMin, ValueType yMin, ValueType zMin,
301 ValueType xMax, ValueType yMax, ValueType zMax)
302 : mMin(xMin, yMin, zMin), mMax(xMax, yMax, zMax)
303 {
304 }
305 /// @brief Splitting constructor for use in TBB ranges
306 /// @note The other bounding box is assumed to be divisible.
307 CoordBBox(CoordBBox& other, const tbb::split&): mMin(other.mMin), mMax(other.mMax)
308 {
309 assert(this->is_divisible());
310 const size_t n = this->maxExtent();
311 mMax[n] = (mMin[n] + mMax[n]) >> 1;
312 other.mMin[n] = mMax[n] + 1;
313 }
314
315 static CoordBBox createCube(const Coord& min, ValueType dim)
316 {
317 return CoordBBox(min, min.offsetBy(dim - 1));
318 }
319
320 /// Return an "infinite" bounding box, as defined by the Coord value range.
321 static CoordBBox inf() { return CoordBBox(Coord::min(), Coord::max()); }
322
323 const Coord& min() const { return mMin; }
324 const Coord& max() const { return mMax; }
325
326 Coord& min() { return mMin; }
327 Coord& max() { return mMax; }
328
329 void reset() { mMin = Coord::max(); mMax = Coord::min(); }
330 void reset(const Coord& min, const Coord& max) { mMin = min; mMax = max; }
331 void resetToCube(const Coord& min, ValueType dim) { mMin = min; mMax = min.offsetBy(dim - 1); }
332
333 /// @brief Return the minimum coordinate.
334 /// @note The start coordinate is inclusive.
335 Coord getStart() const { return mMin; }
336 /// @brief Return the maximum coordinate plus one.
337 /// @note This end coordinate is exclusive.
338 Coord getEnd() const { return mMax.offsetBy(1); }
339
340 /// @brief Return a ZYX-order iterator that points to the minimum coordinate.
341 ZYXIterator begin() const { return ZYXIterator{*this}; }
342 /// @brief Return a ZYX-order iterator that points to the minimum coordinate.
343 ZYXIterator beginZYX() const { return ZYXIterator{*this}; }
344 /// @brief Return an XYZ-order iterator that points to the minimum coordinate.
345 XYZIterator beginXYZ() const { return XYZIterator{*this}; }
346
347 /// @brief Return a ZYX-order iterator that points past the maximum coordinate.
348 ZYXIterator end() const { ZYXIterator it{*this}; it.mPos[0] = mMax[0] + 1; return it; }
349 /// @brief Return a ZYX-order iterator that points past the maximum coordinate.
350 ZYXIterator endZYX() const { return end(); }
351 /// @brief Return an XYZ-order iterator that points past the maximum coordinate.
352 XYZIterator endXYZ() const { XYZIterator it{*this}; it.mPos[2] = mMax[2] + 1; return it; }
353
354 bool operator==(const CoordBBox& rhs) const { return mMin == rhs.mMin && mMax == rhs.mMax; }
355 bool operator!=(const CoordBBox& rhs) const { return !(*this == rhs); }
356
357 /// @brief Return @c true if this bounding box is empty (i.e., encloses no coordinates).
358 bool empty() const
359 {
360#if defined(__GNUC__) && !defined(__INTEL_COMPILER)
361 #pragma GCC diagnostic push
362 #pragma GCC diagnostic ignored "-Wstrict-overflow"
363#endif
364 return (mMin[0] > mMax[0] || mMin[1] > mMax[1] || mMin[2] > mMax[2]);
365#if defined(__GNUC__) && !defined(__INTEL_COMPILER)
366 #pragma GCC diagnostic pop
367#endif
368 }
369 /// @brief Return @c true if this bounding box is nonempty
370 /// (i.e., encloses at least one coordinate).
371 operator bool() const { return !this->empty(); }
372 /// @brief Return @c true if this bounding box is nonempty
373 /// (i.e., encloses at least one coordinate).
374 bool hasVolume() const { return !this->empty(); }
375
376 /// @brief Return the floating-point position of the center of this bounding box.
377 Vec3d getCenter() const { return 0.5 * Vec3d((mMin + mMax).asPointer()); }
378
379 /// @brief Return the dimensions of the coordinates spanned by this bounding box.
380 /// @note Since coordinates are inclusive, a bounding box with min = max
381 /// has dimensions of (1, 1, 1).
