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4 #ifndef OPENVDB_MATH_VEC3_HAS_BEEN_INCLUDED
5 #define OPENVDB_MATH_VEC3_HAS_BEEN_INCLUDED
12 #include <type_traits>
20 template<
typename T>
class Mat3;
23 class Vec3:
public Tuple<3, T>
33 explicit Vec3(T val) { this->mm[0] = this->mm[1] = this->mm[2] = val; }
44 template <
typename Source>
47 this->mm[0] = static_cast<T>(a[0]);
48 this->mm[1] = static_cast<T>(a[1]);
49 this->mm[2] = static_cast<T>(a[2]);
54 template<
typename Source>
57 this->mm[0] = static_cast<T>(v[0]);
58 this->mm[1] = static_cast<T>(v[1]);
59 this->mm[2] = static_cast<T>(v[2]);
65 template<
typename Other>
69 this->mm[0] = this->mm[1] = this->mm[2] = static_cast<T>(val);
74 template<
typename Other>
77 this->mm[0] = static_cast<T>(v[0]);
78 this->mm[1] = static_cast<T>(v[1]);
79 this->mm[2] = static_cast<T>(v[2]);
83 T&
x() {
return this->mm[0]; }
84 T&
y() {
return this->mm[1]; }
85 T&
z() {
return this->mm[2]; }
88 T
x()
const {
return this->mm[0]; }
89 T
y()
const {
return this->mm[1]; }
90 T
z()
const {
return this->mm[2]; }
105 this->mm[0] = x; this->mm[1] = y; this->mm[2] = z;
113 this->mm[0] = 0; this->mm[1] = 0; this->mm[2] = 0;
119 template<
typename Source>
131 bool eq(
const Vec3<T> &v, T eps = static_cast<T>(1.0e-7))
const
144 template <
typename T0,
typename T1>
147 this->mm[0] = v1[0] + v2[0];
148 this->mm[1] = v1[1] + v2[1];
149 this->mm[2] = v1[2] + v2[2];
156 template <
typename T0,
typename T1>
159 this->mm[0] = v1[0] - v2[0];
160 this->mm[1] = v1[1] - v2[1];
161 this->mm[2] = v1[2] - v2[2];
168 template <
typename T0,
typename T1>
171 this->mm[0] =
scale * v[0];
172 this->mm[1] =
scale * v[1];
173 this->mm[2] =
scale * v[2];
178 template <
typename T0,
typename T1>
181 this->mm[0] = v[0] /
scale;
182 this->mm[1] = v[1] /
scale;
183 this->mm[2] = v[2] /
scale;
192 this->mm[0]*v.mm[0] +
193 this->mm[1]*v.mm[1] +
200 return static_cast<T>(sqrt(
double(
201 this->mm[0]*this->mm[0] +
202 this->mm[1]*this->mm[1] +
203 this->mm[2]*this->mm[2])));
212 this->mm[0]*this->mm[0] +
213 this->mm[1]*this->mm[1] +
214 this->mm[2]*this->mm[2];
220 return Vec3<T>(this->mm[1]*v.mm[2] - this->mm[2]*v.mm[1],
221 this->mm[2]*v.mm[0] - this->mm[0]*v.mm[2],
222 this->mm[0]*v.mm[1] - this->mm[1]*v.mm[0]);
231 this->mm[0] = v1.mm[1]*v2.mm[2] - v1.mm[2]*v2.mm[1];
232 this->mm[1] = v1.mm[2]*v2.mm[0] - v1.mm[0]*v2.mm[2];
233 this->mm[2] = v1.mm[0]*v2.mm[1] - v1.mm[1]*v2.mm[0];
238 template <
typename S>
242 const auto value0 = this->mm[0] * scalar;
243 const auto value1 = this->mm[1] * scalar;
244 const auto value2 = this->mm[2] * scalar;
246 this->mm[0] = static_cast<T>(value0);
247 this->mm[1] = static_cast<T>(value1);
248 this->mm[2] = static_cast<T>(value2);
253 template <
typename S>
256 this->mm[0] *= v1[0];
257 this->mm[1] *= v1[1];
258 this->mm[2] *= v1[2];
263 template <
typename S>
266 this->mm[0] /= scalar;
267 this->mm[1] /= scalar;
268 this->mm[2] /= scalar;
273 template <
typename S>
276 this->mm[0] /= v1[0];
277 this->mm[1] /= v1[1];
278 this->mm[2] /= v1[2];
283 template <
typename S>
287 const auto value0 = this->mm[0] + scalar;
288 const auto value1 = this->mm[1] + scalar;
289 const auto value2 = this->mm[2] + scalar;
