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| 1 | // Copyright Contributors to the OpenVDB Project | ||
| 2 | // SPDX-License-Identifier: MPL-2.0 | ||
| 3 | |||
| 4 | #ifndef OPENVDB_MATH_VEC2_HAS_BEEN_INCLUDED | ||
| 5 | #define OPENVDB_MATH_VEC2_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 Mat2; | ||
| 21 | |||
| 22 | template<typename T> | ||
| 23 | class Vec2: public Tuple<2, 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 | Vec2() = default; | ||
| 34 | #else | ||
| 35 | Vec2() {} | ||
| 36 | #endif | ||
| 37 | |||
| 38 | /// @brief Construct a vector all of whose components have the given value. | ||
| 39 |
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1244 | explicit Vec2(T val) { this->mm[0] = this->mm[1] = val; } |
| 40 | |||
| 41 | /// Constructor with two arguments, e.g. Vec2f v(1,2,3); | ||
| 42 | 1126 | Vec2(T x, T y) | |
| 43 | { | ||
| 44 | 1126 | this->mm[0] = x; | |
| 45 |
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1121 | this->mm[1] = y; |
| 46 | } | ||
| 47 | |||
| 48 | /// Constructor with array argument, e.g. float a[2]; Vec2f v(a); | ||
| 49 | template <typename Source> | ||
| 50 | Vec2(Source *a) | ||
| 51 | { | ||
| 52 | this->mm[0] = static_cast<T>(a[0]); | ||
| 53 | this->mm[1] = static_cast<T>(a[1]); | ||
| 54 | } // trivial | ||
| 55 | |||
| 56 | /// Conversion constructor | ||
| 57 | template<typename Source> | ||
| 58 |
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2621440 | explicit Vec2(const Tuple<2, Source> &t) |
| 59 | { | ||
| 60 | 2621440 | this->mm[0] = static_cast<T>(t[0]); | |
| 61 |
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2621440 | this->mm[1] = static_cast<T>(t[1]); |
| 62 | } | ||
| 63 | |||
| 64 | /// @brief Construct a vector all of whose components have the given value, | ||
| 65 | /// which may be of an arithmetic type different from this vector's value type. | ||
| 66 | /// @details Type conversion warnings are suppressed. | ||
| 67 | template<typename Other> | ||
| 68 | 5181 | explicit Vec2(Other val, | |
| 69 | typename std::enable_if<std::is_arithmetic<Other>::value, Conversion>::type = Conversion{}) | ||
| 70 | { | ||
| 71 |
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4529 | this->mm[0] = this->mm[1] = static_cast<T>(val); |
| 72 | } | ||
| 73 | |||
| 74 | /// Reference to the component, e.g. v.x() = 4.5f; | ||
| 75 | T& x() {return this->mm[0];} | ||
| 76 | T& y() {return this->mm[1];} | ||
| 77 | |||
| 78 | /// Get the component, e.g. float f = v.y(); | ||
| 79 |
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147567 | T x() const {return this->mm[0];} |
| 80 |
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147567 | T y() const {return this->mm[1];} |
| 81 | |||
| 82 | /// Alternative indexed reference to the elements | ||
| 83 | T& operator()(int i) {return this->mm[i];} | ||
| 84 | |||
| 85 | /// Alternative indexed constant reference to the elements, | ||
| 86 | T operator()(int i) const {return this->mm[i];} | ||
| 87 | |||
| 88 | T* asPointer() {return this->mm;} | ||