382 Coord dim() const { return empty() ? Coord(0) : (mMax.offsetBy(1) - mMin); }
383 /// @todo deprecate - use dim instead
384 Coord extents() const { return this->dim(); }
385 /// @brief Return the integer volume of coordinates spanned by this bounding box.
386 /// @note Since coordinates are inclusive, a bounding box with min = max has volume one.
387 Index64 volume() const
388 {
389 const Coord d = this->dim();
390 return Index64(d[0]) * Index64(d[1]) * Index64(d[2]);
391 }
392 /// @brief Return @c true if this bounding box can be subdivided [mainly for use by TBB].
393 bool is_divisible() const { return mMin[0]<mMax[0] && mMin[1]<mMax[1] && mMin[2]<mMax[2]; }
394
395 /// @brief Return the index (0, 1 or 2) of the shortest axis.
396 size_t minExtent() const { return this->dim().minIndex(); }
397
398 /// @brief Return the index (0, 1 or 2) of the longest axis.
399 size_t maxExtent() const { return this->dim().maxIndex(); }
400
401 /// @brief Return @c true if point (x, y, z) is inside this bounding box.
402 bool isInside(const Coord& xyz) const
403 {
404 return !(Coord::lessThan(xyz,mMin) || Coord::lessThan(mMax,xyz));
405 }
406
407 /// @brief Return @c true if the given bounding box is inside this bounding box.
408 bool isInside(const CoordBBox& b) const
409 {
410 return !(Coord::lessThan(b.mMin,mMin) || Coord::lessThan(mMax,b.mMax));
411 }
412
413 /// @brief Return @c true if the given bounding box overlaps with this bounding box.
414 bool hasOverlap(const CoordBBox& b) const
415 {
416 return !(Coord::lessThan(mMax,b.mMin) || Coord::lessThan(b.mMax,mMin));
417 }
418
419 /// @brief Pad this bounding box with the specified padding.
420 void expand(ValueType padding)
421 {
422 mMin.offset(-padding);
423 mMax.offset( padding);
424 }
425
426 /// @brief Return a new instance that is expanded by the specified padding.
427 CoordBBox expandBy(ValueType padding) const
428 {
429 return CoordBBox(mMin.offsetBy(-padding),mMax.offsetBy(padding));
430 }
431
432 /// @brief Expand this bounding box to enclose point (x, y, z).
433 void expand(const Coord& xyz)
434 {
435 mMin.minComponent(xyz);
436 mMax.maxComponent(xyz);
437 }
438
439 /// @brief Union this bounding box with the given bounding box.
440 void expand(const CoordBBox& bbox)
441 {
442 mMin.minComponent(bbox.min());
443 mMax.maxComponent(bbox.max());
444 }
445 /// @brief Intersect this bounding box with the given bounding box.
446 void intersect(const CoordBBox& bbox)
447 {
448 mMin.maxComponent(bbox.min());
449 mMax.minComponent(bbox.max());
450 }
451 /// @brief Union this bounding box with the cubical bounding box
452 /// of the given size and with the given minimum coordinates.
453 void expand(const Coord& min, Coord::ValueType dim)
454 {
455 mMin.minComponent(min);
456 mMax.maxComponent(min.offsetBy(dim-1));
457 }
458 /// @brief Translate this bounding box by
459 /// (<i>t<sub>x</sub></i>, <i>t<sub>y</sub></i>, <i>t<sub>z</sub></i>).
460 void translate(const Coord& t) { mMin += t; mMax += t; }
461
462 /// @brief Move this bounding box to the specified min
463 void moveMin(const Coord& min) { mMax += min - mMin; mMin = min; }
464
465 /// @brief Move this bounding box to the specified max
466 void moveMax(const Coord& max) { mMin += max - mMax; mMax = max; }
467
468 /// @brief Populates an array with the eight corner points of this bounding box.
469 /// @details The ordering of the corner points is lexicographic.
470 /// @warning It is assumed that the pointer can be incremented at
471 /// least seven times, i.e. has storage for eight Coord elements!
