4#ifndef OPENVDB_MATH_VEC3_HAS_BEEN_INCLUDED
5#define OPENVDB_MATH_VEC3_HAS_BEEN_INCLUDED
20template<
typename T>
class Mat3;
35 explicit Vec3(T val) { this->mm[0] = this->mm[1] = this->mm[2] = val; }
46 template <
typename Source>
49 this->mm[0] =
static_cast<T
>(a[0]);
50 this->mm[1] =
static_cast<T
>(a[1]);
51 this->mm[2] =
static_cast<T
>(a[2]);
56 template<
typename Source>
59 this->mm[0] =
static_cast<T
>(v[0]);
60 this->mm[1] =
static_cast<T
>(v[1]);
61 this->mm[2] =
static_cast<T
>(v[2]);
67 template<
typename Other>
71 this->mm[0] = this->mm[1] = this->mm[2] =
static_cast<T
>(val);
76 template<
typename Other>
79 this->mm[0] =
static_cast<T
>(v[0]);
80 this->mm[1] =
static_cast<T
>(v[1]);
81 this->mm[2] =
static_cast<T
>(v[2]);
85 T&
x() {
return this->mm[0]; }
86 T&
y() {
return this->mm[1]; }
87 T&
z() {
return this->mm[2]; }
90 T
x()
const {
return this->mm[0]; }
91 T
y()
const {
return this->mm[1]; }
92 T
z()
const {
return this->mm[2]; }
107 this->mm[0] = x; this->mm[1] = y; this->mm[2] = z;
115 this->mm[0] = 0; this->mm[1] = 0; this->mm[2] = 0;
121 template<
typename Source>
133 bool eq(
const Vec3<T> &v, T eps =
static_cast<T
>(1.0e-7))
const
146 template <
typename T0,
typename T1>
149 this->mm[0] = v1[0] + v2[0];
150 this->mm[1] = v1[1] + v2[1];
151 this->mm[2] = v1[2] + v2[2];
158 template <
typename T0,
typename T1>
161 this->mm[0] = v1[0] - v2[0];
162 this->mm[1] = v1[1] - v2[1];
163 this->mm[2] = v1[2] - v2[2];
170 template <
typename T0,
typename T1>
173 this->mm[0] =
scale * v[0];
174 this->mm[1] =
scale * v[1];
175 this->mm[2] =
scale * v[2];
180 template <
typename T0,
typename T1>
183 this->mm[0] = v[0] /
scale;
184 this->mm[1] = v[1] /
scale;
185 this->mm[2] = v[2] /
scale;
194 this->mm[0]*v.
mm[0] +
195 this->mm[1]*v.
mm[1] +
202 return static_cast<T
>(sqrt(
double(
203 this->mm[0]*this->mm[0] +
204 this->mm[1]*this->mm[1] +
205 this->mm[2]*this->mm[2])));
214 this->mm[0]*this->mm[0] +
215 this->mm[1]*this->mm[1] +
216 this->mm[2]*this->mm[2];
222 return Vec3<T>(this->mm[1]*v.
mm[2] - this->mm[2]*v.
mm[1],
223 this->mm[2]*v.
mm[0] - this->mm[0]*v.
mm[2],
224 this->mm[0]*v.
mm[1] - this->mm[1]*v.
mm[0]);
233 this->mm[0] = v1.
mm[1]*v2.
mm[2] - v1.
mm[2]*v2.
mm[1];
234 this->mm[1] = v1.
mm[2]*v2.
mm[0] - v1.
mm[0]*v2.
mm[2];
235 this->mm[2] = v1.
mm[0]*v2.
mm[1] - v1.
mm[1]*v2.