| 89 | const T* asPointer() const {return this->mm;} | ||
| 90 | |||
| 91 | /// "this" vector gets initialized to [x, y, z], | ||
| 92 | /// calling v.init(); has same effect as calling v = Vec2::zero(); | ||
| 93 | const Vec2<T>& init(T x=0, T y=0) | ||
| 94 | { | ||
| 95 | this->mm[0] = x; this->mm[1] = y; | ||
| 96 | return *this; | ||
| 97 | } | ||
| 98 | |||
| 99 | /// Set "this" vector to zero | ||
| 100 | const Vec2<T>& setZero() | ||
| 101 | { | ||
| 102 | this->mm[0] = 0; this->mm[1] = 0; | ||
| 103 | return *this; | ||
| 104 | } | ||
| 105 | |||
| 106 | /// Assignment operator | ||
| 107 | template<typename Source> | ||
| 108 | 1048576 | const Vec2<T>& operator=(const Vec2<Source> &v) | |
| 109 | { | ||
| 110 | // note: don't static_cast because that suppresses warnings | ||
| 111 | 1048576 | this->mm[0] = v[0]; | |
| 112 | 1048576 | this->mm[1] = v[1]; | |
| 113 | |||
| 114 | 1048576 | return *this; | |
| 115 | } | ||
| 116 | |||
| 117 | /// Equality operator, does exact floating point comparisons | ||
| 118 | bool operator==(const Vec2<T> &v) const | ||
| 119 | { | ||
| 120 |
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19326820 | return (isExactlyEqual(this->mm[0], v.mm[0]) && isExactlyEqual(this->mm[1], v.mm[1])); |
| 121 | } | ||
| 122 | |||
| 123 | /// Inequality operator, does exact floating point comparisons | ||
| 124 | bool operator!=(const Vec2<T> &v) const { return !(*this==v); } | ||
| 125 | |||
| 126 | /// Test if "this" vector is equivalent to vector v with tolerance of eps | ||
| 127 | bool eq(const Vec2<T> &v, T eps = static_cast<T>(1.0e-7)) const | ||
| 128 | { | ||
| 129 | ✗ | return isApproxEqual(this->mm[0], v.mm[0], eps) && | |
| 130 | isApproxEqual(this->mm[1], v.mm[1], eps); | ||
| 131 | } // trivial | ||
| 132 | |||
| 133 | /// Negation operator, for e.g. v1 = -v2; | ||
| 134 |
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1030 | Vec2<T> operator-() const {return Vec2<T>(-this->mm[0], -this->mm[1]);} |
| 135 | |||
| 136 | /// this = v1 + v2 | ||
| 137 | /// "this", v1 and v2 need not be distinct objects, e.g. v.add(v1,v); | ||
| 138 | template <typename T0, typename T1> | ||
| 139 | const Vec2<T>& add(const Vec2<T0> &v1, const Vec2<T1> &v2) | ||
| 140 | { | ||
| 141 | this->mm[0] = v1[0] + v2[0]; | ||
| 142 | this->mm[1] = v1[1] + v2[1]; | ||
| 143 | |||
| 144 | return *this; | ||
| 145 | } | ||
| 146 | |||
| 147 | /// this = v1 - v2 | ||
| 148 | /// "this", v1 and v2 need not be distinct objects, e.g. v.sub(v1,v); | ||
| 149 | template <typename T0, typename T1> | ||
| 150 | const Vec2<T>& sub(const Vec2<T0> &v1, const Vec2<T1> &v2) | ||
| 151 | { | ||
| 152 | this->mm[0] = v1[0] - v2[0]; | ||
| 153 | this->mm[1] = v1[1] - v2[1]; | ||
| 154 | |||
| 155 | return *this; | ||
| 156 | } | ||
| 157 | |||
| 158 | /// this = scalar*v, v need not be a distinct object from "this", | ||
| 159 | /// e.g. v.scale(1.5,v1); | ||
| 160 | template <typename T0, typename T1> | ||
| 161 | const Vec2<T>& scale(T0 scalar, const Vec2<T1> &v) | ||
| 162 | { | ||
| 163 | this->mm[0] = scalar * v[0]; | ||
| 164 | this->mm[1] = scalar * v[1]; | ||
