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|---|---|---|---|
| 1 | // Copyright Contributors to the OpenVDB Project | ||
| 2 | // SPDX-License-Identifier: MPL-2.0 | ||
| 3 | |||
| 4 | #ifndef OPENVDB_MATH_VEC3_HAS_BEEN_INCLUDED | ||
| 5 | #define OPENVDB_MATH_VEC3_HAS_BEEN_INCLUDED | ||
| 6 | |||
| 7 | #include <openvdb/Exceptions.h> | ||
| 8 | #include "Math.h" | ||
| 9 | #include "Tuple.h" | ||
| 10 | #include <algorithm> | ||
| 11 | #include <cmath> | ||
| 12 | #include <type_traits> | ||
| 13 | |||
| 14 | |||
| 15 | namespace openvdb { | ||
| 16 | OPENVDB_USE_VERSION_NAMESPACE | ||
| 17 | namespace OPENVDB_VERSION_NAME { | ||
| 18 | namespace math { | ||
| 19 | |||
| 20 | template<typename T> class Mat3; | ||
| 21 | |||
| 22 | template<typename T> | ||
| 23 | class Vec3: public Tuple<3, T> | ||
| 24 | { | ||
| 25 | public: | ||
| 26 | using value_type = T; | ||
| 27 | using ValueType = T; | ||
| 28 | |||
| 29 | /// Trivial constructor, the vector is NOT initialized | ||
| 30 | #if OPENVDB_ABI_VERSION_NUMBER >= 8 | ||
| 31 | /// @note destructor, copy constructor, assignment operator and | ||
| 32 | /// move constructor are left to be defined by the compiler (default) | ||
| 33 | Vec3() = default; | ||
| 34 | #else | ||
| 35 | Vec3() {} | ||
| 36 | #endif | ||
| 37 | |||
| 38 | /// @brief Construct a vector all of whose components have the given value. | ||
| 39 |
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|
35413998 | explicit Vec3(T val) { this->mm[0] = this->mm[1] = this->mm[2] = val; } |
| 40 | |||
| 41 | /// Constructor with three arguments, e.g. Vec3d v(1,2,3); | ||
| 42 |
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|
16454174282 | Vec3(T x, T y, T z) |
| 43 | { | ||
| 44 | 16454174337 | this->mm[0] = x; | |
| 45 | 16454174337 | this->mm[1] = y; | |
| 46 |
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|
4497881263 | this->mm[2] = z; |
| 47 | 2441555 | } | |
| 48 | |||
| 49 | /// Constructor with array argument, e.g. double a[3]; Vec3d v(a); | ||
| 50 | template <typename Source> | ||
| 51 | 454 | Vec3(Source *a) | |
| 52 | { | ||
| 53 | 11365008 | this->mm[0] = static_cast<T>(a[0]); | |
| 54 | 11365008 | this->mm[1] = static_cast<T>(a[1]); | |
| 55 |
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|
11364991 | this->mm[2] = static_cast<T>(a[2]); |
| 56 | } | ||
| 57 | |||
| 58 | /// @brief Construct a Vec3 from a 3-Tuple with a possibly different value type. | ||
| 59 | /// @details Type conversion warnings are suppressed. | ||
| 60 | template<typename Source> | ||
| 61 | explicit Vec3(const Tuple<3, Source> &v) | ||
| 62 | { | ||
| 63 | this->mm[0] = static_cast<T>(v[0]); | ||
| 64 | this->mm[1] = static_cast<T>(v[1]); | ||
| 65 | this->mm[2] = static_cast<T>(v[2]); | ||
| 66 | } | ||
| 67 | |||
| 68 | /// @brief Construct a vector all of whose components have the given value, | ||
| 69 | /// which may be of an arithmetic type different from this vector's value type. | ||
| 70 | /// @details Type conversion warnings are suppressed. | ||
| 71 | template<typename Other> | ||
| 72 | 20424450 | explicit Vec3(Other val, | |
| 73 | typename std::enable_if<std::is_arithmetic<Other>::value, Conversion>::type = Conversion{}) | ||
| 74 | { | ||
| 75 |
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|
9976465 | this->mm[0] = this->mm[1] = this->mm[2] = static_cast<T>(val); |
| 76 | } | ||
| 77 | |||
| 78 | /// @brief Construct a Vec3 from another Vec3 with a possibly different value type. | ||
| 79 | /// @details Type conversion warnings are suppressed. | ||
| 80 | template<typename Other> | ||
| 81 |
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|
75986882 | Vec3(const Vec3<Other>& v) |
| 82 | { | ||
| 83 |
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|
803229418 | this->mm[0] = static_cast<T>(v[0]); |
| 84 | 803229434 | this->mm[1] = static_cast<T>(v[1]); | |
| 85 |