291 this->mm[0] = static_cast<T>(value0);
292 this->mm[1] = static_cast<T>(value1);
293 this->mm[2] = static_cast<T>(value2);
298 template <
typename S>
301 this->mm[0] += v1[0];
302 this->mm[1] += v1[1];
303 this->mm[2] += v1[2];
308 template <
typename S>
311 this->mm[0] -= scalar;
312 this->mm[1] -= scalar;
313 this->mm[2] -= scalar;
318 template <
typename S>
321 this->mm[0] -= v1[0];
322 this->mm[1] -= v1[1];
323 this->mm[2] -= v1[2];
331 this->mm[0] = std::exp(this->mm[0]);
332 this->mm[1] = std::exp(this->mm[1]);
333 this->mm[2] = std::exp(this->mm[2]);
341 this->mm[0] = std::log(this->mm[0]);
342 this->mm[1] = std::log(this->mm[1]);
343 this->mm[2] = std::log(this->mm[2]);
350 return this->mm[0] + this->mm[1] + this->mm[2];
356 return this->mm[0] * this->mm[1] * this->mm[2];
392 return l2 ? *
this / static_cast<T>(sqrt(l2)) :
Vec3<T>(1, 0 ,0);
407 return dot(onto)*(T(1)/l);
414 T l = onto.lengthSqr();
417 return onto*(dot(onto)*(T(1)/l));
428 if ( fabs(this->mm[0]) >= fabs(this->mm[1]) ) {
430 l = this->mm[0]*this->mm[0] + this->mm[2]*this->mm[2];
431 l = static_cast<T>(T(1)/sqrt(
double(l)));
432 u.mm[0] = -this->mm[2]*l;
434 u.mm[2] = +this->mm[0]*l;
437 l = this->mm[1]*this->mm[1] + this->mm[2]*this->mm[2];
438 l = static_cast<T>(T(1)/sqrt(
double(l)));
440 u.mm[1] = +this->mm[2]*l;
441 u.mm[2] = -this->mm[1]*l;
451 if( r.mm[0] > r.mm[1] ) std::swap(r.mm[0], r.mm[1]);
452 if( r.mm[1] > r.mm[2] ) std::swap(r.mm[1], r.mm[2]);
453 if( r.mm[0] > r.mm[1] ) std::swap(r.mm[0], r.mm[1]);
460 return Vec3<T>(this->mm[2], this->mm[1], this->mm[0]);
470 template <
typename T0,
typename T1>
478 template <
typename T0,
typename T1>
482 template <
typename S,
typename T>
486 template <
typename S,
typename T>
495 template <
typename T0,
typename T1>
504 template <
typename S,
typename T>
511 template <
typename S,
typename T>
520 template <
typename T0,
typename T1>
528 template <
typename T0,
typename T1>
537 template <
typename S,
typename T>
546 template <
typename T0,
typename T1>
555 template <
typename S,
typename T>
565 template <
typename T>
569 return static_cast<T>(atan2(c.length(), v1.dot(v2)));
572 template <
typename T>
578 template <
typename T>
596 template <
typename T>
630 template <
typename T>
640 template <
typename T>
651 template <
typename T>
656 template <
typename T>
668 #endif // OPENVDB_MATH_VEC3_HAS_BEEN_INCLUDED
const Vec3< T > & operator+=(S scalar)
Add scalar to each element of this vector.
Definition: Vec3.h:284
const Vec3< T > & sub(const Vec3< T0 > &v1, const Vec3< T1 > &v2)
Definition: Vec3.h:157
T & x()
Reference to the component, e.g. v.x() = 4.5f;.
Definition: Vec3.h:83
static unsigned numElements()
Definition: Vec3.h:398
Vec3< T > cross(const Vec3< T > &v) const
Return the cross product of "this" vector and v;.
Definition: Vec3.h:218
T y() const
Definition: Vec3.h:89
static Vec3< T > zero()
Predefined constants, e.g. Vec3d v = Vec3d::xNegAxis();.
Definition: Vec3.h:464
Vec3(Other val, typename std::enable_if< std::is_arithmetic< Other >::value, Conversion >::type=Conversion{})
Construct a vector all of whose components have the given value, which may be of an arithmetic type d...