| 165 | |||
| 166 | return *this; | ||
| 167 | } | ||
| 168 | |||
| 169 | template <typename T0, typename T1> | ||
| 170 | const Vec2<T> &div(T0 scalar, const Vec2<T1> &v) | ||
| 171 | { | ||
| 172 | this->mm[0] = v[0] / scalar; | ||
| 173 | this->mm[1] = v[1] / scalar; | ||
| 174 | |||
| 175 | return *this; | ||
| 176 | } | ||
| 177 | |||
| 178 | /// Dot product | ||
| 179 | T dot(const Vec2<T> &v) const { return this->mm[0]*v[0] + this->mm[1]*v[1]; } // trivial | ||
| 180 | |||
| 181 | /// Length of the vector | ||
| 182 | T length() const | ||
| 183 | { | ||
| 184 | return static_cast<T>(sqrt(double(this->mm[0]*this->mm[0] + this->mm[1]*this->mm[1]))); | ||
| 185 | } | ||
| 186 | |||
| 187 | /// Squared length of the vector, much faster than length() as it | ||
| 188 | /// does not involve square root | ||
| 189 | T lengthSqr() const { return (this->mm[0]*this->mm[0] + this->mm[1]*this->mm[1]); } | ||
| 190 | |||
| 191 | /// Return a reference to itsef after the exponent has been | ||
| 192 | /// applied to all the vector components. | ||
| 193 | inline const Vec2<T>& exp() | ||
| 194 | { | ||
| 195 | this->mm[0] = std::exp(this->mm[0]); | ||
| 196 | this->mm[1] = std::exp(this->mm[1]); | ||
| 197 | return *this; | ||
| 198 | } | ||
| 199 | |||
| 200 | /// Return a reference to itself after log has been | ||
| 201 | /// applied to all the vector components. | ||
| 202 | inline const Vec2<T>& log() | ||
| 203 | { | ||
| 204 | this->mm[0] = std::log(this->mm[0]); | ||
| 205 | this->mm[1] = std::log(this->mm[1]); | ||
| 206 | return *this; | ||
| 207 | } | ||
| 208 | |||
| 209 | /// Return the sum of all the vector components. | ||
| 210 | inline T sum() const | ||
| 211 | { | ||
| 212 | return this->mm[0] + this->mm[1]; | ||
| 213 | } | ||
| 214 | |||
| 215 | /// Return the product of all the vector components. | ||
| 216 | inline T product() const | ||
| 217 | { | ||
| 218 | return this->mm[0] * this->mm[1]; | ||
| 219 | } | ||
| 220 | |||
| 221 | /// this = normalized this | ||
| 222 | bool normalize(T eps = static_cast<T>(1.0e-8)) | ||
| 223 | { | ||
| 224 | T d = length(); | ||
| 225 | if (isApproxEqual(d, T(0), eps)) { | ||
| 226 | return false; | ||
| 227 | } | ||
| 228 | *this *= (T(1) / d); | ||
| 229 | return true; | ||
| 230 | } | ||
| 231 | |||
| 232 | /// return normalized this, throws if null vector | ||
| 233 | Vec2<T> unit(T eps=0) const | ||
| 234 | { | ||
| 235 | T d; | ||
| 236 | return unit(eps, d); | ||
| 237 | } | ||
| 238 | |||
| 239 | /// return normalized this and length, throws if null vector | ||
| 240 | Vec2<T> unit(T eps, T& len) const | ||
| 241 | { | ||
| 242 | len = length(); | ||
| 243 | if (isApproxEqual(len, T(0), eps)) { | ||
| 244 | OPENVDB_THROW(ArithmeticError, "Normalizing null 2-vector"); | ||
| 245 | } | ||
| 246 | return *this / len; | ||
| 247 | } | ||
| 248 | |||
| 249 | /// return normalized this, or (1, 0) if this is null vector | ||
| 250 | Vec2<T> unitSafe() const | ||
| 251 | { | ||
| 252 | T l2 = lengthSqr(); | ||
| 253 | return l2 ? *this/static_cast<T>(sqrt(l2)) : Vec2<T>(1,0); | ||