472 void getCornerPoints(Coord *p) const
473 {
474 assert(p != nullptr);
475 p->reset(mMin.x(), mMin.y(), mMin.z()); ++p;
476 p->reset(mMin.x(), mMin.y(), mMax.z()); ++p;
477 p->reset(mMin.x(), mMax.y(), mMin.z()); ++p;
478 p->reset(mMin.x(), mMax.y(), mMax.z()); ++p;
479 p->reset(mMax.x(), mMin.y(), mMin.z()); ++p;
480 p->reset(mMax.x(), mMin.y(), mMax.z()); ++p;
481 p->reset(mMax.x(), mMax.y(), mMin.z()); ++p;
482 p->reset(mMax.x(), mMax.y(), mMax.z());
483 }
484
485 //@{
486 /// @brief Bit-wise operations performed on both the min and max members
487 CoordBBox operator>> (size_t n) const { return CoordBBox(mMin>>n, mMax>>n); }
488 CoordBBox operator<< (size_t n) const { return CoordBBox(mMin<<n, mMax<<n); }
489 CoordBBox& operator<<=(size_t n) { mMin <<= n; mMax <<= n; return *this; }
490 CoordBBox& operator>>=(size_t n) { mMin >>= n; mMax >>= n; return *this; }
491 CoordBBox operator& (Coord::Int32 n) const { return CoordBBox(mMin & n, mMax & n); }
492 CoordBBox operator| (Coord::Int32 n) const { return CoordBBox(mMin | n, mMax | n); }
493 CoordBBox& operator&= (Coord::Int32 n) { mMin &= n; mMax &= n; return *this; }
494 CoordBBox& operator|= (Coord::Int32 n) { mMin |= n; mMax |= n; return *this; }
495 //@}
496
497 /// @brief Unserialize this bounding box from the given stream.
498 void read(std::istream& is) { mMin.read(is); mMax.read(is); }
499 /// @brief Serialize this bounding box to the given stream.
500 void write(std::ostream& os) const { mMin.write(os); mMax.write(os); }
501
502 private:
503 Coord mMin, mMax;
504}; // class CoordBBox
505
506
507////////////////////////////////////////
508
509
510 inline std::ostream& operator<<(std::ostream& os, const Coord& xyz)
511{
512 os << xyz.asVec3i(); return os;
513}
514
515
516 inline Coord
517 Abs(const Coord& xyz)
518{
519 return Coord(Abs(xyz[0]), Abs(xyz[1]), Abs(xyz[2]));
520}
521
522
523//@{
524/// Allow a Coord to be added to or subtracted from a Vec3.
525 template<typename T>
526 inline Vec3<typename promote<T, typename Coord::ValueType>::type>
527 operator+(const Vec3<T>& v0, const Coord& v1)
528{
529 Vec3<typename promote<T, typename Coord::ValueType>::type> result(v0);
530 result[0] += v1[0];
531 result[1] += v1[1];
532 result[2] += v1[2];
533 return result;
534}
535
536 template<typename T>
537 inline Vec3<typename promote<T, typename Coord::ValueType>::type>
538 operator+(const Coord& v1, const Vec3<T>& v0)
539{
540 Vec3<typename promote<T, typename Coord::ValueType>::type> result(v0);
541 result[0] += v1[0];
542 result[1] += v1[1];
543 result[2] += v1[2];
544 return result;
545}
546//@}
547
548
549//@{
550/// Allow a Coord to be subtracted from a Vec3.
551 template <typename T>
552 inline Vec3<typename promote<T, Coord::ValueType>::type>
553 operator-(const Vec3<T>& v0, const Coord& v1)
554{
555 Vec3<typename promote<T, Coord::ValueType>::type> result(v0);
556 result[0] -= v1[0];
557 result[1] -= v1[1];
558 result[2] -= v1[2];
559 return result;
560}
561
562 template <typename T>
563 inline Vec3<typename promote<T, Coord::ValueType>::type>
564 operator-(const Coord& v1, const Vec3<T>& v0)
565{
566 Vec3<typename promote<T, Coord::ValueType>::type> result(v0);
567 result[0] -= v1[0];
568 result[1] -= v1[1];
569 result[2] -= v1[2];
570 return -result;
571}
572//@}
573
574 inline std::ostream&
575 operator<<(std::ostream& os, const CoordBBox& b)
576{
577 os << b.min() << " -> " << b.max();
578 return os;
579}
580
581} // namespace math
582} // namespace OPENVDB_VERSION_NAME
583} // namespace openvdb
584
585////////////////////////////////////////
586
587// template specialization of std::hash with Coord, which
588// allows for Coord to be used as the key in std::unordered_map
589 namespace std {// injected in namespace std
590
591 template<>
592 struct hash<openvdb::math::Coord>
593{
594 using Coord = openvdb::math::Coord;
595 using argument_type = Coord;
596 using result_type = std::size_t;
597 std::size_t operator()(const Coord& ijk) const noexcept { return ijk.Coord::hash<>(); }
598};// std::hash<openvdb::math::Coord>
599
600}// namespace std
601
602#endif // OPENVDB_MATH_COORD_HAS_BEEN_INCLUDED
operator>>
OPENVDB_API std::istream & operator>>(std::istream &is, half &h)
Input h from is.
