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MagnumMath.hpp
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MagnumMath.hpp
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/*
Magnum::Math
— a graphics-focused vector math library
https://doc.magnum.graphics/magnum/namespaceMagnum_1_1Math.html
https://doc.magnum.graphics/magnum/namespaceMagnum_1_1EigenIntegration.html
https://doc.magnum.graphics/magnum/namespaceMagnum_1_1GlmIntegration.html
Depends on CorradePair.h.
This is a single-header library generated from the Magnum project. With the
goal being easy integration, it's deliberately free of all comments to keep
the file size small. More info, changelogs and full docs here:
- Project homepage — https://magnum.graphics/magnum/
- Documentation — https://doc.magnum.graphics/
- GitHub project page — https://github.com/mosra/magnum
- GitHub Singles repository — https://github.com/mosra/magnum-singles
The library has a separate non-inline implementation part, enable it *just
once* like this:
#define MAGNUM_MATH_IMPLEMENTATION
#include <MagnumMath.hpp>
If you need the deinlined symbols to be exported from a shared library,
`#define MAGNUM_EXPORT` as appropriate. The STL compatibility bits for time
types are included as well --- opt-in with
`#define MAGNUM_MATH_STL_COMPATIBILITY` before including the file. Contents
of the GlmIntegration and EigenIntegration libraries can be opted in by
specifying either `#define MAGNUM_MATH_GLM_INTEGRATION` or
`#define MAGNUM_MATH_EIGEN_INTEGRATION` before including the file.
Including it multiple times with different macros defined works as well.
v2020.06-3125-g632a2 (2025-01-07)
- New Nanoseconds and Seconds types along with _nsec, _usec, _msec and
_sec literals and opt-in std::chrono compatibility
- Literals are now in inline AngleLiterals, ColorLiterals, HalfLiterals
and TimeLiterals subnamespaces to allow for more fine-grained inclusion
- Most const Vector APIs are now constexpr as well
- The _rgbf and _rgbaf literals are now constexpr
- Vector and [Rectangular]Matrix instances can are now constexpr
constructible directly from plain C arrays of matching sizes
- Added Quaternion::rotation() from two vectors
- Added Quaternion::xyzw() and wxyz() for conversion to a Vector4
- Bezier APIs now use the leaf Vector2 / Vector3 types instead of the
base Vector type
- New Matrix2x1, Matrix3x1, Matrix4x1, Matrix2x1d, Matrix3x1d and
Matrix4x1d typedefs for single-row matrices
- Removed dependency on <utility> in favor of CorradePair.h, which
reduces the preprocessed size by about 500 lines, and enables constexpr
usage in various new places
- Updated Eigen integration to work with MSVC 2022 17.10+
v2020.06-2544-g3e435 (2023-09-11)
- Fixes to the Utility::swap() helper to avoid ambiguity with std::swap()
v2020.06-2502-gfa079385b (2023-08-28)
- New Range1Dui, Range2Dui, Range3Dui, Degh, Radh, Range1Dh, Range2Dh and
Range3Dh typedefs
- New binomialCoefficient(), popcount() and fmod() APIs
- Added r() and g() accessors to Vector2 and rg() to Vector3
- New Color3::fromLinearRgbInt(), toLinearRgbInt() and
Color4::fromLinearRgbaInt(), toLinearRgbaInt() for converting a color
from/to a packed 24-/32-bit representation without a sRGB conversion;
integer-taking fromSrgb() and fromSrgbAlpha() is now renamed to
fromSrgbInt() and fromSrgbAlphaInt() for consistency
- Added an off-center Matrix3::projection() and
Matrix4::orthographicProjection() overloads
- New Matrix4::orthographicProjectionNear(), orthographicProjectionFar(),
perspectiveProjectionNear(), perspectiveProjectionFar() accessors
- Added Quaternion::reflection() and reflectVector() APIs which perform
a reflection with a quaternion instead of a rotation
- Ability to create a DualQuaternion from a rotation quaternion and a
translation vector
- angle() for Quaternion is now called halfAngle() because that's what it
returns, angle() will be eventually reintroduced again but returning
the correct value
- Convenience Distance::pointPoint() and pointPointSquared(),
Intersection::pointCircle() and pointSphere() APIs as a more
self-documenting way of using (a - b).length() or dot()
- New Intersection::rayRange() API
- Conversion between Eigen::AlignedBox and Range
- Added unary operator+ to all math classes
- Matrices can now created from matrices of different sizes with a custom
value on new diagonal elements
- data() accessors of all classes now return sized array references
instead of pointers
- Fixed Matrix4::normalMatrix() to behave correctly in presence of a
reflection
- BoolVector is renamed to BitVector and has new set() and reset() APIs
- 64-bit integers and long doubles are no longer compiled away on
Emscripten
- Fixed QuadraticBezier2Dd, QuadraticBezier3Dd, CubicBezier2Dd and
CubicBezier3Dd typedefs to be actually doubles
- Compatibility with C++20 which removes the <ciso646> header
v2020.06-0-gfac6f4da2 (2020-06-27)
- Various fixes for Clang-CL compatibility
- Expanding the APIs to work with Half and long double types
- Magnum::Math::NoInit is now Magnum::NoInit
- Minor changes for faster performance of dot() and cross() in Debug
- Added reflect() and refract() functions
- slerp() / slerpShortestPath() falls back to linear interpolation for
quaternions that are close together, instead or always returning the
first
- Added Quaternion::toEuler()
- Added transformVector() to DualComplex and DualQuaternion to have the
the same set of APIs as with Matrix3 / Matrix4
- Mutable access to Frustum planes
- Fixed implicit conversion of std::pair to Range*D
- New BoolVector[234], 8-/16-bit and half-float vector and matrix
convenience typedefs
v2019.10-0-g8412e8f99 (2019-10-24)
- New IsScalar, IsVector, IsIntegral, IsFloatingPoint type traits,
correct handling of Deg and Rad types in all APIs
- Guaranteed NaN handling semantic in min()/max()/minmax() APIs
- Using a GCC compiler builtin in sincos()
- swizzle() is replaced with gather() and scatter()
- Added Matrix::{cofactor,comatrix,adjugate}(), Matrix4::normalMatrix()
- New Matrix4::perspectiveProjection() overload taking corner positions
- Handling also Eigen::Ref types; EigenIntegration::eigenCast() is now
just EigenIntegration::cast()
v2019.01-241-g93686746a (2019-04-03)
- Initial release
Generated from Corrade v2020.06-1846-gc4cdf (2025-01-07),
Magnum v2020.06-3125-g632a2 (2025-01-07) and
Magnum Integration v2020.06-282-ged27 (2025-01-05), 8388 / 9812 LoC
*/
/*
This file is part of Magnum.
