Math Namespace Reference

Detailed Description

Different curves.

Half precision (16 bit) float implementation.

Copyright

(C) 2024 Individual contributors, see AUTHORS file

Based on https://github.com/acgessler/half_float

Copyright

(C) 2022 Individual contributors, see AUTHORS file

Classes
class	AngularPFeedbackLoop
	A proportional feedback loop with correct angular interpolation. More...
class	bbox
	Nebula's bounding box class. More...
struct	BezierCubic
struct	byte4
struct	byte4u
class	ClipStatus
	The result of a clip check (Inside, Outside or Clipped). More...
class	Extrapolator
	Extrapolator maintains state about updates for remote entities, and will generate smooth guesses about where those entities will be based on previously received data. More...
struct	float2
struct	float3
struct	float4
class	frustum
	Defines a clipping frustum made of 6 planes. More...
class	half
struct	int2
struct	int3
struct	int4
class	line
	A line in 3d space. More...
struct	mat4
	A 4x4 single point precision float matrix. More...
class	noise
	Perlin noise class. More...
class	PFeedbackLoop
	A P feedback loop (proportional feedback loop) is a simple object which moves a system's current state towards a goal, using the resulting error (difference between goal and state as feedback on the next run. More...
class	PIDFeedbackLoop
	A PID feedback loop (proportional integral derivative feedback loop) More...
class	plane
	A mathematical plane represented by a normal and a distance from origin. More...
struct	point
	Represents a 3D point in space. More...
class	polar
	A polar coordinate inline class, consisting of 2 angles theta (latitude) and rho (longitude). More...
class	quat
	A quaternion is usually used to represent an orientation in 3D space. More...
struct	randxorstate
	fast random generator based on xorshift+ More...
class	rectangle
	A 2d rectangle class. More...
class	sphere
	A 3-dimensional sphere. More...
class	transform
	Simple transform using position, quaternion, and scale. More...
class	transform44
	A 4x4 matrix which is described by translation, rotation and scale. More...
struct	uint2
struct	uint3
struct	uint4
struct	vec2
	A 2-component float vector class. More...
struct	vec3
	A 3D vector. More...
struct	vec4
	A 4D vector. More...
struct	vector
	A vector is a 3D direction in space. More...

Typedefs
typedef rectangle< float >	floatRectangle
typedef rectangle< int >	intRectangle
typedef float	scalar
typedef float	float32
typedef double	float64