operator<<
OPENVDB_API std::ostream & operator<<(std::ostream &os, half h)
Output h to os, formatted as a float.
Math.h
General-purpose arithmetic and comparison routines, most of which accept arbitrary value types (or at...
Platform.h
Vec3.h
openvdb::v11_0::CoordBBox::Iterator::Iterator
Iterator(const CoordBBox &b)
C-tor from a bounding box.
Definition Coord.h:264
openvdb::v11_0::CoordBBox::CoordBBox
CoordBBox()
The default constructor produces an empty bounding box.
Definition Coord.h:296
openvdb::v11_0::Coord::Coord
Coord()
Definition Coord.h:35
openvdb::v11_0::math::CoordBBox::Iterator
Iterator over the Coord domain covered by a CoordBBox.
Definition Coord.h:261
openvdb::v11_0::math::CoordBBox::Iterator::operator!=
bool operator!=(const Iterator &other) const
Return true if this iterator and the given iterator point to different coordinates.
Definition Coord.h:279
openvdb::v11_0::math::CoordBBox::Iterator::operator*
const Coord & operator*() const
Return a const reference to the coordinate currently pointed to.
Definition Coord.h:272
openvdb::v11_0::math::CoordBBox::Iterator::operator++
Iterator & operator++()
Increment the iterator to point to the next coordinate.
Definition Coord.h:268
openvdb::v11_0::math::CoordBBox::Iterator< true >::CoordBBox
friend class CoordBBox
Definition Coord.h:289
openvdb::v11_0::math::CoordBBox::Iterator::operator==
bool operator==(const Iterator &other) const
Return true if this iterator and the given iterator point to the same coordinate.
Definition Coord.h:274
openvdb::v11_0::math::CoordBBox::Iterator::Iterator
Iterator(const CoordBBox &b)
C-tor from a bounding box.
Definition Coord.h:264
openvdb::v11_0::math::CoordBBox
Axis-aligned bounding box of signed integer coordinates.
Definition Coord.h:251
openvdb::v11_0::math::CoordBBox::operator!=
bool operator!=(const CoordBBox &rhs) const
Definition Coord.h:355
openvdb::v11_0::math::CoordBBox::CoordBBox
CoordBBox()
The default constructor produces an empty bounding box.
Definition Coord.h:296
openvdb::v11_0::math::CoordBBox::isInside
bool isInside(const CoordBBox &b) const
Return true if the given bounding box is inside this bounding box.
Definition Coord.h:408
openvdb::v11_0::math::CoordBBox::beginZYX
ZYXIterator beginZYX() const
Return a ZYX-order iterator that points to the minimum coordinate.
Definition Coord.h:343
openvdb::v11_0::math::CoordBBox::minExtent
size_t minExtent() const
Return the index (0, 1 or 2) of the shortest axis.
Definition Coord.h:396
openvdb::v11_0::math::CoordBBox::moveMax
void moveMax(const Coord &max)
Move this bounding box to the specified max.
Definition Coord.h:466
openvdb::v11_0::math::CoordBBox::is_divisible
bool is_divisible() const
Return true if this bounding box can be subdivided [mainly for use by TBB].
Definition Coord.h:393
openvdb::v11_0::math::CoordBBox::ValueType
Coord::ValueType ValueType
Definition Coord.h:254
openvdb::v11_0::math::CoordBBox::extents
Coord extents() const
Definition Coord.h:384
openvdb::v11_0::math::CoordBBox::write
void write(std::ostream &os) const
Serialize this bounding box to the given stream.
Definition Coord.h:500
openvdb::v11_0::math::CoordBBox::translate
void translate(const Coord &t)
Translate this bounding box by (tx, ty, tz).
