Math Support Functionality, e.g. More...

Classes
class	jau::math::geom::AABBox2f
	Axis Aligned Bounding Box. More...

class	jau::math::geom::AABBox3f
	Axis Aligned Bounding Box. More...

class	jau::math::geom::plane::AffineTransform
	Represents a affine 2x3 transformation matrix in column major order (memory layout). More...

class	jau::math::geom::AGeom2f
	Animated geometric object. More...

class	jau::math::geom::Disk2f

class	jau::math::FovHVHalves
	Horizontal and vertical field of view (FOV) halves, allowing a non-centered projection. More...

class	jau::math::geom::Frustum
	Providing frustum `planes` derived by different inputs (`P*MV`, ..) used to classify objects. More...

class	jau::math::geom::Geom2f
	Geometric object. More...

class	jau::math::geom::LineSeg2f

struct	jau::math::geom::LineSeg3f

class	jau::math::geom::LineStrip2f
	A clockwise (CW) polyline. More...

class	jau::math::MathDivByZeroError
	math_error_t::div_by_zero, i.e. More...

class	jau::math::MathDomainError
	math_error_t::invalid More...

class	jau::math::MathError

class	jau::math::MathErrorBase

class	jau::math::MathInexactError
	math_error_t::inexact More...

class	jau::math::MathOverflowError
	math_error_t::overflow More...

class	jau::math::MathRuntimeErrorBase

class	jau::math::MathUnderflowError
	math_error_t::underflow More...

class	jau::math::Matrix4< Value_type, >
	Basic 4x4 value_type matrix implementation using fields for intensive use-cases (host operations). More...

class	jau::math::util::MatrixStack< Value_type, >
	A Matrix stack of compounds, each consisting of 16 * `T` More...

class	jau::math::util::PMVMatrix4< Value_type, >
	PMVMatrix4 implements the basic computer graphics Matrix4 pack using projection (P), modelview (Mv) and texture (T) Matrix4 operations. More...

class	jau::math::Quaternion< Value_type, >
	Quaternion implementation supporting Gimbal-Lock free rotations. More...

class	jau::math::Ray2F< Value_type, >
	Simple compound denoting a ray. More...

class	jau::math::Ray3F< Value_type, >
	Simple compound denoting a ray. More...

class	jau::math::geom::Rect2f

class	jau::math::RectI< Value_type, >
	Rectangle with x, y, width and height value_type components. More...

class	jau::math::util::SimpleStack< Value_type, Element_size, >
	A simple stack of compounds, each consisting of `element_size` * `T` More...

class	jau::math::util::SyncBuffer
	Convenient tuple of a sync_action_t and data buffer. More...

class	jau::math::util::SyncMatrices4< Value_type, >
	SyncBuffer interface with multiple underlying Matrix4. More...

class	jau::math::util::SyncMatrix4< Value_type, >
	SyncBuffer interface with a single underlying Matrix4. More...

class	jau::math::Vector2F< Value_type, >
	2D vector using two value_type components. More...

class	jau::math::Vector2I< Value_type, >
	2D vector using two value_type components. More...

class	jau::math::Vector3F< Value_type, >
	3D vector using three value_type components. More...

class	jau::math::Vector4F< Value_type, >
	4D vector using four value_type components. More...

Typedefs
typedef std::vector< AGeom2f_ref >	jau::math::geom::AGeom2f_list

typedef std::shared_ptr< AGeom2f >	jau::math::geom::AGeom2f_ref

typedef std::shared_ptr< Disk2f >	jau::math::geom::Disk2f_ref

typedef std::vector< Geom2f_ref >	jau::math::geom::Geom2f_list

typedef std::shared_ptr< Geom2f >	jau::math::geom::Geom2f_ref

typedef std::shared_ptr< LineStrip2f >	jau::math::geom::LineStrip2f_ref

typedef Matrix4< float >	jau::math::Mat4f

typedef MatrixStack< float >	jau::math::util::Mat4fStack
	4x4 float matrix stack

typedef PMVMatrix4< float >	jau::math::util::PMVMat4f

template<typename Value_type, std::enable_if_t< std::is_floating_point_v< Value_type > &&sizeof(Value_type)==alignof(Value_type), bool > = true>
using	jau::math::Point2F = Vector2F<Value_type>
	Point2F alias of Vector2F.

typedef Point2F< float >	jau::math::Point2f

template<typename Value_type, std::enable_if_t< std::numeric_limits< Value_type >::is_integer &&sizeof(Value_type)==alignof(Value_type), bool > = true>
using	jau::math::Point2I = Vector2I<Value_type>
	Point2I alias of Vector2I.

typedef Point2I< int >	jau::math::Point2i

template<typename Value_type, std::enable_if_t< std::is_floating_point_v< Value_type > &&sizeof(Value_type)==alignof(Value_type), bool > = true>
using	jau::math::Point3F = Vector3F<Value_type>
	Point3F alias of Vector3F.

typedef Point3F< float >	jau::math::Point3f

template<typename Value_type, std::enable_if_t< std::is_floating_point_v< Value_type > &&sizeof(Value_type)==alignof(Value_type), bool > = true>
using	jau::math::Point4F = Vector4F<Value_type>
	Point4F alias of Vector4F.

typedef Point4F< float >	jau::math::Point4f

typedef Quaternion< float >	jau::math::Quat4f

typedef Ray2F< float >	jau::math::Ray2f

typedef Ray3F< float >	jau::math::Ray3f

typedef std::shared_ptr< Rect2f >	jau::math::geom::Rect2f_ref

typedef RectI< int >	jau::math::Recti

typedef SimpleStack< float, 16 >	jau::math::util::Stack16f
	4x4 float matrix stack based on single float elements

typedef void(*	jau::math::util::sync_action_fptr) ()
	Plain function pointer type matching sync_action_t.

typedef jau::function< void()>	jau::math::util::sync_action_t
	Specific data synchronization action implemented by the data provider to update the buffer with the underlying data before usage, e.g.

typedef SyncMatrix4< float >	jau::math::util::SyncMat4f

typedef SyncMatrices4< float >	jau::math::util::SyncMats4f

typedef Vector2F< float >	jau::math::Vec2f

typedef Vector2I< int >	jau::math::Vec2i

typedef Vector3F< float >	jau::math::Vec3f

typedef jau::darray< Vec3f, jau::nsize_t >	jau::math::geom::Vec3fList

typedef Vector4F< float >	jau::math::Vec4f

Enumerations
enum class	jau::math::geom::plane::AffineTransformType : uint16_t { jau::math::geom::plane::AffineTransformType::unknown = 0 , jau::math::geom::plane::AffineTransformType::identity = 1 << 0 , jau::math::geom::plane::AffineTransformType::translation = 1 << 1 , jau::math::geom::plane::AffineTransformType::uniform_scale = 1 << 2 , jau::math::geom::plane::AffineTransformType::general_scale = 1 << 3 , jau::math::geom::plane::AffineTransformType::quadrant_rotation = 1 << 4 , jau::math::geom::plane::AffineTransformType::general_rotation = 1 << 5 , jau::math::geom::plane::AffineTransformType::general_transform = 1 << 6 , jau::math::geom::plane::AffineTransformType::flip = 1 << 7 , jau::math::geom::plane::AffineTransformType::mask_scale = uniform_scale \| general_scale , jau::math::geom::plane::AffineTransformType::mask_rotation = quadrant_rotation \| general_rotation }

enum class	jau::math::math_error_t : uint16_t { jau::math::math_error_t::none = 0 , jau::math::math_error_t::invalid , jau::math::math_error_t::div_by_zero , jau::math::math_error_t::overflow , jau::math::math_error_t::underflow , jau::math::math_error_t::inexact , jau::math::math_error_t::undefined = 1U << 15 }
	Error types as specified by C++ Math Error Handling More...

enum class	jau::math::geom::orientation_t : uint16_t { jau::math::geom::orientation_t::COL , jau::math::geom::orientation_t::CW , jau::math::geom::orientation_t::CCW }

enum class	jau::math::geom::Winding : uint16_t { jau::math::geom::Winding::CW , jau::math::geom::Winding::CCW }

