nem Namespace Reference

Namespaces
namespace	accurate
namespace	color
namespace	ease
namespace	error
namespace	experimental
namespace	fast
namespace	intr

Classes
struct	is_subset_of
struct	mat
struct	quat_t
struct	safe_t
struct	sincos
struct	storage
struct	storage< _T, 2 >
struct	storage< _T, 3 >
struct	storage< _T, 4 >
struct	unsafe_t
struct	vec

Concepts
concept	scalar_type
concept	CanBeNaN
concept	CanBeNaNIfConfig

Typedefs
using	nem_string = const char*
using	real = float
using	mat2 = mat<real, 2, 2>
using	mat3 = mat<real, 3, 3>
using	mat4 = mat<real, 4, 4>
using	quat = quat_t<nem::real>
using	int2 = nem::vec<int , 2>
using	int3 = nem::vec<int , 3>
using	int4 = nem::vec<int , 4>
using	float2 = nem::vec<float , 2>
using	float3 = nem::vec<float , 3>
using	float4 = nem::vec<float , 4>
using	double2 = nem::vec<double, 2>
using	double3 = nem::vec<double, 3>
using	double4 = nem::vec<double, 4>

Enumerations
enum class	Precision : unsigned char { Fast = 0 , Accurate = 1 }

Functions
const char *	GET_C_STRING (nem_string str)
template<nem::scalar_type T>
constexpr T	abs_to_rel_error (T x, T abs_error)
template<nem::scalar_type T>
constexpr T	eps ()
template<nem::scalar_type T, nem::Precision Prec = nem::default_precision>
constexpr T	abs_error ()
template<nem::scalar_type T, nem::Precision Prec = nem::default_precision>
constexpr T	rel_error (T x)
template<typename T , size_t C, size_t R>
std::string	tostr (const mat< T, C, R > &matrix)
template<typename T , size_t C, size_t R>
std::ostream &	operator<< (std::ostream &os, const mat< T, C, R > &matrix)
template<typename T , size_t C, size_t R>
std::istream &	operator>> (std::istream &is, mat< T, C, R > &matrix)
template<typename T , size_t C, size_t R, typename F >
constexpr nem::mat< T, C, R >	transform_items (nem::mat< T, C, R > m, F &&func)
template<typename T , size_t C, size_t R>
constexpr nem::mat< T, R, C >	transpose (const nem::mat< T, C, R > &m)
template<typename T , size_t N>
constexpr nem::mat< T, N, N >	identity ()
template<typename M >
constexpr nem::mat< typename M::ITEM_TYPE, M::COLUMNS, M::ROWS >	identity ()
template<typename T , size_t C1, size_t R1, size_t C2, size_t R2>
constexpr nem::mat< T, C2, R2 >	upscale (const nem::mat< T, C1, R1 > &m)
template<typename T , size_t N>
constexpr nem::mat< T, N+1, N+1 >	homogenous (const nem::mat< T, N, N > &m)
template<typename T >
constexpr T	determinant (const nem::mat< T, 2, 2 > &m)
template<std::floating_point T>
constexpr nem::mat< T, 2, 2 >	rotate (T radians)
template<std::floating_point T>
constexpr nem::mat< T, 3, 3 >	rotate_x (nem::sincos< T > a)
template<std::floating_point T>
constexpr nem::mat< T, 3, 3 >	rotate_y (nem::sincos< T > a)
template<std::floating_point T>
constexpr nem::mat< T, 3, 3 >	rotate_z (nem::sincos< T > a)
template<std::floating_point T>
constexpr nem::mat< T, 3, 3 >	rotate (T yaw_z, T pitch_y, T roll_x)
template<std::floating_point T>
constexpr nem::mat< T, 3, 3 >	translate_2D (const nem::vec< T, 2 > &value)
template<std::floating_point T>
constexpr nem::mat< T, 4, 4 >	translate_3D (const nem::vec< T, 3 > &value)
template<std::floating_point T, size_t N>
constexpr nem::mat< T, N, N >	scale (const nem::vec< T, N > &value)
template<std::floating_point T>
constexpr nem::mat< T, 4, 4 >	transform (const nem::vec< T, 3 > &translation, const nem::quat_t< T > &rotation, const nem::vec< T, 3 > scaler)
template<std::floating_point T = float, nem::Precision Prec = nem::default_precision>
constexpr T	log2 (T x)
template<std::floating_point T, nem::Precision Prec = nem::default_precision>
constexpr T	log (T base, T value)
template<std::floating_point T, nem::Precision Prec = nem::default_precision>
constexpr T	ln (T value)
template<std::floating_point T, nem::Precision Prec = nem::default_precision>
constexpr T	exp2 (T x)
template<nem::scalar_type T, std::integral E>
constexpr T	pow (T base, E exp)
template<std::floating_point T, nem::Precision Prec = nem::default_precision>
constexpr T	pow (T base, T exp, nem::unsafe_t)
template<std::floating_point T, nem::Precision Prec = nem::default_precision>
constexpr T	pow (T base, T exp, nem::safe_t=nem::safe)
template<typename T >
T	sqrt (T value)
template<std::floating_point T, int Precision = 20>
constexpr T	csqrt (T value)
int	isqrt (unsigned x)
int	icbrt (unsigned x)
template<typename T >
std::ostream &	operator<< (std::ostream &os, const nem::quat_t< T > &q)
template<typename T >
std::istream &	operator>> (std::istream &is, nem::quat_t< T > &q)
template<typename T >
std::string	to_str (const nem::quat_t< T > &q)
template<typename T = nem::real>
constexpr T	sqr_length (const nem::quat_t< T > &q)
template<typename T = nem::real>
T	length (const nem::quat_t< T > &q)
template<typename T = nem::real>
nem::quat_t< T >	normalize (nem::quat_t< T > q)
template<typename T = nem::real>
constexpr nem::quat_t< T >	make_quat (const nem::vec< T, 4 > &vec4)
template<typename T = nem::real>
constexpr nem::quat_t< T >	make_quat (T scalar, T x, T y, T z)
template<typename T = nem::real>
constexpr nem::quat_t< T >	conjugate (const nem::quat_t< T > &q)
	Conjugates the quaternion, yielding a quaternion with the same angle (scalar) but inverse axis (vector)
template<typename T = nem::real>
constexpr nem::quat_t< T >	inverse (const nem::quat_t< T > &q)
template<typename T = nem::real>
nem::quat_t< T >	from_axis_angle (const nem::vec< T, 3 > &axis, T radians)
template<typename T = nem::real>
nem::quat_t< T >	from_euler (T pitch, T yaw, T roll)
template<typename T = nem::real>
constexpr nem::mat< T, 3, 3 >	norm_quaterion_to_rotation_matrix (const nem::quat_t< T > &q)
template<typename T >
constexpr nem::vec< T, 3 >	extract_vector (const nem::quat_t< T > &q)
template<nem::scalar_type T>
constexpr T	degrees (T degrees) noexcept
	Converts degrees to radians. Used to make units explicit.
template<nem::scalar_type T>
constexpr T	radians (T radians) noexcept
	Converts radians to radians (passes the argument unchanged). Used to make units explicit.
template<std::floating_point T, int P = DEFAULT_TRIG_PRECISION>
constexpr T	ft_sin_q1 (T x)
template<std::floating_point T, int P = DEFAULT_TRIG_PRECISION>
constexpr T	ft_cos_q1 (T x)
template<std::floating_point T, int P = DEFAULT_TRIG_PRECISION>
constexpr T	sin (T x)
template<std::floating_point T, int P = DEFAULT_TRIG_PRECISION>
constexpr T	cos (T x)
template<std::floating_point T, int P = DEFAULT_TRIG_PRECISION>
constexpr nem::sincos< T >	get_sincos (T radians)
template<std::floating_point T, int P = DEFAULT_TRIG_PRECISION>
constexpr T	tan (T x)
template<std::floating_point T, int P = DEFAULT_TRIG_PRECISION>
constexpr T	ctg (T x)
template<std::floating_point T, int P = DEFAULT_TRIG_PRECISION>
constexpr T	sec (T x)
template<std::floating_point T, int P = DEFAULT_TRIG_PRECISION>
constexpr T	csc (T x)
template<std::floating_point T, int P = DEFAULT_TRIG_PRECISION>
constexpr T	ft_atan_q1 (T x)
template<std::floating_point T, int P = DEFAULT_TRIG_PRECISION>
constexpr T	atan (T x)
template<std::floating_point T, int P = DEFAULT_TRIG_PRECISION>
constexpr T	atan2 (T y, T x)
template<std::floating_point T>
constexpr T	acos (T x)
template<std::floating_point T>
constexpr T	asin (T x)
template<std::floating_point T, int P = DEFAULT_TRIG_PRECISION>
constexpr T	actg (T x)
template<std::floating_point T, int P = DEFAULT_TRIG_PRECISION>
constexpr T	actg2 (T x, T y)
template<std::floating_point T>
constexpr T	is_infinite (T value) noexcept
template<std::floating_point T>
constexpr T	is_nan (T value) noexcept
template<std::floating_point T>
constexpr T	copysign (T to, T from) noexcept
	Copies the sign of {from} over to {to}. If the signs were the same, it doesn't change.
template<nem::scalar_type T>
constexpr T	sign (T value) noexcept
template<typename T >
constexpr T	abs (T value) noexcept
template<nem::scalar_type T>
constexpr bool	is_zero (T a) noexcept
	Is a nearly 0? Given an Epsilon > 0, within each all numbers are considered indistinguisable from 0, |a| < eps.
template<nem::scalar_type T>
constexpr bool	is_zero_or_neg (T a) noexcept
template<nem::scalar_type T>