Definition Coord.h:460
openvdb::v11_0::math::CoordBBox::hasVolume
bool hasVolume() const
Return true if this bounding box is nonempty (i.e., encloses at least one coordinate).
Definition Coord.h:374
openvdb::v11_0::math::CoordBBox::getCenter
Vec3d getCenter() const
Return the floating-point position of the center of this bounding box.
Definition Coord.h:377
openvdb::v11_0::math::CoordBBox::end
ZYXIterator end() const
Return a ZYX-order iterator that points past the maximum coordinate.
Definition Coord.h:348
openvdb::v11_0::math::CoordBBox::beginXYZ
XYZIterator beginXYZ() const
Return an XYZ-order iterator that points to the minimum coordinate.
Definition Coord.h:345
openvdb::v11_0::math::CoordBBox::expand
void expand(ValueType padding)
Pad this bounding box with the specified padding.
Definition Coord.h:420
openvdb::v11_0::math::CoordBBox::expand
void expand(const Coord &xyz)
Expand this bounding box to enclose point (x, y, z).
Definition Coord.h:433
openvdb::v11_0::math::CoordBBox::CoordBBox
CoordBBox(CoordBBox &other, const tbb::split &)
Splitting constructor for use in TBB ranges.
Definition Coord.h:307
openvdb::v11_0::math::CoordBBox::operator>>=
CoordBBox & operator>>=(size_t n)
Definition Coord.h:490
openvdb::v11_0::math::CoordBBox::endZYX
ZYXIterator endZYX() const
Return a ZYX-order iterator that points past the maximum coordinate.
Definition Coord.h:350
openvdb::v11_0::math::CoordBBox::empty
bool empty() const
Return true if this bounding box is empty (i.e., encloses no coordinates).
Definition Coord.h:358
openvdb::v11_0::math::CoordBBox::max
Coord & max()
Definition Coord.h:327
openvdb::v11_0::math::CoordBBox::moveMin
void moveMin(const Coord &min)
Move this bounding box to the specified min.
Definition Coord.h:463
openvdb::v11_0::math::CoordBBox::min
const Coord & min() const
Definition Coord.h:323
openvdb::v11_0::math::CoordBBox::hasOverlap
bool hasOverlap(const CoordBBox &b) const
Return true if the given bounding box overlaps with this bounding box.
Definition Coord.h:414
openvdb::v11_0::math::CoordBBox::max
const Coord & max() const
Definition Coord.h:324
openvdb::v11_0::math::CoordBBox::maxExtent
size_t maxExtent() const
Return the index (0, 1 or 2) of the longest axis.
Definition Coord.h:399
openvdb::v11_0::math::CoordBBox::endXYZ
XYZIterator endXYZ() const
Return an XYZ-order iterator that points past the maximum coordinate.
Definition Coord.h:352
openvdb::v11_0::math::CoordBBox::operator<<=
CoordBBox & operator<<=(size_t n)
Definition Coord.h:489
openvdb::v11_0::math::CoordBBox::resetToCube
void resetToCube(const Coord &min, ValueType dim)
Definition Coord.h:331
openvdb::v11_0::math::CoordBBox::operator==
bool operator==(const CoordBBox &rhs) const
Definition Coord.h:354
openvdb::v11_0::math::CoordBBox::expand
void expand(const Coord &min, Coord::ValueType dim)
Union this bounding box with the cubical bounding box of the given size and with the given minimum co...
Definition Coord.h:453
openvdb::v11_0::math::CoordBBox::expandBy
CoordBBox expandBy(ValueType padding) const
Return a new instance that is expanded by the specified padding.
Definition Coord.h:427
openvdb::v11_0::math::CoordBBox::volume
Index64 volume() const
Return the integer volume of coordinates spanned by this bounding box.
Definition Coord.h:387
openvdb::v11_0::math::CoordBBox::inf
static CoordBBox inf()
Return an "infinite" bounding box, as defined by the Coord value range.
Definition Coord.h:321
openvdb::v11_0::math::CoordBBox::XYZIterator
Iterator< false > XYZIterator
Definition Coord.h:293
openvdb::v11_0::math::CoordBBox::CoordBBox
CoordBBox(const Coord &min, const Coord &max)
Construct a bounding box with the given min and max bounds.