Copyright © 2007, 2008, 2009, 2010, 2011, 2012, 2013, 2014, 2015, 2016,
2017, 2018, 2019, 2020, 2021, 2022, 2023, 2024, 2025
Vladimír Vondruš <[email protected]>
Copyright © 2016 Ashwin Ravichandran <[email protected]>
Copyright © 2016, 2018, 2020 Jonathan Hale <[email protected]>
Copyright © 2017 sigman78 <[email protected]>
Copyright © 2019 Marco Melorio <[email protected]>
Copyright © 2020 Janos <[email protected]>
Copyright © 2020 Nghia Truong <[email protected]>
Copyright © 2020 Pablo Escobar <[email protected]>
Copyright © 2024 John Turner <[email protected]>
Permission is hereby granted, free of charge, to any person obtaining a
copy of this software and associated documentation files (the "Software"),
to deal in the Software without restriction, including without limitation
the rights to use, copy, modify, merge, publish, distribute, sublicense,
and/or sell copies of the Software, and to permit persons to whom the
Software is furnished to do so, subject to the following conditions:
The above copyright notice and this permission notice shall be included
in all copies or substantial portions of the Software.
THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL
THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING
FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER
DEALINGS IN THE SOFTWARE.
*/
#include <cstddef>
#include <cstdint>
#include <cstdlib>
#include <type_traits>
#include "CorradePair.h"
#if (!defined(CORRADE_ASSERT) || !defined(CORRADE_CONSTEXPR_ASSERT) || !defined(CORRADE_INTERNAL_ASSERT_OUTPUT) || !defined(CORRADE_INTERNAL_ASSERT_UNREACHABLE)) && !defined(NDEBUG)
#include <cassert>
#endif
#if defined(_MSC_VER) && _MSC_VER < 1920
#define CORRADE_MSVC2017_COMPATIBILITY
#endif
#if defined(_MSC_VER) && _MSC_VER < 1910
#define CORRADE_MSVC2015_COMPATIBILITY
#endif
#ifdef _WIN32
#define CORRADE_TARGET_WINDOWS
#endif
#ifdef __EMSCRIPTEN__
#define CORRADE_TARGET_EMSCRIPTEN
#endif
#ifdef __ANDROID__
#define CORRADE_TARGET_ANDROID
#endif
#ifdef __GNUC__
#define CORRADE_TARGET_GCC
#endif
#ifdef __clang__
#define CORRADE_TARGET_CLANG
#endif
#if defined(__clang__) && defined(_MSC_VER)
#define CORRADE_TARGET_CLANG_CL
#endif
#ifdef _MSC_VER
#define CORRADE_TARGET_MSVC
#endif
#if defined(CORRADE_TARGET_MSVC) || (defined(CORRADE_TARGET_ANDROID) && !__LP64__) || defined(CORRADE_TARGET_EMSCRIPTEN) || (defined(CORRADE_TARGET_APPLE) && !defined(CORRADE_TARGET_IOS) && defined(CORRADE_TARGET_ARM))
#define CORRADE_LONG_DOUBLE_SAME_AS_DOUBLE
#endif
#ifndef MAGNUM_EXPORT
#define MAGNUM_EXPORT
#endif
#ifndef Corrade_Utility_StlMath_h
#define Corrade_Utility_StlMath_h
#ifdef _GLIBCXX_USE_STD_SPEC_FUNCS
#undef _GLIBCXX_USE_STD_SPEC_FUNCS
#define _GLIBCXX_USE_STD_SPEC_FUNCS 0
#endif
#include <cmath>
#endif
#ifndef Magnum_Types_h
#define Magnum_Types_h
namespace Magnum {
typedef std::uint8_t UnsignedByte;
typedef std::int8_t Byte;
typedef std::uint16_t UnsignedShort;
typedef std::int16_t Short;
typedef std::uint32_t UnsignedInt;
typedef std::int32_t Int;
typedef std::uint64_t UnsignedLong;
typedef std::int64_t Long;
typedef float Float;
typedef double Double;
}
#endif
#ifndef Magnum_Math_Math_h
#define Magnum_Math_Math_h
namespace Magnum { namespace Math {
template<std::size_t> class BitVector;
template<class> struct Constants;
template<class> class Complex;
template<class> class Dual;
template<class> class DualComplex;
template<class> class DualQuaternion;
template<class> class Frustum;
template<std::size_t, class> class Matrix;
template<class T> using Matrix2x2 = Matrix<2, T>;
template<class T> using Matrix3x3 = Matrix<3, T>;
template<class T> using Matrix4x4 = Matrix<4, T>;
template<class> class Matrix3;
template<class> class Matrix4;
template<class> class Quaternion;
template<std::size_t, std::size_t, class> class RectangularMatrix;
template<class T> using Matrix2x1 = RectangularMatrix<2, 1, T>;
template<class T> using Matrix2x3 = RectangularMatrix<2, 3, T>;
template<class T> using Matrix2x4 = RectangularMatrix<2, 4, T>;