constexpr bool	equal (T a, T b) noexcept
	Are a and b nearly equal? Given an Epsilon > 0, within each all numbers are considered indistinguisable from 0, |a - b| < eps.
template<nem::scalar_type T>
constexpr T	get_max (T a, T b) noexcept
template<nem::scalar_type T>
constexpr T	get_min (T a, T b) noexcept
template<nem::scalar_type T>
constexpr T	average (T a, T b) noexcept
template<typename T >
constexpr T	pow2 (T value) noexcept
template<typename T >
constexpr T	pow3 (T value) noexcept
template<typename T >
constexpr T	pow4 (T value) noexcept
template<typename T >
constexpr T	sqr (T value) noexcept
template<typename T >
constexpr T	cube (T value) noexcept
template<nem::scalar_type T>
constexpr T	truncate (T value) noexcept
template<nem::scalar_type T>
constexpr T	floor (T value) noexcept
	Floors always towards -infinity.
template<nem::scalar_type T>
constexpr T	ceil (T value) noexcept
	Ceils always towards +infinity.
template<nem::scalar_type T>
constexpr T	mod (T a, T b)
	Calculates euclidean modulo of a % b = r, where r belongs to [0, b). Unline standard C++ modulo operator, works with any floating-point numbers and can never yield negative numbers.
template<std::floating_point T>
constexpr T	frac (T value) noexcept
	Returns the fractional part of the floating-point number, with respect to sign 3.5 -> 0.5 4.0 -> 0.0 -2.1 -> -0.1.
template<std::floating_point T>
constexpr T	round (T value) noexcept
template<std::floating_point T>
constexpr T	floor (T value, T step)
template<std::floating_point T>
constexpr T	ceil (T value, T step)
template<std::floating_point T>
constexpr T	round (T value, T step)
template<nem::scalar_type T>
constexpr T	repeat (T value, T lengthExcl)
	Unwinds number to 0 when goes past length. Lengh is excluded: when value == lengthExcl, value becomes 0.
template<nem::scalar_type T>
constexpr T	repeat (T value, T minIncl, T maxExcl)
	Unwinds number to minimum when goes past maximum. Max value is excluded: when value == maxExcl, value becomes minIncl.
template<nem::scalar_type T>
constexpr T	pingpong (T value, T length)
template<nem::scalar_type T>
constexpr T	pingpong (T value, T minIncl, T maxExcl)
template<std::totally_ordered T>
constexpr T	clamp (T value, T minIncl, T maxIncl) noexcept
template<std::totally_ordered T>
constexpr T	clamp01 (T value) noexcept
template<typename T >
constexpr T	smoothstep (T edge0, T edge1, T x)
template<typename T >
constexpr T	lerp (T a, T b, T t)
template<nem::scalar_type T>
constexpr T	remap (T value, T fromMin, T fromMax, T toMin, T toMax)
template<std::floating_point T>
constexpr T	is_whole (T value)
	Is a floating point number whole (same as integer)
template<typename T , size_t N>
std::ostream &	operator<< (std::ostream &os, const nem::vec< T, N > &vec)
template<typename T , size_t N>
std::istream &	operator>> (std::istream &is, nem::vec< T, N > &vec)
template<typename T , size_t N>
std::string	tostr (const nem::vec< T, N > &vec)
template<typename T , size_t N>
bool	is_zero (const nem::vec< T, N > &v)
template<typename T , size_t N>
bool	is_zero (const nem::vec< T, N > &&v)
template<typename T , size_t N>
constexpr nem::vec< T, N >	is_infinite (const nem::vec< T, N > &v)
template<typename T , size_t N>
constexpr nem::vec< T, N >	is_nan (const nem::vec< T, N > &v)
template<std::floating_point T, size_t N>
constexpr nem::vec< T, N >	copysign (const nem::vec< T, N > &to, const nem::vec< T, N > &from)
template<nem::scalar_type T, size_t N>
constexpr nem::vec< T, N >	sign (const nem::vec< T, N > &v)
template<typename T , size_t N>
constexpr nem::vec< T, N >	abs (const nem::vec< T, N > &v)
template<nem::scalar_type T, size_t N>
constexpr bool	is_zero_or_neg (const nem::vec< T, N > &v)
template<nem::scalar_type T, size_t N>
constexpr bool	equal (const nem::vec< T, N > &a, const nem::vec< T, N > &b)
template<nem::scalar_type T, size_t N>
constexpr nem::vec< T, N >	get_max (const nem::vec< T, N > &a, const nem::vec< T, N > &b)
template<nem::scalar_type T, size_t N>
constexpr nem::vec< T, N >	get_min (const nem::vec< T, N > &a, const nem::vec< T, N > &b)
template<nem::scalar_type T, size_t N>
constexpr nem::vec< T, N >	average (const nem::vec< T, N > &a, const nem::vec< T, N > &b)
template<typename T , size_t N>
constexpr nem::vec< T, N >	pow2 (const nem::vec< T, N > &v)
template<typename T , size_t N>
constexpr nem::vec< T, N >	pow3 (const nem::vec< T, N > &v)
template<typename T , size_t N>
constexpr nem::vec< T, N >	pow4 (const nem::vec< T, N > &v)
template<typename T , size_t N>
constexpr nem::vec< T, N >	sqr (const nem::vec< T, N > &v)
template<typename T , size_t N>
constexpr nem::vec< T, N >	cube (const nem::vec< T, N > &v)
template<nem::scalar_type T, size_t N>
constexpr nem::vec< T, N >	truncate (const nem::vec< T, N > &v)
template<nem::scalar_type T, size_t N>
constexpr nem::vec< T, N >	floor (const nem::vec< T, N > &v)
template<nem::scalar_type T, size_t N>
constexpr nem::vec< T, N >	ceil (const nem::vec< T, N > &v)
template<nem::scalar_type T, size_t N>
constexpr nem::vec< T, N >	mod (const nem::vec< T, N > &a, const nem::vec< T, N > &b)
template<std::floating_point T, size_t N>
constexpr nem::vec< T, N >	frac (const nem::vec< T, N > &v)
template<std::floating_point T, size_t N>
constexpr nem::vec< T, N >	round (const nem::vec< T, N > &v)
template<nem::scalar_type T, size_t N>
constexpr nem::vec< T, N >	floor (const nem::vec< T, N > &v, const nem::vec< T, N > &step)
template<nem::scalar_type T, size_t N>
constexpr nem::vec< T, N >	ceil (const nem::vec< T, N > &v, const nem::vec< T, N > &step)
template<nem::scalar_type T, size_t N>
constexpr nem::vec< T, N >	round (const nem::vec< T, N > &v, const nem::vec< T, N > &step)
template<nem::scalar_type T, size_t N>
constexpr nem::vec< T, N >	repeat (const nem::vec< T, N > &value, const nem::vec< T, N > &lengthExcl)
template<nem::scalar_type T, size_t N>
constexpr nem::vec< T, N >	repeat (const nem::vec< T, N > &value, const nem::vec< T, N > &minIncl, const nem::vec< T, N > &maxExcl)
template<nem::scalar_type T, size_t N>
constexpr nem::vec< T, N >	pingpong (const nem::vec< T, N > &value, const nem::vec< T, N > &length)
template<nem::scalar_type T, size_t N>
constexpr nem::vec< T, N >	pingpong (const nem::vec< T, N > &value, const nem::vec< T, N > &minIncl, const nem::vec< T, N > &maxExcl)
template<std::totally_ordered T, size_t N>
constexpr nem::vec< T, N >	clamp (const nem::vec< T, N > &value, const nem::vec< T, N > &minIncl, const nem::vec< T, N > &maxIncl)
template<std::totally_ordered T, size_t N>
constexpr nem::vec< T, N >	clamp01 (const nem::vec< T, N > &value)
template<typename T , size_t N>
constexpr nem::vec< T, N >	smoothstep (const nem::vec< T, N > &edge0, const nem::vec< T, N > &edge1, const nem::vec< T, N > &x)
template<nem::scalar_type T, size_t N>
constexpr nem::vec< T, N >	remap (const nem::vec< T, N > &value, const nem::vec< T, N > &fromMin, const nem::vec< T, N > &fromMax, const nem::vec< T, N > &toMin, const nem::vec< T, N > &toMax)
template<nem::scalar_type T, size_t N>
constexpr nem::vec< T, N >	is_whole (const nem::vec< T, N > &v)
template<typename T , size_t N>
T	dot (const nem::vec< T, N > &a, const nem::vec< T, N > &b)
template<typename T >
nem::vec< T, 3 >	cross (const nem::vec< T, 3 > &a, const nem::vec< T, 3 > &b)
template<typename T , size_t N>
T	horizontal_sum (const nem::vec< T, N > &v)
template<typename T , size_t N>
T	horizontal_mul (const nem::vec< T, N > &v)
template<typename T , size_t N>
nem::vec< T, N >	reflect (const nem::vec< T, N > &vector, const nem::vec< T, N > &normal)
template<typename T , size_t N>
static constexpr nem::vec< T, N >	lerp (const nem::vec< T, N > &a, const nem::vec< T, N > &b, float t)
template<typename T , size_t N>
constexpr T	sqr_length (const nem::vec< T, N > &vec)
template<typename T , size_t N>
T	length (const nem::vec< T, N > &vec)
template<typename T , size_t N>
nem::vec< T, N >	normalize (const nem::vec< T, N > &vec)
template<typename T >
bool	orthogonal_3d_basis (const nem::vec< T, 3 > &vector, nem::vec< T, 3 > &b1, nem::vec< T, 3 > &b2)