Functions
template<typename T, std::enable_if_t< std::is_floating_point_v< T >, bool > = true>
constexpr Vector2F< T >	jau::math::abs (const Vector2F< T > &lhs) noexcept

template<typename T, std::enable_if_t< std::is_floating_point_v< T >, bool > = true>
constexpr Vector2I< T >	jau::math::abs (const Vector2I< T > &lhs) noexcept

template<typename T, std::enable_if_t< std::is_floating_point_v< T >, bool > = true>
constexpr Vector3F< T >	jau::math::abs (const Vector3F< T > &lhs) noexcept

template<typename T, std::enable_if_t< std::is_floating_point_v< T >, bool > = true>
constexpr Vector4F< T >	jau::math::abs (const Vector4F< T > &lhs) noexcept

constexpr double	jau::math::geom::area2D (const Vec3fList &vertices) noexcept
	Computes the area of a list of vertices via shoelace formula.

constexpr Winding	jau::math::geom::get2DWinding (const Vec3f &a, const Vec3f &b, const Vec3f &c) noexcept
	Compute the winding of the 3 given points.

constexpr Winding	jau::math::geom::getArea2DWinding (const Vec3fList &vertices) noexcept
	Compute the winding using the area2D() function over all vertices for complex shapes.

constexpr jau::math::Vec3f	jau::math::util::getEulerAngleOrientation (const jau::math::Vec3f &eulerRotation) noexcept
	Returns an orientation vector for given eurler X/Y/Z angles in radians.

constexpr float	jau::math::util::getOrthoWinZ (float orthoZ, float zNear, float zFar) noexcept
	Returns orthogonal distance (1f/zNear-1f/orthoZ) / (1f/zNear-1f/zFar);.

Quat &	jau::math::Matrix4< Value_type, >::getRotation (Quat &res) const noexcept
	Returns the rotation [m00 .

constexpr float	jau::math::util::getZBufferEpsilon (int zBits, float z, float zNear) noexcept
	Returns resolution of Z buffer of given parameter, see Love Your Z-Buffer.

constexpr int	jau::math::util::getZBufferValue (int zBits, float z, float zNear, float zFar) noexcept
	Returns Z buffer value of given parameter, see Love Your Z-Buffer.

constexpr double	jau::math::geom::inCircle2DVal (const Vec3f &a, const Vec3f &b, const Vec3f &c, const Vec3f &d) noexcept

constexpr bool	jau::math::geom::is2DCCW (const Vec3f &a, const Vec3f &b, const Vec3f &c) noexcept
	Check if points are in ccw order.

constexpr bool	jau::math::geom::isInCircle2D (const Vec3f &a, const Vec3f &b, const Vec3f &c, const Vec3f &d) noexcept
	Check if vertices in triangle circumcircle given `d` vertex, from paper by Guibas and Stolfi (1985).

constexpr bool	jau::math::geom::isInTriangle3 (const Vec3f &a, const Vec3f &b, const Vec3f &c, const Vec3f &p1, const Vec3f &p2, const Vec3f &p3) noexcept
	Check if one of three vertices are in triangle using barycentric coordinates computation.

	jau::math::geom::plane::JAU_MAKE_BITFIELD_ENUM_STRING (AffineTransformType, identity, translation, uniform_scale, general_scale, quadrant_rotation, general_rotation, general_transform, flip)

	jau::math::geom::JAU_MAKE_ENUM_STRING (orientation_t, COL, CW, CCW)

	jau::math::geom::JAU_MAKE_ENUM_STRING (Winding, CW, CCW)

template<typename T, std::enable_if_t< std::is_floating_point_v< T >, bool > = true>
constexpr Vector2F< T >	jau::math::max (const Vector2F< T > &lhs, const Vector2F< T > &rhs) noexcept

template<typename T, std::enable_if_t< std::numeric_limits< T >::is_integer, bool > = true>
constexpr Vector2I< T >	jau::math::max (const Vector2I< T > &lhs, const Vector2I< T > &rhs) noexcept

template<typename T, std::enable_if_t< std::is_floating_point_v< T >, bool > = true>
constexpr Vector3F< T >	jau::math::max (const Vector3F< T > &lhs, const Vector3F< T > &rhs) noexcept

template<typename T, std::enable_if_t< std::is_floating_point_v< T >, bool > = true>
constexpr Vector4F< T >	jau::math::max (const Vector4F< T > &lhs, const Vector4F< T > &rhs) noexcept

constexpr Vec3f	jau::math::geom::midpoint (const Vec3f &a, const Vec3f &b) noexcept

template<typename T, std::enable_if_t< std::is_floating_point_v< T >, bool > = true>
constexpr Vector2F< T >	jau::math::min (const Vector2F< T > &lhs, const Vector2F< T > &rhs) noexcept

template<typename T, std::enable_if_t< std::numeric_limits< T >::is_integer, bool > = true>
constexpr Vector2I< T >	jau::math::min (const Vector2I< T > &lhs, const Vector2I< T > &rhs) noexcept

template<typename T, std::enable_if_t< std::is_floating_point_v< T >, bool > = true>
constexpr Vector3F< T >	jau::math::min (const Vector3F< T > &lhs, const Vector3F< T > &rhs) noexcept

template<typename T, std::enable_if_t< std::is_floating_point_v< T >, bool > = true>
constexpr Vector4F< T >	jau::math::min (const Vector4F< T > &lhs, const Vector4F< T > &rhs) noexcept

template<typename T, std::enable_if_t< std::numeric_limits< T >::is_integer, bool > = true>
constexpr Vector2I< T >	jau::math::operator* (const float s, const Vector2I< T > &rhs) noexcept

template<typename T, std::enable_if_t< std::is_floating_point_v< T >, bool > = true>
constexpr Matrix4< T >	jau::math::operator* (const Matrix4< T > &lhs, const Matrix4< T > &rhs) noexcept

template<typename T, std::enable_if_t< std::is_floating_point_v< T >, bool > = true>
constexpr Matrix4< T >	jau::math::operator* (const Matrix4< T > &lhs, const T s) noexcept

template<typename T, std::enable_if_t< std::is_floating_point_v< T >, bool > = true>
constexpr Quaternion< T >	jau::math::operator* (const Quaternion< T > &lhs, const Quaternion< T > &rhs) noexcept

template<typename T, std::enable_if_t< std::is_floating_point_v< T >, bool > = true>
constexpr Quaternion< T >	jau::math::operator* (const Quaternion< T > &lhs, const T s) noexcept

template<typename T, std::enable_if_t< std::is_floating_point_v< T >, bool > = true>
constexpr Matrix4< T >	jau::math::operator* (const T s, const Matrix4< T > &rhs) noexcept

template<typename T, std::enable_if_t< std::is_floating_point_v< T >, bool > = true>
constexpr Quaternion< T >	jau::math::operator* (const T s, const Quaternion< T > &rhs) noexcept

template<typename T, std::enable_if_t< std::is_floating_point_v< T >, bool > = true>
constexpr Vector2F< T >	jau::math::operator* (const T s, const Vector2F< T > &rhs) noexcept

template<typename T, std::enable_if_t< std::is_floating_point_v< T >, bool > = true>
constexpr Vector3F< T >	jau::math::operator* (const T s, const Vector3F< T > &rhs) noexcept

template<typename T, std::enable_if_t< std::is_floating_point_v< T >, bool > = true>
constexpr Vector4F< T >	jau::math::operator* (const T s, const Vector4F< T > &rhs) noexcept

template<typename T, std::enable_if_t< std::is_floating_point_v< T >, bool > = true>
constexpr Vector2F< T >	jau::math::operator* (const Vector2F< T > &lhs, const T s) noexcept

template<typename T, std::enable_if_t< std::numeric_limits< T >::is_integer, bool > = true>
constexpr Vector2I< T >	jau::math::operator* (const Vector2I< T > &lhs, const float s) noexcept

template<typename T, std::enable_if_t< std::is_floating_point_v< T >, bool > = true>
constexpr Vector3F< T >	jau::math::operator* (const Vector3F< T > &lhs, const T s) noexcept

template<typename T, std::enable_if_t< std::is_floating_point_v< T >, bool > = true>
constexpr Vector4F< T >	jau::math::operator* (const Vector4F< T > &lhs, const T s) noexcept