template<class T> using Matrix3x1 = RectangularMatrix<3, 1, T>;
template<class T> using Matrix3x2 = RectangularMatrix<3, 2, T>;
template<class T> using Matrix3x4 = RectangularMatrix<3, 4, T>;
template<class T> using Matrix4x1 = RectangularMatrix<4, 1, T>;
template<class T> using Matrix4x2 = RectangularMatrix<4, 2, T>;
template<class T> using Matrix4x3 = RectangularMatrix<4, 3, T>;
template<template<class> class, class> class Unit;
template<class> class Deg;
template<class> class Rad;
template<class> class Nanoseconds;
template<class> class Seconds;
class Half;
template<std::size_t, class> class Vector;
template<class> class Vector2;
template<class> class Vector3;
template<class> class Vector4;
template<class> struct ColorHsv;
template<class> class Color3;
template<class> class Color4;
template<UnsignedInt, UnsignedInt, class> class Bezier;
template<UnsignedInt dimensions, class T> using QuadraticBezier = Bezier<2, dimensions, T>;
template<UnsignedInt dimensions, class T> using CubicBezier = Bezier<3, dimensions, T>;
template<class T> using QuadraticBezier2D = QuadraticBezier<2, T>;
template<class T> using QuadraticBezier3D = QuadraticBezier<3, T>;
template<class T> using CubicBezier2D = CubicBezier<2, T>;
template<class T> using CubicBezier3D = CubicBezier<3, T>;
template<class> class CubicHermite;
template<class T> using CubicHermite1D = CubicHermite<T>;
template<class T> using CubicHermite2D = CubicHermite<Vector2<T>>;
template<class T> using CubicHermite3D = CubicHermite<Vector3<T>>;
template<class T> using CubicHermiteComplex = CubicHermite<Complex<T>>;
template<class T> using CubicHermiteQuaternion = CubicHermite<Quaternion<T>>;
template<UnsignedInt, class> class Range;
template<class T> using Range1D = Range<1, T>;
template<class> class Range2D;
template<class> class Range3D;
}}
#endif
#ifndef MagnumMath_hpp
#define MagnumMath_hpp
#define CORRADE_HAS_TYPE(className, ...) \
template<class U> class className { \
template<class T> static char get(T&&, __VA_ARGS__* = nullptr); \
static short get(...); \
public: \
enum: bool { value = sizeof(get(std::declval<U>())) == sizeof(char) }; \
}
namespace Magnum {
using namespace Corrade;
typedef Math::Half Half;
typedef Math::BitVector<2> BitVector2;
typedef Math::BitVector<3> BitVector3;
typedef Math::BitVector<4> BitVector4;
typedef Math::Vector2<Float> Vector2;
typedef Math::Vector3<Float> Vector3;
typedef Math::Vector4<Float> Vector4;
typedef Math::Vector2<UnsignedByte> Vector2ub;
typedef Math::Vector3<UnsignedByte> Vector3ub;
typedef Math::Vector4<UnsignedByte> Vector4ub;
typedef Math::Vector2<Byte> Vector2b;
typedef Math::Vector3<Byte> Vector3b;
typedef Math::Vector4<Byte> Vector4b;
typedef Math::Vector2<UnsignedShort> Vector2us;
typedef Math::Vector3<UnsignedShort> Vector3us;
typedef Math::Vector4<UnsignedShort> Vector4us;
typedef Math::Vector2<Short> Vector2s;
typedef Math::Vector3<Short> Vector3s;
typedef Math::Vector4<Short> Vector4s;
typedef Math::Vector2<UnsignedInt> Vector2ui;
typedef Math::Vector3<UnsignedInt> Vector3ui;
typedef Math::Vector4<UnsignedInt> Vector4ui;
typedef Math::Vector2<Int> Vector2i;
typedef Math::Vector3<Int> Vector3i;
typedef Math::Vector4<Int> Vector4i;
typedef Math::Color3<Float> Color3;
typedef Math::Color4<Float> Color4;
typedef Math::Color3<UnsignedByte> Color3ub;
typedef Math::Color4<UnsignedByte> Color4ub;
typedef Math::Color3<UnsignedShort> Color3us;
typedef Math::Color4<UnsignedShort> Color4us;
typedef Math::Matrix3<Float> Matrix3;
typedef Math::Matrix4<Float> Matrix4;
typedef Math::Matrix2x1<Float> Matrix2x1;
typedef Math::Matrix2x2<Float> Matrix2x2;
typedef Math::Matrix2x3<Float> Matrix2x3;
typedef Math::Matrix2x4<Float> Matrix2x4;
typedef Math::Matrix3x1<Float> Matrix3x1;
typedef Math::Matrix3x2<Float> Matrix3x2;
typedef Math::Matrix3x3<Float> Matrix3x3;
typedef Math::Matrix3x4<Float> Matrix3x4;
typedef Math::Matrix4x1<Float> Matrix4x1;
typedef Math::Matrix4x2<Float> Matrix4x2;
typedef Math::Matrix4x3<Float> Matrix4x3;
typedef Math::Matrix4x4<Float> Matrix4x4;