Variables
constexpr bool	ERR_THROW = true
constexpr bool	ERR_LOG = true
constexpr bool	ERR_USE_NAN = true
constexpr bool	ERR_SAFE_FALLBACK = false
constexpr bool	USE_C_STRING = true
constexpr safe_t	safe {}
constexpr unsafe_t	unsafe {}
constexpr nem::Precision	default_precision = nem::Precision::Fast
template<class From , class To >
constexpr bool	is_subset_of_v = is_subset_of<From, To>::value
template<std::floating_point T>
constexpr T	SQRT2 = (T)1.414213562373095
template<std::floating_point T>
constexpr T	SQRT3 = (T)1.73205080756887
template<std::floating_point T>
constexpr T	SQRT5 = (T)2.236067977499789
template<std::floating_point T>
constexpr T	PI = (T)3.141592653589793
template<std::floating_point T>
constexpr T	HALF_PI = (T)nem::PI<T> * (T)0.5
template<std::floating_point T>
constexpr T	QUARTER_PI = (T)nem::PI<T> * (T)0.25
template<std::floating_point T>
constexpr T	TWO_PI = (T)nem::PI<T> * (T)2.0
template<std::floating_point T>
constexpr T	E = (T)2.718281828459045
template<std::floating_point T>
constexpr T	ESQR = nem::E<T> * nem::E<T>
template<std::floating_point T>
constexpr T	PHI = (T)1.618033988749894
template<std::floating_point T>
constexpr T	DEG_TO_RAD = nem::TWO_PI<T> / (T)360.0
template<std::floating_point T>
constexpr T	RAD_TO_DEG = (T)1.0 / nem::DEG_TO_RAD<T>
template<std::floating_point T>
constexpr T	LN2 = (T)0.6931471805599453094
template<std::floating_point T>
constexpr T	LOG2E = (T)1.44269504088896340735992
	log(2, e)
static constexpr const char *	MATRIX_COLUMN_SEPARATOR = ", "
static constexpr const char *	MATRIX_ROW_SEPARATOR = "\n"
static constexpr const char *	MATRIX_L_BRACE = "["
static constexpr const char *	MATRIX_R_BRACE = "]"
static constexpr const char *	QUAT_SEPARATOR = " + "
static constexpr const char *	QUAT_L_BRACE = "("
static constexpr const char *	QUAT_R_BRACE = ")"
static constexpr int	DEFAULT_TRIG_PRECISION = 1
static constexpr float	DEFAULT_TRIG_EPSILON = 0.01f
static constexpr const char *	VECTOR_SEPARATOR = ", "
static constexpr const char *	VECTOR_L_BRACE = "("
static constexpr const char *	VECTOR_R_BRACE = ")"

Typedef Documentation

double2

using nem::double2 = nem::vec<double, 2>

Definition at line 261 of file vec.hpp.

double3

using nem::double3 = nem::vec<double, 3>

Definition at line 262 of file vec.hpp.

double4

using nem::double4 = nem::vec<double, 4>

Definition at line 263 of file vec.hpp.

float2

using nem::float2 = nem::vec<float , 2>

Definition at line 258 of file vec.hpp.

float3

using nem::float3 = nem::vec<float , 3>

Definition at line 259 of file vec.hpp.

float4

using nem::float4 = nem::vec<float , 4>

Definition at line 260 of file vec.hpp.

int2

using nem::int2 = nem::vec<int , 2>

Definition at line 255 of file vec.hpp.

int3

using nem::int3 = nem::vec<int , 3>

Definition at line 256 of file vec.hpp.

int4

using nem::int4 = nem::vec<int , 4>

Definition at line 257 of file vec.hpp.

mat2

using nem::mat2 = mat<real, 2, 2>

Definition at line 149 of file mat.hpp.

mat3

using nem::mat3 = mat<real, 3, 3>

Definition at line 150 of file mat.hpp.

mat4

using nem::mat4 = mat<real, 4, 4>

Definition at line 151 of file mat.hpp.

nem_string

using nem::nem_string = const char*

Definition at line 47 of file config.hpp.

quat

using nem::quat = quat_t<nem::real>

Definition at line 112 of file quat.hpp.

real

using nem::real = float

Definition at line 55 of file config.hpp.

Enumeration Type Documentation

Precision

enum class nem::Precision : unsigned char

strong

Enumerator
Fast
Accurate

Definition at line 66 of file config.hpp.