Definition Coord.h:298
openvdb::v11_0::math::CoordBBox::CoordBBox
CoordBBox(ValueType xMin, ValueType yMin, ValueType zMin, ValueType xMax, ValueType yMax, ValueType zMax)
Construct from individual components of the min and max bounds.
Definition Coord.h:300
openvdb::v11_0::math::CoordBBox::min
Coord & min()
Definition Coord.h:326
openvdb::v11_0::math::CoordBBox::expand
void expand(const CoordBBox &bbox)
Union this bounding box with the given bounding box.
Definition Coord.h:440
openvdb::v11_0::math::CoordBBox::isInside
bool isInside(const Coord &xyz) const
Return true if point (x, y, z) is inside this bounding box.
Definition Coord.h:402
openvdb::v11_0::math::CoordBBox::dim
Coord dim() const
Return the dimensions of the coordinates spanned by this bounding box.
Definition Coord.h:382
openvdb::v11_0::math::CoordBBox::getStart
Coord getStart() const
Return the minimum coordinate.
Definition Coord.h:335
openvdb::v11_0::math::CoordBBox::getEnd
Coord getEnd() const
Return the maximum coordinate plus one.
Definition Coord.h:338
openvdb::v11_0::math::CoordBBox::ZYXIterator
Iterator< true > ZYXIterator
Definition Coord.h:292
openvdb::v11_0::math::CoordBBox::Index64
uint64_t Index64
Definition Coord.h:253
openvdb::v11_0::math::CoordBBox::intersect
void intersect(const CoordBBox &bbox)
Intersect this bounding box with the given bounding box.
Definition Coord.h:446
openvdb::v11_0::math::CoordBBox::reset
void reset()
Definition Coord.h:329
openvdb::v11_0::math::CoordBBox::getCornerPoints
void getCornerPoints(Coord *p) const
Populates an array with the eight corner points of this bounding box.
Definition Coord.h:472
openvdb::v11_0::math::CoordBBox::createCube
static CoordBBox createCube(const Coord &min, ValueType dim)
Definition Coord.h:315
openvdb::v11_0::math::CoordBBox::begin
ZYXIterator begin() const
Return a ZYX-order iterator that points to the minimum coordinate.
Definition Coord.h:341
openvdb::v11_0::math::CoordBBox::reset
void reset(const Coord &min, const Coord &max)
Definition Coord.h:330
openvdb::v11_0::math::CoordBBox::read
void read(std::istream &is)
Unserialize this bounding box from the given stream.
Definition Coord.h:498
openvdb::v11_0::math::Coord
Signed (x, y, z) 32-bit integer coordinates.
Definition Coord.h:25
openvdb::v11_0::math::Coord::ValueType
Int32 ValueType
Definition Coord.h:32
openvdb::v11_0::math::Coord::operator-
Coord operator-(const Coord &rhs) const
Definition Coord.h:115
openvdb::v11_0::math::Coord::offset
Coord & offset(Int32 dx, Int32 dy, Int32 dz)
Definition Coord.h:83
openvdb::v11_0::math::Coord::z
Int32 & z()
Definition Coord.h:136
openvdb::v11_0::math::Coord::asVec3d
Vec3d asVec3d() const
Definition Coord.h:143
openvdb::v11_0::math::Coord::operator-
Coord operator-() const
Definition Coord.h:119
openvdb::v11_0::math::Coord::y
Int32 y() const
Definition Coord.h:131
openvdb::v11_0::math::Coord::hash
size_t hash() const
Return a hash value for this coordinate.
Definition Coord.h:232
openvdb::v11_0::math::Coord::asVec3s
Vec3s asVec3s() const
Definition Coord.h:144
openvdb::v11_0::math::Coord::round
static Coord round(const Vec3< T > &xyz)
Return xyz rounded to the closest integer coordinates (cell centered conversion).
Definition Coord.h:50
openvdb::v11_0::math::Coord::operator[]
Int32 operator[](size_t i) const
Definition Coord.h:133
openvdb::v11_0::math::Coord::asVec3I
Vec3I asVec3I() const
Definition Coord.h:146
openvdb::v11_0::math::Coord::ceil
static Coord ceil(const Vec3< T > &xyz)
Return the largest integer coordinates that are not greater than xyz+1 (node centered conversion).