typedef Math::Matrix2x2<Byte> Matrix2x2b;
typedef Math::Matrix2x3<Byte> Matrix2x3b;
typedef Math::Matrix2x4<Byte> Matrix2x4b;
typedef Math::Matrix3x2<Byte> Matrix3x2b;
typedef Math::Matrix3x3<Byte> Matrix3x3b;
typedef Math::Matrix3x4<Byte> Matrix3x4b;
typedef Math::Matrix4x2<Byte> Matrix4x2b;
typedef Math::Matrix4x3<Byte> Matrix4x3b;
typedef Math::Matrix4x4<Byte> Matrix4x4b;
typedef Math::Matrix2x2<Short> Matrix2x2s;
typedef Math::Matrix2x3<Short> Matrix2x3s;
typedef Math::Matrix2x4<Short> Matrix2x4s;
typedef Math::Matrix3x2<Short> Matrix3x2s;
typedef Math::Matrix3x3<Short> Matrix3x3s;
typedef Math::Matrix3x4<Short> Matrix3x4s;
typedef Math::Matrix4x2<Short> Matrix4x2s;
typedef Math::Matrix4x3<Short> Matrix4x3s;
typedef Math::Matrix4x4<Short> Matrix4x4s;
typedef Math::QuadraticBezier2D<Float> QuadraticBezier2D;
typedef Math::QuadraticBezier3D<Float> QuadraticBezier3D;
typedef Math::CubicBezier2D<Float> CubicBezier2D;
typedef Math::CubicBezier3D<Float> CubicBezier3D;
typedef Math::CubicHermite1D<Float> CubicHermite1D;
typedef Math::CubicHermite2D<Float> CubicHermite2D;
typedef Math::CubicHermite3D<Float> CubicHermite3D;
typedef Math::CubicHermiteComplex<Float> CubicHermiteComplex;
typedef Math::CubicHermiteQuaternion<Float> CubicHermiteQuaternion;
typedef Math::Complex<Float> Complex;
typedef Math::DualComplex<Float> DualComplex;
typedef Math::Quaternion<Float> Quaternion;
typedef Math::DualQuaternion<Float> DualQuaternion;
typedef Math::Constants<Float> Constants;
typedef Math::Deg<Float> Deg;
typedef Math::Rad<Float> Rad;
typedef Math::Range1D<Float> Range1D;
typedef Math::Range2D<Float> Range2D;
typedef Math::Range3D<Float> Range3D;
typedef Math::Range1D<UnsignedInt> Range1Dui;
typedef Math::Range2D<UnsignedInt> Range2Dui;
typedef Math::Range3D<UnsignedInt> Range3Dui;
typedef Math::Range1D<Int> Range1Di;
typedef Math::Range2D<Int> Range2Di;
typedef Math::Range3D<Int> Range3Di;
typedef Math::Frustum<Float> Frustum;
typedef Math::Nanoseconds<Long> Nanoseconds;
typedef Math::Seconds<Float> Seconds;
typedef Math::Vector2<Half> Vector2h;
typedef Math::Vector3<Half> Vector3h;
typedef Math::Vector4<Half> Vector4h;
typedef Math::Color3<Half> Color3h;
typedef Math::Color4<Half> Color4h;
typedef Math::Matrix2x2<Half> Matrix2x2h;
typedef Math::Matrix2x3<Half> Matrix2x3h;
typedef Math::Matrix2x4<Half> Matrix2x4h;
typedef Math::Matrix3x2<Half> Matrix3x2h;
typedef Math::Matrix3x3<Half> Matrix3x3h;
typedef Math::Matrix3x4<Half> Matrix3x4h;
typedef Math::Matrix4x2<Half> Matrix4x2h;
typedef Math::Matrix4x3<Half> Matrix4x3h;
typedef Math::Matrix4x4<Half> Matrix4x4h;
typedef Math::Deg<Half> Degh;
typedef Math::Rad<Half> Radh;
typedef Math::Range1D<Half> Range1Dh;
typedef Math::Range2D<Half> Range2Dh;
typedef Math::Range3D<Half> Range3Dh;
typedef Math::Vector2<Double> Vector2d;
typedef Math::Vector3<Double> Vector3d;
typedef Math::Vector4<Double> Vector4d;
typedef Math::Matrix3<Double> Matrix3d;
typedef Math::Matrix4<Double> Matrix4d;
typedef Math::Matrix2x1<Double> Matrix2x1d;
typedef Math::Matrix2x2<Double> Matrix2x2d;
typedef Math::Matrix2x3<Double> Matrix2x3d;
typedef Math::Matrix2x4<Double> Matrix2x4d;
typedef Math::Matrix3x1<Double> Matrix3x1d;
typedef Math::Matrix3x2<Double> Matrix3x2d;
typedef Math::Matrix3x3<Double> Matrix3x3d;
typedef Math::Matrix3x4<Double> Matrix3x4d;
typedef Math::Matrix4x1<Double> Matrix4x1d;
typedef Math::Matrix4x2<Double> Matrix4x2d;
typedef Math::Matrix4x3<Double> Matrix4x3d;
typedef Math::Matrix4x4<Double> Matrix4x4d;
typedef Math::QuadraticBezier2D<Double> QuadraticBezier2Dd;
typedef Math::QuadraticBezier3D<Double> QuadraticBezier3Dd;
typedef Math::CubicBezier2D<Double> CubicBezier2Dd;
typedef Math::CubicBezier3D<Double> CubicBezier3Dd;
typedef Math::CubicHermite1D<Double> CubicHermite1Dd;
typedef Math::CubicHermite2D<Double> CubicHermite2Dd;
typedef Math::CubicHermite3D<Double> CubicHermite3Dd;
typedef Math::CubicHermiteComplex<Double> CubicHermiteComplexd;
typedef Math::CubicHermiteQuaternion<Double> CubicHermiteQuaterniond;