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|
36334599 | this->mm[2] = static_cast<T>(v[2]); |
| 86 | 2289852 | } | |
| 87 | |||
| 88 | /// Reference to the component, e.g. v.x() = 4.5f; | ||
| 89 | T& x() { return this->mm[0]; } | ||
| 90 | T& y() { return this->mm[1]; } | ||
| 91 | T& z() { return this->mm[2]; } | ||
| 92 | |||
| 93 | /// Get the component, e.g. float f = v.y(); | ||
| 94 |
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2498986257 | T x() const { return this->mm[0]; } |
| 95 |
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2579393817 | T y() const { return this->mm[1]; } |
| 96 |
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2744996482 | T z() const { return this->mm[2]; } |
| 97 | |||
| 98 | 705 | T* asPointer() { return this->mm; } | |
| 99 | const T* asPointer() const { return this->mm; } | ||
| 100 | |||
| 101 | /// Alternative indexed reference to the elements | ||
| 102 |
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213556683 | T& operator()(int i) { return this->mm[i]; } |
| 103 | |||
| 104 | /// Alternative indexed constant reference to the elements, | ||
| 105 |
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9995446 | T operator()(int i) const { return this->mm[i]; } |
| 106 | |||
| 107 | /// "this" vector gets initialized to [x, y, z], | ||
| 108 | /// calling v.init(); has same effect as calling v = Vec3::zero(); | ||
| 109 | const Vec3<T>& init(T x=0, T y=0, T z=0) | ||
| 110 | { | ||
| 111 | this->mm[0] = x; this->mm[1] = y; this->mm[2] = z; | ||
| 112 | return *this; | ||
| 113 | } | ||
| 114 | |||
| 115 | |||
| 116 | /// Set "this" vector to zero | ||
| 117 | const Vec3<T>& setZero() | ||
| 118 | { | ||
| 119 | 14078658 | this->mm[0] = 0; this->mm[1] = 0; this->mm[2] = 0; | |
| 120 | 2213 | return *this; | |
| 121 | } | ||
| 122 | |||
| 123 | /// @brief Assignment operator | ||
| 124 | /// @details Type conversion warnings are not suppressed. | ||
| 125 | template<typename Source> | ||
| 126 | 786944 | const Vec3<T>& operator=(const Vec3<Source> &v) | |
| 127 | { | ||
| 128 | // note: don't static_cast because that suppresses warnings | ||
| 129 | 786964 | this->mm[0] = v[0]; | |
| 130 | 786964 | this->mm[1] = v[1]; | |
| 131 | 786964 | this->mm[2] = v[2]; | |
| 132 | |||
| 133 | 786962 | return *this; | |
| 134 | } | ||
| 135 | |||
| 136 | /// Test if "this" vector is equivalent to vector v with tolerance of eps | ||
| 137 |
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61580152 | bool eq(const Vec3<T> &v, T eps = static_cast<T>(1.0e-7)) const |
| 138 | { | ||
| 139 |
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18748975 | return isRelOrApproxEqual(this->mm[0], v.mm[0], eps, eps) && |
| 140 |
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39220687 | isRelOrApproxEqual(this->mm[1], v.mm[1], eps, eps) && |
| 141 | 61580152 | isRelOrApproxEqual(this->mm[2], v.mm[2], eps, eps); | |
| 142 | } | ||
| 143 | |||
| 144 | |||
| 145 | /// Negation operator, for e.g. v1 = -v2; | ||
| 146 |
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1076601 | Vec3<T> operator-() const { return Vec3<T>(-this->mm[0], -this->mm[1], -this->mm[2]); } |
| 147 | |||
| 148 | /// this = v1 + v2 | ||
| 149 | /// "this", v1 and v2 need not be distinct objects, e.g. v.add(v1,v); | ||
| 150 | template <typename T0, typename T1> | ||
| 151 | const Vec3<T>& add(const Vec3<T0> &v1, const Vec3<T1> &v2) | ||
| 152 | { | ||
| 153 | this->mm[0] = v1[0] + v2[0]; | ||
| 154 | this->mm[1] = v1[1] + v2[1]; | ||
| 155 | this->mm[2] = v1[2] + v2[2]; | ||
| 156 | |||
| 157 | return *this; | ||
| 158 | } | ||
| 159 | |||
| 160 | /// this = v1 - v2 | ||
| 161 | /// "this", v1 and v2 need not be distinct objects, e.g. v.sub(v1,v); | ||
| 162 | template <typename T0, typename T1> | ||
| 163 | const Vec3<T>& sub(const Vec3<T0> &v1, const Vec3<T1> &v2) | ||
| 164 | { | ||
| 165 | this->mm[0] = v1[0] - v2[0]; | ||
