OpenVDB: openvdb/math/Coord.h Source File

OpenVDB 9.0.0

Coord.h
Go to the documentation of this file.
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
18namespace openvdb {
19 OPENVDB_USE_VERSION_NAMESPACE
20namespace OPENVDB_VERSION_NAME {
21namespace math {
22
23/// @brief Signed (x, y, z) 32-bit integer coordinates
24 class Coord
25{
26public:
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 explicit Coord(Int32 xyz): mVec{{xyz, xyz, xyz}} {}
37 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 taken from the SIGGRAPH paper:
228 /// "VDB: High-resolution sparse volumes with dynamic topology"
229 template<int Log2N = 20>
230 size_t hash() const
231 {
232 return ((1<<Log2N)-1) & (mVec[0]*73856093 ^ mVec[1]*19349663 ^ mVec[2]*83492791);
233 }
234
235private:
236 std::array<Int32, 3> mVec;
237}; // class Coord
238
239
240////////////////////////////////////////
241
242
243/// @brief Axis-aligned bounding box of signed integer coordinates
244/// @note The range of the integer coordinates, [min, max], is inclusive.
245/// Thus, a bounding box with min = max is not empty but rather encloses
246/// a single coordinate.
247 class CoordBBox
248{
249public:
250 using Index64 = uint64_t;
251 using ValueType = Coord::ValueType;
252
253 /// @brief Iterator over the Coord domain covered by a CoordBBox
254 /// @note If ZYXOrder is @c true, @e z is the fastest-moving coordinate,
255 /// otherwise the traversal is in XYZ order (i.e., @e x is fastest-moving).
256 template<bool ZYXOrder>
257 class Iterator
258 {
259 public:
260 /// @brief C-tor from a bounding box
261 Iterator(const CoordBBox& b): mPos(b.min()), mMin(b.min()), mMax(b.max()) {}
262 /// @brief Increment the iterator to point to the next coordinate.
263 /// @details Iteration stops one past the maximum coordinate
264 /// along the axis determined by the template parameter.
265 Iterator& operator++() { ZYXOrder ? next<2,1,0>() : next<0,1,2>(); return *this; }
266 /// @brief Return @c true if the iterator still points to a valid coordinate.
267 operator bool() const { return ZYXOrder ? (mPos[0] <= mMax[0]) : (mPos[2] <= mMax[2]); }
268 /// @brief Return a const reference to the coordinate currently pointed to.
269 const Coord& operator*() const { return mPos; }
270 /// Return @c true if this iterator and the given iterator point to the same coordinate.
271 bool operator==(const Iterator& other) const
272 {
273 return ((mPos == other.mPos) && (mMin == other.mMin) && (mMax == other.mMax));
274 }
275 /// Return @c true if this iterator and the given iterator point to different coordinates.
276 bool operator!=(const Iterator& other) const { return !(*this == other); }
277 private:
278 template<size_t a, size_t b, size_t c>
279 void next()
280 {
281 if (mPos[a] < mMax[a]) { ++mPos[a]; } // this is the most common case
282 else if (mPos[b] < mMax[b]) { mPos[a] = mMin[a]; ++mPos[b]; }
283 else if (mPos[c] <= mMax[c]) { mPos[a] = mMin[a]; mPos[b] = mMin[b]; ++mPos[c]; }
284 }
285 Coord mPos, mMin, mMax;
286 friend class CoordBBox; // for CoordBBox::end()
287 };// CoordBBox::Iterator
288
289 using ZYXIterator = Iterator</*ZYX=*/true>;
290 using XYZIterator = Iterator</*ZYX=*/false>;
291
292 /// @brief The default constructor produces an empty bounding box.
293 CoordBBox(): mMin(Coord::max()), mMax(Coord::min()) {}
294 /// @brief Construct a bounding box with the given @a min and @a max bounds.
295 CoordBBox(const Coord& min, const Coord& max): mMin(min), mMax(max) {}
296 /// @brief Construct from individual components of the min and max bounds.
297 CoordBBox(ValueType xMin, ValueType yMin, ValueType zMin,
298 ValueType xMax, ValueType yMax, ValueType zMax)
299 : mMin(xMin, yMin, zMin), mMax(xMax, yMax, zMax)
300 {
301 }
302 /// @brief Splitting constructor for use in TBB ranges
303 /// @note The other bounding box is assumed to be divisible.