template<typename T, std::enable_if_t< std::is_floating_point_v< T >, bool > = true>
constexpr Quaternion< T >	jau::math::operator+ (const Quaternion< T > &lhs, const Quaternion< T > &rhs) noexcept

template<typename T, std::enable_if_t< std::is_floating_point_v< T >, bool > = true>
constexpr Vector2F< T >	jau::math::operator+ (const Vector2F< T > &lhs, const Vector2F< T > &rhs) noexcept

template<typename T, std::enable_if_t< std::numeric_limits< T >::is_integer, bool > = true>
constexpr Vector2I< T >	jau::math::operator+ (const Vector2I< T > &lhs, const Vector2I< T > &rhs) noexcept

template<typename T, std::enable_if_t< std::is_floating_point_v< T >, bool > = true>
constexpr Vector3F< T >	jau::math::operator+ (const Vector3F< T > &lhs, const Vector3F< T > &rhs) noexcept

template<typename T, std::enable_if_t< std::is_floating_point_v< T >, bool > = true>
constexpr Vector4F< T >	jau::math::operator+ (const Vector4F< T > &lhs, const Vector4F< T > &rhs) noexcept

template<typename T, std::enable_if_t< std::is_floating_point_v< T >, bool > = true>
constexpr Quaternion< T >	jau::math::operator- (const Quaternion< T > &lhs, const Quaternion< T > &rhs) noexcept

template<typename T, std::enable_if_t< std::is_floating_point_v< T >, bool > = true>
constexpr Vector2F< T >	jau::math::operator- (const Vector2F< T > &lhs) noexcept

template<typename T, std::enable_if_t< std::is_floating_point_v< T >, bool > = true>
constexpr Vector2F< T >	jau::math::operator- (const Vector2F< T > &lhs, const Vector2F< T > &rhs) noexcept

template<typename T, std::enable_if_t< std::numeric_limits< T >::is_integer, bool > = true>
constexpr Vector2I< T >	jau::math::operator- (const Vector2I< T > &lhs) noexcept

template<typename T, std::enable_if_t< std::numeric_limits< T >::is_integer, bool > = true>
constexpr Vector2I< T >	jau::math::operator- (const Vector2I< T > &lhs, const Vector2I< T > &rhs) noexcept

template<typename T, std::enable_if_t< std::is_floating_point_v< T >, bool > = true>
constexpr Vector3F< T >	jau::math::operator- (const Vector3F< T > &lhs) noexcept

template<typename T, std::enable_if_t< std::is_floating_point_v< T >, bool > = true>
constexpr Vector3F< T >	jau::math::operator- (const Vector3F< T > &lhs, const Vector3F< T > &rhs) noexcept

template<typename T, std::enable_if_t< std::is_floating_point_v< T >, bool > = true>
constexpr Vector4F< T >	jau::math::operator- (const Vector4F< T > &lhs) noexcept

template<typename T, std::enable_if_t< std::is_floating_point_v< T >, bool > = true>
constexpr Vector4F< T >	jau::math::operator- (const Vector4F< T > &lhs, const Vector4F< T > &rhs) noexcept

template<typename T, std::enable_if_t< std::is_floating_point_v< T >, bool > = true>
constexpr Vector2F< T >	jau::math::operator/ (const T s, const Vector2F< T > &rhs) noexcept

template<typename T, std::enable_if_t< std::is_floating_point_v< T >, bool > = true>
constexpr Vector2I< T >	jau::math::operator/ (const T s, const Vector2I< T > &rhs) noexcept

template<typename T, std::enable_if_t< std::is_floating_point_v< T >, bool > = true>
constexpr Vector3F< T >	jau::math::operator/ (const T s, const Vector3F< T > &rhs) noexcept

template<typename T, std::enable_if_t< std::is_floating_point_v< T >, bool > = true>
constexpr Vector4F< T >	jau::math::operator/ (const T s, const Vector4F< T > &rhs) noexcept

template<typename T, std::enable_if_t< std::is_floating_point_v< T >, bool > = true>
constexpr Vector2F< T >	jau::math::operator/ (const Vector2F< T > &lhs, const T s) noexcept

template<typename T, std::enable_if_t< std::numeric_limits< T >::is_integer, bool > = true>
constexpr Vector2I< T >	jau::math::operator/ (const Vector2I< T > &lhs, const float s) noexcept

template<typename T, std::enable_if_t< std::is_floating_point_v< T >, bool > = true>
constexpr Vector3F< T >	jau::math::operator/ (const Vector3F< T > &lhs, const T s) noexcept

template<typename T, std::enable_if_t< std::is_floating_point_v< T >, bool > = true>
constexpr Vector4F< T >	jau::math::operator/ (const Vector4F< T > &lhs, const T s) noexcept

template<typename T, std::enable_if_t< std::is_floating_point_v< T >, bool > = true>
std::ostream &	jau::math::operator<< (std::ostream &out, const Matrix4< T > &v) noexcept

template<typename T, std::enable_if_t< std::is_floating_point_v< T >, bool > = true>
std::ostream &	jau::math::operator<< (std::ostream &out, const Quaternion< T > &v) noexcept

template<typename T, std::enable_if_t< std::is_floating_point_v< T >, bool > = true>
std::ostream &	jau::math::operator<< (std::ostream &out, const Ray2F< T > &v) noexcept

template<typename T, std::enable_if_t< std::is_floating_point_v< T >, bool > = true>
std::ostream &	jau::math::operator<< (std::ostream &out, const Ray3F< T > &v) noexcept

template<typename T, std::enable_if_t< std::numeric_limits< T >::is_integer, bool > = true>
std::ostream &	jau::math::operator<< (std::ostream &out, const RectI< T > &v) noexcept

template<typename T, std::enable_if_t< std::is_floating_point_v< T >, bool > = true>
std::ostream &	jau::math::operator<< (std::ostream &out, const Vector2F< T > &v) noexcept

template<typename T, std::enable_if_t< std::numeric_limits< T >::is_integer, bool > = true>
std::ostream &	jau::math::operator<< (std::ostream &out, const Vector2I< T > &v) noexcept

template<typename T, std::enable_if_t< std::is_floating_point_v< T >, bool > = true>
std::ostream &	jau::math::operator<< (std::ostream &out, const Vector3F< T > &v) noexcept

template<typename T, std::enable_if_t< std::is_floating_point_v< T >, bool > = true>
std::ostream &	jau::math::operator<< (std::ostream &out, const Vector4F< T > &v) noexcept

template<typename Value_type, std::enable_if_t< std::is_floating_point_v< Value_type >, bool > = true>
std::ostream &	jau::math::util::operator<< (std::ostream &out, const PMVMatrix4< Value_type > &v) noexcept

constexpr orientation_t	jau::math::geom::orientation (const Point2f &a, const Point2f &b, const Point2f &c) noexcept
	Return the orientation of the given point triplet a, b and c using triArea()

Matrix4 &	jau::math::Matrix4< Value_type, >::setToRotation (const Quat &q)
	Set this matrix to rotation using the given Quaternion.

constexpr double	jau::math::geom::sqlend (double x, double y) noexcept

constexpr bool	jau::math::geom::testSeg2SegIntersection2D (const Vec3f &p, const Vec3f &p2, const Vec3f &q, const Vec3f &q2) noexcept
	2D line segment intersection test w/o considering collinear-case

constexpr bool	jau::math::geom::testSeg2SegIntersection2D (Vec2f *result, const Vec2f &p, const Vec2f &p2, const Vec2f &q, const Vec2f &q2, const bool do_collinear=false) noexcept
	See p + t r = q + u s and its terse C# implementation

constexpr bool	jau::math::geom::testTri2SegIntersection2D (const Vec3f &a, const Vec3f &b, const Vec3f &c, const Vec3f &d, const Vec3f &e)
	Check if a segment intersects with a triangle using `FloatUtil#EPSILON` w/o considering collinear-case.

std::string	jau::math::to_string (const math_error_t v) noexcept
	Returns std::string representation of math_error_t.

template<typename T, std::enable_if_t< std::is_floating_point_v< T >, bool > = true>
constexpr Vector3F< T >	jau::math::to_vec3 (const Vector4F< T > &v) noexcept
	out = { this.x, this.y, this.z } dropping w, returns out.

constexpr double	jau::math::geom::tri_area (const Point2f &a, const Point2f &b, const Point2f &c)
	Computes oriented double area of a triangle, i.e.

constexpr double	jau::math::geom::triArea (double ax, double ay, double bx, double by, double cx, double cy) noexcept

constexpr double	jau::math::geom::triArea (float ax, float ay, float bx, float by, float cx, float cy) noexcept

constexpr double	jau::math::geom::triArea2D (const Vec3f &a, const Vec3f &b, const Vec3f &c) noexcept
	Computes oriented double area of a triangle, i.e.