| 166 | this->mm[1] = v1[1] - v2[1]; | ||
| 167 | this->mm[2] = v1[2] - v2[2]; | ||
| 168 | |||
| 169 | return *this; | ||
| 170 | } | ||
| 171 | |||
| 172 | /// this = scalar*v, v need not be a distinct object from "this", | ||
| 173 | /// e.g. v.scale(1.5,v1); | ||
| 174 | template <typename T0, typename T1> | ||
| 175 | const Vec3<T>& scale(T0 scale, const Vec3<T1> &v) | ||
| 176 | { | ||
| 177 | this->mm[0] = scale * v[0]; | ||
| 178 | this->mm[1] = scale * v[1]; | ||
| 179 | this->mm[2] = scale * v[2]; | ||
| 180 | |||
| 181 | return *this; | ||
| 182 | } | ||
| 183 | |||
| 184 | template <typename T0, typename T1> | ||
| 185 | const Vec3<T> &div(T0 scale, const Vec3<T1> &v) | ||
| 186 | { | ||
| 187 | this->mm[0] = v[0] / scale; | ||
| 188 | this->mm[1] = v[1] / scale; | ||
| 189 | this->mm[2] = v[2] / scale; | ||
| 190 | |||
| 191 | return *this; | ||
| 192 | } | ||
| 193 | |||
| 194 | /// Dot product | ||
| 195 | T dot(const Vec3<T> &v) const | ||
| 196 | { | ||
| 197 | return | ||
| 198 | 448399002 | this->mm[0]*v.mm[0] + | |
| 199 | 448399002 | this->mm[1]*v.mm[1] + | |
| 200 |
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410976852 | this->mm[2]*v.mm[2]; |
| 201 | } | ||
| 202 | |||
| 203 | /// Length of the vector | ||
| 204 | ✗ | T length() const | |
| 205 | { | ||
| 206 | 84475080 | return static_cast<T>(sqrt(double( | |
| 207 |
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140786237 | this->mm[0]*this->mm[0] + |
| 208 | 140786251 | this->mm[1]*this->mm[1] + | |
| 209 |
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59127067 | this->mm[2]*this->mm[2]))); |
| 210 | } | ||
| 211 | |||
| 212 | |||
| 213 | /// Squared length of the vector, much faster than length() as it | ||
| 214 | /// does not involve square root | ||
| 215 | T lengthSqr() const | ||
| 216 | { | ||
| 217 | return | ||
| 218 | 83663202 | this->mm[0]*this->mm[0] + | |
| 219 | 83663202 | this->mm[1]*this->mm[1] + | |
| 220 |
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71494432 | this->mm[2]*this->mm[2]; |
| 221 | } | ||
| 222 | |||
| 223 | /// Return the cross product of "this" vector and v; | ||
| 224 | Vec3<T> cross(const Vec3<T> &v) const | ||
| 225 | { | ||
| 226 | 68 | return Vec3<T>(this->mm[1]*v.mm[2] - this->mm[2]*v.mm[1], | |
| 227 | 1520945 | this->mm[2]*v.mm[0] - this->mm[0]*v.mm[2], | |
| 228 |
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1520947 | this->mm[0]*v.mm[1] - this->mm[1]*v.mm[0]); |
| 229 | } | ||
| 230 | |||
| 231 | |||
| 232 | /// this = v1 cross v2, v1 and v2 must be distinct objects than "this" | ||
| 233 | const Vec3<T>& cross(const Vec3<T> &v1, const Vec3<T> &v2) | ||
| 234 | { | ||
| 235 | // assert(this!=&v1); | ||
| 236 | // assert(this!=&v2); | ||
| 237 | 14 | this->mm[0] = v1.mm[1]*v2.mm[2] - v1.mm[2]*v2.mm[1]; | |
| 238 | 14 | this->mm[1] = v1.mm[2]*v2.mm[0] - v1.mm[0]*v2.mm[2]; | |
| 239 |
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14 | this->mm[2] = v1.mm[0]*v2.mm[1] - v1.mm[1]*v2.mm[0]; |
| 240 | return *this; | ||
| 241 | } | ||
| 242 | |||
| 243 | /// Multiply each element of this vector by @a scalar. | ||
| 244 | template <typename S> | ||
| 245 | const Vec3<T> &operator*=(S scalar) | ||
| 246 | { | ||
| 247 | OPENVDB_NO_TYPE_CONVERSION_WARNING_BEGIN | ||
| 248 | 896928988 | const auto value0 = this->mm[0] * scalar; | |
| 249 | 896928988 | const auto value1 = this->mm[1] * scalar; | |
| 250 |
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12336619 | const auto value2 = this->mm[2] * scalar; |
| 251 | OPENVDB_NO_TYPE_CONVERSION_WARNING_END | ||
| 252 | 61669200 | this->mm[0] = static_cast<T>(value0); | |
| 253 | 61669200 | this->mm[1] = static_cast<T>(value1); | |
| 254 |
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61669169 | this->mm[2] = static_cast<T>(value2); |
| 255 | 90657 | return *this; | |
| 256 | } | ||
| 257 | |||