304 CoordBBox(CoordBBox& other, const tbb::split&): mMin(other.mMin), mMax(other.mMax)
305 {
306 assert(this->is_divisible());
307 const size_t n = this->maxExtent();
308 mMax[n] = (mMin[n] + mMax[n]) >> 1;
309 other.mMin[n] = mMax[n] + 1;
310 }
311
312 static CoordBBox createCube(const Coord& min, ValueType dim)
313 {
314 return CoordBBox(min, min.offsetBy(dim - 1));
315 }
316
317 /// Return an "infinite" bounding box, as defined by the Coord value range.
318 static CoordBBox inf() { return CoordBBox(Coord::min(), Coord::max()); }
319
320 const Coord& min() const { return mMin; }
321 const Coord& max() const { return mMax; }
322
323 Coord& min() { return mMin; }
324 Coord& max() { return mMax; }
325
326 void reset() { mMin = Coord::max(); mMax = Coord::min(); }
327 void reset(const Coord& min, const Coord& max) { mMin = min; mMax = max; }
328 void resetToCube(const Coord& min, ValueType dim) { mMin = min; mMax = min.offsetBy(dim - 1); }
329
330 /// @brief Return the minimum coordinate.
331 /// @note The start coordinate is inclusive.
332 Coord getStart() const { return mMin; }
333 /// @brief Return the maximum coordinate plus one.
334 /// @note This end coordinate is exclusive.
335 Coord getEnd() const { return mMax.offsetBy(1); }
336
337 /// @brief Return a ZYX-order iterator that points to the minimum coordinate.
338 ZYXIterator begin() const { return ZYXIterator{*this}; }
339 /// @brief Return a ZYX-order iterator that points to the minimum coordinate.
340 ZYXIterator beginZYX() const { return ZYXIterator{*this}; }
341 /// @brief Return an XYZ-order iterator that points to the minimum coordinate.
342 XYZIterator beginXYZ() const { return XYZIterator{*this}; }
343
344 /// @brief Return a ZYX-order iterator that points past the maximum coordinate.
345 ZYXIterator end() const { ZYXIterator it{*this}; it.mPos[0] = mMax[0] + 1; return it; }
346 /// @brief Return a ZYX-order iterator that points past the maximum coordinate.
347 ZYXIterator endZYX() const { return end(); }
348 /// @brief Return an XYZ-order iterator that points past the maximum coordinate.
349 XYZIterator endXYZ() const { XYZIterator it{*this}; it.mPos[2] = mMax[2] + 1; return it; }
350
351 bool operator==(const CoordBBox& rhs) const { return mMin == rhs.mMin && mMax == rhs.mMax; }
352 bool operator!=(const CoordBBox& rhs) const { return !(*this == rhs); }
353
354 /// @brief Return @c true if this bounding box is empty (i.e., encloses no coordinates).
355 bool empty() const
356 {
357#if defined(__GNUC__) && !defined(__INTEL_COMPILER)
358 #pragma GCC diagnostic push
359 #pragma GCC diagnostic ignored "-Wstrict-overflow"
360#endif
361 return (mMin[0] > mMax[0] || mMin[1] > mMax[1] || mMin[2] > mMax[2]);
362#if defined(__GNUC__) && !defined(__INTEL_COMPILER)
363 #pragma GCC diagnostic pop
364#endif
365 }
366 /// @brief Return @c true if this bounding box is nonempty
367 /// (i.e., encloses at least one coordinate).
368 operator bool() const { return !this->empty(); }
369 /// @brief Return @c true if this bounding box is nonempty
370 /// (i.e., encloses at least one coordinate).
371 bool hasVolume() const { return !this->empty(); }
372
373 /// @brief Return the floating-point position of the center of this bounding box.
374 Vec3d getCenter() const { return 0.5 * Vec3d((mMin + mMax).asPointer()); }
375
376 /// @brief Return the dimensions of the coordinates spanned by this bounding box.
377 /// @note Since coordinates are inclusive, a bounding box with min = max
378 /// has dimensions of (1, 1, 1).
379 Coord dim() const { return empty() ? Coord(0) : (mMax.offsetBy(1) - mMin); }
380 /// @todo deprecate - use dim instead
381 Coord extents() const { return this->dim(); }
382 /// @brief Return the integer volume of coordinates spanned by this bounding box.
383 /// @note Since coordinates are inclusive, a bounding box with min = max has volume one.
384 Index64 volume() const
385 {
386 const Coord d = this->dim();
387 return Index64(d[0]) * Index64(d[1]) * Index64(d[2]);
388 }
389 /// @brief Return @c true if this bounding box can be subdivided [mainly for use by TBB].