Detailed Description

Math Support Functionality, e.g.

linear algebra, meta group

Further support is coming from

Typedef Documentation

◆ Geom2f_ref

typedef std::shared_ptr<Geom2f> jau::math::geom::Geom2f_ref

Definition at line 154 of file geom2f.hpp.

◆ Geom2f_list

typedef std::vector<Geom2f_ref> jau::math::geom::Geom2f_list

Definition at line 155 of file geom2f.hpp.

◆ AGeom2f_ref

typedef std::shared_ptr<AGeom2f> jau::math::geom::AGeom2f_ref

Definition at line 408 of file geom2f.hpp.

◆ AGeom2f_list

typedef std::vector<AGeom2f_ref> jau::math::geom::AGeom2f_list

Definition at line 409 of file geom2f.hpp.

◆ Disk2f_ref

typedef std::shared_ptr<Disk2f> jau::math::geom::Disk2f_ref

Definition at line 498 of file geom2f.hpp.

◆ Rect2f_ref

typedef std::shared_ptr<Rect2f> jau::math::geom::Rect2f_ref

Definition at line 701 of file geom2f.hpp.

◆ LineStrip2f_ref

typedef std::shared_ptr<LineStrip2f> jau::math::geom::LineStrip2f_ref

Definition at line 842 of file geom2f.hpp.

◆ Vec3fList

typedef jau::darray<Vec3f, jau::nsize_t> jau::math::geom::Vec3fList

Definition at line 32 of file geom3f2D.hpp.

◆ Mat4f

typedef Matrix4<float> jau::math::Mat4f

Examples: GearsES2.cpp, GearsES2.hpp, GraphShapes01.cpp, and Primitives02.cpp.

Definition at line 1973 of file mat4f.hpp.

◆ Quat4f

typedef Quaternion<float> jau::math::Quat4f

Examples: GraphShapes01.cpp, and Primitives02.cpp.

Definition at line 1186 of file quaternion.hpp.

◆ Recti

typedef RectI<int> jau::math::Recti

Examples: GearsES2.hpp, GraphShapes01.cpp, Primitives02.cpp, and RedSquareES2.hpp.

Definition at line 139 of file recti.hpp.

◆ PMVMat4f

typedef PMVMatrix4<float> jau::math::util::PMVMat4f

Examples: GearsES2.hpp, GraphShapes01.cpp, Primitives02.cpp, and RedSquareES2.hpp.

Definition at line 1461 of file pmvmat4f.hpp.

◆ Stack16f

typedef SimpleStack<float, 16 > jau::math::util::Stack16f

4x4 float matrix stack based on single float elements

Definition at line 95 of file sstack.hpp.

◆ Mat4fStack

typedef MatrixStack<float> jau::math::util::Mat4fStack

4x4 float matrix stack

Definition at line 152 of file sstack.hpp.

◆ sync_action_t

typedef jau::function<void()> jau::math::util::sync_action_t

Specific data synchronization action implemented by the data provider to update the buffer with the underlying data before usage, e.g.

uploading the GLUniformData data to the GPU.

Definition at line 34 of file syncbuffer.hpp.

◆ sync_action_fptr

typedef void(* jau::math::util::sync_action_fptr) ()

Plain function pointer type matching sync_action_t.

Definition at line 37 of file syncbuffer.hpp.

◆ SyncMat4f

typedef SyncMatrix4<float> jau::math::util::SyncMat4f

Definition at line 118 of file syncbuffer.hpp.

◆ SyncMats4f

typedef SyncMatrices4<float> jau::math::util::SyncMats4f

Definition at line 158 of file syncbuffer.hpp.

◆ Vec2f

typedef Vector2F<float> jau::math::Vec2f

Definition at line 416 of file vec2f.hpp.

◆ Point2F

template<typename Value_type, std::enable_if_t< std::is_floating_point_v< Value_type > &&sizeof(Value_type)==alignof(Value_type), bool > = true>

using jau::math::Point2F = Vector2F<Value_type>

Point2F alias of Vector2F.

Definition at line 429 of file vec2f.hpp.

◆ Point2f

typedef Point2F<float> jau::math::Point2f

Definition at line 431 of file vec2f.hpp.

◆ Ray2f

typedef Ray2F<float> jau::math::Ray2f

Definition at line 483 of file vec2f.hpp.

◆ Vec2i

typedef Vector2I<int> jau::math::Vec2i

Examples: GearsES2.cpp.

Definition at line 328 of file vec2i.hpp.

◆ Point2I

template<typename Value_type, std::enable_if_t< std::numeric_limits< Value_type >::is_integer &&sizeof(Value_type)==alignof(Value_type), bool > = true>

using jau::math::Point2I = Vector2I<Value_type>

Point2I alias of Vector2I.

Definition at line 341 of file vec2i.hpp.

◆ Point2i

typedef Point2I<int> jau::math::Point2i

Definition at line 343 of file vec2i.hpp.

◆ Vec3f

typedef Vector3F<float> jau::math::Vec3f

Examples: GearsES2.cpp, GearsES2.hpp, GraphShapes01.cpp, and Primitives02.cpp.

Definition at line 436 of file vec3f.hpp.

◆ Point3F

template<typename Value_type, std::enable_if_t< std::is_floating_point_v< Value_type > &&sizeof(Value_type)==alignof(Value_type), bool > = true>

using jau::math::Point3F = Vector3F<Value_type>

Point3F alias of Vector3F.

Definition at line 449 of file vec3f.hpp.

◆ Point3f

typedef Point3F<float> jau::math::Point3f

Definition at line 451 of file vec3f.hpp.

◆ Ray3f

typedef Ray3F<float> jau::math::Ray3f

Examples: GearsES2.cpp.

Definition at line 502 of file vec3f.hpp.

◆ Vec4f

typedef Vector4F<float> jau::math::Vec4f

Examples: GearsES2.hpp, GraphShapes01.cpp, and Primitives02.cpp.

Definition at line 375 of file vec4f.hpp.

◆ Point4F

template<typename Value_type, std::enable_if_t< std::is_floating_point_v< Value_type > &&sizeof(Value_type)==alignof(Value_type), bool > = true>

using jau::math::Point4F = Vector4F<Value_type>

Point4F alias of Vector4F.

Definition at line 388 of file vec4f.hpp.

◆ Point4f

typedef Point4F<float> jau::math::Point4f

Definition at line 390 of file vec4f.hpp.

Enumeration Type Documentation

◆ orientation_t

enum class jau::math::geom::orientation_t : uint16_t

strong

Enumerator
COL	Collinear.
CW	Clockwise.
CCW	Counter-Clockwise.

Definition at line 25 of file geom.hpp.

◆ Winding

enum class jau::math::geom::Winding : uint16_t

strong

Enumerator
CW	Clockwise.
CCW	Counter-Clockwise.

Definition at line 35 of file geom.hpp.

◆ AffineTransformType

enum class jau::math::geom::plane::AffineTransformType : uint16_t

strong

Enumerator
unknown	The `AffineTransformType::unknown` is the initial value.
identity
translation
uniform_scale
general_scale
quadrant_rotation
general_rotation
general_transform
flip
mask_scale
mask_rotation

Definition at line 31 of file affine_transform.hpp.