| 258 | /// Multiply each element of this vector by the corresponding element of the given vector. | ||
| 259 | template <typename S> | ||
| 260 | const Vec3<T> &operator*=(const Vec3<S> &v1) | ||
| 261 | { | ||
| 262 | ✗ | this->mm[0] *= v1[0]; | |
| 263 | ✗ | this->mm[1] *= v1[1]; | |
| 264 | ✗ | this->mm[2] *= v1[2]; | |
| 265 | return *this; | ||
| 266 | } | ||
| 267 | |||
| 268 | /// Divide each element of this vector by @a scalar. | ||
| 269 | template <typename S> | ||
| 270 | const Vec3<T> &operator/=(S scalar) | ||
| 271 | { | ||
| 272 | 16483404 | this->mm[0] /= scalar; | |
| 273 | 16483404 | this->mm[1] /= scalar; | |
| 274 |
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1546824 | this->mm[2] /= scalar; |
| 275 | return *this; | ||
| 276 | } | ||
| 277 | |||
| 278 | /// Divide each element of this vector by the corresponding element of the given vector. | ||
| 279 | template <typename S> | ||
| 280 | const Vec3<T> &operator/=(const Vec3<S> &v1) | ||
| 281 | { | ||
| 282 | 12 | this->mm[0] /= v1[0]; | |
| 283 | 12 | this->mm[1] /= v1[1]; | |
| 284 | 12 | this->mm[2] /= v1[2]; | |
| 285 | 2 | return *this; | |
| 286 | } | ||
| 287 | |||
| 288 | /// Add @a scalar to each element of this vector. | ||
| 289 | template <typename S> | ||
| 290 | const Vec3<T> &operator+=(S scalar) | ||
| 291 | { | ||
| 292 | OPENVDB_NO_TYPE_CONVERSION_WARNING_BEGIN | ||
| 293 | 543813 | const auto value0 = this->mm[0] + scalar; | |
| 294 | 10284838 | const auto value1 = this->mm[1] + scalar; | |
| 295 |
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10274838 | const auto value2 = this->mm[2] + scalar; |
| 296 | OPENVDB_NO_TYPE_CONVERSION_WARNING_END | ||
| 297 | 10281776 | this->mm[0] = static_cast<T>(value0); | |
| 298 | 10281776 | this->mm[1] = static_cast<T>(value1); | |
| 299 | 16462 | this->mm[2] = static_cast<T>(value2); | |
| 300 | 16 | return *this; | |
| 301 | } | ||
| 302 | |||
| 303 | /// Add each element of the given vector to the corresponding element of this vector. | ||
| 304 | template <typename S> | ||
| 305 | const Vec3<T> &operator+=(const Vec3<S> &v1) | ||
| 306 | { | ||
| 307 | 1356058485 | this->mm[0] += v1[0]; | |
| 308 | 1356058485 | this->mm[1] += v1[1]; | |
| 309 |
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82638239 | this->mm[2] += v1[2]; |
| 310 | 257105386 | return *this; | |
| 311 | } | ||
| 312 | |||
| 313 | /// Subtract @a scalar from each element of this vector. | ||
| 314 | template <typename S> | ||
| 315 | const Vec3<T> &operator-=(S scalar) | ||
| 316 | { | ||
| 317 | 9758225 | this->mm[0] -= scalar; | |
| 318 | 9758225 | this->mm[1] -= scalar; | |
| 319 | 9758225 | this->mm[2] -= scalar; | |
| 320 | return *this; | ||
| 321 | } | ||
| 322 | |||
| 323 | /// Subtract each element of the given vector from the corresponding element of this vector. | ||
| 324 | template <typename S> | ||
| 325 | const Vec3<T> &operator-=(const Vec3<S> &v1) | ||
| 326 | { | ||
| 327 |
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1196877293 | this->mm[0] -= v1[0]; |
| 328 |
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1197057456 | this->mm[1] -= v1[1]; |
| 329 |
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344496570 | this->mm[2] -= v1[2]; |
| 330 | return *this; | ||
| 331 | } | ||
| 332 | |||
| 333 | /// Return a reference to itself after the exponent has been | ||
| 334 | /// applied to all the vector components. | ||
| 335 | ✗ | inline const Vec3<T>& exp() | |
| 336 | { | ||
| 337 | ✗ | this->mm[0] = std::exp(this->mm[0]); | |
| 338 | ✗ | this->mm[1] = std::exp(this->mm[1]); | |
| 339 | ✗ | this->mm[2] = std::exp(this->mm[2]); | |
| 340 | ✗ | return *this; | |
| 341 | } | ||
| 342 | |||
| 343 | /// Return a reference to itself after log has been | ||
| 344 | /// applied to all the vector components. | ||
| 345 | inline const Vec3<T>& log() | ||
| 346 | { | ||
| 347 | this->mm[0] = std::log(this->mm[0]); | ||