390 bool is_divisible() const { return mMin[0]<mMax[0] && mMin[1]<mMax[1] && mMin[2]<mMax[2]; }
391
392 /// @brief Return the index (0, 1 or 2) of the shortest axis.
393 size_t minExtent() const { return this->dim().minIndex(); }
394
395 /// @brief Return the index (0, 1 or 2) of the longest axis.
396 size_t maxExtent() const { return this->dim().maxIndex(); }
397
398 /// @brief Return @c true if point (x, y, z) is inside this bounding box.
399 bool isInside(const Coord& xyz) const
400 {
401 return !(Coord::lessThan(xyz,mMin) || Coord::lessThan(mMax,xyz));
402 }
403
404 /// @brief Return @c true if the given bounding box is inside this bounding box.
405 bool isInside(const CoordBBox& b) const
406 {
407 return !(Coord::lessThan(b.mMin,mMin) || Coord::lessThan(mMax,b.mMax));
408 }
409
410 /// @brief Return @c true if the given bounding box overlaps with this bounding box.
411 bool hasOverlap(const CoordBBox& b) const
412 {
413 return !(Coord::lessThan(mMax,b.mMin) || Coord::lessThan(b.mMax,mMin));
414 }
415
416 /// @brief Pad this bounding box with the specified padding.
417 void expand(ValueType padding)
418 {
419 mMin.offset(-padding);
420 mMax.offset( padding);
421 }
422
423 /// @brief Return a new instance that is expanded by the specified padding.
424 CoordBBox expandBy(ValueType padding) const
425 {
426 return CoordBBox(mMin.offsetBy(-padding),mMax.offsetBy(padding));
427 }
428
429 /// @brief Expand this bounding box to enclose point (x, y, z).
430 void expand(const Coord& xyz)
431 {
432 mMin.minComponent(xyz);
433 mMax.maxComponent(xyz);
434 }
435
436 /// @brief Union this bounding box with the given bounding box.
437 void expand(const CoordBBox& bbox)
438 {
439 mMin.minComponent(bbox.min());
440 mMax.maxComponent(bbox.max());
441 }
442 /// @brief Intersect this bounding box with the given bounding box.
443 void intersect(const CoordBBox& bbox)
444 {
445 mMin.maxComponent(bbox.min());
446 mMax.minComponent(bbox.max());
447 }
448 /// @brief Union this bounding box with the cubical bounding box
449 /// of the given size and with the given minimum coordinates.
450 void expand(const Coord& min, Coord::ValueType dim)
451 {
452 mMin.minComponent(min);
453 mMax.maxComponent(min.offsetBy(dim-1));
454 }
455 /// @brief Translate this bounding box by
456 /// (<i>t<sub>x</sub></i>, <i>t<sub>y</sub></i>, <i>t<sub>z</sub></i>).
457 void translate(const Coord& t) { mMin += t; mMax += t; }
458
459 /// @brief Move this bounding box to the specified min
460 void moveMin(const Coord& min) { mMax += min - mMin; mMin = min; }
461
462 /// @brief Move this bounding box to the specified max
463 void moveMax(const Coord& max) { mMin += max - mMax; mMax = max; }
464
465 /// @brief Populates an array with the eight corner points of this bounding box.
466 /// @details The ordering of the corner points is lexicographic.
467 /// @warning It is assumed that the pointer can be incremented at
468 /// least seven times, i.e. has storage for eight Coord elements!
469 void getCornerPoints(Coord *p) const
470 {
471 assert(p != nullptr);
472 p->reset(mMin.x(), mMin.y(), mMin.z()); ++p;
473 p->reset(mMin.x(), mMin.y(), mMax.z()); ++p;
474 p->reset(mMin.x(), mMax.y(), mMin.z()); ++p;
475 p->reset(mMin.x(), mMax.y(), mMax.z()); ++p;
476 p->reset(mMax.x(), mMin.y(), mMin.z()); ++p;
477 p->reset(mMax.x(), mMin.y(), mMax.z()); ++p;
478 p->reset(mMax.x(), mMax.y(), mMin.z()); ++p;
479 p->reset(mMax.x(), mMax.y(), mMax.z());
480 }
481
482 //@{
483 /// @brief Bit-wise operations performed on both the min and max members
484 CoordBBox operator>> (size_t n) const { return CoordBBox(mMin>>n, mMax>>n); }
485 CoordBBox operator<< (size_t n) const { return CoordBBox(mMin<<n, mMax<<n); }
486 CoordBBox& operator<<=(size_t n) { mMin <<= n; mMax <<= n; return *this; }
487 CoordBBox& operator>>=(size_t n) { mMin >>= n; mMax >>= n; return *this; }
488 CoordBBox operator& (Coord::Int32 n) const { return CoordBBox(mMin & n, mMax & n); }
489 CoordBBox operator| (Coord::Int32 n) const { return CoordBBox(mMin | n, mMax | n); }
490 CoordBBox& operator&= (Coord::Int32 n) { mMin &= n; mMax &= n; return *this; }
491 CoordBBox& operator|= (Coord::Int32 n) { mMin |= n; mMax |= n; return *this; }
492 //@}
493
494 /// @brief Unserialize this bounding box from the given stream.