Definition: Vec3.h:66
Vec3< T > Exp(Vec3< T > v)
Return a vector with the exponent applied to each of the components of the input vector.
Definition: Vec3.h:652
static unsigned numColumns()
Definition: Vec3.h:397
Vec3(const Tuple< 3, Source > &v)
Construct a Vec3 from a 3-Tuple with a possibly different value type.
Definition: Vec3.h:55
T sum() const
Return the sum of all the vector components.
Definition: Vec3.h:348
Vec3< T > getArbPerpendicular() const
Definition: Vec3.h:423
Dummy class for tag dispatch of conversion constructors.
Definition: Tuple.h:22
const Vec3< T > & setZero()
Set "this" vector to zero.
Definition: Vec3.h:111
Vec3(T x, T y, T z)
Constructor with three arguments, e.g. Vec3d v(1,2,3);.
Definition: Vec3.h:36
Vec3< T > unit(T eps, T &len) const
return normalized this and length, throws if null vector
Definition: Vec3.h:379
const Vec3< T > & operator*=(const Vec3< S > &v1)
Multiply each element of this vector by the corresponding element of the given vector.
Definition: Vec3.h:254
Vec3(const Vec3< Other > &v)
Construct a Vec3 from another Vec3 with a possibly different value type.
Definition: Vec3.h:75
const Vec3< T > & operator/=(S scalar)
Divide each element of this vector by scalar.
Definition: Vec3.h:264
const Vec3< T > & cross(const Vec3< T > &v1, const Vec3< T > &v2)
this = v1 cross v2, v1 and v2 must be distinct objects than "this"
Definition: Vec3.h:227
Vec3< typename promote< S, T >::type > operator-(const Vec3< T > &v, S scalar)
Subtract scalar from each element of the given vector and return the result.
Definition: Vec3.h:556
T & y()
Definition: Vec3.h:84
const Vec3< T > & div(T0 scale, const Vec3< T1 > &v)
Definition: Vec3.h:179
const Vec3< T > & operator-=(const Vec3< S > &v1)
Subtract each element of the given vector from the corresponding element of this vector.
Definition: Vec3.h:319
T operator()(int i) const
Alternative indexed constant reference to the elements,.
Definition: Vec3.h:99
bool isRelOrApproxEqual(const Type &a, const Type &b, const Type &absTol, const Type &relTol)
Definition: Math.h:398
Vec3< T > sorted() const
Return a vector with the components of this in ascending order.
Definition: Vec3.h:448
Vec3< T > minComponent(const Vec3< T > &v1, const Vec3< T > &v2)
Return component-wise minimum of the two vectors.
Definition: Vec3.h:631
Vec3< typename promote< S, T >::type > operator+(const Vec3< T > &v, S scalar)
Add scalar to each element of the given vector and return the result.
Definition: Vec3.h:538
bool eq(const Vec3< T > &v, T eps=static_cast< T >(1.0e-7)) const
Test if "this" vector is equivalent to vector v with tolerance of eps.
Definition: Vec3.h:131
Vec3< T > Log(Vec3< T > v)
Return a vector with log applied to each of the components of the input vector.
Definition: Vec3.h:657
const Vec3< T > & operator=(const Vec3< Source > &v)
Assignment operator.
Definition: Vec3.h:120
General-purpose arithmetic and comparison routines, most of which accept arbitrary value types (or at...
T lengthSqr() const
Definition: Vec3.h:209
Vec3< T > Abs(const Vec3< T > &v)
Definition: Vec3.h:589
T & z()
Definition: Vec3.h:85
T angle(const Vec3< T > &v1, const Vec3< T > &v2)
Definition: Vec3.h:566
Vec3< T > maxComponent(const Vec3< T > &v1, const Vec3< T > &v2)
Return component-wise maximum of the two vectors.
Definition: Vec3.h:641
T * asPointer()
Definition: Vec3.h:92
const Vec3< T > & operator-=(S scalar)
Subtract scalar from each element of this vector.
Definition: Vec3.h:309
bool operator==(const Vec3< T0 > &v0, const Vec3< T1 > &v1)
Equality operator, does exact floating point comparisons.