Function Documentation

abs() [1/2]

template<typename T , size_t N>

nem::vec< T, N > nem::abs ( const nem::vec< T, N > & v )

constexpr

Definition at line 90 of file vec_utils.hpp.

abs() [2/2]

template<typename T >

T nem::abs ( T value )

constexprnoexcept

Definition at line 38 of file utils.hpp.

abs_error()

template<nem::scalar_type T, nem::Precision Prec = nem::default_precision>

T nem::abs_error ( )

constexpr

Definition at line 144 of file config.hpp.

abs_to_rel_error()

template<nem::scalar_type T>

T nem::abs_to_rel_error ( T x, T abs_error )

constexpr

Definition at line 75 of file config.hpp.

acos()

template<std::floating_point T>

T nem::acos ( T x )

constexpr

Minimax polynomial approximation of acos, valid on [-1, 1], with a max error of roughly 6.7e-5. A widely used public-domain approximation (see e.g. "Efficient approximations for the arc cosine function", Lee, 2008, and countless graphics-programming write-ups building on it).

Definition at line 273 of file trig.hpp.

actg()

template<std::floating_point T, int P = DEFAULT_TRIG_PRECISION>

T nem::actg ( T x )

constexpr

Definition at line 294 of file trig.hpp.

actg2()

template<std::floating_point T, int P = DEFAULT_TRIG_PRECISION>

T nem::actg2 ( T x, T y )

constexpr

Two-argument arc-cotangent: the angle whose cotangent is x / y, equivalent to nem::atan2 with the arguments given in x/y order instead of y/x.

Definition at line 302 of file trig.hpp.

asin()

template<std::floating_point T>

T nem::asin ( T x )

constexpr

Definition at line 288 of file trig.hpp.

atan()

template<std::floating_point T, int P = DEFAULT_TRIG_PRECISION>

T nem::atan ( T x )

constexpr

Definition at line 240 of file trig.hpp.

atan2()

template<std::floating_point T, int P = DEFAULT_TRIG_PRECISION>

T nem::atan2 ( T y, T x )

constexpr

Two-argument arctangent: the angle of the point (x, y), in (-PI, PI], resolved using the sign of both arguments instead of just their ratio.

Definition at line 254 of file trig.hpp.

average() [1/2]

template<nem::scalar_type T, size_t N>

nem::vec< T, N > nem::average ( const nem::vec< T, N > & a, const nem::vec< T, N > & b )

constexpr

Definition at line 153 of file vec_utils.hpp.

average() [2/2]

template<nem::scalar_type T>

T nem::average ( T a, T b )

constexprnoexcept

Definition at line 62 of file utils.hpp.

ceil() [1/4]

template<nem::scalar_type T, size_t N>

nem::vec< T, N > nem::ceil ( const nem::vec< T, N > & v )

constexpr

Definition at line 249 of file vec_utils.hpp.

ceil() [2/4]

template<nem::scalar_type T, size_t N>

nem::vec< T, N > nem::ceil ( const nem::vec< T, N > & v, const nem::vec< T, N > & step )

constexpr

Definition at line 308 of file vec_utils.hpp.

ceil() [3/4]

template<nem::scalar_type T>

T nem::ceil ( T value )

constexprnoexcept

Ceils always towards +infinity.

Definition at line 101 of file utils.hpp.

ceil() [4/4]

template<std::floating_point T>

T nem::ceil ( T value, T step )

constexpr

Ceils the value to a uniform linear grid with step {step}. Same as normal ceil, when step = 1. Step has to always be positive. (v = 0.9, s = 1.0) -> 1.0 (v = 0.2, s = 1.0) -> 1.0 (v = 0.4, s = 0.25) -> 0.5 (v = 0.1, s = 0.25) -> 0.5 (v = -0.1, s = 0.25) -> 0.0 (v = 423.163123, s = 0.1) -> 423.2

Ceils the value to a uniform linear grid with step {step}. Same as normal ceil, when step = 1. Step has to always be positive. (v = 5, s = 3) -> 3 (v = -4, s = 3) -> -6

Definition at line 189 of file utils.hpp.

clamp() [1/2]

template<std::totally_ordered T, size_t N>

nem::vec< T, N > nem::clamp ( const nem::vec< T, N > & value, const nem::vec< T, N > & minIncl, const nem::vec< T, N > & maxIncl )

constexpr

Definition at line 378 of file vec_utils.hpp.

clamp() [2/2]

template<std::totally_ordered T>

T nem::clamp ( T value, T minIncl, T maxIncl )

constexprnoexcept

Definition at line 261 of file utils.hpp.

clamp01() [1/2]

template<std::totally_ordered T, size_t N>

nem::vec< T, N > nem::clamp01 ( const nem::vec< T, N > & value )

constexpr

Definition at line 389 of file vec_utils.hpp.

clamp01() [2/2]

template<std::totally_ordered T>

T nem::clamp01 ( T value )

constexprnoexcept

Definition at line 267 of file utils.hpp.

conjugate()

template<typename T = nem::real>

nem::quat_t< T > nem::conjugate ( const nem::quat_t< T > & q )

constexpr

Conjugates the quaternion, yielding a quaternion with the same angle (scalar) but inverse axis (vector)

Definition at line 48 of file quat_utils.hpp.

copysign() [1/2]

template<std::floating_point T, size_t N>

nem::vec< T, N > nem::copysign ( const nem::vec< T, N > & to, const nem::vec< T, N > & from )

constexpr

---

Sign operations

Definition at line 68 of file vec_utils.hpp.

copysign() [2/2]

template<std::floating_point T>

T nem::copysign ( T to, T from )

constexprnoexcept

Copies the sign of {from} over to {to}. If the signs were the same, it doesn't change.

---

Sign operations

Definition at line 31 of file utils.hpp.

cos()

template<std::floating_point T, int P = DEFAULT_TRIG_PRECISION>

T nem::cos ( T x )

constexpr

Definition at line 100 of file trig.hpp.

cross()

template<typename T >

nem::vec< T, 3 > nem::cross ( const nem::vec< T, 3 > & a, const nem::vec< T, 3 > & b )

inline

Definition at line 457 of file vec_utils.hpp.

csc()

template<std::floating_point T, int P = DEFAULT_TRIG_PRECISION>

T nem::csc ( T x )

constexpr

Definition at line 201 of file trig.hpp.

csqrt()

template<std::floating_point T, int Precision = 20>

T nem::csqrt ( T value )

constexpr

Definition at line 197 of file power.hpp.

ctg()

template<std::floating_point T, int P = DEFAULT_TRIG_PRECISION>

T nem::ctg ( T x )

constexpr

Definition at line 179 of file trig.hpp.

cube() [1/2]

template<typename T , size_t N>

nem::vec< T, N > nem::cube ( const nem::vec< T, N > & v )

constexpr

Definition at line 212 of file vec_utils.hpp.

cube() [2/2]

template<typename T >

T nem::cube ( T value )

constexprnoexcept

Definition at line 73 of file utils.hpp.

degrees()

template<nem::scalar_type T>

T nem::degrees ( T degrees )

constexprnoexcept

Converts degrees to radians. Used to make units explicit.

Definition at line 28 of file trig.hpp.

determinant()

template<typename T >

T nem::determinant ( const nem::mat< T, 2, 2 > & m )

constexpr

Definition at line 88 of file mat_utils.hpp.

dot()

template<typename T , size_t N>

T nem::dot ( const nem::vec< T, N > & a, const nem::vec< T, N > & b )

inline

Definition at line 446 of file vec_utils.hpp.

eps()

template<nem::scalar_type T>

T nem::eps ( )

constexpr

Definition at line 90 of file config.hpp.

equal() [1/2]

template<nem::scalar_type T, size_t N>

bool nem::equal ( const nem::vec< T, N > & a, const nem::vec< T, N > & b )

constexpr

Definition at line 118 of file vec_utils.hpp.

equal() [2/2]

template<nem::scalar_type T>

bool nem::equal ( T a, T b )

constexprnoexcept

Are a and b nearly equal? Given an Epsilon > 0, within each all numbers are considered indistinguisable from 0, |a - b| < eps.