495 void read(std::istream& is) { mMin.read(is); mMax.read(is); }
496 /// @brief Serialize this bounding box to the given stream.
497 void write(std::ostream& os) const { mMin.write(os); mMax.write(os); }
498
499private:
500 Coord mMin, mMax;
501}; // class CoordBBox
502
503
504////////////////////////////////////////
505
506
507 inline std::ostream& operator<<(std::ostream& os, const Coord& xyz)
508{
509 os << xyz.asVec3i(); return os;
510}
511
512
513inline Coord
514Abs(const Coord& xyz)
515{
516 return Coord(Abs(xyz[0]), Abs(xyz[1]), Abs(xyz[2]));
517}
518
519
520//@{
521/// Allow a Coord to be added to or subtracted from a Vec3.
522template<typename T>
523inline Vec3<typename promote<T, typename Coord::ValueType>::type>
524 operator+(const Vec3<T>& v0, const Coord& v1)
525{
526 Vec3<typename promote<T, typename Coord::ValueType>::type> result(v0);
527 result[0] += v1[0];
528 result[1] += v1[1];
529 result[2] += v1[2];
530 return result;
531}
532
533template<typename T>
534inline Vec3<typename promote<T, typename Coord::ValueType>::type>
535 operator+(const Coord& v1, const Vec3<T>& v0)
536{
537 Vec3<typename promote<T, typename Coord::ValueType>::type> result(v0);
538 result[0] += v1[0];
539 result[1] += v1[1];
540 result[2] += v1[2];
541 return result;
542}
543//@}
544
545
546//@{
547/// Allow a Coord to be subtracted from a Vec3.
548template <typename T>
549inline Vec3<typename promote<T, Coord::ValueType>::type>
550 operator-(const Vec3<T>& v0, const Coord& v1)
551{
552 Vec3<typename promote<T, Coord::ValueType>::type> result(v0);
553 result[0] -= v1[0];
554 result[1] -= v1[1];
555 result[2] -= v1[2];
556 return result;
557}
558
559template <typename T>
560inline Vec3<typename promote<T, Coord::ValueType>::type>
561 operator-(const Coord& v1, const Vec3<T>& v0)
562{
563 Vec3<typename promote<T, Coord::ValueType>::type> result(v0);
564 result[0] -= v1[0];
565 result[1] -= v1[1];
566 result[2] -= v1[2];
567 return -result;
568}
569//@}
570
571 inline std::ostream&
572 operator<<(std::ostream& os, const CoordBBox& b)
573{
574 os << b.min() << " -> " << b.max();
575 return os;
576}
577
578} // namespace math
579} // namespace OPENVDB_VERSION_NAME
580} // namespace openvdb
581
582////////////////////////////////////////
583
584// template specialization of std::hash with Coord, which
585// allows for Coord to be used as the key in std::unordered_map
586 namespace std {// injected in namespace std
587
588template<>
589 struct hash<openvdb::math::Coord>
590{
591 using Coord = openvdb::math::Coord;
592 using argument_type = Coord;
593 using result_type = std::size_t;
594 std::size_t operator()(const Coord& ijk) const noexcept { return ijk.Coord::hash<>(); }
595};// std::hash<openvdb::math::Coord>
596
597}// namespace std
598
599#endif // OPENVDB_MATH_COORD_HAS_BEEN_INCLUDED
Math.h
General-purpose arithmetic and comparison routines, most of which accept arbitrary value types (or at...
Platform.h
Vec3.h
openvdb::v9_0::math::CoordBBox::Iterator
Iterator over the Coord domain covered by a CoordBBox.
Definition: Coord.h:258
openvdb::v9_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:276
openvdb::v9_0::math::CoordBBox::Iterator::operator*
const Coord & operator*() const
Return a const reference to the coordinate currently pointed to.
Definition: Coord.h:269
openvdb::v9_0::math::CoordBBox::Iterator::operator++
Iterator & operator++()
Increment the iterator to point to the next coordinate.