| 254 | } | ||
| 255 | |||
| 256 | /// Multiply each element of this vector by @a scalar. | ||
| 257 | template <typename S> | ||
| 258 | const Vec2<T> &operator*=(S scalar) | ||
| 259 | { | ||
| 260 | this->mm[0] *= scalar; | ||
| 261 | this->mm[1] *= scalar; | ||
| 262 | return *this; | ||
| 263 | } | ||
| 264 | |||
| 265 | /// Multiply each element of this vector by the corresponding element of the given vector. | ||
| 266 | template <typename S> | ||
| 267 | const Vec2<T> &operator*=(const Vec2<S> &v1) | ||
| 268 | { | ||
| 269 | this->mm[0] *= v1[0]; | ||
| 270 | this->mm[1] *= v1[1]; | ||
| 271 | return *this; | ||
| 272 | } | ||
| 273 | |||
| 274 | /// Divide each element of this vector by @a scalar. | ||
| 275 | template <typename S> | ||
| 276 | const Vec2<T> &operator/=(S scalar) | ||
| 277 | { | ||
| 278 | this->mm[0] /= scalar; | ||
| 279 | this->mm[1] /= scalar; | ||
| 280 | return *this; | ||
| 281 | } | ||
| 282 | |||
| 283 | /// Divide each element of this vector by the corresponding element of the given vector. | ||
| 284 | template <typename S> | ||
| 285 | const Vec2<T> &operator/=(const Vec2<S> &v1) | ||
| 286 | { | ||
| 287 | this->mm[0] /= v1[0]; | ||
| 288 | this->mm[1] /= v1[1]; | ||
| 289 | return *this; | ||
| 290 | } | ||
| 291 | |||
| 292 | /// Add @a scalar to each element of this vector. | ||
| 293 | template <typename S> | ||
| 294 | const Vec2<T> &operator+=(S scalar) | ||
| 295 | { | ||
| 296 | 524290 | this->mm[0] += scalar; | |
| 297 | 524290 | this->mm[1] += scalar; | |
| 298 | return *this; | ||
| 299 | } | ||
| 300 | |||
| 301 | /// Add each element of the given vector to the corresponding element of this vector. | ||
| 302 | template <typename S> | ||
| 303 | const Vec2<T> &operator+=(const Vec2<S> &v1) | ||
| 304 | { | ||
| 305 | 4 | this->mm[0] += v1[0]; | |
| 306 | 4 | this->mm[1] += v1[1]; | |
| 307 | return *this; | ||
| 308 | } | ||
| 309 | |||
| 310 | /// Subtract @a scalar from each element of this vector. | ||
| 311 | template <typename S> | ||
| 312 | const Vec2<T> &operator-=(S scalar) | ||
| 313 | { | ||
| 314 | this->mm[0] -= scalar; | ||
| 315 | this->mm[1] -= scalar; | ||
| 316 | return *this; | ||
| 317 | } | ||
| 318 | |||
| 319 | /// Subtract each element of the given vector from the corresponding element of this vector. | ||
| 320 | template <typename S> | ||
| 321 | const Vec2<T> &operator-=(const Vec2<S> &v1) | ||
| 322 | { | ||
| 323 | 2 | this->mm[0] -= v1[0]; | |
| 324 | 2 | this->mm[1] -= v1[1]; | |
| 325 | return *this; | ||
| 326 | } | ||
| 327 | |||
| 328 | // Number of cols, rows, elements | ||
| 329 | static unsigned numRows() { return 1; } | ||
| 330 | static unsigned numColumns() { return 2; } | ||
| 331 | static unsigned numElements() { return 2; } | ||
| 332 | |||
| 333 | /// Returns the scalar component of v in the direction of onto, onto need | ||
| 334 | /// not be unit. e.g float c = Vec2f::component(v1,v2); | ||
| 335 | T component(const Vec2<T> &onto, T eps = static_cast<T>(1.0e-8)) const | ||
| 336 | { | ||
| 337 | T l = onto.length(); | ||
