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Vec3.h
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// Copyright Contributors to the OpenVDB Project
// SPDX-License-Identifier: MPL-2.0
#ifndef OPENVDB_MATH_VEC3_HAS_BEEN_INCLUDED
#define OPENVDB_MATH_VEC3_HAS_BEEN_INCLUDED
#include <openvdb/Exceptions.h>
#include "Math.h"
#include "Tuple.h"
#include <algorithm>
#include <cmath>
#include <type_traits>
namespace openvdb {
OPENVDB_USE_VERSION_NAMESPACE
namespace OPENVDB_VERSION_NAME {
namespace math {
template<typename T> class Mat3;
template<typename T>
class Vec3: public Tuple<3, T>
{
public:
using value_type = T;
using ValueType = T;
/// Trivial constructor, the vector is NOT initialized
/// @note destructor, copy constructor, assignment operator and
/// move constructor are left to be defined by the compiler (default)
Vec3() = default;
/// @brief Construct a vector all of whose components have the given value.
explicit Vec3(T val) { this->mm[0] = this->mm[1] = this->mm[2] = val; }
/// Constructor with three arguments, e.g. Vec3d v(1,2,3);
Vec3(T x, T y, T z)
{
this->mm[0] = x;
this->mm[1] = y;
this->mm[2] = z;
}
/// Constructor with array argument, e.g. double a[3]; Vec3d v(a);
template <typename Source>
Vec3(Source *a)
{
this->mm[0] = static_cast<T>(a[0]);
this->mm[1] = static_cast<T>(a[1]);
this->mm[2] = static_cast<T>(a[2]);
}
/// @brief Construct a Vec3 from a 3-Tuple with a possibly different value type.
/// @details Type conversion warnings are suppressed.
template<typename Source>
explicit Vec3(const Tuple<3, Source> &v)
{
this->mm[0] = static_cast<T>(v[0]);
this->mm[1] = static_cast<T>(v[1]);
this->mm[2] = static_cast<T>(v[2]);
}
/// @brief Construct a vector all of whose components have the given value,
/// which may be of an arithmetic type different from this vector's value type.
/// @details Type conversion warnings are suppressed.
template<typename Other>
explicit Vec3(Other val,
typename std::enable_if<std::is_arithmetic<Other>::value, Conversion>::type = Conversion{})
{
this->mm[0] = this->mm[1] = this->mm[2] = static_cast<T>(val);
}
/// @brief Construct a Vec3 from another Vec3 with a possibly different value type.
/// @details Type conversion warnings are suppressed.
template<typename Other>
Vec3(const Vec3<Other>& v)
{
this->mm[0] = static_cast<T>(v[0]);
this->mm[1] = static_cast<T>(v[1]);
this->mm[2] = static_cast<T>(v[2]);
}
/// Reference to the component, e.g. v.x() = 4.5f;
T& x() { return this->mm[0]; }
T& y() { return this->mm[1]; }
T& z() { return this->mm[2]; }
/// Get the component, e.g. float f = v.y();
T x() const { return this->mm[0]; }
T y() const { return this->mm[1]; }
T z() const { return this->mm[2]; }
T* asPointer() { return this->mm; }
const T* asPointer() const { return this->mm; }
/// Alternative indexed reference to the elements
T& operator()(int i) { return this->mm[i]; }
/// Alternative indexed constant reference to the elements,
T operator()(int i) const { return this->mm[i]; }
/// "this" vector gets initialized to [x, y, z],
/// calling v.init(); has same effect as calling v = Vec3::zero();
const Vec3<T>& init(T x=0, T y=0, T z=0)
{
this->mm[0] = x; this->mm[1] = y; this->mm[2] = z;
return *this;
}
/// Set "this" vector to zero
const Vec3<T>& setZero()
{
this->mm[0] = 0; this->mm[1] = 0; this->mm[2] = 0;
return *this;
}
/// @brief Assignment operator
/// @details Type conversion warnings are not suppressed.