| 348 | this->mm[1] = std::log(this->mm[1]); | ||
| 349 | this->mm[2] = std::log(this->mm[2]); | ||
| 350 | return *this; | ||
| 351 | } | ||
| 352 | |||
| 353 | /// Return the sum of all the vector components. | ||
| 354 | inline T sum() const | ||
| 355 | { | ||
| 356 | ✗ | return this->mm[0] + this->mm[1] + this->mm[2]; | |
| 357 | } | ||
| 358 | |||
| 359 | /// Return the product of all the vector components. | ||
| 360 | inline T product() const | ||
| 361 | { | ||
| 362 |
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88 | return this->mm[0] * this->mm[1] * this->mm[2]; |
| 363 | } | ||
| 364 | |||
| 365 | /// this = normalized this | ||
| 366 |
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6767766 | bool normalize(T eps = T(1.0e-7)) |
| 367 | { | ||
| 368 | ✗ | T d = length(); | |
| 369 |
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6767766 | if (isApproxEqual(d, T(0), eps)) { |
| 370 | return false; | ||
| 371 | } | ||
| 372 | 6297892 | *this *= (T(1) / d); | |
| 373 | 6297892 | return true; | |
| 374 | } | ||
| 375 | |||
| 376 | |||
| 377 | /// return normalized this, throws if null vector | ||
| 378 | Vec3<T> unit(T eps=0) const | ||
| 379 | { | ||
| 380 | T d; | ||
| 381 |
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8377396 | return unit(eps, d); |
| 382 | } | ||
| 383 | |||
| 384 | /// return normalized this and length, throws if null vector | ||
| 385 | 8377495 | Vec3<T> unit(T eps, T& len) const | |
| 386 | { | ||
| 387 |
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8377495 | len = length(); |
| 388 |
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8377495 | if (isApproxEqual(len, T(0), eps)) { |
| 389 | ✗ | OPENVDB_THROW(ArithmeticError, "Normalizing null 3-vector"); | |
| 390 | } | ||
| 391 | 8377495 | return *this / len; | |
| 392 | } | ||
| 393 | |||
| 394 | /// return normalized this, or (1, 0, 0) if this is null vector | ||
| 395 | Vec3<T> unitSafe() const | ||
| 396 | { | ||
| 397 | T l2 = lengthSqr(); | ||
| 398 | return l2 ? *this / static_cast<T>(sqrt(l2)) : Vec3<T>(1, 0 ,0); | ||
| 399 | } | ||
| 400 | |||
| 401 | // Number of cols, rows, elements | ||
| 402 | static unsigned numRows() { return 1; } | ||
| 403 | static unsigned numColumns() { return 3; } | ||
| 404 | static unsigned numElements() { return 3; } | ||
| 405 | |||
| 406 | /// Returns the scalar component of v in the direction of onto, onto need | ||
| 407 | /// not be unit. e.g double c = Vec3d::component(v1,v2); | ||
| 408 | T component(const Vec3<T> &onto, T eps = static_cast<T>(1.0e-7)) const | ||
| 409 | { | ||
| 410 | T l = onto.length(); | ||
| 411 | if (isApproxEqual(l, T(0), eps)) return 0; | ||
| 412 | |||
| 413 | return dot(onto)*(T(1)/l); | ||
| 414 | } | ||
| 415 | |||
| 416 | /// Return the projection of v onto the vector, onto need not be unit | ||
| 417 | /// e.g. Vec3d a = vprojection(n); | ||
| 418 | Vec3<T> projection(const Vec3<T> &onto, T eps = static_cast<T>(1.0e-7)) const | ||
| 419 | { | ||
| 420 | T l = onto.lengthSqr(); | ||
| 421 | if (isApproxEqual(l, T(0), eps)) return Vec3::zero(); | ||
| 422 | |||
| 423 | return onto*(dot(onto)*(T(1)/l)); | ||
| 424 | } | ||
| 425 | |||
| 426 | /// Return an arbitrary unit vector perpendicular to v | ||
| 427 | /// Vector this must be a unit vector | ||
| 428 | /// e.g. v = v.normalize(); Vec3d n = v.getArbPerpendicular(); | ||
| 429 | Vec3<T> getArbPerpendicular() const | ||
| 430 | { | ||
| 431 | Vec3<T> u; | ||
| 432 | T l; | ||
| 433 | |||
| 434 | if ( fabs(this->mm[0]) >= fabs(this->mm[1]) ) { | ||
| 435 | // v.x or v.z is the largest magnitude component, swap them | ||
| 436 | l = this->mm[0]*this->mm[0] + this->mm[2]*this->mm[2]; | ||
| 437 | l = static_cast<T>(T(1)/sqrt(double(l))); | ||
| 438 | u.mm[0] = -this->mm[2]*l; | ||
| 439 | u.mm[1] = T(0); | ||
| 440 | u.mm[2] = +this->mm[0]*l; | ||
| 441 | } else { | ||
| 442 | // W.y or W.z is the largest magnitude component, swap them | ||