| 338 | if (isApproxEqual(l, T(0), eps)) return 0; | ||
| 339 | |||
| 340 | return dot(onto)*(T(1)/l); | ||
| 341 | } | ||
| 342 | |||
| 343 | /// Return the projection of v onto the vector, onto need not be unit | ||
| 344 | /// e.g. Vec2f v = Vec2f::projection(v,n); | ||
| 345 | Vec2<T> projection(const Vec2<T> &onto, T eps = static_cast<T>(1.0e-8)) const | ||
| 346 | { | ||
| 347 | T l = onto.lengthSqr(); | ||
| 348 | if (isApproxEqual(l, T(0), eps)) return Vec2::zero(); | ||
| 349 | |||
| 350 | return onto*(dot(onto)*(T(1)/l)); | ||
| 351 | } | ||
| 352 | |||
| 353 | /// Return an arbitrary unit vector perpendicular to v | ||
| 354 | /// Vector v must be a unit vector | ||
| 355 | /// e.g. v.normalize(); Vec2f n = Vec2f::getArbPerpendicular(v); | ||
| 356 | Vec2<T> getArbPerpendicular() const { return Vec2<T>(-this->mm[1], this->mm[0]); } | ||
| 357 | |||
| 358 | /// Predefined constants, e.g. Vec2f v = Vec2f::xNegAxis(); | ||
| 359 | static Vec2<T> zero() { return Vec2<T>(0, 0); } | ||
| 360 | static Vec2<T> ones() { return Vec2<T>(1, 1); } | ||
| 361 | }; | ||
| 362 | |||
| 363 | /// Multiply each element of the given vector by @a scalar and return the result. | ||
| 364 | template <typename S, typename T> | ||
| 365 | inline Vec2<typename promote<S, T>::type> operator*(S scalar, const Vec2<T> &v) | ||
| 366 | { | ||
| 367 | return v * scalar; | ||
| 368 | } | ||
| 369 | |||
| 370 | /// Multiply each element of the given vector by @a scalar and return the result. | ||
| 371 | template <typename S, typename T> | ||
| 372 | inline Vec2<typename promote<S, T>::type> operator*(const Vec2<T> &v, S scalar) | ||
| 373 | { | ||
| 374 | Vec2<typename promote<S, T>::type> result(v); | ||
| 375 | result *= scalar; | ||
| 376 | return result; | ||
| 377 | } | ||
| 378 | |||
| 379 | /// Multiply corresponding elements of @a v0 and @a v1 and return the result. | ||
| 380 | template <typename T0, typename T1> | ||
| 381 | inline Vec2<typename promote<T0, T1>::type> operator*(const Vec2<T0> &v0, const Vec2<T1> &v1) | ||
| 382 | { | ||
| 383 | Vec2<typename promote<T0, T1>::type> result(v0[0] * v1[0], v0[1] * v1[1]); | ||
| 384 |
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2 | return result; |
| 385 | } | ||
| 386 | |||
| 387 | /// Divide @a scalar by each element of the given vector and return the result. | ||
| 388 | template <typename S, typename T> | ||
| 389 | inline Vec2<typename promote<S, T>::type> operator/(S scalar, const Vec2<T> &v) | ||
| 390 | { | ||
| 391 | return Vec2<typename promote<S, T>::type>(scalar/v[0], scalar/v[1]); | ||
| 392 | } | ||
| 393 | |||
| 394 | /// Divide each element of the given vector by @a scalar and return the result. | ||
| 395 | template <typename S, typename T> | ||
| 396 | inline Vec2<typename promote<S, T>::type> operator/(const Vec2<T> &v, S scalar) | ||
| 397 | { | ||
| 398 | Vec2<typename promote<S, T>::type> result(v); | ||
| 399 | result /= scalar; | ||
| 400 | return result; | ||
| 401 | } | ||
| 402 | |||
| 403 | /// Divide corresponding elements of @a v0 and @a v1 and return the result. | ||