typedef Math::Complex<Double> Complexd;
typedef Math::DualComplex<Double> DualComplexd;
typedef Math::Quaternion<Double> Quaterniond;
typedef Math::DualQuaternion<Double> DualQuaterniond;
typedef Math::Constants<Double> Constantsd;
typedef Math::Deg<Double> Degd;
typedef Math::Rad<Double> Radd;
typedef Math::Range1D<Double> Range1Dd;
typedef Math::Range2D<Double> Range2Dd;
typedef Math::Range3D<Double> Range3Dd;
typedef Math::Frustum<Double> Frustumd;
}
#endif
#ifndef Magnum_Math_Constants_h
#define Magnum_Math_Constants_h
namespace Magnum { namespace Math {
template<class> struct Constants;
#ifndef CORRADE_TARGET_EMSCRIPTEN
template<> struct Constants<long double> {
static constexpr long double pi() { return 3.14159265358979323846l; }
};
#endif
template<> struct Constants<Double> {
Constants() = delete;
static constexpr Double pi() { return 3.1415926535897932; }
static constexpr Double piHalf() { return 1.5707963267948966; }
static constexpr Double piQuarter() { return 0.7853981633974483; }
static constexpr Double tau() { return 6.2831853071795864; }
static constexpr Double e() { return 2.7182818284590452; }
static constexpr Double sqrt2() { return 1.4142135623730950; }
static constexpr Double sqrt3() { return 1.7320508075688773; }
static constexpr Double sqrtHalf() { return 0.7071067811865475; }
static constexpr Double nan() {
#ifdef CORRADE_TARGET_CLANG_CL
return __builtin_nan("0");
#else
return Double(NAN);
#endif
}
static constexpr Double inf() {
#if defined(CORRADE_TARGET_CLANG_CL) && __clang_major__ < 9
return __builtin_huge_val();
#else
return HUGE_VAL;
#endif
}
};
template<> struct Constants<Float> {
Constants() = delete;
static constexpr Float pi() { return 3.141592654f; }
static constexpr Float piHalf() { return 1.570796327f; }
static constexpr Float piQuarter() { return 0.785398163f; }
static constexpr Float tau() { return 6.283185307f; }
static constexpr Float e() { return 2.718281828f; }
static constexpr Float sqrt2() { return 1.414213562f; }
static constexpr Float sqrt3() { return 1.732050808f; }
static constexpr Float sqrtHalf() { return 0.707106781f; }
static constexpr Float nan() {
#ifdef CORRADE_TARGET_CLANG_CL
return __builtin_nanf("0");
#else
return NAN;
#endif
}
static constexpr Float inf() {
#if defined(CORRADE_TARGET_CLANG_CL) && __clang_major__ < 9
return __builtin_huge_valf();
#else
return HUGE_VALF;
#endif
}
};
}}
#endif
#ifndef Magnum_Math_TypeTraits_h
#define Magnum_Math_TypeTraits_h
namespace Magnum { namespace Math {
template<class T> struct IsScalar
: std::false_type
{};
template<> struct IsScalar<char>: std::true_type {};
template<> struct IsScalar<signed char>: std::true_type {};
template<> struct IsScalar<unsigned char>: std::true_type {};
template<> struct IsScalar<short>: std::true_type {};
template<> struct IsScalar<unsigned short>: std::true_type {};
template<> struct IsScalar<int>: std::true_type {};
template<> struct IsScalar<unsigned int>: std::true_type {};
template<> struct IsScalar<long>: std::true_type {};
template<> struct IsScalar<unsigned long>: std::true_type {};
template<> struct IsScalar<long long>: std::true_type {};
template<> struct IsScalar<unsigned long long>: std::true_type {};
template<> struct IsScalar<float>: std::true_type {};
template<> struct IsScalar<Half>: std::true_type {};
template<> struct IsScalar<double>: std::true_type {};
template<> struct IsScalar<long double>: std::true_type {};
template<template<class> class Derived, class T> struct IsScalar<Unit<Derived, T>>: std::true_type {};
template<class T> struct IsScalar<Deg<T>>: std::true_type {};
template<class T> struct IsScalar<Rad<T>>: std::true_type {};
template<> struct IsScalar<Nanoseconds<Long>>: std::true_type {};
template<> struct IsScalar<Seconds<Float>>: std::true_type {};
template<class T> struct IsVector
: std::false_type
{};
template<std::size_t size, class T> struct IsVector<Vector<size, T>>: std::true_type {};
template<class T> struct IsVector<Vector2<T>>: std::true_type {};