Definition: Coord.h:265
openvdb::v9_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:271
openvdb::v9_0::math::CoordBBox::Iterator::Iterator
Iterator(const CoordBBox &b)
C-tor from a bounding box.
Definition: Coord.h:261
openvdb::v9_0::math::CoordBBox
Axis-aligned bounding box of signed integer coordinates.
Definition: Coord.h:248
openvdb::v9_0::math::CoordBBox::operator!=
bool operator!=(const CoordBBox &rhs) const
Definition: Coord.h:352
openvdb::v9_0::math::CoordBBox::CoordBBox
CoordBBox()
The default constructor produces an empty bounding box.
Definition: Coord.h:293
openvdb::v9_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:405
openvdb::v9_0::math::CoordBBox::beginZYX
ZYXIterator beginZYX() const
Return a ZYX-order iterator that points to the minimum coordinate.
Definition: Coord.h:340
openvdb::v9_0::math::CoordBBox::minExtent
size_t minExtent() const
Return the index (0, 1 or 2) of the shortest axis.
Definition: Coord.h:393
openvdb::v9_0::math::CoordBBox::moveMax
void moveMax(const Coord &max)
Move this bounding box to the specified max.
Definition: Coord.h:463
openvdb::v9_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:390
openvdb::v9_0::math::CoordBBox::ValueType
Coord::ValueType ValueType
Definition: Coord.h:251
openvdb::v9_0::math::CoordBBox::extents
Coord extents() const
Definition: Coord.h:381
openvdb::v9_0::math::CoordBBox::write
void write(std::ostream &os) const
Serialize this bounding box to the given stream.
Definition: Coord.h:497
openvdb::v9_0::math::CoordBBox::translate
void translate(const Coord &t)
Translate this bounding box by (tx, ty, tz).
Definition: Coord.h:457
openvdb::v9_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:371
openvdb::v9_0::math::CoordBBox::getCenter
Vec3d getCenter() const
Return the floating-point position of the center of this bounding box.
Definition: Coord.h:374
openvdb::v9_0::math::CoordBBox::end
ZYXIterator end() const
Return a ZYX-order iterator that points past the maximum coordinate.
Definition: Coord.h:345
openvdb::v9_0::math::CoordBBox::beginXYZ
XYZIterator beginXYZ() const
Return an XYZ-order iterator that points to the minimum coordinate.
Definition: Coord.h:342
openvdb::v9_0::math::CoordBBox::expand
void expand(ValueType padding)
Pad this bounding box with the specified padding.
Definition: Coord.h:417
openvdb::v9_0::math::CoordBBox::expand
void expand(const Coord &xyz)
Expand this bounding box to enclose point (x, y, z).
Definition: Coord.h:430
openvdb::v9_0::math::CoordBBox::CoordBBox
CoordBBox(CoordBBox &other, const tbb::split &)
Splitting constructor for use in TBB ranges.
Definition: Coord.h:304
openvdb::v9_0::math::CoordBBox::operator>>=
CoordBBox & operator>>=(size_t n)
Definition: Coord.h:487
openvdb::v9_0::math::CoordBBox::endZYX
ZYXIterator endZYX() const
Return a ZYX-order iterator that points past the maximum coordinate.
Definition: Coord.h:347
openvdb::v9_0::math::CoordBBox::empty
bool empty() const
Return true if this bounding box is empty (i.e., encloses no coordinates).
Definition: Coord.h:355
openvdb::v9_0::math::CoordBBox::max
Coord & max()
Definition: Coord.h:324
openvdb::v9_0::math::CoordBBox::moveMin
void moveMin(const Coord &min)
Move this bounding box to the specified min.
Definition: Coord.h:460
openvdb::v9_0::math::CoordBBox::min
const Coord & min() const
Definition: Coord.h:320
openvdb::v9_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:411
openvdb::v9_0::math::CoordBBox::max
const Coord & max() const
Definition: Coord.h:321
openvdb::v9_0::math::CoordBBox::maxExtent
size_t maxExtent() const
Return the index (0, 1 or 2) of the longest axis.
Definition: Coord.h:396
openvdb::v9_0::math::CoordBBox::endXYZ
XYZIterator endXYZ() const
Return an XYZ-order iterator that points past the maximum coordinate.
Definition: Coord.h:349
openvdb::v9_0::math::CoordBBox::operator<<=
CoordBBox & operator<<=(size_t n)
Definition: Coord.h:486
openvdb::v9_0::math::CoordBBox::resetToCube
void resetToCube(const Coord &min, ValueType dim)
Definition: Coord.h:328
openvdb::v9_0::math::CoordBBox::operator==
bool operator==(const CoordBBox &rhs) const
Definition: Coord.h:351
openvdb::v9_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:450
openvdb::v9_0::math::CoordBBox::expandBy
CoordBBox expandBy(ValueType padding) const
Return a new instance that is expanded by the specified padding.