mm[0];
240 template <
typename S>
244 const auto value0 = this->mm[0] * scalar;
245 const auto value1 = this->mm[1] * scalar;
246 const auto value2 = this->mm[2] * scalar;
248 this->mm[0] =
static_cast<T
>(value0);
249 this->mm[1] =
static_cast<T
>(value1);
250 this->mm[2] =
static_cast<T
>(value2);
255 template <
typename S>
258 this->mm[0] *= v1[0];
259 this->mm[1] *= v1[1];
260 this->mm[2] *= v1[2];
265 template <
typename S>
268 this->mm[0] /= scalar;
269 this->mm[1] /= scalar;
270 this->mm[2] /= scalar;
275 template <
typename S>
278 this->mm[0] /= v1[0];
279 this->mm[1] /= v1[1];
280 this->mm[2] /= v1[2];
285 template <
typename S>
289 const auto value0 = this->mm[0] + scalar;
290 const auto value1 = this->mm[1] + scalar;
291 const auto value2 = this->mm[2] + scalar;
293 this->mm[0] =
static_cast<T
>(value0);
294 this->mm[1] =
static_cast<T
>(value1);
295 this->mm[2] =
static_cast<T
>(value2);
300 template <
typename S>
303 this->mm[0] += v1[0];
304 this->mm[1] += v1[1];
305 this->mm[2] += v1[2];
310 template <
typename S>
313 this->mm[0] -= scalar;
314 this->mm[1] -= scalar;
315 this->mm[2] -= scalar;
320 template <
typename S>
323 this->mm[0] -= v1[0];
324 this->mm[1] -= v1[1];
325 this->mm[2] -= v1[2];
333 this->mm[0] = std::exp(this->mm[0]);
334 this->mm[1] = std::exp(this->mm[1]);
335 this->mm[2] = std::exp(this->mm[2]);
343 this->mm[0] = std::log(this->mm[0]);
344 this->mm[1] = std::log(this->mm[1]);
345 this->mm[2] = std::log(this->mm[2]);
352 return this->mm[0] + this->mm[1] + this->mm[2];
358 return this->mm[0] * this->mm[1] * this->mm[2];
394 return l2 ? *
this /
static_cast<T
>(sqrt(l2)) :
Vec3<T>(1, 0 ,0);
409 return dot(onto)*(T(1)/l);
419 return onto*(dot(onto)*(T(1)/l));
430 if ( fabs(this->mm[0]) >= fabs(this->mm[1]) ) {
432 l = this->mm[0]*this->mm[0] + this->mm[2]*this->mm[2];
433 l =
static_cast<T
>(T(1)/sqrt(
double(l)));
434 u.
mm[0] = -this->mm[2]*l;
436 u.
mm[2] = +this->mm[0]*l;
439 l = this->mm[1]*this->mm[1] + this->mm[2]*this->mm[2];
440 l =
static_cast<T
>(T(1)/sqrt(
double(l)));
442 u.
mm[1] = +this->mm[2]*l;
443 u.
mm[2] = -this->mm[1]*l;
453 if( r.
mm[0] > r.
mm[1] ) std::swap(r.
mm[0], r.
mm[1]);
454 if( r.
mm[1] > r.
mm[2] ) std::swap(r.
mm[1], r.
mm[2]);
455 if( r.
mm[0] > r.
mm[1] ) std::swap(r.
mm[0], r.
mm[1]);
462 return Vec3<T>(this->mm[2], this->mm[1], this->mm[0]);
472template <
typename T0,
typename T1>
480template <
typename T0,
typename T1>
484template <
typename S,
typename T>
488template <
typename S,
typename T>
497template <
typename T0,
typename T1>
506template <
typename S,
typename T>
513template <
typename S,
typename T>
522template <
typename T0,
typename T1>
530template <
typename T0,
typename T1>
539template <
typename S,
typename T>
548template <
typename T0,
typename T1>
557template <
typename S,
typename T>
571 return static_cast<T
>(atan2(c.
length(), v1.
dot(v2)));
636 std::min(v1.
x(), v2.
x()),
637 std::min(v1.
y(), v2.
y()),
638 std::min(v1.
z(), v2.
z()));
646 std::max(v1.
x(), v2.
x()),
647 std::max(v1.
y(), v2.
y()),
648 std::max(v1.
z(), v2.
z()));
General-purpose arithmetic and comparison routines, most of which accept arbitrary value types (or at...