| 404 | template <typename T0, typename T1> | ||
| 405 | inline Vec2<typename promote<T0, T1>::type> operator/(const Vec2<T0> &v0, const Vec2<T1> &v1) | ||
| 406 | { | ||
| 407 | Vec2<typename promote<T0, T1>::type> result(v0[0] / v1[0], v0[1] / v1[1]); | ||
| 408 |
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2 | return result; |
| 409 | } | ||
| 410 | |||
| 411 | /// Add corresponding elements of @a v0 and @a v1 and return the result. | ||
| 412 | template <typename T0, typename T1> | ||
| 413 | inline Vec2<typename promote<T0, T1>::type> operator+(const Vec2<T0> &v0, const Vec2<T1> &v1) | ||
| 414 | { | ||
| 415 | Vec2<typename promote<T0, T1>::type> result(v0); | ||
| 416 | result += v1; | ||
| 417 |
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4 | return result; |
| 418 | } | ||
| 419 | |||
| 420 | /// Add @a scalar to each element of the given vector and return the result. | ||
| 421 | template <typename S, typename T> | ||
| 422 | inline Vec2<typename promote<S, T>::type> operator+(const Vec2<T> &v, S scalar) | ||
| 423 | { | ||
| 424 | 524288 | Vec2<typename promote<S, T>::type> result(v); | |
| 425 | result += scalar; | ||
| 426 |
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524290 | return result; |
| 427 | } | ||
| 428 | |||
| 429 | /// Subtract corresponding elements of @a v0 and @a v1 and return the result. | ||
| 430 | template <typename T0, typename T1> | ||
| 431 | inline Vec2<typename promote<T0, T1>::type> operator-(const Vec2<T0> &v0, const Vec2<T1> &v1) | ||
| 432 | { | ||
| 433 | Vec2<typename promote<T0, T1>::type> result(v0); | ||
| 434 | result -= v1; | ||
| 435 |
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2 | return result; |
| 436 | } | ||
| 437 | |||
| 438 | /// Subtract @a scalar from each element of the given vector and return the result. | ||
| 439 | template <typename S, typename T> | ||
| 440 | inline Vec2<typename promote<S, T>::type> operator-(const Vec2<T> &v, S scalar) | ||
| 441 | { | ||
| 442 | Vec2<typename promote<S, T>::type> result(v); | ||
| 443 | result -= scalar; | ||
| 444 | return result; | ||
| 445 | } | ||
| 446 | |||
| 447 | /// Angle between two vectors, the result is between [0, pi], | ||
| 448 | /// e.g. float a = Vec2f::angle(v1,v2); | ||
| 449 | template <typename T> | ||
| 450 | inline T angle(const Vec2<T> &v1, const Vec2<T> &v2) | ||
| 451 | { | ||
| 452 | T c = v1.dot(v2); | ||
| 453 | return acos(c); | ||
| 454 | } | ||
| 455 | |||
| 456 | template <typename T> | ||
| 457 | inline bool | ||
| 458 | isApproxEqual(const Vec2<T>& a, const Vec2<T>& b) | ||
| 459 | { | ||
| 460 | return a.eq(b); | ||
| 461 | } | ||
| 462 | template <typename T> | ||
| 463 | inline bool | ||
| 464 | isApproxEqual(const Vec2<T>& a, const Vec2<T>& b, const Vec2<T>& eps) | ||
| 465 | { | ||
| 466 |
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147567 | return isApproxEqual(a.x(), b.x(), eps.x()) && |
| 467 | isApproxEqual(a.y(), b.y(), eps.y()); | ||
| 468 | } | ||
| 469 | |||
| 470 | template<typename T> | ||
| 471 | inline Vec2<T> | ||