Definition: Coord.h:424
openvdb::v9_0::math::CoordBBox::volume
Index64 volume() const
Return the integer volume of coordinates spanned by this bounding box.
Definition: Coord.h:384
openvdb::v9_0::math::CoordBBox::inf
static CoordBBox inf()
Return an "infinite" bounding box, as defined by the Coord value range.
Definition: Coord.h:318
openvdb::v9_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:295
openvdb::v9_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:297
openvdb::v9_0::math::CoordBBox::min
Coord & min()
Definition: Coord.h:323
openvdb::v9_0::math::CoordBBox::expand
void expand(const CoordBBox &bbox)
Union this bounding box with the given bounding box.
Definition: Coord.h:437
openvdb::v9_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:399
openvdb::v9_0::math::CoordBBox::dim
Coord dim() const
Return the dimensions of the coordinates spanned by this bounding box.
Definition: Coord.h:379
openvdb::v9_0::math::CoordBBox::getStart
Coord getStart() const
Return the minimum coordinate.
Definition: Coord.h:332
openvdb::v9_0::math::CoordBBox::getEnd
Coord getEnd() const
Return the maximum coordinate plus one.
Definition: Coord.h:335
openvdb::v9_0::math::CoordBBox::Index64
uint64_t Index64
Definition: Coord.h:250
openvdb::v9_0::math::CoordBBox::intersect
void intersect(const CoordBBox &bbox)
Intersect this bounding box with the given bounding box.
Definition: Coord.h:443
openvdb::v9_0::math::CoordBBox::reset
void reset()
Definition: Coord.h:326
openvdb::v9_0::math::CoordBBox::getCornerPoints
void getCornerPoints(Coord *p) const
Populates an array with the eight corner points of this bounding box.
Definition: Coord.h:469
openvdb::v9_0::math::CoordBBox::createCube
static CoordBBox createCube(const Coord &min, ValueType dim)
Definition: Coord.h:312
openvdb::v9_0::math::CoordBBox::begin
ZYXIterator begin() const
Return a ZYX-order iterator that points to the minimum coordinate.
Definition: Coord.h:338
openvdb::v9_0::math::CoordBBox::reset
void reset(const Coord &min, const Coord &max)
Definition: Coord.h:327
openvdb::v9_0::math::CoordBBox::read
void read(std::istream &is)
Unserialize this bounding box from the given stream.
Definition: Coord.h:495
openvdb::v9_0::math::Coord
Signed (x, y, z) 32-bit integer coordinates.
Definition: Coord.h:25
openvdb::v9_0::math::Coord::ValueType
Int32 ValueType
Definition: Coord.h:32
openvdb::v9_0::math::Coord::operator-
Coord operator-(const Coord &rhs) const
Definition: Coord.h:115
openvdb::v9_0::math::Coord::offset
Coord & offset(Int32 dx, Int32 dy, Int32 dz)
Definition: Coord.h:83
openvdb::v9_0::math::Coord::z
Int32 & z()
Definition: Coord.h:136
openvdb::v9_0::math::Coord::asVec3d
Vec3d asVec3d() const
Definition: Coord.h:143
openvdb::v9_0::math::Coord::operator-
Coord operator-() const
Definition: Coord.h:119
openvdb::v9_0::math::Coord::y
Int32 y() const
Definition: Coord.h:131
openvdb::v9_0::math::Coord::hash
size_t hash() const
Return a hash value for this coordinate.
Definition: Coord.h:230
openvdb::v9_0::math::Coord::asVec3s
Vec3s asVec3s() const
Definition: Coord.h:144
openvdb::v9_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::v9_0::math::Coord::operator[]
Int32 operator[](size_t i) const
Definition: Coord.h:133
openvdb::v9_0::math::Coord::asVec3I
Vec3I asVec3I() const
Definition: Coord.h:146
openvdb::v9_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::v9_0::math::Coord::operator-=
Coord & operator-=(const Coord &rhs)
Definition: Coord.h:104
openvdb::v9_0::math::Coord::Limits
std::numeric_limits< ValueType > Limits
Definition: Coord.h:33
openvdb::v9_0::math::Coord::asPointer
Int32 * asPointer()
Definition: Coord.h:142
openvdb::v9_0::math::Coord::Coord
Coord(const Vec3I &v)
Definition: Coord.h:39
openvdb::v9_0::math::Coord::asXYZ
void asXYZ(Int32 &x, Int32 &y, Int32 &z) const
Definition: Coord.h:147
openvdb::v9_0::math::Coord::operator+
Coord operator+(const Coord &rhs) const
Definition: Coord.h:111
openvdb::v9_0::math::Coord::offsetBy
Coord offsetBy(Int32 dx, Int32 dy, Int32 dz) const
Definition: Coord.h:91
openvdb::v9_0::math::Coord::write
void write(std::ostream &os) const
Definition: Coord.h:220
openvdb::v9_0::math::Coord::maxIndex
size_t maxIndex() const
Return the index (0, 1 or 2) with the largest value.