Functions
half	operator+ (half one, half two)
half	operator- (half one, half two)
half	operator* (half one, half two)
half	operator/ (half one, half two)
half	operator+ (half one, float two)
half	operator- (half one, float two)
half	operator* (half one, float two)
half	operator/ (half one, float two)
float	operator+ (float one, half two)
float	operator- (float one, half two)
float	operator* (float one, half two)
float	operator/ (float one, half two)
mat4	reflect (const vec4 &p)
	based on this http://www.opengl.org/discussion_boards/showthread.php/169605-reflection-matrix-how-to-derive
void	decompose (const mat4 &mat, vec3 &outScale, quat &outRotation, vec3 &outTranslation)
mat4	affine (const vec3 &scale, const vec3 &rotationCenter, const quat &rotation, const vec3 &translation)
mat4	affine (const vec3 &scale, const quat &rotation, const vec3 &translation)
mat4	affine (const vec3 &scale, const vec3 &rotation, const vec3 &translation)
mat4	affinetransformation (scalar scale, const vec3 &rotationCenter, const quat &rotation, const vec3 &translation)
mat4	rotationquat (const quat &q)
	TODO: rewrite using SSE.
mat4	transformation (const vec3 &scalingCenter, const quat &scalingRotation, const vec3 &scale, const vec3 &rotationCenter, const quat &rotation, const vec3 &trans)
bool	ispointinside (const vec4 &p, const mat4 &m)
mat4	fromeuler (const vec3 &v)
vec3	aseuler (const mat4 &m)
mat4	skewsymmetric (const vec3 &v)
__forceinline bool	isidentity (const mat4 &m)
__forceinline scalar	determinant (const mat4 &m)
__forceinline mat4	inverse (const mat4 &m)
__forceinline mat4	lookatlh (const point &eye, const point &at, const vector &up)
__forceinline mat4	lookatrh (const point &eye, const point &at, const vector &up)
__forceinline mat4	operator* (const mat4 &m0, const mat4 &m1)
__forceinline vec4	operator* (const mat4 &m, const vec4 &v)
__forceinline vec4	operator* (const mat4 &m, const vec3 &v)
__forceinline vec4	operator* (const mat4 &m, const point &p)
__forceinline vector	operator* (const mat4 &m, const vector &v)
__forceinline mat4	ortholh (scalar w, scalar h, scalar zn, scalar zf)
__forceinline mat4	orthorh (scalar w, scalar h, scalar zn, scalar zf)
__forceinline mat4	orthooffcenterlh (scalar l, scalar r, scalar t, scalar b, scalar zn, scalar zf)
__forceinline mat4	orthooffcenterrh (scalar l, scalar r, scalar t, scalar b, scalar zn, scalar zf)
__forceinline mat4	perspfovlh (scalar fovy, scalar aspect, scalar zn, scalar zf)
__forceinline mat4	perspfovrh (scalar fovy, scalar aspect, scalar zn, scalar zf)
__forceinline mat4	persplh (scalar w, scalar h, scalar zn, scalar zf)
__forceinline mat4	persprh (scalar w, scalar h, scalar zn, scalar zf)
__forceinline mat4	perspoffcenterlh (scalar l, scalar r, scalar b, scalar t, scalar zn, scalar zf)
__forceinline mat4	perspoffcenterrh (scalar l, scalar r, scalar b, scalar t, scalar zn, scalar zf)
__forceinline mat4	rotationaxis (const vec3 &axis, scalar angle)
__forceinline mat4	rotationx (scalar angle)
__forceinline mat4	rotationy (scalar angle)
__forceinline mat4	rotationz (scalar angle)
__forceinline mat4	rotationyawpitchroll (scalar yaw, scalar pitch, scalar roll)
__forceinline mat4	scaling (scalar scale)
__forceinline mat4	scaling (scalar sx, scalar sy, scalar sz)
__forceinline mat4	scaling (const vec3 &s)
__forceinline mat4	translation (scalar x, scalar y, scalar z)
__forceinline mat4	translation (const vec3 &t)
__forceinline mat4	trs (const vec3 &position, const quat &rotation, const vec3 &scale)
	A short hand for creating a TRS (translation, rotation, scale) matrix from pos, rot and scale.
__forceinline mat4	transpose (const mat4 &m)
vector	get_normal (const plane &plane)
point	get_point (const plane &plane)
bool	intersectline (const plane &plane, const point &startPoint, const point &endPoint, point &outIntersectPoint)
bool	intersectplane (const plane &p1, const plane &p2, line &outLine)
	TODO: Test and make sure it produces correct intersection line.
ClipStatus::Type	clip (const plane &plane, const line &l, line &outClippedLine)