template<class T> struct IsVector<Vector3<T>>: std::true_type {};
template<class T> struct IsVector<Vector4<T>>: std::true_type {};
template<class T> struct IsVector<Color3<T>>: std::true_type {};
template<class T> struct IsVector<Color4<T>>: std::true_type {};
template<class T> struct IsIntegral
: std::false_type
{};
template<> struct IsIntegral<char>: std::true_type {};
template<> struct IsIntegral<signed char>: std::true_type {};
template<> struct IsIntegral<unsigned char>: std::true_type {};
template<> struct IsIntegral<short>: std::true_type {};
template<> struct IsIntegral<unsigned short>: std::true_type {};
template<> struct IsIntegral<int>: std::true_type {};
template<> struct IsIntegral<unsigned int>: std::true_type {};
template<> struct IsIntegral<long>: std::true_type {};
template<> struct IsIntegral<unsigned long>: std::true_type {};
template<> struct IsIntegral<long long>: std::true_type {};
template<> struct IsIntegral<unsigned long long>: std::true_type {};
template<std::size_t size, class T> struct IsIntegral<Vector<size, T>>: IsIntegral<T> {};
template<> struct IsIntegral<Nanoseconds<Long>>: std::true_type {};
template<class T> struct IsIntegral<Vector2<T>>: IsIntegral<T> {};
template<class T> struct IsIntegral<Vector3<T>>: IsIntegral<T> {};
template<class T> struct IsIntegral<Vector4<T>>: IsIntegral<T> {};
template<class T> struct IsIntegral<Color3<T>>: IsIntegral<T> {};
template<class T> struct IsIntegral<Color4<T>>: IsIntegral<T> {};
template<class T> struct IsFloatingPoint
: std::false_type
{};
template<> struct IsFloatingPoint<Float>: std::true_type {};
template<> struct IsFloatingPoint<Half>: std::true_type {};
template<> struct IsFloatingPoint<Double>: std::true_type {};
template<> struct IsFloatingPoint<long double>: std::true_type {};
template<std::size_t size, class T> struct IsFloatingPoint<Vector<size, T>>: IsFloatingPoint<T> {};
template<class T> struct IsFloatingPoint<Vector2<T>>: IsFloatingPoint<T> {};
template<class T> struct IsFloatingPoint<Vector3<T>>: IsFloatingPoint<T> {};
template<class T> struct IsFloatingPoint<Vector4<T>>: IsFloatingPoint<T> {};
template<class T> struct IsFloatingPoint<Color3<T>>: IsFloatingPoint<T> {};
template<class T> struct IsFloatingPoint<Color4<T>>: IsFloatingPoint<T> {};
template<template<class> class Derived, class T> struct IsFloatingPoint<Unit<Derived, T>>: IsFloatingPoint<T> {};
template<class T> struct IsFloatingPoint<Deg<T>>: IsFloatingPoint<T> {};
template<class T> struct IsFloatingPoint<Rad<T>>: IsFloatingPoint<T> {};
template<> struct IsFloatingPoint<Seconds<Float>>: std::true_type {};
template<class T> struct IsUnitless
: std::integral_constant<bool, IsScalar<T>::value || IsVector<T>::value>
{};
template<template<class> class Derived, class T> struct IsUnitless<Unit<Derived, T>>: std::false_type {};
template<class T> struct IsUnitless<Deg<T>>: std::false_type {};
template<class T> struct IsUnitless<Rad<T>>: std::false_type {};
template<class T> struct IsUnitless<Nanoseconds<T>>: std::false_type {};
template<class T> struct IsUnitless<Seconds<T>>: std::false_type {};
namespace Implementation {
template<class T> struct UnderlyingType {
static_assert(IsScalar<T>::value, "type is not scalar");
typedef T Type;
};
template<template<class> class Derived, class T> struct UnderlyingType<Unit<Derived, T>> {
typedef T Type;
};
template<class T> struct UnderlyingType<Deg<T>> { typedef T Type; };
template<class T> struct UnderlyingType<Rad<T>> { typedef T Type; };
template<class T> struct UnderlyingType<Nanoseconds<T>> { typedef T Type; };
template<class T> struct UnderlyingType<Seconds<T>> { typedef T Type; };
template<std::size_t size, class T> struct UnderlyingType<Vector<size, T>> {
typedef T Type;
};
template<class T> struct UnderlyingType<Vector2<T>> { typedef T Type; };
template<class T> struct UnderlyingType<Vector3<T>> { typedef T Type; };
template<class T> struct UnderlyingType<Vector4<T>> { typedef T Type; };
template<class T> struct UnderlyingType<Color3<T>> { typedef T Type; };