Definition at line 56 of file utils.hpp.

exp2()

template<std::floating_point T, nem::Precision Prec = nem::default_precision>

T nem::exp2 ( T x )

constexpr

---

Exponentiation

Definition at line 106 of file power.hpp.

extract_vector()

template<typename T >

nem::vec< T, 3 > nem::extract_vector ( const nem::quat_t< T > & q )

constexpr

Definition at line 99 of file quat_utils.hpp.

floor() [1/4]

template<nem::scalar_type T, size_t N>

nem::vec< T, N > nem::floor ( const nem::vec< T, N > & v )

constexpr

Definition at line 238 of file vec_utils.hpp.

floor() [2/4]

template<nem::scalar_type T, size_t N>

nem::vec< T, N > nem::floor ( const nem::vec< T, N > & v, const nem::vec< T, N > & step )

constexpr

---

Rounding, flooring and ceiling with step

Definition at line 297 of file vec_utils.hpp.

floor() [3/4]

template<nem::scalar_type T>

T nem::floor ( T value )

constexprnoexcept

Floors always towards -infinity.

Definition at line 87 of file utils.hpp.

floor() [4/4]

template<std::floating_point T>

T nem::floor ( T value, T step )

constexprnoexcept

---

Rounding, flooring and ceiling with step

Floors the value to a uniform linear grid with step {step}. Same as normal floor, when step = 1. Step has to always be positive. (v = 0.9, s = 1.0) -> 0.0 (v = 0.2, s = 1.0) -> 0.0 (v = 0.4, s = 0.25) -> 0.25 (v = 0.1, s = 0.25) -> 0.0 (v = -0.1, s = 0.25) -> -0.25 (v = 423.163123, s = 0.1) -> 423.1

Floors the value to a uniform linear grid with step {step}. Same as normal floor, when step = 1. Step has to always be positive. (v = 5, s = 3) -> 3 (v = -4, s = 3) -> -6

Definition at line 165 of file utils.hpp.

frac() [1/2]

template<std::floating_point T, size_t N>

nem::vec< T, N > nem::frac ( const nem::vec< T, N > & v )

constexpr

Definition at line 271 of file vec_utils.hpp.

frac() [2/2]

template<std::floating_point T>

T nem::frac ( T value )

constexprnoexcept

Returns the fractional part of the floating-point number, with respect to sign 3.5 -> 0.5 4.0 -> 0.0 -2.1 -> -0.1.

Definition at line 133 of file utils.hpp.

from_axis_angle()

template<typename T = nem::real>

nem::quat_t< T > nem::from_axis_angle	(	const nem::vec< T, 3 > &	axis,
		T	radians )

Definition at line 60 of file quat_utils.hpp.

from_euler()

template<typename T = nem::real>

nem::quat_t< T > nem::from_euler	(	T	pitch,
		T	yaw,
		T	roll )

Definition at line 72 of file quat_utils.hpp.

ft_atan_q1()

template<std::floating_point T, int P = DEFAULT_TRIG_PRECISION>

T nem::ft_atan_q1 ( T x )

constexpr

---

Inverse trigonometric functions

Core polynomial approximation of atan(x), valid on [-1, 1]. nem::atan reduces any other argument into this range first via atan(x) = sign(x) * HALF_PI - atan(1 / x). Minimax coefficients fitted for P = 1, 2, 3 (max error roughly 5e-3, 6e-4, 8e-5).

Definition at line 219 of file trig.hpp.

ft_cos_q1()

template<std::floating_point T, int P = DEFAULT_TRIG_PRECISION>

T nem::ft_cos_q1 ( T x )

constexpr

Definition at line 63 of file trig.hpp.

ft_sin_q1()

template<std::floating_point T, int P = DEFAULT_TRIG_PRECISION>

T nem::ft_sin_q1 ( T x )

constexpr

Definition at line 43 of file trig.hpp.

GET_C_STRING()

const char * nem::GET_C_STRING ( nem_string str )

inline

Definition at line 49 of file config.hpp.

get_max() [1/2]

template<nem::scalar_type T, size_t N>

nem::vec< T, N > nem::get_max ( const nem::vec< T, N > & a, const nem::vec< T, N > & b )

constexpr

Definition at line 131 of file vec_utils.hpp.

get_max() [2/2]

template<nem::scalar_type T>

T nem::get_max ( T a, T b )

constexprnoexcept

Definition at line 58 of file utils.hpp.

get_min() [1/2]

template<nem::scalar_type T, size_t N>

nem::vec< T, N > nem::get_min ( const nem::vec< T, N > & a, const nem::vec< T, N > & b )

constexpr

Definition at line 142 of file vec_utils.hpp.

get_min() [2/2]

template<nem::scalar_type T>

T nem::get_min ( T a, T b )

constexprnoexcept

Definition at line 60 of file utils.hpp.

get_sincos()

template<std::floating_point T, int P = DEFAULT_TRIG_PRECISION>

nem::sincos< T > nem::get_sincos ( T radians )

constexpr

Computes sin and cos together in a single range reduction pass, instead of paying for it twice (once per nem::sin/nemcos call). Both quadrant-1 polynomials still have to be evaluated once each (they're different polynomials), but the division + rounding + multiply-subtract range reduction and the sign/abs extraction only happen once.

Definition at line 120 of file trig.hpp.

homogenous()

template<typename T , size_t N>

nem::mat< T, N+1, N+1 > nem::homogenous ( const nem::mat< T, N, N > & m )

constexpr

Definition at line 74 of file mat_utils.hpp.

horizontal_mul()

template<typename T , size_t N>

T nem::horizontal_mul ( const nem::vec< T, N > & v )

inline

Definition at line 478 of file vec_utils.hpp.

horizontal_sum()

template<typename T , size_t N>

T nem::horizontal_sum ( const nem::vec< T, N > & v )

inline

Definition at line 467 of file vec_utils.hpp.

icbrt()

int nem::icbrt ( unsigned x )

inline

binary search for the approximation of integer cubic root. original implementation from "Hacker's Delight, Ch. 11: Integer Cube Root"

Definition at line 247 of file power.hpp.

identity() [1/2]

template<typename T , size_t N>

nem::mat< T, N, N > nem::identity ( )

constexpr

Definition at line 39 of file mat_utils.hpp.

identity() [2/2]

template<typename M >

nem::mat< typename M::ITEM_TYPE, M::COLUMNS, M::ROWS > nem::identity ( )

constexpr

Definition at line 50 of file mat_utils.hpp.

inverse()

template<typename T = nem::real>

nem::quat_t< T > nem::inverse ( const nem::quat_t< T > & q )

constexpr

Definition at line 54 of file quat_utils.hpp.

is_infinite() [1/2]

template<typename T , size_t N>

nem::vec< T, N > nem::is_infinite ( const nem::vec< T, N > & v )

constexpr

---

Metadata

Definition at line 42 of file vec_utils.hpp.

is_infinite() [2/2]

template<std::floating_point T>

T nem::is_infinite ( T value )

constexprnoexcept

---

Metadata

Definition at line 19 of file utils.hpp.

is_nan() [1/2]

template<typename T , size_t N>

nem::vec< T, N > nem::is_nan ( const nem::vec< T, N > & v )

constexpr

Definition at line 53 of file vec_utils.hpp.

is_nan() [2/2]

template<std::floating_point T>

T nem::is_nan ( T value )

constexprnoexcept

Definition at line 20 of file utils.hpp.

is_whole() [1/2]

template<nem::scalar_type T, size_t N>

nem::vec< T, N > nem::is_whole ( const nem::vec< T, N > & v )

constexpr

---

Properties

Definition at line 435 of file vec_utils.hpp.

is_whole() [2/2]

template<std::floating_point T>

T nem::is_whole ( T value )

constexpr

Is a floating point number whole (same as integer)

Is an integer number whole. Always true, here for compatibility.