| 472 | Abs(const Vec2<T>& v) | ||
| 473 | { | ||
| 474 | return Vec2<T>(Abs(v[0]), Abs(v[1])); | ||
| 475 | } | ||
| 476 | |||
| 477 | /// Orthonormalize vectors v1 and v2 and store back the resulting basis | ||
| 478 | /// e.g. Vec2f::orthonormalize(v1,v2); | ||
| 479 | template <typename T> | ||
| 480 | inline void orthonormalize(Vec2<T> &v1, Vec2<T> &v2) | ||
| 481 | { | ||
| 482 | // If the input vectors are v0, v1, and v2, then the Gram-Schmidt | ||
| 483 | // orthonormalization produces vectors u0, u1, and u2 as follows, | ||
| 484 | // | ||
| 485 | // u0 = v0/|v0| | ||
| 486 | // u1 = (v1-(u0*v1)u0)/|v1-(u0*v1)u0| | ||
| 487 | // | ||
| 488 | // where |A| indicates length of vector A and A*B indicates dot | ||
| 489 | // product of vectors A and B. | ||
| 490 | |||
| 491 | // compute u0 | ||
| 492 | v1.normalize(); | ||
| 493 | |||
| 494 | // compute u1 | ||
| 495 | T d0 = v1.dot(v2); | ||
| 496 | v2 -= v1*d0; | ||
| 497 | v2.normalize(); | ||
| 498 | } | ||
| 499 | |||
| 500 | |||
| 501 | /// \remark We are switching to a more explicit name because the semantics | ||
| 502 | /// are different from std::min/max. In that case, the function returns a | ||
| 503 | /// reference to one of the objects based on a comparator. Here, we must | ||
| 504 | /// fabricate a new object which might not match either of the inputs. | ||
| 505 | |||
| 506 | /// Return component-wise minimum of the two vectors. | ||
| 507 | template <typename T> | ||
| 508 | inline Vec2<T> minComponent(const Vec2<T> &v1, const Vec2<T> &v2) | ||
| 509 | { | ||
| 510 | return Vec2<T>( | ||
| 511 | std::min(v1.x(), v2.x()), | ||
| 512 | std::min(v1.y(), v2.y())); | ||
| 513 | } | ||
| 514 | |||
| 515 | /// Return component-wise maximum of the two vectors. | ||
| 516 | template <typename T> | ||
| 517 | inline Vec2<T> maxComponent(const Vec2<T> &v1, const Vec2<T> &v2) | ||
| 518 | { | ||
| 519 | return Vec2<T>( | ||
| 520 | std::max(v1.x(), v2.x()), | ||
| 521 | std::max(v1.y(), v2.y())); | ||
| 522 | } | ||
| 523 | |||
| 524 | /// @brief Return a vector with the exponent applied to each of | ||
| 525 | /// the components of the input vector. | ||
| 526 | template <typename T> | ||
| 527 | inline Vec2<T> Exp(Vec2<T> v) { return v.exp(); } | ||
| 528 | |||
| 529 | /// @brief Return a vector with log applied to each of | ||
| 530 | /// the components of the input vector. | ||
| 531 | template <typename T> | ||
| 532 | inline Vec2<T> Log(Vec2<T> v) { return v.log(); } | ||
| 533 | |||
| 534 | using Vec2i = Vec2<int32_t>; | ||
| 535 | using Vec2ui = Vec2<uint32_t>; | ||
| 536 | using Vec2s = Vec2<float>; | ||
| 537 | using Vec2d = Vec2<double>; | ||
| 538 | |||
| 539 | #if OPENVDB_ABI_VERSION_NUMBER >= 8 | ||
| 540 | OPENVDB_IS_POD(Vec2i) | ||
| 541 | OPENVDB_IS_POD(Vec2ui) | ||
| 542 | OPENVDB_IS_POD(Vec2s) | ||
| 543 | OPENVDB_IS_POD(Vec2d) | ||
| 544 | #endif | ||
| 545 | |||
| 546 | } // namespace math | ||
| 547 | } // namespace OPENVDB_VERSION_NAME | ||
| 548 | } // namespace openvdb | ||
| 549 | |||
| 550 | #endif // OPENVDB_MATH_VEC2_HAS_BEEN_INCLUDED | ||
| 551 |