Definition: Vec3.h:471
void orthonormalize(Vec3< T > &v1, Vec3< T > &v2, Vec3< T > &v3)
Definition: Vec3.h:597
Vec3< T > unit(T eps=0) const
return normalized this, throws if null vector
Definition: Vec3.h:372
MatType unit(const MatType &mat, typename MatType::value_type eps=1.0e-8)
Return a copy of the given matrix with its upper 3×3 rows normalized.
Definition: Mat.h:653
#define OPENVDB_USE_VERSION_NAMESPACE
Definition: version.h:154
const Vec3< T > & init(T x=0, T y=0, T z=0)
Definition: Vec3.h:103
Vec3< T > projection(const Vec3< T > &onto, T eps=static_cast< T >(1.0e-7)) const
Definition: Vec3.h:412
const Vec3< T > & add(const Vec3< T0 > &v1, const Vec3< T1 > &v2)
Definition: Vec3.h:145
T length() const
Length of the vector.
Definition: Vec3.h:198
Vec3< T > reversed() const
Return the vector (z, y, x)
Definition: Vec3.h:458
Vec3(Source *a)
Constructor with array argument, e.g. double a[3]; Vec3d v(a);.
Definition: Vec3.h:45
Vec3< typename promote< T0, T1 >::type > operator/(const Vec3< T0 > &v0, const Vec3< T1 > &v1)
Divide corresponding elements of v0 and v1 and return the result.
Definition: Vec3.h:521
const Vec3< T > & operator/=(const Vec3< S > &v1)
Divide each element of this vector by the corresponding element of the given vector.
Definition: Vec3.h:274
bool operator!=(const Vec3< T0 > &v0, const Vec3< T1 > &v1)
Inequality operator, does exact floating point comparisons.
Definition: Vec3.h:479
T x() const
Get the component, e.g. float f = v.y();.
Definition: Vec3.h:88
Vec3()
Trivial constructor, the vector is NOT initialized.
Definition: Vec3.h:30
const Vec3< T > & log()
Definition: Vec3.h:339
bool isExactlyEqual(const T0 &a, const T1 &b)
Return true if a is exactly equal to b.
Definition: Math.h:388
const T * asPointer() const
Definition: Vec3.h:93
const Vec3< T > & operator+=(const Vec3< S > &v1)
Add each element of the given vector to the corresponding element of this vector.
Definition: Vec3.h:299
Vec3< T > unitSafe() const
return normalized this, or (1, 0, 0) if this is null vector
Definition: Vec3.h:389
#define OPENVDB_VERSION_NAME
The version namespace name for this library version.
Definition: version.h:102
MatType scale(const Vec3< typename MatType::value_type > &s)
Return a matrix that scales by s.
Definition: Mat.h:620
Real value_type
Definition: Vec3.h:26
static Vec3< T > ones()
Definition: Vec3.h:465
T dot(const Vec3< T > &v) const
Dot product.
Definition: Vec3.h:189
bool normalize(T eps=T(1.0e-7))
this = normalized this
Definition: Vec3.h:360
Vec3(T val)
Construct a vector all of whose components have the given value.
Definition: Vec3.h:33
Real ValueType
Definition: Vec3.h:27
T product() const
Return the product of all the vector components.
Definition: Vec3.h:354
T & operator()(int i)
Alternative indexed reference to the elements.
Definition: Vec3.h:96
Vec3< typename promote< T0, T1 >::type > operator*(const Vec3< T0 > &v0, const Vec3< T1 > &v1)
Multiply corresponding elements of v0 and v1 and return the result.
Definition: Vec3.h:496
Definition: Exceptions.h:13
const Vec3< T > & exp()
Definition: Vec3.h:329
const Vec3< T > & operator*=(S scalar)
Multiply each element of this vector by scalar.
Definition: Vec3.h:239
bool isApproxEqual(const Vec3< T > &a, const Vec3< T > &b, const Vec3< T > &eps)
Definition: Vec3.h:580
T z() const
Definition: Vec3.h:90
Vec3< T > operator-() const
Negation operator, for e.g. v1 = -v2;.
Definition: Vec3.h:140
static unsigned numRows()
Definition: Vec3.h:396
#define OPENVDB_THROW(exception, message)
Definition: Exceptions.h:82
T component(const Vec3< T > &onto, T eps=static_cast< T >(1.0e-7)) const
Definition: Vec3.h:402
Definition: Exceptions.h:56
const Vec3< T > & scale(T0 scale, const Vec3< T1 > &v)
Definition: Vec3.h:169