| 443 | l = this->mm[1]*this->mm[1] + this->mm[2]*this->mm[2]; | ||
| 444 | l = static_cast<T>(T(1)/sqrt(double(l))); | ||
| 445 | u.mm[0] = T(0); | ||
| 446 | u.mm[1] = +this->mm[2]*l; | ||
| 447 | u.mm[2] = -this->mm[1]*l; | ||
| 448 | } | ||
| 449 | |||
| 450 | return u; | ||
| 451 | } | ||
| 452 | |||
| 453 | /// Return a vector with the components of this in ascending order | ||
| 454 | 348 | Vec3<T> sorted() const | |
| 455 | { | ||
| 456 | 447 | Vec3<T> r(*this); | |
| 457 |
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447 | if( r.mm[0] > r.mm[1] ) std::swap(r.mm[0], r.mm[1]); |
| 458 |
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447 | if( r.mm[1] > r.mm[2] ) std::swap(r.mm[1], r.mm[2]); |
| 459 |
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447 | if( r.mm[0] > r.mm[1] ) std::swap(r.mm[0], r.mm[1]); |
| 460 | 348 | return r; | |
| 461 | } | ||
| 462 | |||
| 463 | /// Return the vector (z, y, x) | ||
| 464 | Vec3<T> reversed() const | ||
| 465 | { | ||
| 466 |
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12 | return Vec3<T>(this->mm[2], this->mm[1], this->mm[0]); |
| 467 | } | ||
| 468 | |||
| 469 | /// Predefined constants, e.g. Vec3d v = Vec3d::xNegAxis(); | ||
| 470 |
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6 | static Vec3<T> zero() { return Vec3<T>(0, 0, 0); } |
| 471 | static Vec3<T> ones() { return Vec3<T>(1, 1, 1); } | ||
| 472 | }; | ||
| 473 | |||
| 474 | |||
| 475 | /// Equality operator, does exact floating point comparisons | ||
| 476 | template <typename T0, typename T1> | ||
| 477 |
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8 | inline bool operator==(const Vec3<T0> &v0, const Vec3<T1> &v1) |
| 478 | { | ||
| 479 |
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|
121063472 | return isExactlyEqual(v0[0], v1[0]) && isExactlyEqual(v0[1], v1[1]) |
| 480 |
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201855003 | && isExactlyEqual(v0[2], v1[2]); |
| 481 | } | ||
| 482 | |||
| 483 | /// Inequality operator, does exact floating point comparisons | ||
| 484 | template <typename T0, typename T1> | ||
| 485 | inline bool operator!=(const Vec3<T0> &v0, const Vec3<T1> &v1) { return !(v0==v1); } | ||
| 486 | |||
| 487 | /// Multiply each element of the given vector by @a scalar and return the result. | ||
| 488 | template <typename S, typename T> | ||
| 489 | inline Vec3<typename promote<S, T>::type> operator*(S scalar, const Vec3<T> &v) { return v*scalar; } | ||
| 490 | |||
| 491 | /// Multiply each element of the given vector by @a scalar and return the result. | ||
| 492 | template <typename S, typename T> | ||
| 493 | inline Vec3<typename promote<S, T>::type> operator*(const Vec3<T> &v, S scalar) | ||
| 494 | { | ||
| 495 |
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2601306 | Vec3<typename promote<S, T>::type> result(v); |
| 496 | result *= scalar; | ||
| 497 |
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21924758 | return result; |
| 498 | } | ||
| 499 | |||
| 500 | /// Multiply corresponding elements of @a v0 and @a v1 and return the result. | ||
| 501 | template <typename T0, typename T1> | ||
| 502 | inline Vec3<typename promote<T0, T1>::type> operator*(const Vec3<T0> &v0, const Vec3<T1> &v1) | ||
| 503 | { | ||
| 504 |
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407187303 | Vec3<typename promote<T0, T1>::type> result(v0[0] * v1[0], v0[1] * v1[1], v0[2] * v1[2]); |
| 505 |
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12143545 | return result; |
| 506 | } | ||
| 507 | |||
| 508 | |||
| 509 | /// Divide @a scalar by each element of the given vector and return the result. | ||
| 510 | template <typename S, typename T> | ||
| 511 | inline Vec3<typename promote<S, T>::type> operator/(S scalar, const Vec3<T> &v) | ||
| 512 | { | ||
| 513 |