template<class T> struct UnderlyingType<Color4<T>> { typedef T Type; };
template<std::size_t cols, std::size_t rows, class T> struct UnderlyingType<RectangularMatrix<cols, rows, T>> {
typedef T Type;
};
template<std::size_t size, class T> struct UnderlyingType<Matrix<size, T>> {
typedef T Type;
};
template<class T> struct UnderlyingType<Matrix3<T>> { typedef T Type; };
template<class T> struct UnderlyingType<Matrix4<T>> { typedef T Type; };
}
template<class T> using UnderlyingTypeOf = typename Implementation::UnderlyingType<T>::Type;
namespace Implementation {
template<class T> struct TypeTraitsDefault {
TypeTraitsDefault() = delete;
constexpr static bool equals(T a, T b) {
return a == b;
}
constexpr static bool equalsZero(T a, T) {
return !a;
}
};
}
template<class T> struct TypeTraits: Implementation::TypeTraitsDefault<T> {
};
template<class T> inline typename std::enable_if<IsScalar<T>::value, bool>::type equal(T a, T b) {
return TypeTraits<T>::equals(a, b);
}
template<class T> inline typename std::enable_if<IsScalar<T>::value, bool>::type notEqual(T a, T b) {
return !TypeTraits<T>::equals(a, b);
}
namespace Implementation {
template<class> struct TypeTraitsName;
#define _c(type) template<> struct TypeTraitsName<type> { \
constexpr static const char* name() { return #type; } \
};
_c(UnsignedByte)
_c(Byte)
_c(UnsignedShort)
_c(Short)
_c(UnsignedInt)
_c(Int)
_c(UnsignedLong)
_c(Long)
_c(Float)
_c(Half)
_c(Double)
_c(long double)
#undef _c
template<class T> struct TypeTraitsIntegral: TypeTraitsDefault<T>, TypeTraitsName<T> {
constexpr static T epsilon() { return T(1); }
};
}
template<> struct TypeTraits<UnsignedByte>: Implementation::TypeTraitsIntegral<UnsignedByte> {
typedef Float FloatingPointType;
};
template<> struct TypeTraits<Byte>: Implementation::TypeTraitsIntegral<Byte> {
typedef Float FloatingPointType;
};
template<> struct TypeTraits<UnsignedShort>: Implementation::TypeTraitsIntegral<UnsignedShort> {
typedef Float FloatingPointType;
};
template<> struct TypeTraits<Short>: Implementation::TypeTraitsIntegral<Short> {
typedef Float FloatingPointType;
};
template<> struct TypeTraits<UnsignedInt>: Implementation::TypeTraitsIntegral<UnsignedInt> {
typedef Double FloatingPointType;
};
template<> struct TypeTraits<Int>: Implementation::TypeTraitsIntegral<Int> {
typedef Double FloatingPointType;
};
template<> struct TypeTraits<UnsignedLong>: Implementation::TypeTraitsIntegral<UnsignedLong> {
typedef long double FloatingPointType;
};
template<> struct TypeTraits<Long>: Implementation::TypeTraitsIntegral<Long> {
typedef long double FloatingPointType;
};
namespace Implementation {
template<class T> struct TypeTraitsFloatingPoint: TypeTraitsName<T> {
TypeTraitsFloatingPoint() = delete;
static bool equals(T a, T b);
static bool equalsZero(T a, T epsilon);
};
template<class T> bool TypeTraitsFloatingPoint<T>::equals(const T a, const T b) {
if(a == b) return true;
const T absA = std::abs(a);
const T absB = std::abs(b);
const T difference = std::abs(a - b);
if(a == T{} || b == T{} || difference < TypeTraits<T>::epsilon())
return difference < TypeTraits<T>::epsilon();
return difference/(absA + absB) < TypeTraits<T>::epsilon();
}
template<class T> bool TypeTraitsFloatingPoint<T>::equalsZero(const T a, const T magnitude) {
if(a == T(0.0)) return true;
const T absA = std::abs(a);
if(absA < TypeTraits<T>::epsilon())
return absA < TypeTraits<T>::epsilon();
return absA*T(0.5)/magnitude < TypeTraits<T>::epsilon();
}
}
template<> struct TypeTraits<Float>: Implementation::TypeTraitsFloatingPoint<Float> {
typedef Float FloatingPointType;
constexpr static Float epsilon() { return 1.0e-5f; }
};
template<> struct TypeTraits<Half>: Implementation::TypeTraitsName<Half>, Implementation::TypeTraitsDefault<Half> {
typedef Half FloatingPointType;
};
template<> struct TypeTraits<Double>: Implementation::TypeTraitsFloatingPoint<Double> {
typedef Double FloatingPointType;
constexpr static Double epsilon() { return 1.0e-14; }
};
template<> struct TypeTraits<long double>: Implementation::TypeTraitsFloatingPoint<long double> {