template<typename Source>
const Vec3<T>& operator=(const Vec3<Source> &v)
{
// note: don't static_cast because that suppresses warnings
this->mm[0] = v[0];
this->mm[1] = v[1];
this->mm[2] = v[2];
return *this;
}
/// Test if "this" vector is equivalent to vector v with tolerance of eps
bool eq(const Vec3<T> &v, T eps = static_cast<T>(1.0e-7)) const
{
return isRelOrApproxEqual(this->mm[0], v.mm[0], eps, eps) &&
isRelOrApproxEqual(this->mm[1], v.mm[1], eps, eps) &&
isRelOrApproxEqual(this->mm[2], v.mm[2], eps, eps);
}
/// Negation operator, for e.g. v1 = -v2;
Vec3<T> operator-() const { return Vec3<T>(-this->mm[0], -this->mm[1], -this->mm[2]); }
/// this = v1 + v2
/// "this", v1 and v2 need not be distinct objects, e.g. v.add(v1,v);
template <typename T0, typename T1>
const Vec3<T>& add(const Vec3<T0> &v1, const Vec3<T1> &v2)
{
this->mm[0] = v1[0] + v2[0];
this->mm[1] = v1[1] + v2[1];
this->mm[2] = v1[2] + v2[2];
return *this;
}
/// this = v1 - v2
/// "this", v1 and v2 need not be distinct objects, e.g. v.sub(v1,v);
template <typename T0, typename T1>
const Vec3<T>& sub(const Vec3<T0> &v1, const Vec3<T1> &v2)
{
this->mm[0] = v1[0] - v2[0];
this->mm[1] = v1[1] - v2[1];
this->mm[2] = v1[2] - v2[2];
return *this;
}
/// this = scalar*v, v need not be a distinct object from "this",
/// e.g. v.scale(1.5,v1);
template <typename T0, typename T1>
const Vec3<T>& scale(T0 scale, const Vec3<T1> &v)
{
this->mm[0] = scale * v[0];
this->mm[1] = scale * v[1];
this->mm[2] = scale * v[2];
return *this;
}
template <typename T0, typename T1>
const Vec3<T> &div(T0 scale, const Vec3<T1> &v)
{
this->mm[0] = v[0] / scale;
this->mm[1] = v[1] / scale;
this->mm[2] = v[2] / scale;
return *this;
}
/// Dot product
T dot(const Vec3<T> &v) const
{
return
this->mm[0]*v.mm[0] +
this->mm[1]*v.mm[1] +
this->mm[2]*v.mm[2];
}
/// Length of the vector
T length() const
{
return static_cast<T>(sqrt(double(
this->mm[0]*this->mm[0] +
this->mm[1]*this->mm[1] +
this->mm[2]*this->mm[2])));
}
/// Squared length of the vector, much faster than length() as it
/// does not involve square root
T lengthSqr() const
{
return
this->mm[0]*this->mm[0] +
this->mm[1]*this->mm[1] +
this->mm[2]*this->mm[2];
}
/// Return the cross product of "this" vector and v;
Vec3<T> cross(const Vec3<T> &v) const
{
return Vec3<T>(this->mm[1]*v.mm[2] - this->mm[2]*v.mm[1],
this->mm[2]*v.mm[0] - this->mm[0]*v.mm[2],
this->mm[0]*v.mm[1] - this->mm[1]*v.mm[0]);
}
/// this = v1 cross v2, v1 and v2 must be distinct objects than "this"
const Vec3<T>& cross(const Vec3<T> &v1, const Vec3<T> &v2)
{
// assert(this!=&v1);
// assert(this!=&v2);
this->mm[0] = v1.mm[1]*v2.mm[2] - v1.mm[2]*v2.mm[1];
this->mm[1] = v1.mm[2]*v2.mm[0] - v1.mm[0]*v2.mm[2];
this->mm[2] = v1.mm[0]*v2.mm[1] - v1.mm[1]*v2.mm[0];
return *this;
}
/// Multiply each element of this vector by @a scalar.
template <typename S>
const Vec3<T> &operator*=(S scalar)
{
OPENVDB_NO_TYPE_CONVERSION_WARNING_BEGIN
const auto value0 = this->mm[0] * scalar;
const auto value1 = this->mm[1] * scalar;
const auto value2 = this->mm[2] * scalar;
OPENVDB_NO_TYPE_CONVERSION_WARNING_END
this->mm[0] = static_cast<T>(value0);
this->mm[1] = static_cast<T>(value1);
this->mm[2] = static_cast<T>(value2);
return *this;
}
/// Multiply each element of this vector by the corresponding element of the given vector.
template <typename S>
const Vec3<T> &operator*=(const Vec3<S> &v1)
{
this->mm[0] *= v1[0];
this->mm[1] *= v1[1];
this->mm[2] *= v1[2];
return *this;
}
/// Divide each element of this vector by @a scalar.