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2157086 | return Vec3<typename promote<S, T>::type>(scalar/v[0], scalar/v[1], scalar/v[2]); |
| 514 | } | ||
| 515 | |||
| 516 | /// Divide each element of the given vector by @a scalar and return the result. | ||
| 517 | template <typename S, typename T> | ||
| 518 | inline Vec3<typename promote<S, T>::type> operator/(const Vec3<T> &v, S scalar) | ||
| 519 | { | ||
| 520 | 13789177 | Vec3<typename promote<S, T>::type> result(v); | |
| 521 | result /= scalar; | ||
| 522 |
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7 | return result; |
| 523 | } | ||
| 524 | |||
| 525 | /// Divide corresponding elements of @a v0 and @a v1 and return the result. | ||
| 526 | template <typename T0, typename T1> | ||
| 527 | inline Vec3<typename promote<T0, T1>::type> operator/(const Vec3<T0> &v0, const Vec3<T1> &v1) | ||
| 528 | { | ||
| 529 | 1698293 | Vec3<typename promote<T0, T1>::type> result(v0[0] / v1[0], v0[1] / v1[1], v0[2] / v1[2]); | |
| 530 |
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74769 | return result; |
| 531 | } | ||
| 532 | |||
| 533 | /// Add corresponding elements of @a v0 and @a v1 and return the result. | ||
| 534 | template <typename T0, typename T1> | ||
| 535 | inline Vec3<typename promote<T0, T1>::type> operator+(const Vec3<T0> &v0, const Vec3<T1> &v1) | ||
| 536 | { | ||
| 537 |
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30329227 | Vec3<typename promote<T0, T1>::type> result(v0); |
| 538 | result += v1; | ||
| 539 |
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25942707 | return result; |
| 540 | } | ||
| 541 | |||
| 542 | /// Add @a scalar to each element of the given vector and return the result. | ||
| 543 | template <typename S, typename T> | ||
| 544 | inline Vec3<typename promote<S, T>::type> operator+(const Vec3<T> &v, S scalar) | ||
| 545 | { | ||
| 546 |
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279358 | Vec3<typename promote<S, T>::type> result(v); |
| 547 | result += scalar; | ||
| 548 |
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262170 | return result; |
| 549 | } | ||
| 550 | |||
| 551 | /// Subtract corresponding elements of @a v0 and @a v1 and return the result. | ||
| 552 | template <typename T0, typename T1> | ||
| 553 | inline Vec3<typename promote<T0, T1>::type> operator-(const Vec3<T0> &v0, const Vec3<T1> &v1) | ||
| 554 | { | ||
| 555 |
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837396855 | Vec3<typename promote<T0, T1>::type> result(v0); |
| 556 | result -= v1; | ||
| 557 |
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79564430 | return result; |
| 558 | } | ||
| 559 | |||
| 560 | /// Subtract @a scalar from each element of the given vector and return the result. | ||
| 561 | template <typename S, typename T> | ||
| 562 | inline Vec3<typename promote<S, T>::type> operator-(const Vec3<T> &v, S scalar) | ||
| 563 | { | ||
| 564 |
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9758225 | Vec3<typename promote<S, T>::type> result(v); |
| 565 | result -= scalar; | ||
| 566 | ✗ | return result; | |
| 567 | } | ||
| 568 | |||
| 569 | /// Angle between two vectors, the result is between [0, pi], | ||
| 570 | /// e.g. double a = Vec3d::angle(v1,v2); | ||
| 571 | template <typename T> | ||
| 572 | inline T angle(const Vec3<T> &v1, const Vec3<T> &v2) | ||
| 573 | { | ||
| 574 | Vec3<T> c = v1.cross(v2); | ||
| 575 | return static_cast<T>(atan2(c.length(), v1.dot(v2))); | ||
| 576 | } | ||
| 577 | |||
| 578 | template <typename T> | ||
| 579 | inline bool | ||
| 580 | isApproxEqual(const Vec3<T>& a, const Vec3<T>& b) | ||
| 581 | { | ||
| 582 |
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15771163 | return a.eq(b); |
| 583 | } | ||
| 584 | template <typename T> | ||
| 585 | inline bool | ||
| 586 | isApproxEqual(const Vec3<T>& a, const Vec3<T>& b, const Vec3<T>& eps) | ||
| 587 | { | ||
| 588 |
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5435823 | return isApproxEqual(a.x(), b.x(), eps.x()) && |