Definition: Coord.h:217
openvdb::v9_0::math::Coord::offsetBy
Coord offsetBy(Int32 n) const
Definition: Coord.h:95
openvdb::v9_0::math::Coord::operator<
bool operator<(const Coord &rhs) const
Lexicographic less than.
Definition: Coord.h:156
openvdb::v9_0::math::Coord::minComponent
void minComponent(const Coord &other)
Perform a component-wise minimum with the other Coord.
Definition: Coord.h:175
openvdb::v9_0::math::Coord::data
Int32 * data()
Definition: Coord.h:140
openvdb::v9_0::math::Coord::operator+=
Coord & operator+=(const Coord &rhs)
Definition: Coord.h:97
openvdb::v9_0::math::Coord::operator>=
bool operator>=(const Coord &rhs) const
Lexicographic greater than or equal to.
Definition: Coord.h:172
openvdb::v9_0::math::Coord::x
Int32 & x()
Definition: Coord.h:134
openvdb::v9_0::math::Coord::operator<<=
Coord & operator<<=(size_t n)
Definition: Coord.h:123
openvdb::v9_0::math::Coord::Coord
Coord()
Definition: Coord.h:35
openvdb::v9_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::v9_0::math::Coord::maxComponent
void maxComponent(const Coord &other)
Perform a component-wise maximum with the other Coord.
Definition: Coord.h:183
openvdb::v9_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::v9_0::math::Coord::Coord
Coord(const Int32 *v)
Definition: Coord.h:40
openvdb::v9_0::math::Coord::Index32
uint32_t Index32
Definition: Coord.h:28
openvdb::v9_0::math::Coord::asPointer
const Int32 * asPointer() const
Definition: Coord.h:141
openvdb::v9_0::math::Coord::x
Int32 x() const
Definition: Coord.h:130
openvdb::v9_0::math::Coord::asVec3i
Vec3i asVec3i() const
Definition: Coord.h:145
openvdb::v9_0::math::Coord::minIndex
size_t minIndex() const
Return the index (0, 1 or 2) with the smallest value.
Definition: Coord.h:214
openvdb::v9_0::math::Coord::operator!=
bool operator!=(const Coord &rhs) const
Definition: Coord.h:153
openvdb::v9_0::math::Coord::min
static Coord min()
Return the smallest possible coordinate.
Definition: Coord.h:43
openvdb::v9_0::math::Coord::reset
Coord & reset(Int32 xyz)
Reset all three coordinates with the same specified argument.
Definition: Coord.h:77
openvdb::v9_0::math::Coord::Coord
Coord(Int32 xyz)
Definition: Coord.h:36
openvdb::v9_0::math::Coord::setZ
Coord & setZ(Int32 z)
Definition: Coord.h:81
openvdb::v9_0::math::Coord::Int32
int32_t Int32
Definition: Coord.h:27
openvdb::v9_0::math::Coord::setY
Coord & setY(Int32 y)
Definition: Coord.h:80
openvdb::v9_0::math::Coord::operator==
bool operator==(const Coord &rhs) const
Definition: Coord.h:149
openvdb::v9_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::v9_0::math::Coord::operator<=
bool operator<=(const Coord &rhs) const
Lexicographic less than or equal to.
Definition: Coord.h:163
openvdb::v9_0::math::Coord::max
static Coord max()
Return the largest possible coordinate.