template <typename S>
const Vec3<T> &operator/=(S scalar)
{
this->mm[0] /= scalar;
this->mm[1] /= scalar;
this->mm[2] /= scalar;
return *this;
}
/// Divide each element of this vector by the corresponding element of the given vector.
template <typename S>
const Vec3<T> &operator/=(const Vec3<S> &v1)
{
this->mm[0] /= v1[0];
this->mm[1] /= v1[1];
this->mm[2] /= v1[2];
return *this;
}
/// Add @a scalar to each element of this vector.
template <typename S>
const Vec3<T> &operator+=(S scalar)
{
OPENVDB_NO_TYPE_CONVERSION_WARNING_BEGIN
const auto value0 = this->mm[0] + scalar;
const auto value1 = this->mm[1] + scalar;
const auto value2 = this->mm[2] + scalar;
OPENVDB_NO_TYPE_CONVERSION_WARNING_END
this->mm[0] = static_cast<T>(value0);
this->mm[1] = static_cast<T>(value1);
this->mm[2] = static_cast<T>(value2);
return *this;
}
/// Add each element of the given vector to the corresponding element of this vector.
template <typename S>
const Vec3<T> &operator+=(const Vec3<S> &v1)
{
this->mm[0] += v1[0];
this->mm[1] += v1[1];
this->mm[2] += v1[2];
return *this;
}
/// Subtract @a scalar from each element of this vector.
template <typename S>
const Vec3<T> &operator-=(S scalar)
{
this->mm[0] -= scalar;
this->mm[1] -= scalar;
this->mm[2] -= scalar;
return *this;
}
/// Subtract each element of the given vector from the corresponding element of this vector.
template <typename S>
const Vec3<T> &operator-=(const Vec3<S> &v1)
{
this->mm[0] -= v1[0];
this->mm[1] -= v1[1];
this->mm[2] -= v1[2];
return *this;
}
/// Return a reference to itself after the exponent has been
/// applied to all the vector components.
inline const Vec3<T>& exp()
{
this->mm[0] = std::exp(this->mm[0]);
this->mm[1] = std::exp(this->mm[1]);
this->mm[2] = std::exp(this->mm[2]);
return *this;
}
/// Return a reference to itself after log has been
/// applied to all the vector components.
inline const Vec3<T>& log()
{
this->mm[0] = std::log(this->mm[0]);
this->mm[1] = std::log(this->mm[1]);
this->mm[2] = std::log(this->mm[2]);
return *this;
}
/// Return the sum of all the vector components.
inline T sum() const
{
return this->mm[0] + this->mm[1] + this->mm[2];
}
/// Return the product of all the vector components.
inline T product() const
{
return this->mm[0] * this->mm[1] * this->mm[2];
}
/// this = normalized this
bool normalize(T eps = T(1.0e-7))
{
T d = length();
if (isApproxEqual(d, T(0), eps)) {
return false;
}
*this *= (T(1) / d);
return true;
}
/// return normalized this, throws if null vector
Vec3<T> unit(T eps=0) const
{
T d;
return unit(eps, d);
}
/// return normalized this and length, throws if null vector
Vec3<T> unit(T eps, T& len) const
{
len = length();
if (isApproxEqual(len, T(0), eps)) {
OPENVDB_THROW(ArithmeticError, "Normalizing null 3-vector");
}
return *this / len;
}
/// return normalized this, or (1, 0, 0) if this is null vector
Vec3<T> unitSafe() const
{
T l2 = lengthSqr();
return l2 ? *this / static_cast<T>(sqrt(l2)) : Vec3<T>(1, 0 ,0);
}
// Number of cols, rows, elements
static unsigned numRows() { return 1; }
static unsigned numColumns() { return 3; }
static unsigned numElements() { return 3; }
/// Returns the scalar component of v in the direction of onto, onto need
/// not be unit. e.g double c = Vec3d::component(v1,v2);
T component(const Vec3<T> &onto, T eps = static_cast<T>(1.0e-7)) const
{
T l = onto.length();
if (isApproxEqual(l, T(0), eps)) return 0;
return dot(onto)*(T(1)/l);
}