Definition Coord.h:63
openvdb::v11_0::math::Coord::Vec3I
Vec3< Index32 > Vec3I
Definition Coord.h:30
openvdb::v11_0::math::Coord::operator-=
Coord & operator-=(const Coord &rhs)
Definition Coord.h:104
openvdb::v11_0::math::Coord::Limits
std::numeric_limits< ValueType > Limits
Definition Coord.h:33
openvdb::v11_0::math::Coord::asPointer
Int32 * asPointer()
Definition Coord.h:142
openvdb::v11_0::math::Coord::Coord
Coord(const Vec3I &v)
Definition Coord.h:39
openvdb::v11_0::math::Coord::asXYZ
void asXYZ(Int32 &x, Int32 &y, Int32 &z) const
Definition Coord.h:147
openvdb::v11_0::math::Coord::operator+
Coord operator+(const Coord &rhs) const
Definition Coord.h:111
openvdb::v11_0::math::Coord::offsetBy
Coord offsetBy(Int32 dx, Int32 dy, Int32 dz) const
Definition Coord.h:91
openvdb::v11_0::math::Coord::write
void write(std::ostream &os) const
Definition Coord.h:220
openvdb::v11_0::math::Coord::maxIndex
size_t maxIndex() const
Return the index (0, 1 or 2) with the largest value.
Definition Coord.h:217
openvdb::v11_0::math::Coord::offsetBy
Coord offsetBy(Int32 n) const
Definition Coord.h:95
openvdb::v11_0::math::Coord::operator<
bool operator<(const Coord &rhs) const
Lexicographic less than.
Definition Coord.h:156
openvdb::v11_0::math::Coord::minComponent
void minComponent(const Coord &other)
Perform a component-wise minimum with the other Coord.
Definition Coord.h:175
openvdb::v11_0::math::Coord::data
Int32 * data()
Definition Coord.h:140
openvdb::v11_0::math::Coord::operator+=
Coord & operator+=(const Coord &rhs)
Definition Coord.h:97
openvdb::v11_0::math::Coord::operator>=
bool operator>=(const Coord &rhs) const
Lexicographic greater than or equal to.
Definition Coord.h:172
openvdb::v11_0::math::Coord::Coord
constexpr Coord(Int32 x, Int32 y, Int32 z)
Definition Coord.h:37
openvdb::v11_0::math::Coord::x
Int32 & x()
Definition Coord.h:134
openvdb::v11_0::math::Coord::operator<<=
Coord & operator<<=(size_t n)
Definition Coord.h:123
openvdb::v11_0::math::Coord::Coord
Coord()
Definition Coord.h:35
openvdb::v11_0::math::Coord::maxComponent
static Coord maxComponent(const Coord &lhs, const Coord &rhs)
Return the component-wise maximum of the two Coords.
Definition Coord.h:199
openvdb::v11_0::math::Coord::maxComponent
void maxComponent(const Coord &other)
Perform a component-wise maximum with the other Coord.
Definition Coord.h:183
openvdb::v11_0::math::Coord::Coord
constexpr Coord(Int32 xyz)
Definition Coord.h:36
openvdb::v11_0::math::Coord::reset
Coord & reset(Int32 x, Int32 y, Int32 z)
Reset all three coordinates with the specified arguments.
Definition Coord.h:69
openvdb::v11_0::math::Coord::Vec3i
Vec3< Int32 > Vec3i
Definition Coord.h:29
openvdb::v11_0::math::Coord::Coord
Coord(const Int32 *v)
Definition Coord.h:40
openvdb::v11_0::math::Coord::Index32
uint32_t Index32
Definition Coord.h:28
openvdb::v11_0::math::Coord::asPointer
const Int32 * asPointer() const
Definition Coord.h:141
openvdb::v11_0::math::Coord::x
Int32 x() const
Definition Coord.h:130
openvdb::v11_0::math::Coord::asVec3i
Vec3i asVec3i() const
Definition Coord.h:145
openvdb::v11_0::math::Coord::minIndex
size_t minIndex() const
Return the index (0, 1 or 2) with the smallest value.
Definition Coord.h:214
openvdb::v11_0::math::Coord::operator!=
bool operator!=(const Coord &rhs) const
Definition Coord.h:153
openvdb::v11_0::math::Coord::min
static Coord min()
Return the smallest possible coordinate.