Definition: Coord.h:46
openvdb::v9_0::math::Coord::operator[]
Int32 & operator[](size_t i)
Definition: Coord.h:137
openvdb::v9_0::math::Coord::Coord
Coord(Int32 x, Int32 y, Int32 z)
Definition: Coord.h:37
openvdb::v9_0::math::Coord::Coord
Coord(const Vec3i &v)
Definition: Coord.h:38
openvdb::v9_0::math::Coord::lessThan
static bool lessThan(const Coord &a, const Coord &b)
Definition: Coord.h:208
openvdb::v9_0::math::Coord::z
Int32 z() const
Definition: Coord.h:132
openvdb::v9_0::math::Coord::setX
Coord & setX(Int32 x)
Definition: Coord.h:79
openvdb::v9_0::math::Coord::offset
Coord & offset(Int32 n)
Definition: Coord.h:90
openvdb::v9_0::math::Coord::data
const Int32 * data() const
Definition: Coord.h:139
openvdb::v9_0::math::Coord::operator>
bool operator>(const Coord &rhs) const
Lexicographic greater than.
Definition: Coord.h:170
openvdb::v9_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::v9_0::math::Coord::operator>>=
Coord & operator>>=(size_t n)
Definition: Coord.h:124
openvdb::v9_0::math::Coord::y
Int32 & y()
Definition: Coord.h:135
openvdb::v9_0::math::Coord::read
void read(std::istream &is)
Definition: Coord.h:219
openvdb::v9_0::math::Mat3::operator+
Mat3< typename promote< T0, T1 >::type > operator+(const Mat3< T0 > &m0, const Mat3< T1 > &m1)
Add corresponding elements of m0 and m1 and return the result.
Definition: Mat3.h:591
openvdb::v9_0::math::Mat3::operator-
Mat3< typename promote< T0, T1 >::type > operator-(const Mat3< T0 > &m0, const Mat3< T1 > &m1)
Subtract corresponding elements of m0 and m1 and return the result.
Definition: Mat3.h:601
openvdb::v9_0::math::Vec3
Definition: Vec3.h:24
hash
__hostdev__ uint32_t hash(uint32_t x)
Definition: common.h:13
nanovdb::CoordBBox
BBox< Coord > CoordBBox
Definition: NanoVDB.h:1658
openvdb::v9_0::math::internal::operator>>
OPENVDB_API std::istream & operator>>(std::istream &is, half &h)
openvdb::v9_0::math::Ceil
int Ceil(float x)
Return the ceiling of x.
Definition: Math.h:859
openvdb::v9_0::math::Round
float Round(float x)
Return x rounded to the nearest integer.
Definition: Math.h:822
openvdb::v9_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:956
openvdb::v9_0::math::Abs
Coord Abs(const Coord &xyz)
Definition: Coord.h:514
openvdb::v9_0::math::Vec3d
Vec3< double > Vec3d
Definition: Vec3.h:668
openvdb::v9_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:938
openvdb::v9_0::math::Vec3i
Vec3< int32_t > Vec3i
Definition: Vec3.h:665
openvdb::v9_0::math::operator<<
std::ostream & operator<<(std::ostream &os, const CoordBBox &b)
Definition: Coord.h:572
openvdb::v9_0::math::Vec3s
Vec3< float > Vec3s
Definition: Vec3.h:667
openvdb::v9_0::math::Floor
int Floor(float x)
Return the floor of x.
Definition: Math.h:851
openvdb::v9_0::tools::composite::max
const std::enable_if<!VecTraits< T >::IsVec, T >::type & max(const T &a, const T &b)
Definition: Composite.h:107
openvdb::v9_0::tools::composite::min
const std::enable_if<!VecTraits< T >::IsVec, T >::type & min(const T &a, const T &b)
Definition: Composite.h:103
openvdb::v9_0::Index32
uint32_t Index32
Definition: Types.h:52
openvdb::v9_0::Vec3I
math::Vec3< Index32 > Vec3I
Definition: Types.h:73
openvdb::v9_0::Int32
int32_t Int32
Definition: Types.h:56
openvdb::v9_0::Index64
uint64_t Index64
Definition: Types.h:53
openvdb
Definition: Exceptions.h:13
std
Definition: Coord.h:586
std::hash< openvdb::math::Coord >::result_type
std::size_t result_type
Definition: Coord.h:593
std::hash< openvdb::math::Coord >::operator()
std::size_t operator()(const Coord &ijk) const noexcept
Definition: Coord.h:594
std::hash< openvdb::math::Coord >::Coord
openvdb::math::Coord Coord
Definition: Coord.h:591
std::hash< openvdb::math::Coord >::argument_type
Coord argument_type
Definition: Coord.h:592
OPENVDB_VERSION_NAME
#define OPENVDB_VERSION_NAME
The version namespace name for this library version.
Definition: version.h.in:116
OPENVDB_USE_VERSION_NAMESPACE
#define OPENVDB_USE_VERSION_NAMESPACE
Definition: version.h.in:202