/// Return the projection of v onto the vector, onto need not be unit
/// e.g. Vec3d a = vprojection(n);
Vec3<T> projection(const Vec3<T> &onto, T eps = static_cast<T>(1.0e-7)) const
{
T l = onto.lengthSqr();
if (isApproxEqual(l, T(0), eps)) return Vec3::zero();
return onto*(dot(onto)*(T(1)/l));
}
/// Return an arbitrary unit vector perpendicular to v
/// Vector this must be a unit vector
/// e.g. v = v.normalize(); Vec3d n = v.getArbPerpendicular();
Vec3<T> getArbPerpendicular() const
{
Vec3<T> u;
T l;
if ( fabs(this->mm[0]) >= fabs(this->mm[1]) ) {
// v.x or v.z is the largest magnitude component, swap them
l = this->mm[0]*this->mm[0] + this->mm[2]*this->mm[2];
l = static_cast<T>(T(1)/sqrt(double(l)));
u.mm[0] = -this->mm[2]*l;
u.mm[1] = T(0);
u.mm[2] = +this->mm[0]*l;
} else {
// W.y or W.z is the largest magnitude component, swap them
l = this->mm[1]*this->mm[1] + this->mm[2]*this->mm[2];
l = static_cast<T>(T(1)/sqrt(double(l)));
u.mm[0] = T(0);
u.mm[1] = +this->mm[2]*l;
u.mm[2] = -this->mm[1]*l;
}
return u;
}
/// Return a vector with the components of this in ascending order
Vec3<T> sorted() const
{
Vec3<T> r(*this);
if( r.mm[0] > r.mm[1] ) std::swap(r.mm[0], r.mm[1]);
if( r.mm[1] > r.mm[2] ) std::swap(r.mm[1], r.mm[2]);
if( r.mm[0] > r.mm[1] ) std::swap(r.mm[0], r.mm[1]);
return r;
}
/// Return the vector (z, y, x)
Vec3<T> reversed() const
{
return Vec3<T>(this->mm[2], this->mm[1], this->mm[0]);
}
/// Predefined constants, e.g. Vec3d v = Vec3d::xNegAxis();
static Vec3<T> zero() { return Vec3<T>(0, 0, 0); }
static Vec3<T> ones() { return Vec3<T>(1, 1, 1); }
};
/// Equality operator, does exact floating point comparisons
template <typename T0, typename T1>
inline bool operator==(const Vec3<T0> &v0, const Vec3<T1> &v1)
{
return isExactlyEqual(v0[0], v1[0]) && isExactlyEqual(v0[1], v1[1])
&& isExactlyEqual(v0[2], v1[2]);
}
/// Inequality operator, does exact floating point comparisons
template <typename T0, typename T1>
inline bool operator!=(const Vec3<T0> &v0, const Vec3<T1> &v1) { return !(v0==v1); }
/// Multiply each element of the given vector by @a scalar and return the result.
template <typename S, typename T>
inline Vec3<typename promote<S, T>::type> operator*(S scalar, const Vec3<T> &v) { return v*scalar; }
/// Multiply each element of the given vector by @a scalar and return the result.
template <typename S, typename T>
inline Vec3<typename promote<S, T>::type> operator*(const Vec3<T> &v, S scalar)
{
Vec3<typename promote<S, T>::type> result(v);
result *= scalar;
return result;
}
/// Multiply corresponding elements of @a v0 and @a v1 and return the result.
template <typename T0, typename T1>
inline Vec3<typename promote<T0, T1>::type> operator*(const Vec3<T0> &v0, const Vec3<T1> &v1)
{
Vec3<typename promote<T0, T1>::type> result(v0[0] * v1[0], v0[1] * v1[1], v0[2] * v1[2]);
return result;
}
/// Divide @a scalar by each element of the given vector and return the result.
template <typename S, typename T>
inline Vec3<typename promote<S, T>::type> operator/(S scalar, const Vec3<T> &v)
{
return Vec3<typename promote<S, T>::type>(scalar/v[0], scalar/v[1], scalar/v[2]);
}
/// Divide each element of the given vector by @a scalar and return the result.
template <typename S, typename T>
inline Vec3<typename promote<S, T>::type> operator/(const Vec3<T> &v, S scalar)
{
Vec3<typename promote<S, T>::type> result(v);
result /= scalar;
return result;
}
/// Divide corresponding elements of @a v0 and @a v1 and return the result.