◆ math_error_t

enum class jau::math::math_error_t : uint16_t

strong

Error types as specified by C++ Math Error Handling

Enumerator
none	no math error
invalid	See FE_INVALID, i.e. MathDomainError, std::domain_error : std::logic_error
div_by_zero	See FE_DIVBYZERO, i.e. MathDivByZeroError, std::domain_error : std::logic_error
overflow	See FE_OVERFLOW, i.e. MathOverflowError, std::overflow_error : std::runtime_error
underflow	See FE_UNDERFLOW, i.e. MathUnderflowError, std::underflow_error : std::runtime_error
inexact	See FE_INEXACT, i.e. MathInexactError, std::runtime_error
undefined	undefined math error

Definition at line 33 of file math_error.hpp.

Function Documentation

◆ JAU_MAKE_ENUM_STRING() [1/2]

jau::math::geom::JAU_MAKE_ENUM_STRING	(	orientation_t	,
		COL	,
		CW	,
		CCW	)

◆ JAU_MAKE_ENUM_STRING() [2/2]

jau::math::geom::JAU_MAKE_ENUM_STRING	(	Winding	,
		CW	,
		CCW	)

◆ tri_area()

double jau::math::geom::tri_area	(	const Point2f &	a,
		const Point2f &	b,
		const Point2f &	c )

constexpr

Computes oriented double area of a triangle, i.e.

the 2x2 determinant with b-a and c-a per column.

      | bx-ax, cx-ax |
det = | by-ay, cy-ay |

Parameters

a	first vertex
b	second vertex
c	third vertex

Returns: area > 0 CCW, ..

Definition at line 42 of file geom2f.hpp.

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◆ orientation()

orientation_t jau::math::geom::orientation	(	const Point2f &	a,
		const Point2f &	b,
		const Point2f &	c )

constexprnoexcept

Return the orientation of the given point triplet a, b and c using triArea()

Definition at line 49 of file geom2f.hpp.

◆ testSeg2SegIntersection2D() [1/2]

bool jau::math::geom::testSeg2SegIntersection2D	(	Vec2f *	result,
		const Vec2f &	p,
		const Vec2f &	p2,
		const Vec2f &	q,
		const Vec2f &	q2,
		const bool	do_collinear = false )

constexprnoexcept

See p + t r = q + u s and its terse C# implementation

Definition at line 61 of file geom2f.hpp.

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◆ midpoint()

Vec3f jau::math::geom::midpoint	(	const Vec3f &	a,
		const Vec3f &	b )

constexprnoexcept

Definition at line 126 of file geom3f.hpp.

◆ isInTriangle3()

bool jau::math::geom::isInTriangle3	(	const Vec3f &	a,
		const Vec3f &	b,
		const Vec3f &	c,
		const Vec3f &	p1,
		const Vec3f &	p2,
		const Vec3f &	p3 )

constexprnoexcept

Check if one of three vertices are in triangle using barycentric coordinates computation.

Parameters

a	first triangle vertex
b	second triangle vertex
c	third triangle vertex
p1	the vertex in question
p2	the vertex in question
p3	the vertex in question

Returns: true if p1 or p2 or p3 is in triangle (a, b, c), false otherwise.

Definition at line 140 of file geom3f.hpp.

◆ area2D()

double jau::math::geom::area2D ( const Vec3fList & vertices )

constexprnoexcept

Computes the area of a list of vertices via shoelace formula.

This method is utilized e.g. to reliably compute the Winding of complex shapes.

Implementation uses double precision.

Parameters

vertices

Returns: positive area if ccw else negative area value

See also: #getWinding()

Definition at line 45 of file geom3f2D.hpp.

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◆ getArea2DWinding()

Winding jau::math::geom::getArea2DWinding ( const Vec3fList & vertices )

constexprnoexcept

Compute the winding using the area2D() function over all vertices for complex shapes.

Uses the area(List) function over all points on complex shapes for a reliable result!

Implementation uses double precision.

Parameters

vertices array of Vertices

Returns: Winding::CCW or Winding::CLW

See also: area2D()

Definition at line 68 of file geom3f2D.hpp.

◆ sqlend()

double jau::math::geom::sqlend	(	double	x,
		double	y )

constexprnoexcept

Definition at line 73 of file geom3f2D.hpp.

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◆ triArea() [1/2]

double jau::math::geom::triArea	(	double	ax,
		double	ay,
		double	bx,
		double	by,
		double	cx,
		double	cy )

constexprnoexcept

Definition at line 76 of file geom3f2D.hpp.

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◆ triArea() [2/2]

double jau::math::geom::triArea	(	float	ax,
		float	ay,
		float	bx,
		float	by,
		float	cx,
		float	cy )

constexprnoexcept

Definition at line 79 of file geom3f2D.hpp.

◆ triArea2D()

double jau::math::geom::triArea2D	(	const Vec3f &	a,
		const Vec3f &	b,
		const Vec3f &	c )

constexprnoexcept

Computes oriented double area of a triangle, i.e.

the 2x2 determinant with b-a and c-a per column.

      | bx-ax, cx-ax |
det = | by-ay, cy-ay |

Parameters

a	first vertex
b	second vertex
c	third vertex

Returns: area > 0 CCW, ..

Definition at line 94 of file geom3f2D.hpp.

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◆ inCircle2DVal()

double jau::math::geom::inCircle2DVal	(	const Vec3f &	a,
		const Vec3f &	b,
		const Vec3f &	c,
		const Vec3f &	d )

constexprnoexcept

Definition at line 97 of file geom3f2D.hpp.

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◆ isInCircle2D()

bool jau::math::geom::isInCircle2D	(	const Vec3f &	a,
		const Vec3f &	b,
		const Vec3f &	c,
		const Vec3f &	d )

constexprnoexcept

Check if vertices in triangle circumcircle given d vertex, from paper by Guibas and Stolfi (1985).

Implementation uses double precision.

Parameters

a	triangle vertex 1
b	triangle vertex 2
c	triangle vertex 3
d	vertex in question

Returns: true if the vertex d is inside the circle defined by the vertices a, b, c.

Definition at line 117 of file geom3f2D.hpp.

◆ is2DCCW()

bool jau::math::geom::is2DCCW	(	const Vec3f &	a,
		const Vec3f &	b,
		const Vec3f &	c )

constexprnoexcept

Check if points are in ccw order.

Consider using getWinding(List) using the area(List) function over all points on complex shapes for a reliable result!

Parameters

a	first vertex
b	second vertex
c	third vertex

Returns: true if the points a,b,c are in a ccw order

See also: #getWinding(List)

Definition at line 133 of file geom3f2D.hpp.

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◆ get2DWinding()

Winding jau::math::geom::get2DWinding	(	const Vec3f &	a,
		const Vec3f &	b,
		const Vec3f &	c )

constexprnoexcept

Compute the winding of the 3 given points.

Consider using getWinding(List) using the area(List) function over all points on complex shapes for a reliable result!

Parameters

a	first vertex
b	second vertex
c	third vertex

Returns: Winding#CCW or Winding#CW

See also: #getWinding(List)

Definition at line 149 of file geom3f2D.hpp.

◆ testSeg2SegIntersection2D() [2/2]

bool jau::math::geom::testSeg2SegIntersection2D	(	const Vec3f &	p,
		const Vec3f &	p2,
		const Vec3f &	q,
		const Vec3f &	q2 )

constexprnoexcept

2D line segment intersection test w/o considering collinear-case

See p + t r = q + u s and its terse C# implementation

Implementation uses float precision.

Parameters

p	vertex 1 of first segment
p2	vertex 2 of first segment
q	vertex 1 of second segment
q2	vertex 2 of second segment

Returns: true if line segments are intersecting, otherwise false

Definition at line 168 of file geom3f2D.hpp.

◆ testTri2SegIntersection2D()

bool jau::math::geom::testTri2SegIntersection2D	(	const Vec3f &	a,
		const Vec3f &	b,
		const Vec3f &	c,
		const Vec3f &	d,
		const Vec3f &	e )

constexpr

Check if a segment intersects with a triangle using FloatUtil#EPSILON w/o considering collinear-case.

Implementation uses float precision.