---

Properties

Definition at line 307 of file utils.hpp.

is_zero() [1/3]

template<typename T , size_t N>

bool nem::is_zero ( const nem::vec< T, N > && v )

inline

Definition at line 25 of file vec_utils.hpp.

is_zero() [2/3]

template<typename T , size_t N>

bool nem::is_zero ( const nem::vec< T, N > & v )

inline

Definition at line 12 of file vec_utils.hpp.

is_zero() [3/3]

template<nem::scalar_type T>

bool nem::is_zero ( T a )

constexprnoexcept

Is a nearly 0? Given an Epsilon > 0, within each all numbers are considered indistinguisable from 0, |a| < eps.

---

Comparisons

Definition at line 48 of file utils.hpp.

is_zero_or_neg() [1/2]

template<nem::scalar_type T, size_t N>

bool nem::is_zero_or_neg ( const nem::vec< T, N > & v )

constexpr

---

Comparisons

Definition at line 105 of file vec_utils.hpp.

is_zero_or_neg() [2/2]

template<nem::scalar_type T>

bool nem::is_zero_or_neg ( T a )

constexprnoexcept

Definition at line 51 of file utils.hpp.

isqrt()

int nem::isqrt ( unsigned x )

inline

binary search for the approximation of integer square root. original implementation from "Hacker's Delight, Ch. 11: Integer square root, simple binary search."

Definition at line 230 of file power.hpp.

length() [1/2]

template<typename T = nem::real>

T nem::length ( const nem::quat_t< T > & q )

inline

Definition at line 19 of file quat_utils.hpp.

length() [2/2]

template<typename T , size_t N>

T nem::length

(

const nem::vec< T, N > &

vec

)

Definition at line 517 of file vec_utils.hpp.

lerp() [1/2]

template<typename T , size_t N>

static constexpr nem::vec< T, N > nem::lerp ( const nem::vec< T, N > & a, const nem::vec< T, N > & b, float t )

staticconstexpr

Definition at line 495 of file vec_utils.hpp.

lerp() [2/2]

template<typename T >

T nem::lerp ( T a, T b, T t )

constexpr

Definition at line 286 of file utils.hpp.

ln()

template<std::floating_point T, nem::Precision Prec = nem::default_precision>

T nem::ln ( T value )

constexpr

Definition at line 86 of file power.hpp.

log()

template<std::floating_point T, nem::Precision Prec = nem::default_precision>

T nem::log ( T base, T value )

constexpr

Definition at line 72 of file power.hpp.

log2()

template<std::floating_point T = float, nem::Precision Prec = nem::default_precision>

T nem::log2 ( T x )

constexpr

---

Logs

Definition at line 50 of file power.hpp.

make_quat() [1/2]

template<typename T = nem::real>

nem::quat_t< T > nem::make_quat ( const nem::vec< T, 4 > & vec4 )

constexpr

Definition at line 33 of file quat_utils.hpp.

make_quat() [2/2]

template<typename T = nem::real>

nem::quat_t< T > nem::make_quat ( T scalar, T x, T y, T z )

constexpr

Definition at line 39 of file quat_utils.hpp.

mod() [1/2]

template<nem::scalar_type T, size_t N>

nem::vec< T, N > nem::mod ( const nem::vec< T, N > & a, const nem::vec< T, N > & b )

constexpr

Definition at line 260 of file vec_utils.hpp.

mod() [2/2]

template<nem::scalar_type T>

T nem::mod ( T a, T b )

constexpr

Calculates euclidean modulo of a % b = r, where r belongs to [0, b). Unline standard C++ modulo operator, works with any floating-point numbers and can never yield negative numbers.

Definition at line 115 of file utils.hpp.

norm_quaterion_to_rotation_matrix()

template<typename T = nem::real>

nem::mat< T, 3, 3 > nem::norm_quaterion_to_rotation_matrix ( const nem::quat_t< T > & q )

constexpr

Definition at line 81 of file quat_utils.hpp.

normalize() [1/2]

template<typename T , size_t N>

nem::vec< T, N > nem::normalize

(

const nem::vec< T, N > &

vec

)

Definition at line 523 of file vec_utils.hpp.

normalize() [2/2]

template<typename T = nem::real>

nem::quat_t< T > nem::normalize ( nem::quat_t< T > q )

inline

Definition at line 25 of file quat_utils.hpp.

operator<<() [1/3]

template<typename T , size_t C, size_t R>

std::ostream & nem::operator<<	(	std::ostream &	os,
		const mat< T, C, R > &	matrix )

Definition at line 32 of file mat_io.hpp.

operator<<() [2/3]

template<typename T >

std::ostream & nem::operator<<	(	std::ostream &	os,
		const nem::quat_t< T > &	q )

Definition at line 16 of file quat_io.hpp.

operator<<() [3/3]

template<typename T , size_t N>

std::ostream & nem::operator<<	(	std::ostream &	os,
		const nem::vec< T, N > &	vec )

Definition at line 16 of file vec_io.hpp.

operator>>() [1/3]

template<typename T , size_t C, size_t R>

std::istream & nem::operator>>	(	std::istream &	is,
		mat< T, C, R > &	matrix )

Definition at line 48 of file mat_io.hpp.

operator>>() [2/3]

template<typename T >

std::istream & nem::operator>>	(	std::istream &	is,
		nem::quat_t< T > &	q )

Definition at line 28 of file quat_io.hpp.

operator>>() [3/3]

template<typename T , size_t N>

std::istream & nem::operator>>	(	std::istream &	is,
		nem::vec< T, N > &	vec )

Definition at line 28 of file vec_io.hpp.

orthogonal_3d_basis()

template<typename T >

bool nem::orthogonal_3d_basis	(	const nem::vec< T, 3 > &	vector,
		nem::vec< T, 3 > &	b1,
		nem::vec< T, 3 > &	b2 )

Definition at line 553 of file vec_utils.hpp.

pingpong() [1/4]

template<nem::scalar_type T, size_t N>

nem::vec< T, N > nem::pingpong ( const nem::vec< T, N > & value, const nem::vec< T, N > & length )

constexpr

Definition at line 356 of file vec_utils.hpp.

pingpong() [2/4]

template<nem::scalar_type T, size_t N>

nem::vec< T, N > nem::pingpong ( const nem::vec< T, N > & value, const nem::vec< T, N > & minIncl, const nem::vec< T, N > & maxExcl )

constexpr

Definition at line 367 of file vec_utils.hpp.

pingpong() [3/4]

template<nem::scalar_type T>

T nem::pingpong ( T value, T length )

constexpr

Definition at line 250 of file utils.hpp.

pingpong() [4/4]

template<nem::scalar_type T>

T nem::pingpong ( T value, T minIncl, T maxExcl )

constexpr

Definition at line 256 of file utils.hpp.

pow() [1/3]

template<nem::scalar_type T, std::integral E>

T nem::pow ( T base, E exp )

constexpr

Definition at line 131 of file power.hpp.

pow() [2/3]

template<std::floating_point T, nem::Precision Prec = nem::default_precision>

T nem::pow ( T base, T exp, nem::safe_t = nem::safe )

constexpr

Definition at line 144 of file power.hpp.

pow() [3/3]

template<std::floating_point T, nem::Precision Prec = nem::default_precision>

T nem::pow ( T base, T exp, nem::unsafe_t  )

constexpr

Definition at line 138 of file power.hpp.

pow2() [1/2]

template<typename T , size_t N>

nem::vec< T, N > nem::pow2 ( const nem::vec< T, N > & v )

constexpr

---

Powers

Definition at line 168 of file vec_utils.hpp.

pow2() [2/2]

template<typename T >

T nem::pow2 ( T value )

constexprnoexcept

---

Powers

Definition at line 69 of file utils.hpp.

pow3() [1/2]

template<typename T , size_t N>

nem::vec< T, N > nem::pow3 ( const nem::vec< T, N > & v )

constexpr

Definition at line 179 of file vec_utils.hpp.

pow3() [2/2]

template<typename T >

T nem::pow3 ( T value )

constexprnoexcept

Definition at line 70 of file utils.hpp.

pow4() [1/2]

template<typename T , size_t N>

nem::vec< T, N > nem::pow4 ( const nem::vec< T, N > & v )

constexpr

Definition at line 190 of file vec_utils.hpp.

pow4() [2/2]

template<typename T >

T nem::pow4 ( T value )

constexprnoexcept

Definition at line 71 of file utils.hpp.

radians()

template<nem::scalar_type T>

T nem::radians ( T radians )

constexprnoexcept

Converts radians to radians (passes the argument unchanged). Used to make units explicit.