template <typename T0, typename T1>
inline Vec3<typename promote<T0, T1>::type> operator/(const Vec3<T0> &v0, const Vec3<T1> &v1)
{
Vec3<typename promote<T0, T1>::type> result(v0[0] / v1[0], v0[1] / v1[1], v0[2] / v1[2]);
return result;
}
/// Add corresponding elements of @a v0 and @a v1 and return the result.
template <typename T0, typename T1>
inline Vec3<typename promote<T0, T1>::type> operator+(const Vec3<T0> &v0, const Vec3<T1> &v1)
{
Vec3<typename promote<T0, T1>::type> result(v0);
result += v1;
return result;
}
/// Add @a scalar to each element of the given vector and return the result.
template <typename S, typename T>
inline Vec3<typename promote<S, T>::type> operator+(const Vec3<T> &v, S scalar)
{
Vec3<typename promote<S, T>::type> result(v);
result += scalar;
return result;
}
/// Subtract corresponding elements of @a v0 and @a v1 and return the result.
template <typename T0, typename T1>
inline Vec3<typename promote<T0, T1>::type> operator-(const Vec3<T0> &v0, const Vec3<T1> &v1)
{
Vec3<typename promote<T0, T1>::type> result(v0);
result -= v1;
return result;
}
/// Subtract @a scalar from each element of the given vector and return the result.
template <typename S, typename T>
inline Vec3<typename promote<S, T>::type> operator-(const Vec3<T> &v, S scalar)
{
Vec3<typename promote<S, T>::type> result(v);
result -= scalar;
return result;
}
/// Angle between two vectors, the result is between [0, pi],
/// e.g. double a = Vec3d::angle(v1,v2);
template <typename T>
inline T angle(const Vec3<T> &v1, const Vec3<T> &v2)
{
Vec3<T> c = v1.cross(v2);
return static_cast<T>(atan2(c.length(), v1.dot(v2)));
}
template <typename T>
inline bool
isApproxEqual(const Vec3<T>& a, const Vec3<T>& b)
{
return a.eq(b);
}
template <typename T>
inline bool
isApproxEqual(const Vec3<T>& a, const Vec3<T>& b, const Vec3<T>& eps)
{
return isApproxEqual(a.x(), b.x(), eps.x()) &&
isApproxEqual(a.y(), b.y(), eps.y()) &&
isApproxEqual(a.z(), b.z(), eps.z());
}
template<typename T>
inline Vec3<T>
Abs(const Vec3<T>& v)
{
return Vec3<T>(Abs(v[0]), Abs(v[1]), Abs(v[2]));
}
/// Orthonormalize vectors v1, v2 and v3 and store back the resulting
/// basis e.g. Vec3d::orthonormalize(v1,v2,v3);
template <typename T>
inline void orthonormalize(Vec3<T> &v1, Vec3<T> &v2, Vec3<T> &v3)
{
// If the input vectors are v0, v1, and v2, then the Gram-Schmidt
// orthonormalization produces vectors u0, u1, and u2 as follows,
//
// u0 = v0/|v0|
// u1 = (v1-(u0*v1)u0)/|v1-(u0*v1)u0|
// u2 = (v2-(u0*v2)u0-(u1*v2)u1)/|v2-(u0*v2)u0-(u1*v2)u1|
//
// where |A| indicates length of vector A and A*B indicates dot
// product of vectors A and B.
// compute u0
v1.normalize();
// compute u1
T d0 = v1.dot(v2);
v2 -= v1*d0;
v2.normalize();
// compute u2
T d1 = v2.dot(v3);
d0 = v1.dot(v3);
v3 -= v1*d0 + v2*d1;
v3.normalize();
}
/// @remark We are switching to a more explicit name because the semantics
/// are different from std::min/max. In that case, the function returns a
/// reference to one of the objects based on a comparator. Here, we must
/// fabricate a new object which might not match either of the inputs.