Parameters

a	vertex 1 of the triangle
b	vertex 2 of the triangle
c	vertex 3 of the triangle
d	vertex 1 of first segment
e	vertex 2 of first segment

Returns: true if the segment intersects at least one segment of the triangle, false otherwise

See also: #testSeg2SegIntersection(Vert2fImmutable, Vert2fImmutable, Vert2fImmutable, Vert2fImmutable, float, boolean)

Definition at line 220 of file geom3f2D.hpp.

◆ JAU_MAKE_BITFIELD_ENUM_STRING()

jau::math::geom::plane::JAU_MAKE_BITFIELD_ENUM_STRING	(	AffineTransformType	,
		identity	,
		translation	,
		uniform_scale	,
		general_scale	,
		quadrant_rotation	,
		general_rotation	,
		general_transform	,
		flip	)

◆ operator*() [1/14]

template<typename T, std::enable_if_t< std::is_floating_point_v< T >, bool > = true>

Matrix4< T > jau::math::operator*	(	const Matrix4< T > &	lhs,
		const Matrix4< T > &	rhs )

constexprnoexcept

Definition at line 1951 of file mat4f.hpp.

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◆ operator*() [2/14]

template<typename T, std::enable_if_t< std::is_floating_point_v< T >, bool > = true>

Matrix4< T > jau::math::operator*	(	const Matrix4< T > &	lhs,
		const T	s )

constexprnoexcept

Definition at line 1957 of file mat4f.hpp.

◆ operator*() [3/14]

template<typename T, std::enable_if_t< std::is_floating_point_v< T >, bool > = true>

Matrix4< T > jau::math::operator*	(	const T	s,
		const Matrix4< T > &	rhs )

constexprnoexcept

Definition at line 1963 of file mat4f.hpp.

◆ operator<<() [1/10]

template<typename T, std::enable_if_t< std::is_floating_point_v< T >, bool > = true>

std::ostream & jau::math::operator<<	(	std::ostream &	out,
		const Matrix4< T > &	v )

noexcept

Definition at line 1969 of file mat4f.hpp.

◆ to_string()

std::string jau::math::to_string ( const math_error_t v )

noexcept

Returns std::string representation of math_error_t.

Definition at line 906 of file basic_types.cpp.

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◆ operator+() [1/5]

template<typename T, std::enable_if_t< std::is_floating_point_v< T >, bool > = true>

Quaternion< T > jau::math::operator+	(	const Quaternion< T > &	lhs,
		const Quaternion< T > &	rhs )

constexprnoexcept

Definition at line 1152 of file quaternion.hpp.

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◆ operator-() [1/9]

template<typename T, std::enable_if_t< std::is_floating_point_v< T >, bool > = true>

Quaternion< T > jau::math::operator-	(	const Quaternion< T > &	lhs,
		const Quaternion< T > &	rhs )

constexprnoexcept

Definition at line 1158 of file quaternion.hpp.

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◆ operator*() [4/14]

template<typename T, std::enable_if_t< std::is_floating_point_v< T >, bool > = true>

Quaternion< T > jau::math::operator*	(	const Quaternion< T > &	lhs,
		const Quaternion< T > &	rhs )

constexprnoexcept

Definition at line 1164 of file quaternion.hpp.

◆ operator*() [5/14]

template<typename T, std::enable_if_t< std::is_floating_point_v< T >, bool > = true>

Quaternion< T > jau::math::operator*	(	const Quaternion< T > &	lhs,
		const T	s )

constexprnoexcept

Definition at line 1170 of file quaternion.hpp.

◆ operator*() [6/14]

template<typename T, std::enable_if_t< std::is_floating_point_v< T >, bool > = true>

Quaternion< T > jau::math::operator*	(	const T	s,
		const Quaternion< T > &	rhs )

constexprnoexcept

Definition at line 1176 of file quaternion.hpp.

◆ operator<<() [2/10]

template<typename T, std::enable_if_t< std::is_floating_point_v< T >, bool > = true>

std::ostream & jau::math::operator<<	(	std::ostream &	out,
		const Quaternion< T > &	v )

noexcept

Definition at line 1182 of file quaternion.hpp.

◆ operator<<() [3/10]

template<typename T, std::enable_if_t< std::numeric_limits< T >::is_integer, bool > = true>

std::ostream & jau::math::operator<<	(	std::ostream &	out,
		const RectI< T > &	v )

noexcept

Definition at line 135 of file recti.hpp.

◆ getZBufferEpsilon()

float jau::math::util::getZBufferEpsilon	(	int	zBits,
		float	z,
		float	zNear )

constexprnoexcept

Returns resolution of Z buffer of given parameter, see Love Your Z-Buffer.

 return z * z / ( zNear * (1<<zBits) - z )

Examples:

1.5256461E-4 = 16 zBits, -0.2 zDist, 0.1 zNear
6.1033297E-6 = 16 zBits, -1.0 zDist, 0.1 zNear

Parameters

zBits	number of bits of Z precision, i.e. z-buffer depth
z	distance from the eye to the object
zNear	distance from eye to near clip plane

Returns: smallest resolvable Z separation at this range.

Definition at line 46 of file float_util.hpp.

◆ getZBufferValue()

int jau::math::util::getZBufferValue	(	int	zBits,
		float	z,
		float	zNear,
		float	zFar )

constexprnoexcept

Returns Z buffer value of given parameter, see Love Your Z-Buffer.

 float a = zFar / ( zFar - zNear )
 float b = zFar * zNear / ( zNear - zFar )
 return (int) ( (1<<zBits) * ( a + b / z ) )

Parameters

zBits	number of bits of Z precision, i.e. z-buffer depth
z	distance from the eye to the object
zNear	distance from eye to near clip plane
zFar	distance from eye to far clip plane

Returns: z buffer value

Definition at line 64 of file float_util.hpp.

◆ getOrthoWinZ()

float jau::math::util::getOrthoWinZ	(	float	orthoZ,
		float	zNear,
		float	zFar )

constexprnoexcept

Returns orthogonal distance (1f/zNear-1f/orthoZ) / (1f/zNear-1f/zFar);.

Definition at line 74 of file float_util.hpp.

◆ getEulerAngleOrientation()

jau::math::Vec3f jau::math::util::getEulerAngleOrientation ( const jau::math::Vec3f & eulerRotation )

constexprnoexcept

Returns an orientation vector for given eurler X/Y/Z angles in radians.

Returned vector reflect each axis and is either 1 for not-flipped or -1 for flipped orientation..

Examples: GearsES2.cpp.

Definition at line 83 of file float_util.hpp.

◆ operator<<() [4/10]

template<typename Value_type, std::enable_if_t< std::is_floating_point_v< Value_type >, bool > = true>

std::ostream & jau::math::util::operator<<	(	std::ostream &	out,
		const PMVMatrix4< Value_type > &	v )

inlinenoexcept

Definition at line 1457 of file pmvmat4f.hpp.

◆ operator+() [2/5]

template<typename T, std::enable_if_t< std::is_floating_point_v< T >, bool > = true>

Vector2F< T > jau::math::operator+	(	const Vector2F< T > &	lhs,
		const Vector2F< T > &	rhs )

constexprnoexcept

Definition at line 340 of file vec2f.hpp.

◆ operator-() [2/9]

template<typename T, std::enable_if_t< std::is_floating_point_v< T >, bool > = true>

Vector2F< T > jau::math::operator-	(	const Vector2F< T > &	lhs,
		const Vector2F< T > &	rhs )

constexprnoexcept

Definition at line 352 of file vec2f.hpp.

◆ operator-() [3/9]

template<typename T, std::enable_if_t< std::is_floating_point_v< T >, bool > = true>

Vector2F< T > jau::math::operator- ( const Vector2F< T > & lhs )

constexprnoexcept

Definition at line 358 of file vec2f.hpp.

◆ operator*() [7/14]

template<typename T, std::enable_if_t< std::is_floating_point_v< T >, bool > = true>

Vector2F< T > jau::math::operator*	(	const Vector2F< T > &	lhs,
		const T	s )

constexprnoexcept

Definition at line 366 of file vec2f.hpp.

◆ operator*() [8/14]

template<typename T, std::enable_if_t< std::is_floating_point_v< T >, bool > = true>

Vector2F< T > jau::math::operator*	(	const T	s,
		const Vector2F< T > &	rhs )

constexprnoexcept

Definition at line 372 of file vec2f.hpp.