#define OPENVDB_IS_POD(Type)
Definition: Math.h:56
Definition: Exceptions.h:56
T mm[SIZE]
Copies this tuple into an array of a compatible type.
Definition: Tuple.h:164
Vec3< T > sorted() const
Return a vector with the components of this in ascending order.
Definition: Vec3.h:450
const Vec3< T > & div(T0 scale, const Vec3< T1 > &v)
Definition: Vec3.h:181
T & x()
Reference to the component, e.g. v.x() = 4.5f;.
Definition: Vec3.h:85
const Vec3< T > & sub(const Vec3< T0 > &v1, const Vec3< T1 > &v2)
Definition: Vec3.h:159
const Vec3< T > & setZero()
Set "this" vector to zero.
Definition: Vec3.h:113
const Vec3< T > & operator/=(S scalar)
Divide each element of this vector by scalar.
Definition: Vec3.h:266
Vec3< T > reversed() const
Return the vector (z, y, x)
Definition: Vec3.h:460
const Vec3< T > & add(const Vec3< T0 > &v1, const Vec3< T1 > &v2)
Definition: Vec3.h:147
T length() const
Length of the vector.
Definition: Vec3.h:200
Vec3(Source *a)
Constructor with array argument, e.g. double a[3]; Vec3d v(a);.
Definition: Vec3.h:47
T dot(const Vec3< T > &v) const
Dot product.
Definition: Vec3.h:191
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:256
const Vec3< T > & operator*=(S scalar)
Multiply each element of this vector by scalar.
Definition: Vec3.h:241
T sum() const
Return the sum of all the vector components.
Definition: Vec3.h:350
static unsigned numColumns()
Definition: Vec3.h:399
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:276
const Vec3< T > & init(T x=0, T y=0, T z=0)
Definition: Vec3.h:105
Vec3(T x, T y, T z)
Constructor with three arguments, e.g. Vec3d v(1,2,3);.
Definition: Vec3.h:38
Vec3< T > unit(T eps, T &len) const
return normalized this and length, throws if null vector
Definition: Vec3.h:381
T * asPointer()
Definition: Vec3.h:94
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:133
static unsigned numRows()
Definition: Vec3.h:398
Vec3< T > getArbPerpendicular() const
Definition: Vec3.h:425
const Vec3< T > & log()
Definition: Vec3.h:341
T & operator()(int i)
Alternative indexed reference to the elements.
Definition: Vec3.h:98
T & y()
Definition: Vec3.h:86
T component(const Vec3< T > &onto, T eps=static_cast< T >(1.0e-7)) const
Definition: Vec3.h:404
Vec3(T val)
Construct a vector all of whose components have the given value.
Definition: Vec3.h:35
T & z()
Definition: Vec3.h:87
T operator()(int i) const
Alternative indexed constant reference to the elements,.
Definition: Vec3.h:101
T product() const
Return the product of all the vector components.
Definition: Vec3.h:356
Vec3< T > cross(const Vec3< T > &v) const
Return the cross product of "this" vector and v;.
Definition: Vec3.h:220
const T * asPointer() const
Definition: Vec3.h:95
T lengthSqr() const
Definition: Vec3.h:211
Vec3(const Vec3< Other > &v)
Construct a Vec3 from another Vec3 with a possibly different value type.
Definition: Vec3.h:77
static Vec3< T > zero()
Predefined constants, e.g. Vec3d v = Vec3d::xNegAxis();.
Definition: Vec3.h:466
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:229
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:68
T x() const
Get the component, e.g. float f = v.y();.
Definition: Vec3.h:90
Vec3(const Tuple< 3, Source > &v)
Construct a Vec3 from a 3-Tuple with a possibly different value type.
Definition: Vec3.h:57
const Vec3< T > & operator+=(S scalar)
Add scalar to each element of this vector.
Definition: Vec3.h:286
const Vec3< T > & operator=(const Vec3< Source > &v)
Assignment operator.