/// Return component-wise minimum of the two vectors.
template <typename T>
inline Vec3<T> minComponent(const Vec3<T> &v1, const Vec3<T> &v2)
{
return Vec3<T>(
std::min(v1.x(), v2.x()),
std::min(v1.y(), v2.y()),
std::min(v1.z(), v2.z()));
}
/// Return component-wise maximum of the two vectors.
template <typename T>
inline Vec3<T> maxComponent(const Vec3<T> &v1, const Vec3<T> &v2)
{
return Vec3<T>(
std::max(v1.x(), v2.x()),
std::max(v1.y(), v2.y()),
std::max(v1.z(), v2.z()));
}
/// @brief Return a vector with the exponent applied to each of
/// the components of the input vector.
template <typename T>
inline Vec3<T> Exp(Vec3<T> v) { return v.exp(); }
/// @brief Return a vector with log applied to each of
/// the components of the input vector.
template <typename T>
inline Vec3<T> Log(Vec3<T> v) { return v.log(); }
using Vec3i = Vec3<int32_t>;
using Vec3ui = Vec3<uint32_t>;
using Vec3s = Vec3<float>;
using Vec3d = Vec3<double>;
OPENVDB_IS_POD(Vec3i)
OPENVDB_IS_POD(Vec3ui)
OPENVDB_IS_POD(Vec3s)
OPENVDB_IS_POD(Vec3d)
} // namespace math
} // namespace OPENVDB_VERSION_NAME
} // namespace openvdb
#endif // OPENVDB_MATH_VEC3_HAS_BEEN_INCLUDED
Math.h
General-purpose arithmetic and comparison routines, most of which accept arbitrary value types (or at...
OPENVDB_IS_POD
#define OPENVDB_IS_POD(Type)
Definition Math.h:56
OPENVDB_NO_TYPE_CONVERSION_WARNING_BEGIN
#define OPENVDB_NO_TYPE_CONVERSION_WARNING_BEGIN
Bracket code with OPENVDB_NO_TYPE_CONVERSION_WARNING_BEGIN/_END, to inhibit warnings about type conve...
Definition Platform.h:204
OPENVDB_NO_TYPE_CONVERSION_WARNING_END
#define OPENVDB_NO_TYPE_CONVERSION_WARNING_END
Definition Platform.h:205
Tuple.h
openvdb::v10_0::ArithmeticError
Definition Exceptions.h:56
openvdb::v10_0::math::Vec3< Real >::mm
Real mm[SIZE]
Definition Tuple.h:164
openvdb::v10_0::math::Tuple< 3, T >::Tuple
Tuple()=default
openvdb::v10_0::math::Vec3
Definition Vec3.h:24
openvdb::v10_0::math::Vec3::sorted
Vec3< T > sorted() const
Return a vector with the components of this in ascending order.
Definition Vec3.h:450
openvdb::v10_0::math::Vec3::div
const Vec3< T > & div(T0 scale, const Vec3< T1 > &v)
Definition Vec3.h:181
openvdb::v10_0::math::Vec3< Real >::x
Real & x()
Definition Vec3.h:85
openvdb::v10_0::math::Vec3::sub
const Vec3< T > & sub(const Vec3< T0 > &v1, const Vec3< T1 > &v2)
Definition Vec3.h:159
openvdb::v10_0::math::Vec3::setZero
const Vec3< T > & setZero()
Set "this" vector to zero.
Definition Vec3.h:113
openvdb::v10_0::math::Vec3::operator/=
const Vec3< T > & operator/=(S scalar)
Divide each element of this vector by scalar.
Definition Vec3.h:266
openvdb::v10_0::math::Vec3::reversed
Vec3< T > reversed() const
Return the vector (z, y, x).
Definition Vec3.h:460
openvdb::v10_0::math::Vec3::add
const Vec3< T > & add(const Vec3< T0 > &v1, const Vec3< T1 > &v2)
Definition Vec3.h:147
openvdb::v10_0::math::Vec3::length
T length() const
Length of the vector.
Definition Vec3.h:200
openvdb::v10_0::math::Vec3::Vec3
Vec3(Source *a)
Constructor with array argument, e.g. double a[3]; Vec3d v(a);.
Definition Vec3.h:47
openvdb::v10_0::math::Vec3::dot
T dot(const Vec3< T > &v) const
Dot product.
Definition Vec3.h:191
openvdb::v10_0::math::Vec3::operator*=
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
openvdb::v10_0::math::Vec3::operator*=
const Vec3< T > & operator*=(S scalar)
Multiply each element of this vector by scalar.
Definition Vec3.h:241
openvdb::v10_0::math::Vec3::sum
T sum() const
Return the sum of all the vector components.