typedef long double FloatingPointType;
#ifndef CORRADE_LONG_DOUBLE_SAME_AS_DOUBLE
constexpr static long double epsilon() { return 1.0e-17l; }
#else
constexpr static long double epsilon() { return 1.0e-14l; }
#endif
};
namespace Implementation {
template<class T> inline bool isNormalizedSquared(T lengthSquared) {
return std::abs(lengthSquared - T(1)) < T(2)*TypeTraits<T>::epsilon();
}
}
}}
#endif
#ifndef Corrade_Tags_h
#define Corrade_Tags_h
namespace Corrade {
struct DefaultInitT {
struct Init {};
constexpr explicit DefaultInitT(Init) {}
};
struct ValueInitT {
struct Init {};
constexpr explicit ValueInitT(Init) {}
};
struct NoInitT {
struct Init {};
constexpr explicit NoInitT(Init) {}
};
struct NoCreateT {
struct Init {};
constexpr explicit NoCreateT(Init) {}
};
struct DirectInitT {
struct Init {};
constexpr explicit DirectInitT(Init) {}
};
struct InPlaceInitT {
struct Init {};
constexpr explicit InPlaceInitT(Init) {}
};
constexpr DefaultInitT DefaultInit{DefaultInitT::Init{}};
constexpr ValueInitT ValueInit{ValueInitT::Init{}};
constexpr NoInitT NoInit{NoInitT::Init{}};
constexpr NoCreateT NoCreate{NoCreateT::Init{}};
constexpr DirectInitT DirectInit{DirectInitT::Init{}};
constexpr InPlaceInitT InPlaceInit{InPlaceInitT::Init{}};
}
#endif
#ifndef Magnum_Tags_h
#define Magnum_Tags_h
namespace Magnum {
using Corrade::DefaultInitT;
using Corrade::NoInitT;
using Corrade::NoCreateT;
struct NoAllocateT {
struct Init {};
constexpr explicit NoAllocateT(Init) {}
};
using Corrade::DefaultInit;
using Corrade::NoInit;
using Corrade::NoCreate;
constexpr NoAllocateT NoAllocate{NoAllocateT::Init{}};
}
#endif
#ifndef Magnum_Math_Tags_h
#define Magnum_Math_Tags_h
namespace Magnum { namespace Math {
struct ZeroInitT {
struct Init{};
constexpr explicit ZeroInitT(Init) {}
};
struct IdentityInitT {
struct Init{};
constexpr explicit IdentityInitT(Init) {}
};
constexpr ZeroInitT ZeroInit{ZeroInitT::Init{}};
constexpr IdentityInitT IdentityInit{IdentityInitT::Init{}};
}}
#endif
#ifndef Magnum_Math_Unit_h
#define Magnum_Math_Unit_h
namespace Magnum { namespace Math {
template<template<class> class Derived, class T> class Unit {
template<template<class> class, class> friend class Unit;
public:
typedef T Type;
constexpr /*implicit*/ Unit() noexcept: _value(T(0)) {}
constexpr explicit Unit(ZeroInitT) noexcept: _value(T(0)) {}
explicit Unit(Magnum::NoInitT) noexcept {}
constexpr explicit Unit(T value) noexcept: _value(value) {}
template<class U> constexpr explicit Unit(Unit<Derived, U> value) noexcept: _value(T(value._value)) {}
constexpr explicit operator T() const { return _value; }
constexpr bool operator==(Unit<Derived, T> other) const {
return TypeTraits<T>::equals(_value, other._value);
}
constexpr bool operator!=(Unit<Derived, T> other) const {
return !operator==(other);
}
constexpr bool operator<(Unit<Derived, T> other) const {
return _value < other._value;
}
constexpr bool operator>(Unit<Derived, T> other) const {
return _value > other._value;
}
constexpr bool operator<=(Unit<Derived, T> other) const {
return !operator>(other);
}
constexpr bool operator>=(Unit<Derived, T> other) const {
return !operator<(other);
}
constexpr Unit<Derived, T> operator+() const { return *this; }
constexpr Unit<Derived, T> operator-() const {
return Unit<Derived, T>(-_value);
}
Unit<Derived, T>& operator+=(Unit<Derived, T> other) {
_value += other._value;
return *this;
}
constexpr Unit<Derived, T> operator+(Unit<Derived, T> other) const {
return Unit<Derived, T>(_value + other._value);
}
Unit<Derived, T>& operator-=(Unit<Derived, T> other) {
_value -= other._value;
return *this;
}
constexpr Unit<Derived, T> operator-(Unit<Derived, T> other) const {
return Unit<Derived, T>(_value - other._value);
}
Unit<Derived, T>& operator*=(T number) {
_value *= number;
return *this;
}
constexpr Unit<Derived, T> operator*(T number) const {
return Unit<Derived, T>(_value*number);
}
constexpr friend Unit<Derived, T> operator*(
typename std::common_type<T>::type