Definition: Vec3.h:122
T z() const
Definition: Vec3.h:92
static Vec3< T > ones()
Definition: Vec3.h:467
Vec3< T > unitSafe() const
return normalized this, or (1, 0, 0) if this is null vector
Definition: Vec3.h:391
T y() const
Definition: Vec3.h:91
Vec3< T > operator-() const
Negation operator, for e.g. v1 = -v2;.
Definition: Vec3.h:142
const Vec3< T > & scale(T0 scale, const Vec3< T1 > &v)
Definition: Vec3.h:171
Vec3< T > projection(const Vec3< T > &onto, T eps=static_cast< T >(1.0e-7)) const
Definition: Vec3.h:414
static unsigned numElements()
Definition: Vec3.h:400
Vec3< T > unit(T eps=0) const
return normalized this, throws if null vector
Definition: Vec3.h:374
const Vec3< T > & operator-=(S scalar)
Subtract scalar from each element of this vector.
Definition: Vec3.h:311
bool normalize(T eps=T(1.0e-7))
this = normalized this
Definition: Vec3.h:362
T ValueType
Definition: Vec3.h:27
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:321
const Vec3< T > & exp()
Definition: Vec3.h:331
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:301
T value_type
Definition: Vec3.h:26
Vec2< T > Log(Vec2< T > v)
Return a vector with log applied to each of the components of the input vector.
Definition: Vec2.h:528
bool operator==(const Vec3< T0 > &v0, const Vec3< T1 > &v1)
Equality operator, does exact floating point comparisons.
Definition: Vec3.h:473
void orthonormalize(Vec2< T > &v1, Vec2< T > &v2)
Definition: Vec2.h:476
Mat3< typename promote< T0, T1 >::type > operator*(const Mat3< T0 > &m0, const Mat3< T1 > &m1)
Multiply m0 by m1 and return the resulting matrix.
Definition: Mat3.h:597
bool isApproxEqual(const Type &a, const Type &b, const Type &tolerance)
Return true if a is equal to b to within the given tolerance.
Definition: Math.h:406
bool isRelOrApproxEqual(const Type &a, const Type &b, const Type &absTol, const Type &relTol)
Definition: Math.h:453
Vec3< typename promote< T, Coord::ValueType >::type > operator-(const Vec3< T > &v0, const Coord &v1)
Allow a Coord to be subtracted from a Vec3.
Definition: Coord.h:551
MatType scale(const Vec3< typename MatType::value_type > &s)
Return a matrix that scales by s.
Definition: Mat.h:615
Vec3< typename promote< T, typename Coord::ValueType >::type > operator+(const Vec3< T > &v0, const Coord &v1)
Allow a Coord to be added to or subtracted from a Vec3.
Definition: Coord.h:525
Type Exp(const Type &x)
Return ex.
Definition: Math.h:710
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:648
Coord Abs(const Coord &xyz)
Definition: Coord.h:515
T angle(const Vec2< T > &v1, const Vec2< T > &v2)
Definition: Vec2.h:446
Vec2< typename promote< S, T >::type > operator/(S scalar, const Vec2< T > &v)
Divide scalar by each element of the given vector and return the result.
Definition: Vec2.h:385
bool isExactlyEqual(const T0 &a, const T1 &b)
Return true if a is exactly equal to b.
Definition: Math.h:443
Vec2< T > minComponent(const Vec2< T > &v1, const Vec2< T > &v2)
Return component-wise minimum of the two vectors.
Definition: Vec2.h:504
bool operator!=(const Vec3< T0 > &v0, const Vec3< T1 > &v1)
Inequality operator, does exact floating point comparisons.
Definition: Vec3.h:481
Vec2< T > maxComponent(const Vec2< T > &v1, const Vec2< T > &v2)
Return component-wise maximum of the two vectors.
Definition: Vec2.h:513
Definition: Exceptions.h:13
#define OPENVDB_THROW(exception, message)
Definition: Exceptions.h:74
Dummy class for tag dispatch of conversion constructors.
Definition: Tuple.h:23
#define OPENVDB_VERSION_NAME
The version namespace name for this library version.
Definition: version.h.in:121
#define OPENVDB_USE_VERSION_NAMESPACE
Definition: version.h.in:212