Definition Vec3.h:350
openvdb::v10_0::math::Vec3::numColumns
static unsigned numColumns()
Definition Vec3.h:399
openvdb::v10_0::math::Vec3::operator/=
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
openvdb::v10_0::math::Vec3::init
const Vec3< T > & init(T x=0, T y=0, T z=0)
Definition Vec3.h:105
openvdb::v10_0::math::Vec3::Vec3
Vec3(T x, T y, T z)
Constructor with three arguments, e.g. Vec3d v(1,2,3);.
Definition Vec3.h:38
openvdb::v10_0::math::Vec3::unit
Vec3< T > unit(T eps, T &len) const
return normalized this and length, throws if null vector
Definition Vec3.h:381
openvdb::v10_0::math::Vec3::asPointer
T * asPointer()
Definition Vec3.h:94
openvdb::v10_0::math::Vec3::eq
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
openvdb::v10_0::math::Vec3::numRows
static unsigned numRows()
Definition Vec3.h:398
openvdb::v10_0::math::Vec3::getArbPerpendicular
Vec3< T > getArbPerpendicular() const
Definition Vec3.h:425
openvdb::v10_0::math::Vec3::log
const Vec3< T > & log()
Definition Vec3.h:341
openvdb::v10_0::math::Vec3::operator()
T & operator()(int i)
Alternative indexed reference to the elements.
Definition Vec3.h:98
openvdb::v10_0::math::Vec3< Real >::y
Real & y()
Definition Vec3.h:86
openvdb::v10_0::math::Vec3::component
T component(const Vec3< T > &onto, T eps=static_cast< T >(1.0e-7)) const
Definition Vec3.h:404
openvdb::v10_0::math::Vec3::Vec3
Vec3(T val)
Construct a vector all of whose components have the given value.
Definition Vec3.h:35
openvdb::v10_0::math::Vec3< Real >::z
Real & z()
Definition Vec3.h:87
openvdb::v10_0::math::Vec3::operator()
T operator()(int i) const
Alternative indexed constant reference to the elements,.
Definition Vec3.h:101
openvdb::v10_0::math::Vec3::product
T product() const
Return the product of all the vector components.
Definition Vec3.h:356
openvdb::v10_0::math::Vec3::cross
Vec3< T > cross(const Vec3< T > &v) const
Return the cross product of "this" vector and v;.
Definition Vec3.h:220
openvdb::v10_0::math::Vec3::asPointer
const T * asPointer() const
Definition Vec3.h:95
openvdb::v10_0::math::Vec3::lengthSqr
T lengthSqr() const
Definition Vec3.h:211
openvdb::v10_0::math::Vec3::Vec3
Vec3(const Vec3< Other > &v)
Construct a Vec3 from another Vec3 with a possibly different value type.
Definition Vec3.h:77
openvdb::v10_0::math::Vec3::zero
static Vec3< T > zero()
Predefined constants, e.g. Vec3d v = Vec3d::xNegAxis();.
Definition Vec3.h:466
openvdb::v10_0::math::Vec3::Vec3
Vec3()=default
openvdb::v10_0::math::Vec3::cross
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
openvdb::v10_0::math::Vec3::Vec3
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
openvdb::v10_0::math::Vec3::x
T x() const
Get the component, e.g. float f = v.y();.
Definition Vec3.h:90
openvdb::v10_0::math::Vec3::Vec3
Vec3(const Tuple< 3, Source > &v)
Construct a Vec3 from a 3-Tuple with a possibly different value type.
Definition Vec3.h:57
openvdb::v10_0::math::Vec3::operator+=
const Vec3< T > & operator+=(S scalar)
Add scalar to each element of this vector.
Definition Vec3.h:286
openvdb::v10_0::math::Vec3::operator=
const Vec3< T > & operator=(const Vec3< Source > &v)
Assignment operator.
Definition Vec3.h:122
openvdb::v10_0::math::Vec3::z
T z() const
Definition Vec3.h:92
openvdb::v10_0::math::Vec3::ones
static Vec3< T > ones()
Definition Vec3.h:467
openvdb::v10_0::math::Vec3::unitSafe
Vec3< T > unitSafe() const
return normalized this, or (1, 0, 0) if this is null vector
Definition Vec3.h:391
openvdb::v10_0::math::Vec3::y
T y() const
Definition Vec3.h:91
openvdb::v10_0::math::Vec3::operator-
Vec3< T > operator-() const
Negation operator, for e.g. v1 = -v2;.