◆ operator/() [1/8]

template<typename T, std::enable_if_t< std::is_floating_point_v< T >, bool > = true>

Vector2F< T > jau::math::operator/	(	const Vector2F< T > &	lhs,
		const T	s )

constexprnoexcept

Definition at line 378 of file vec2f.hpp.

◆ operator/() [2/8]

template<typename T, std::enable_if_t< std::is_floating_point_v< T >, bool > = true>

Vector2F< T > jau::math::operator/	(	const T	s,
		const Vector2F< T > &	rhs )

constexprnoexcept

Definition at line 384 of file vec2f.hpp.

◆ min() [1/4]

template<typename T, std::enable_if_t< std::is_floating_point_v< T >, bool > = true>

Vector2F< T > jau::math::min	(	const Vector2F< T > &	lhs,
		const Vector2F< T > &	rhs )

constexprnoexcept

Definition at line 392 of file vec2f.hpp.

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◆ max() [1/4]

template<typename T, std::enable_if_t< std::is_floating_point_v< T >, bool > = true>

Vector2F< T > jau::math::max	(	const Vector2F< T > &	lhs,
		const Vector2F< T > &	rhs )

constexprnoexcept

Definition at line 398 of file vec2f.hpp.

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◆ abs() [1/4]

template<typename T, std::enable_if_t< std::is_floating_point_v< T >, bool > = true>

Vector2F< T > jau::math::abs ( const Vector2F< T > & lhs )

constexprnoexcept

Definition at line 404 of file vec2f.hpp.

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◆ operator<<() [5/10]

template<typename T, std::enable_if_t< std::is_floating_point_v< T >, bool > = true>

std::ostream & jau::math::operator<<	(	std::ostream &	out,
		const Vector2F< T > &	v )

noexcept

Definition at line 410 of file vec2f.hpp.

◆ operator<<() [6/10]

template<typename T, std::enable_if_t< std::is_floating_point_v< T >, bool > = true>

std::ostream & jau::math::operator<<	(	std::ostream &	out,
		const Ray2F< T > &	v )

noexcept

Definition at line 479 of file vec2f.hpp.

◆ operator+() [3/5]

template<typename T, std::enable_if_t< std::numeric_limits< T >::is_integer, bool > = true>

Vector2I< T > jau::math::operator+	(	const Vector2I< T > &	lhs,
		const Vector2I< T > &	rhs )

constexprnoexcept

Definition at line 254 of file vec2i.hpp.

◆ operator-() [4/9]

template<typename T, std::enable_if_t< std::numeric_limits< T >::is_integer, bool > = true>

Vector2I< T > jau::math::operator-	(	const Vector2I< T > &	lhs,
		const Vector2I< T > &	rhs )

constexprnoexcept

Definition at line 266 of file vec2i.hpp.

◆ operator-() [5/9]

template<typename T, std::enable_if_t< std::numeric_limits< T >::is_integer, bool > = true>

Vector2I< T > jau::math::operator- ( const Vector2I< T > & lhs )

constexprnoexcept

Definition at line 272 of file vec2i.hpp.

◆ operator*() [9/14]

template<typename T, std::enable_if_t< std::numeric_limits< T >::is_integer, bool > = true>

Vector2I< T > jau::math::operator*	(	const Vector2I< T > &	lhs,
		const float	s )

constexprnoexcept

Definition at line 280 of file vec2i.hpp.

◆ operator*() [10/14]

template<typename T, std::enable_if_t< std::numeric_limits< T >::is_integer, bool > = true>

Vector2I< T > jau::math::operator*	(	const float	s,
		const Vector2I< T > &	rhs )

constexprnoexcept

Definition at line 286 of file vec2i.hpp.

◆ operator/() [3/8]

template<typename T, std::enable_if_t< std::numeric_limits< T >::is_integer, bool > = true>

Vector2I< T > jau::math::operator/	(	const Vector2I< T > &	lhs,
		const float	s )

constexprnoexcept

Definition at line 292 of file vec2i.hpp.

◆ operator/() [4/8]

template<typename T, std::enable_if_t< std::is_floating_point_v< T >, bool > = true>

Vector2I< T > jau::math::operator/	(	const T	s,
		const Vector2I< T > &	rhs )

constexprnoexcept

Definition at line 298 of file vec2i.hpp.

◆ min() [2/4]

template<typename T, std::enable_if_t< std::numeric_limits< T >::is_integer, bool > = true>

Vector2I< T > jau::math::min	(	const Vector2I< T > &	lhs,
		const Vector2I< T > &	rhs )

constexprnoexcept

Definition at line 306 of file vec2i.hpp.

◆ max() [2/4]

template<typename T, std::enable_if_t< std::numeric_limits< T >::is_integer, bool > = true>

Vector2I< T > jau::math::max	(	const Vector2I< T > &	lhs,
		const Vector2I< T > &	rhs )

constexprnoexcept

Definition at line 312 of file vec2i.hpp.

◆ abs() [2/4]

template<typename T, std::enable_if_t< std::is_floating_point_v< T >, bool > = true>

Vector2I< T > jau::math::abs ( const Vector2I< T > & lhs )

constexprnoexcept

Definition at line 318 of file vec2i.hpp.

◆ operator<<() [7/10]

template<typename T, std::enable_if_t< std::numeric_limits< T >::is_integer, bool > = true>

std::ostream & jau::math::operator<<	(	std::ostream &	out,
		const Vector2I< T > &	v )

noexcept

Definition at line 324 of file vec2i.hpp.

◆ operator+() [4/5]

template<typename T, std::enable_if_t< std::is_floating_point_v< T >, bool > = true>

Vector3F< T > jau::math::operator+	(	const Vector3F< T > &	lhs,
		const Vector3F< T > &	rhs )

constexprnoexcept

Definition at line 356 of file vec3f.hpp.

◆ operator-() [6/9]

template<typename T, std::enable_if_t< std::is_floating_point_v< T >, bool > = true>

Vector3F< T > jau::math::operator-	(	const Vector3F< T > &	lhs,
		const Vector3F< T > &	rhs )

constexprnoexcept

Definition at line 368 of file vec3f.hpp.

◆ operator-() [7/9]

template<typename T, std::enable_if_t< std::is_floating_point_v< T >, bool > = true>

Vector3F< T > jau::math::operator- ( const Vector3F< T > & lhs )

constexprnoexcept

Definition at line 374 of file vec3f.hpp.

◆ operator*() [11/14]

template<typename T, std::enable_if_t< std::is_floating_point_v< T >, bool > = true>

Vector3F< T > jau::math::operator*	(	const Vector3F< T > &	lhs,
		const T	s )

constexprnoexcept

Definition at line 382 of file vec3f.hpp.

◆ operator*() [12/14]

template<typename T, std::enable_if_t< std::is_floating_point_v< T >, bool > = true>

Vector3F< T > jau::math::operator*	(	const T	s,
		const Vector3F< T > &	rhs )

constexprnoexcept

Definition at line 388 of file vec3f.hpp.

◆ operator/() [5/8]

template<typename T, std::enable_if_t< std::is_floating_point_v< T >, bool > = true>

Vector3F< T > jau::math::operator/	(	const Vector3F< T > &	lhs,
		const T	s )

constexprnoexcept

Definition at line 394 of file vec3f.hpp.

◆ operator/() [6/8]

template<typename T, std::enable_if_t< std::is_floating_point_v< T >, bool > = true>

Vector3F< T > jau::math::operator/	(	const T	s,
		const Vector3F< T > &	rhs )

constexprnoexcept

Definition at line 400 of file vec3f.hpp.

◆ min() [3/4]

template<typename T, std::enable_if_t< std::is_floating_point_v< T >, bool > = true>

Vector3F< T > jau::math::min	(	const Vector3F< T > &	lhs,
		const Vector3F< T > &	rhs )

constexprnoexcept

Definition at line 408 of file vec3f.hpp.

◆ max() [3/4]

template<typename T, std::enable_if_t< std::is_floating_point_v< T >, bool > = true>

Vector3F< T > jau::math::max	(	const Vector3F< T > &	lhs,
		const Vector3F< T > &	rhs )

constexprnoexcept

Definition at line 414 of file vec3f.hpp.