Definition at line 35 of file trig.hpp.

reflect()

template<typename T , size_t N>

nem::vec< T, N > nem::reflect ( const nem::vec< T, N > & vector, const nem::vec< T, N > & normal )

inline

Definition at line 489 of file vec_utils.hpp.

rel_error()

template<nem::scalar_type T, nem::Precision Prec = nem::default_precision>

T nem::rel_error ( T x )

constexpr

Definition at line 158 of file config.hpp.

remap() [1/2]

template<nem::scalar_type T, size_t N>

nem::vec< T, N > nem::remap ( const nem::vec< T, N > & value, const nem::vec< T, N > & fromMin, const nem::vec< T, N > & fromMax, const nem::vec< T, N > & toMin, const nem::vec< T, N > & toMax )

constexpr

---

Linear mapping

Definition at line 419 of file vec_utils.hpp.

remap() [2/2]

template<nem::scalar_type T>

T nem::remap ( T value, T fromMin, T fromMax, T toMin, T toMax )

constexpr

---

Linear mapping

Definition at line 292 of file utils.hpp.

repeat() [1/4]

template<nem::scalar_type T, size_t N>

nem::vec< T, N > nem::repeat ( const nem::vec< T, N > & value, const nem::vec< T, N > & lengthExcl )

constexpr

---

Repeat, pingpong, clamp

Definition at line 334 of file vec_utils.hpp.

repeat() [2/4]

template<nem::scalar_type T, size_t N>

nem::vec< T, N > nem::repeat ( const nem::vec< T, N > & value, const nem::vec< T, N > & minIncl, const nem::vec< T, N > & maxExcl )

constexpr

Definition at line 345 of file vec_utils.hpp.

repeat() [3/4]

template<nem::scalar_type T>

T nem::repeat ( T value, T lengthExcl )

constexpr

Unwinds number to 0 when goes past length. Lengh is excluded: when value == lengthExcl, value becomes 0.

---

Repeat, pingpong, clamp

Definition at line 237 of file utils.hpp.

repeat() [4/4]

template<nem::scalar_type T>

T nem::repeat ( T value, T minIncl, T maxExcl )

constexpr

Unwinds number to minimum when goes past maximum. Max value is excluded: when value == maxExcl, value becomes minIncl.

Definition at line 245 of file utils.hpp.

rotate() [1/2]

template<std::floating_point T>

nem::mat< T, 2, 2 > nem::rotate ( T radians )

constexpr

Definition at line 94 of file mat_utils.hpp.

rotate() [2/2]

template<std::floating_point T>

nem::mat< T, 3, 3 > nem::rotate ( T yaw_z, T pitch_y, T roll_x )

constexpr

Definition at line 119 of file mat_utils.hpp.

rotate_x()

template<std::floating_point T>

nem::mat< T, 3, 3 > nem::rotate_x ( nem::sincos< T > a )

constexpr

Definition at line 101 of file mat_utils.hpp.

rotate_y()

template<std::floating_point T>

nem::mat< T, 3, 3 > nem::rotate_y ( nem::sincos< T > a )

constexpr

Definition at line 107 of file mat_utils.hpp.

rotate_z()

template<std::floating_point T>

nem::mat< T, 3, 3 > nem::rotate_z ( nem::sincos< T > a )

constexpr

Definition at line 113 of file mat_utils.hpp.

round() [1/4]

template<std::floating_point T, size_t N>

nem::vec< T, N > nem::round ( const nem::vec< T, N > & v )

constexpr

Definition at line 282 of file vec_utils.hpp.

round() [2/4]

template<nem::scalar_type T, size_t N>

nem::vec< T, N > nem::round ( const nem::vec< T, N > & v, const nem::vec< T, N > & step )

constexpr

Definition at line 319 of file vec_utils.hpp.

round() [3/4]

template<std::floating_point T>

T nem::round ( T value )

constexprnoexcept

Rounds the floating-point number to the closest integer. |0.5| will round up, meaning: 0.3 -> 0.0 0.5 -> 1.0 -0.1 -> 0 -0.6 -> -1.0 -0.5 -> 0

Definition at line 144 of file utils.hpp.

round() [4/4]

template<std::floating_point T>

T nem::round ( T value, T step )

constexpr

Rounds the value to a uniform linear grid with step {step}. Same as normal round, when step = 1. Step has to always be positive. (v = 0.9, s = 1.0) -> 1.0 (v = 0.2, s = 1.0) -> 0.0 (v = 0.2, s = 0.25) -> 0.25 (v = 0.1, s = 0.25) -> 0.0 (v = -0.1, s = 0.25) -> 0.0 (v = 423.163123, s = 0.1) -> 423.2

Rounds the value to a uniform linear grid with step {step}. Same as normal round, when step = 1. Step has to always be positive. (v = 5, s = 3) -> 6 (v = -4, s = 3) -> -3

Definition at line 213 of file utils.hpp.

scale()

template<std::floating_point T, size_t N>

nem::mat< T, N, N > nem::scale ( const nem::vec< T, N > & value )

constexpr

Definition at line 139 of file mat_utils.hpp.

sec()

template<std::floating_point T, int P = DEFAULT_TRIG_PRECISION>

T nem::sec ( T x )

constexpr

Definition at line 190 of file trig.hpp.

sign() [1/2]

template<nem::scalar_type T, size_t N>

nem::vec< T, N > nem::sign ( const nem::vec< T, N > & v )

constexpr

Definition at line 79 of file vec_utils.hpp.

sign() [2/2]

template<nem::scalar_type T>

T nem::sign ( T value )

constexprnoexcept

Definition at line 36 of file utils.hpp.

sin()

template<std::floating_point T, int P = DEFAULT_TRIG_PRECISION>

T nem::sin ( T x )

constexpr

Definition at line 83 of file trig.hpp.

smoothstep() [1/2]

template<typename T , size_t N>

nem::vec< T, N > nem::smoothstep ( const nem::vec< T, N > & edge0, const nem::vec< T, N > & edge1, const nem::vec< T, N > & x )

constexpr

---

Interpolation

Definition at line 404 of file vec_utils.hpp.

smoothstep() [2/2]

template<typename T >

T nem::smoothstep ( T edge0, T edge1, T x )

constexpr

---

Interpolation

Definition at line 276 of file utils.hpp.

sqr() [1/2]

template<typename T , size_t N>

nem::vec< T, N > nem::sqr ( const nem::vec< T, N > & v )

constexpr

Definition at line 201 of file vec_utils.hpp.

sqr() [2/2]

template<typename T >

T nem::sqr ( T value )

constexprnoexcept

Definition at line 72 of file utils.hpp.

sqr_length() [1/2]

template<typename T = nem::real>

T nem::sqr_length ( const nem::quat_t< T > & q )

constexpr

Definition at line 13 of file quat_utils.hpp.

sqr_length() [2/2]

template<typename T , size_t N>

T nem::sqr_length ( const nem::vec< T, N > & vec )

constexpr

Definition at line 506 of file vec_utils.hpp.

sqrt()

template<typename T >

T nem::sqrt ( T value )

inline

---

Roots

Definition at line 180 of file power.hpp.

tan()

template<std::floating_point T, int P = DEFAULT_TRIG_PRECISION>

T nem::tan ( T x )

constexpr

---

Tangent, cotangent, secant, cosecant

Definition at line 168 of file trig.hpp.