Definition Vec3.h:142
openvdb::v10_0::math::Vec3::scale
const Vec3< T > & scale(T0 scale, const Vec3< T1 > &v)
Definition Vec3.h:171
openvdb::v10_0::math::Vec3::projection
Vec3< T > projection(const Vec3< T > &onto, T eps=static_cast< T >(1.0e-7)) const
Definition Vec3.h:414
openvdb::v10_0::math::Vec3::numElements
static unsigned numElements()
Definition Vec3.h:400
openvdb::v10_0::math::Vec3::unit
Vec3< T > unit(T eps=0) const
return normalized this, throws if null vector
Definition Vec3.h:374
openvdb::v10_0::math::Vec3::operator-=
const Vec3< T > & operator-=(S scalar)
Subtract scalar from each element of this vector.
Definition Vec3.h:311
openvdb::v10_0::math::Vec3::normalize
bool normalize(T eps=T(1.0e-7))
this = normalized this
Definition Vec3.h:362
openvdb::v10_0::math::Vec3< Real >::ValueType
Real ValueType
Definition Vec3.h:27
openvdb::v10_0::math::Vec3::operator-=
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
openvdb::v10_0::math::Vec3::exp
const Vec3< T > & exp()
Definition Vec3.h:331
openvdb::v10_0::math::Vec3::operator+=
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
openvdb::v10_0::math::Vec3< Real >::value_type
Real value_type
Definition Vec3.h:26
openvdb::v10_0::math::Log
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
openvdb::v10_0::math::operator==
bool operator==(const Vec3< T0 > &v0, const Vec3< T1 > &v1)
Equality operator, does exact floating point comparisons.
Definition Vec3.h:473
openvdb::v10_0::math::orthonormalize
void orthonormalize(Vec2< T > &v1, Vec2< T > &v2)
Definition Vec2.h:476
openvdb::v10_0::math::operator*
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
openvdb::v10_0::math::isApproxEqual
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
openvdb::v10_0::math::isRelOrApproxEqual
bool isRelOrApproxEqual(const Type &a, const Type &b, const Type &absTol, const Type &relTol)
Definition Math.h:453
openvdb::v10_0::math::operator-
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
openvdb::v10_0::math::operator+
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
openvdb::v10_0::math::Vec3ui
Vec3< uint32_t > Vec3ui
Definition Vec3.h:662
openvdb::v10_0::math::Exp
Type Exp(const Type &x)
Return ex.
Definition Math.h:710
openvdb::v10_0::math::Vec3d
Vec3< double > Vec3d
Definition Vec3.h:664
openvdb::v10_0::math::Abs
Coord Abs(const Coord &xyz)
Definition Coord.h:515
openvdb::v10_0::math::angle
T angle(const Vec2< T > &v1, const Vec2< T > &v2)
Definition Vec2.h:446
openvdb::v10_0::math::operator/
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
openvdb::v10_0::math::isExactlyEqual
bool isExactlyEqual(const T0 &a, const T1 &b)
Return true if a is exactly equal to b.
Definition Math.h:443
openvdb::v10_0::math::minComponent
Vec2< T > minComponent(const Vec2< T > &v1, const Vec2< T > &v2)
Return component-wise minimum of the two vectors.
Definition Vec2.h:504
openvdb::v10_0::math::operator!=
bool operator!=(const Vec3< T0 > &v0, const Vec3< T1 > &v1)
Inequality operator, does exact floating point comparisons.
Definition Vec3.h:481
openvdb::v10_0::math::Vec3i
Vec3< int32_t > Vec3i
Definition Vec3.h:661
openvdb::v10_0::math::maxComponent
Vec2< T > maxComponent(const Vec2< T > &v1, const Vec2< T > &v2)
Return component-wise maximum of the two vectors.
Definition Vec2.h:513
openvdb::v10_0::math::Vec3s
Vec3< float > Vec3s
Definition Vec3.h:663
openvdb
Definition Exceptions.h:13
Exceptions.h
OPENVDB_THROW
#define OPENVDB_THROW(exception, message)
Definition Exceptions.h:74
openvdb::v10_0::math::Conversion
Dummy class for tag dispatch of conversion constructors.
Definition Tuple.h:23
OPENVDB_VERSION_NAME
#define OPENVDB_VERSION_NAME
The version namespace name for this library version.
Definition version.h.in:121
OPENVDB_USE_VERSION_NAMESPACE
#define OPENVDB_USE_VERSION_NAMESPACE
Definition version.h.in:212