◆ abs() [3/4]

template<typename T, std::enable_if_t< std::is_floating_point_v< T >, bool > = true>

Vector3F< T > jau::math::abs ( const Vector3F< T > & lhs )

constexprnoexcept

Definition at line 420 of file vec3f.hpp.

◆ operator<<() [8/10]

template<typename T, std::enable_if_t< std::is_floating_point_v< T >, bool > = true>

std::ostream & jau::math::operator<<	(	std::ostream &	out,
		const Vector3F< T > &	v )

noexcept

Definition at line 426 of file vec3f.hpp.

◆ operator<<() [9/10]

template<typename T, std::enable_if_t< std::is_floating_point_v< T >, bool > = true>

std::ostream & jau::math::operator<<	(	std::ostream &	out,
		const Ray3F< T > &	v )

noexcept

Definition at line 498 of file vec3f.hpp.

◆ operator+() [5/5]

template<typename T, std::enable_if_t< std::is_floating_point_v< T >, bool > = true>

Vector4F< T > jau::math::operator+	(	const Vector4F< T > &	lhs,
		const Vector4F< T > &	rhs )

constexprnoexcept

Definition at line 288 of file vec4f.hpp.

◆ operator-() [8/9]

template<typename T, std::enable_if_t< std::is_floating_point_v< T >, bool > = true>

Vector4F< T > jau::math::operator-	(	const Vector4F< T > &	lhs,
		const Vector4F< T > &	rhs )

constexprnoexcept

Definition at line 300 of file vec4f.hpp.

◆ operator-() [9/9]

template<typename T, std::enable_if_t< std::is_floating_point_v< T >, bool > = true>

Vector4F< T > jau::math::operator- ( const Vector4F< T > & lhs )

constexprnoexcept

Definition at line 306 of file vec4f.hpp.

◆ operator*() [13/14]

template<typename T, std::enable_if_t< std::is_floating_point_v< T >, bool > = true>

Vector4F< T > jau::math::operator*	(	const Vector4F< T > &	lhs,
		const T	s )

constexprnoexcept

Definition at line 314 of file vec4f.hpp.

◆ operator*() [14/14]

template<typename T, std::enable_if_t< std::is_floating_point_v< T >, bool > = true>

Vector4F< T > jau::math::operator*	(	const T	s,
		const Vector4F< T > &	rhs )

constexprnoexcept

Definition at line 320 of file vec4f.hpp.

◆ operator/() [7/8]

template<typename T, std::enable_if_t< std::is_floating_point_v< T >, bool > = true>

Vector4F< T > jau::math::operator/	(	const Vector4F< T > &	lhs,
		const T	s )

constexprnoexcept

Definition at line 326 of file vec4f.hpp.

◆ operator/() [8/8]

template<typename T, std::enable_if_t< std::is_floating_point_v< T >, bool > = true>

Vector4F< T > jau::math::operator/	(	const T	s,
		const Vector4F< T > &	rhs )

constexprnoexcept

Definition at line 332 of file vec4f.hpp.

◆ min() [4/4]

template<typename T, std::enable_if_t< std::is_floating_point_v< T >, bool > = true>

Vector4F< T > jau::math::min	(	const Vector4F< T > &	lhs,
		const Vector4F< T > &	rhs )

constexprnoexcept

Definition at line 340 of file vec4f.hpp.

◆ max() [4/4]

template<typename T, std::enable_if_t< std::is_floating_point_v< T >, bool > = true>

Vector4F< T > jau::math::max	(	const Vector4F< T > &	lhs,
		const Vector4F< T > &	rhs )

constexprnoexcept

Definition at line 346 of file vec4f.hpp.

◆ abs() [4/4]

template<typename T, std::enable_if_t< std::is_floating_point_v< T >, bool > = true>

Vector4F< T > jau::math::abs ( const Vector4F< T > & lhs )

constexprnoexcept

Definition at line 352 of file vec4f.hpp.

◆ to_vec3()

template<typename T, std::enable_if_t< std::is_floating_point_v< T >, bool > = true>

Vector3F< T > jau::math::to_vec3 ( const Vector4F< T > & v )

constexprnoexcept

out = { this.x, this.y, this.z } dropping w, returns out.

Definition at line 359 of file vec4f.hpp.

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◆ operator<<() [10/10]

template<typename T, std::enable_if_t< std::is_floating_point_v< T >, bool > = true>

std::ostream & jau::math::operator<<	(	std::ostream &	out,
		const Vector4F< T > &	v )

noexcept

Definition at line 365 of file vec4f.hpp.

◆ setToRotation()

template<typename Value_type, std::enable_if_t< std::is_floating_point_v< Value_type >, bool > = true>

Matrix4< Value_type, sf_type > & jau::math::Matrix4< Value_type, sf_type >::setToRotation ( const Quat & q )

Set this matrix to rotation using the given Quaternion.

Implementation Details:

makes identity matrix if magnitudeSquared() is is zero using epsilon
The fields [m00 .. m22] define the rotation

Parameters

q	the Quaternion representing the rotation

Returns: this matrix for chaining

See also: Matrix-FAQ Q54; Quaternion#toMatrix(float[]); getRotation()

Definition at line 1193 of file quaternion.hpp.

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◆ getRotation()

template<typename Value_type, std::enable_if_t< std::is_floating_point_v< Value_type >, bool > = true>

Matrix4< Value_type, sf_type >::Quat & jau::math::Matrix4< Value_type, sf_type >::getRotation ( Quat & res ) const

noexcept

Returns the rotation [m00 .

. m22] fields converted to a Quaternion.

Parameters

res	resulting Quaternion

Returns: the resulting Quaternion for chaining.

See also: Quaternion#setFromMat(float, float, float, float, float, float, float, float, float); #setToRotation(Quaternion)

Definition at line 1207 of file quaternion.hpp.

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Classes

Typedefs

Enumerations

Functions

Detailed Description

Typedef Documentation

◆ Geom2f_ref

◆ Geom2f_list

◆ AGeom2f_ref

◆ AGeom2f_list

◆ Disk2f_ref

◆ Rect2f_ref

◆ LineStrip2f_ref

◆ Vec3fList

◆ Mat4f

◆ Quat4f

◆ Recti

◆ PMVMat4f

◆ Stack16f

◆ Mat4fStack

◆ sync_action_t

◆ sync_action_fptr

◆ SyncMat4f

◆ SyncMats4f

◆ Vec2f

◆ Point2F

◆ Point2f

◆ Ray2f

◆ Vec2i

◆ Point2I

◆ Point2i

◆ Vec3f

◆ Point3F

◆ Point3f

◆ Ray3f

◆ Vec4f

◆ Point4F

◆ Point4f

Enumeration Type Documentation

◆ orientation_t

◆ Winding

◆ AffineTransformType

◆ math_error_t

Function Documentation

◆ JAU_MAKE_ENUM_STRING() [1/2]

◆ JAU_MAKE_ENUM_STRING() [2/2]

◆ tri_area()

◆ orientation()

◆ testSeg2SegIntersection2D() [1/2]

◆ midpoint()

◆ isInTriangle3()

◆ area2D()

◆ getArea2DWinding()

◆ sqlend()

◆ triArea() [1/2]

◆ triArea() [2/2]

◆ triArea2D()

◆ inCircle2DVal()

◆ isInCircle2D()

◆ is2DCCW()

◆ get2DWinding()

◆ testSeg2SegIntersection2D() [2/2]

◆ testTri2SegIntersection2D()

◆ JAU_MAKE_BITFIELD_ENUM_STRING()

◆ operator*() [1/14]

◆ operator*() [2/14]

◆ operator*() [3/14]

◆ operator<<() [1/10]

◆ to_string()

◆ operator+() [1/5]

◆ operator-() [1/9]

◆ operator*() [4/14]

◆ operator*() [5/14]

◆ operator*() [6/14]

◆ operator<<() [2/10]

◆ operator<<() [3/10]

◆ getZBufferEpsilon()

◆ getZBufferValue()

◆ getOrthoWinZ()

◆ getEulerAngleOrientation()