to_str()

template<typename T >

std::string nem::to_str

(

const nem::quat_t< T > &

q

)

Definition at line 38 of file quat_io.hpp.

tostr() [1/2]

template<typename T , size_t C, size_t R>

std::string nem::tostr

(

const mat< T, C, R > &

matrix

)

Definition at line 15 of file mat_io.hpp.

tostr() [2/2]

template<typename T , size_t N>

std::string nem::tostr

(

const nem::vec< T, N > &

vec

)

Definition at line 38 of file vec_io.hpp.

transform()

template<std::floating_point T>

nem::mat< T, 4, 4 > nem::transform ( const nem::vec< T, 3 > & translation, const nem::quat_t< T > & rotation, const nem::vec< T, 3 > scaler )

constexpr

Definition at line 150 of file mat_utils.hpp.

transform_items()

template<typename T , size_t C, size_t R, typename F >

nem::mat< T, C, R > nem::transform_items ( nem::mat< T, C, R > m, F && func )

constexpr

Definition at line 12 of file mat_utils.hpp.

translate_2D()

template<std::floating_point T>

nem::mat< T, 3, 3 > nem::translate_2D ( const nem::vec< T, 2 > & value )

constexpr

Definition at line 127 of file mat_utils.hpp.

translate_3D()

template<std::floating_point T>

nem::mat< T, 4, 4 > nem::translate_3D ( const nem::vec< T, 3 > & value )

constexpr

Definition at line 133 of file mat_utils.hpp.

transpose()

template<typename T , size_t C, size_t R>

nem::mat< T, R, C > nem::transpose ( const nem::mat< T, C, R > & m )

constexpr

Definition at line 25 of file mat_utils.hpp.

truncate() [1/2]

template<nem::scalar_type T, size_t N>

nem::vec< T, N > nem::truncate ( const nem::vec< T, N > & v )

constexpr

---

Float truncation, fractional part, modulo (remainder), rounding, flooring, ceiling

Definition at line 227 of file vec_utils.hpp.

truncate() [2/2]

template<nem::scalar_type T>

T nem::truncate ( T value )

constexprnoexcept

---

Float truncation, fractional part, modulo (remainder), rounding, flooring, ceiling

Definition at line 79 of file utils.hpp.

upscale()

template<typename T , size_t C1, size_t R1, size_t C2, size_t R2>

nem::mat< T, C2, R2 > nem::upscale ( const nem::mat< T, C1, R1 > & m )

constexpr

Definition at line 57 of file mat_utils.hpp.

Variable Documentation

default_precision

nem::Precision nem::default_precision = nem::Precision::Fast

inlineconstexpr

Definition at line 72 of file config.hpp.

DEFAULT_TRIG_EPSILON

float nem::DEFAULT_TRIG_EPSILON = 0.01f

staticconstexpr

Definition at line 24 of file trig.hpp.

DEFAULT_TRIG_PRECISION

int nem::DEFAULT_TRIG_PRECISION = 1

staticconstexpr

Definition at line 23 of file trig.hpp.

DEG_TO_RAD

template<std::floating_point T>

T nem::DEG_TO_RAD = nem::TWO_PI<T> / (T)360.0

constexpr

Definition at line 17 of file consts.hpp.

E

template<std::floating_point T>

T nem::E = (T)2.718281828459045

constexpr

Definition at line 14 of file consts.hpp.

ERR_LOG

bool nem::ERR_LOG = true

constexpr

Definition at line 24 of file config.hpp.

ERR_SAFE_FALLBACK

bool nem::ERR_SAFE_FALLBACK = false

constexpr

Definition at line 38 of file config.hpp.

ERR_THROW

bool nem::ERR_THROW = true

constexpr

Definition at line 18 of file config.hpp.

ERR_USE_NAN

bool nem::ERR_USE_NAN = true

constexpr

Definition at line 30 of file config.hpp.

ESQR

template<std::floating_point T>

T nem::ESQR = nem::E<T> * nem::E<T>

constexpr

Definition at line 15 of file consts.hpp.

HALF_PI

template<std::floating_point T>

T nem::HALF_PI = (T)nem::PI<T> * (T)0.5

constexpr

Definition at line 11 of file consts.hpp.

is_subset_of_v

template<class From , class To >

bool nem::is_subset_of_v = is_subset_of<From, To>::value

constexpr

Definition at line 180 of file config.hpp.

LN2

template<std::floating_point T>

T nem::LN2 = (T)0.6931471805599453094

constexpr

Definition at line 19 of file consts.hpp.

LOG2E

template<std::floating_point T>

T nem::LOG2E = (T)1.44269504088896340735992

constexpr

log(2, e)

Definition at line 22 of file consts.hpp.

MATRIX_COLUMN_SEPARATOR

const char* nem::MATRIX_COLUMN_SEPARATOR = ", "

staticconstexpr

Definition at line 9 of file mat_io.hpp.

MATRIX_L_BRACE

const char* nem::MATRIX_L_BRACE = "["

staticconstexpr

Definition at line 11 of file mat_io.hpp.

MATRIX_R_BRACE

const char* nem::MATRIX_R_BRACE = "]"

staticconstexpr

Definition at line 12 of file mat_io.hpp.

MATRIX_ROW_SEPARATOR

const char* nem::MATRIX_ROW_SEPARATOR = "\n"

staticconstexpr

Definition at line 10 of file mat_io.hpp.

PHI

template<std::floating_point T>

T nem::PHI = (T)1.618033988749894

constexpr

Definition at line 16 of file consts.hpp.

PI

template<std::floating_point T>

T nem::PI = (T)3.141592653589793

constexpr

Definition at line 10 of file consts.hpp.

QUARTER_PI

template<std::floating_point T>

T nem::QUARTER_PI = (T)nem::PI<T> * (T)0.25

constexpr

Definition at line 12 of file consts.hpp.

QUAT_L_BRACE

const char* nem::QUAT_L_BRACE = "("

staticconstexpr

Definition at line 12 of file quat_io.hpp.

QUAT_R_BRACE

const char* nem::QUAT_R_BRACE = ")"

staticconstexpr

Definition at line 13 of file quat_io.hpp.

QUAT_SEPARATOR

const char* nem::QUAT_SEPARATOR = " + "

staticconstexpr

Definition at line 11 of file quat_io.hpp.

RAD_TO_DEG

template<std::floating_point T>

T nem::RAD_TO_DEG = (T)1.0 / nem::DEG_TO_RAD<T>

constexpr

Definition at line 18 of file consts.hpp.

safe

safe_t nem::safe {}

inlineconstexpr

Definition at line 63 of file config.hpp.

SQRT2

template<std::floating_point T>

T nem::SQRT2 = (T)1.414213562373095

constexpr

Definition at line 7 of file consts.hpp.

SQRT3

template<std::floating_point T>

T nem::SQRT3 = (T)1.73205080756887

constexpr

Definition at line 8 of file consts.hpp.

SQRT5

template<std::floating_point T>

T nem::SQRT5 = (T)2.236067977499789

constexpr

Definition at line 9 of file consts.hpp.

TWO_PI

template<std::floating_point T>

T nem::TWO_PI = (T)nem::PI<T> * (T)2.0

constexpr

Definition at line 13 of file consts.hpp.

unsafe

unsafe_t nem::unsafe {}

inlineconstexpr

Definition at line 64 of file config.hpp.

USE_C_STRING

bool nem::USE_C_STRING = true

constexpr

Definition at line 48 of file config.hpp.

VECTOR_L_BRACE

const char* nem::VECTOR_L_BRACE = "("

staticconstexpr

Definition at line 12 of file vec_io.hpp.

VECTOR_R_BRACE

const char* nem::VECTOR_R_BRACE = ")"

staticconstexpr

Definition at line 13 of file vec_io.hpp.

VECTOR_SEPARATOR

const char* nem::VECTOR_SEPARATOR = ", "

staticconstexpr

Definition at line 11 of file vec_io.hpp.