Definition Coord.h:43
openvdb::v11_0::math::Coord::reset
Coord & reset(Int32 xyz)
Reset all three coordinates with the same specified argument.
Definition Coord.h:77
openvdb::v11_0::math::Coord::setZ
Coord & setZ(Int32 z)
Definition Coord.h:81
openvdb::v11_0::math::Coord::Int32
int32_t Int32
Definition Coord.h:27
openvdb::v11_0::math::Coord::setY
Coord & setY(Int32 y)
Definition Coord.h:80
openvdb::v11_0::math::Coord::operator==
bool operator==(const Coord &rhs) const
Definition Coord.h:149
openvdb::v11_0::math::Coord::floor
static Coord floor(const Vec3< T > &xyz)
Return the largest integer coordinates that are not greater than xyz (node centered conversion).
Definition Coord.h:56
openvdb::v11_0::math::Coord::operator<=
bool operator<=(const Coord &rhs) const
Lexicographic less than or equal to.
Definition Coord.h:163
openvdb::v11_0::math::Coord::max
static Coord max()
Return the largest possible coordinate.
Definition Coord.h:46
openvdb::v11_0::math::Coord::operator[]
Int32 & operator[](size_t i)
Definition Coord.h:137
openvdb::v11_0::math::Coord::Coord
Coord(const Vec3i &v)
Definition Coord.h:38
openvdb::v11_0::math::Coord::lessThan
static bool lessThan(const Coord &a, const Coord &b)
Definition Coord.h:208
openvdb::v11_0::math::Coord::z
Int32 z() const
Definition Coord.h:132
openvdb::v11_0::math::Coord::setX
Coord & setX(Int32 x)
Definition Coord.h:79
openvdb::v11_0::math::Coord::offset
Coord & offset(Int32 n)
Definition Coord.h:90
openvdb::v11_0::math::Coord::data
const Int32 * data() const
Definition Coord.h:139
openvdb::v11_0::math::Coord::operator>
bool operator>(const Coord &rhs) const
Lexicographic greater than.
Definition Coord.h:170
openvdb::v11_0::math::Coord::minComponent
static Coord minComponent(const Coord &lhs, const Coord &rhs)
Return the component-wise minimum of the two Coords.
Definition Coord.h:191
openvdb::v11_0::math::Coord::operator>>=
Coord & operator>>=(size_t n)
Definition Coord.h:124
openvdb::v11_0::math::Coord::y
Int32 & y()
Definition Coord.h:135
openvdb::v11_0::math::Coord::read
void read(std::istream &is)
Definition Coord.h:219
openvdb::v11_0::math::Vec3
Definition Vec3.h:24
hash
__hostdev__ uint32_t hash(uint32_t x)
Definition common.h:14
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::Ceil
int Ceil(float x)
Return the ceiling of x.
Definition Math.h:856
openvdb::v11_0::math::operator-
Vec3< typename promote< T, Coord::ValueType >::type > operator-(const Vec3< T > &v0, const Coord &v1)
Allow a Coord to be subtracted from a Vec3.
Definition Coord.h:553
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::operator+
Vec3< typename promote< T, typename Coord::ValueType >::type > operator+(const Vec3< T > &v0, const Coord &v1)
Allow a Coord to be added to or subtracted from a Vec3.
Definition Coord.h:527
openvdb::v11_0::math::Vec3d
Vec3< double > Vec3d
Definition Vec3.h:664
openvdb::v11_0::math::Abs
Coord Abs(const Coord &xyz)
Definition Coord.h:517
openvdb::v11_0::math::Round
float Round(float x)
Return x rounded to the nearest integer.
Definition Math.h:819
openvdb::v11_0::math::Vec3s
Vec3< float > Vec3s
Definition Vec3.h:663
openvdb::v11_0::math::Floor
int Floor(float x)
Return the floor of x.
Definition Math.h:848
openvdb
Definition Exceptions.h:13
std
Definition Coord.h:589
std::hash< openvdb::math::Coord >::result_type
std::size_t result_type
Definition Coord.h:596
std::hash< openvdb::math::Coord >::operator()
std::size_t operator()(const Coord &ijk) const noexcept
Definition Coord.h:597
std::hash< openvdb::math::Coord >::Coord
openvdb::math::Coord Coord
Definition Coord.h:594
std::hash< openvdb::math::Coord >::argument_type
Coord argument_type
Definition Coord.h:595
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