| 589 |
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12856744 | isApproxEqual(a.y(), b.y(), eps.y()) && |
| 590 | isApproxEqual(a.z(), b.z(), eps.z()); | ||
| 591 | } | ||
| 592 | |||
| 593 | template<typename T> | ||
| 594 | inline Vec3<T> | ||
| 595 | Abs(const Vec3<T>& v) | ||
| 596 | { | ||
| 597 | 7 | return Vec3<T>(Abs(v[0]), Abs(v[1]), Abs(v[2])); | |
| 598 | } | ||
| 599 | |||
| 600 | /// Orthonormalize vectors v1, v2 and v3 and store back the resulting | ||
| 601 | /// basis e.g. Vec3d::orthonormalize(v1,v2,v3); | ||
| 602 | template <typename T> | ||
| 603 | inline void orthonormalize(Vec3<T> &v1, Vec3<T> &v2, Vec3<T> &v3) | ||
| 604 | { | ||
| 605 | // If the input vectors are v0, v1, and v2, then the Gram-Schmidt | ||
| 606 | // orthonormalization produces vectors u0, u1, and u2 as follows, | ||
| 607 | // | ||
| 608 | // u0 = v0/|v0| | ||
| 609 | // u1 = (v1-(u0*v1)u0)/|v1-(u0*v1)u0| | ||
| 610 | // u2 = (v2-(u0*v2)u0-(u1*v2)u1)/|v2-(u0*v2)u0-(u1*v2)u1| | ||
| 611 | // | ||
| 612 | // where |A| indicates length of vector A and A*B indicates dot | ||
| 613 | // product of vectors A and B. | ||
| 614 | |||
| 615 | // compute u0 | ||
| 616 | v1.normalize(); | ||
| 617 | |||
| 618 | // compute u1 | ||
| 619 | T d0 = v1.dot(v2); | ||
| 620 | v2 -= v1*d0; | ||
| 621 | v2.normalize(); | ||
| 622 | |||
| 623 | // compute u2 | ||
| 624 | T d1 = v2.dot(v3); | ||
| 625 | d0 = v1.dot(v3); | ||
| 626 | v3 -= v1*d0 + v2*d1; | ||
| 627 | v3.normalize(); | ||
| 628 | } | ||
| 629 | |||
| 630 | /// @remark We are switching to a more explicit name because the semantics | ||
| 631 | /// are different from std::min/max. In that case, the function returns a | ||
| 632 | /// reference to one of the objects based on a comparator. Here, we must | ||
| 633 | /// fabricate a new object which might not match either of the inputs. | ||
| 634 | |||
| 635 | /// Return component-wise minimum of the two vectors. | ||
| 636 | template <typename T> | ||
| 637 | 2241586 | inline Vec3<T> minComponent(const Vec3<T> &v1, const Vec3<T> &v2) | |
| 638 | { | ||
| 639 | return Vec3<T>( | ||
| 640 | 4483172 | std::min(v1.x(), v2.x()), | |
| 641 | 4483172 | std::min(v1.y(), v2.y()), | |
| 642 |
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2251960 | std::min(v1.z(), v2.z())); |
| 643 | } | ||
| 644 | |||
| 645 | /// Return component-wise maximum of the two vectors. | ||
| 646 | template <typename T> | ||
| 647 | 1133442 | inline Vec3<T> maxComponent(const Vec3<T> &v1, const Vec3<T> &v2) | |
| 648 | { | ||
| 649 | return Vec3<T>( | ||
| 650 | 2266884 | std::max(v1.x(), v2.x()), | |
| 651 | 2266884 | std::max(v1.y(), v2.y()), | |
| 652 |
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1744178 | std::max(v1.z(), v2.z())); |
| 653 | } | ||
| 654 | |||
| 655 | /// @brief Return a vector with the exponent applied to each of | ||
| 656 | /// the components of the input vector. | ||
| 657 | template <typename T> | ||
| 658 | ✗ | inline Vec3<T> Exp(Vec3<T> v) { return v.exp(); } | |
| 659 | |||
| 660 | /// @brief Return a vector with log applied to each of | ||
| 661 | /// the components of the input vector. | ||
| 662 | template <typename T> | ||
| 663 | inline Vec3<T> Log(Vec3<T> v) { return v.log(); } | ||
| 664 | |||
| 665 | using Vec3i = Vec3<int32_t>; | ||
| 666 | using Vec3ui = Vec3<uint32_t>; | ||
| 667 | using Vec3s = Vec3<float>; | ||
| 668 | using Vec3d = Vec3<double>; | ||
| 669 | |||
| 670 | #if OPENVDB_ABI_VERSION_NUMBER >= 8 | ||
| 671 | OPENVDB_IS_POD(Vec3i) | ||
| 672 | OPENVDB_IS_POD(Vec3ui) | ||
| 673 | OPENVDB_IS_POD(Vec3s) | ||
| 674 | OPENVDB_IS_POD(Vec3d) | ||
| 675 | #endif | ||
| 676 | |||
| 677 | } // namespace math | ||
| 678 | } // namespace OPENVDB_VERSION_NAME | ||
| 679 | } // namespace openvdb | ||
| 680 | |||
| 681 | #endif // OPENVDB_MATH_VEC3_HAS_BEEN_INCLUDED | ||
| 682 |