__forceinline scalar	dot (const plane &p, const vec4 &v1)
__forceinline plane	normalize (const plane &p)
__forceinline plane	operator* (const mat4 &m, const plane &p)
__forceinline point	operator+ (const point &lhs, const vector &rhs)
__forceinline point	operator- (const point &lhs, const vector &rhs)
__forceinline vector	operator- (const point &lhs, const point &rhs)
__forceinline scalar	dot (const point &p0, const point &p1)
__forceinline scalar	dot (const vector &v, const point &p)
__forceinline scalar	dot (const point &p, const vector &v)
__forceinline point	maximize (const point &v0, const point &v1)
__forceinline point	minimize (const point &v0, const point &v1)
__forceinline bool	less_any (const point &v0, const point &v1)
__forceinline bool	less_all (const point &v0, const point &v1)
__forceinline bool	lessequal_any (const point &v0, const point &v1)
__forceinline bool	lessequal_all (const point &v0, const point &v1)
__forceinline bool	greater_any (const point &v0, const point &v1)
__forceinline bool	greater_all (const point &v0, const point &v1)
__forceinline bool	greaterequal_any (const point &v0, const point &v1)
__forceinline bool	greaterequal_all (const point &v0, const point &v1)
__forceinline bool	equal_any (const point &v0, const point &v1)
__forceinline bool	nearequal (const point &v0, const point &v1, float epsilon)
__forceinline point	less (const point &v0, const point &v1)
__forceinline point	greater (const point &v0, const point &v1)
__forceinline point	equal (const point &v0, const point &v1)
__forceinline vec3	xyz (const point &v)
quat	rotationmatrix (const mat4 &m)
quat	quatyawpitchroll (scalar y, scalar x, scalar z)
vec3	to_euler (const quat &q)
quat	from_euler (const vec3 &v)
quat	slerp (const quat &q1, const quat &q2, scalar t)
	quat slerp TODO: rewrite using sse/avx
vec3	rotate (quat const &q, vec3 const &v)
	Rotate a vector by a quaternion.
__forceinline bool	isidentity (const quat &q)
__forceinline scalar	length (const quat &q)
__forceinline scalar	lengthsq (const quat &q)
__forceinline quat	quatUndenormalize (const quat &q)
__forceinline quat	barycentric (const quat &q0, const quat &q1, const quat &q2, scalar f, scalar g)
__forceinline quat	conjugate (const quat &q)
__forceinline scalar	dot (const quat &q0, const quat &q1)
__forceinline quat	quatExp (const quat &q)
__forceinline quat	identity ()
__forceinline quat	inverse (const quat &q)
__forceinline quat	ln (const quat &q)
__forceinline quat	operator* (const quat &q0, const quat &q1)
__forceinline quat	normalize (const quat &q)
__forceinline quat	rotationquataxis (const vec3 &axis, scalar angle)
	quat from rotation axis + angle.
__forceinline void	squadsetup (const quat &q0, const quat &q1, const quat &q2, const quat &q3, quat &aOut, quat &bOut, quat &cOut)
__forceinline quat	squad (const quat &q1, const quat &a, const quat &b, const quat &c, scalar t)
__forceinline void	to_axisangle (const quat &q, vec4 &outAxis, scalar &outAngle)
__forceinline scalar	rand ()
	Return a pseudo random number between 0 and 1.
__forceinline scalar	rand (scalar min, scalar max)
	Return a pseudo random number between min and max.
__forceinline scalar	sin (scalar x)
__forceinline scalar	cos (scalar x)
__forceinline scalar	tan (scalar x)
__forceinline scalar	asin (scalar x)
__forceinline scalar	acos (scalar x)
__forceinline scalar	atan (scalar x)
__forceinline scalar	sqrt (scalar x)
__forceinline int	fchop (scalar f)
	Chop float to int.
__forceinline scalar	fmod (scalar x, scalar y)
__forceinline scalar	modangle (scalar a)
	Normalize an angular value into the range rad(0) to rad(360).
__forceinline scalar	log2 (scalar f)
	log2() function.
__forceinline scalar	exp2 (scalar x)
__forceinline scalar	log (scalar x)
	get logarithm of x
__forceinline scalar	exp (scalar x)
__forceinline int	frnd (scalar f)
	Round float to integer.
__forceinline scalar	pow (scalar x, scalar y)
__forceinline bool	fequal (scalar f0, scalar f1, scalar tol)
	A fuzzy floating point equality check.
template<typename TYPE >
__forceinline TYPE	max (TYPE a, TYPE b)
template<typename TYPE0 , typename ... TYPEN>
__forceinline TYPE0	max (TYPE0 first, TYPE0 second, TYPEN... rest)
template<>
__forceinline unsigned int	max (unsigned int a, unsigned int b)
	branchless max for uint32
template<typename TYPE >
__forceinline TYPE	min (TYPE a, TYPE b)
template<>
__forceinline unsigned int	min (unsigned int a, unsigned int b)
	branchless min for uints
template<>
__forceinline uint16_t	min (uint16_t a, uint16_t b)
	branchless min for uints
template<typename TYPE0 , typename ... TYPEN>
__forceinline TYPE0	min (TYPE0 first, TYPE0 second, TYPEN... rest)
__forceinline scalar	abs (scalar a)
__forceinline double	abs (double a)
__forceinline int	abs (int a)
__forceinline scalar	sgn (scalar a)
__forceinline constexpr scalar	deg2rad (scalar d)
__forceinline constexpr scalar	rad2deg (scalar r)
__forceinline float	clamp (float val, float minVal, float maxVal)
	Float clamping.
__forceinline int64_t	clamp (int64_t val, int64_t minVal, int64_t maxVal)
	int clamping.
__forceinline int32_t	clamp (int32_t val, int32_t minVal, int32_t maxVal)
	int clamping.
__forceinline float	ceil (float val)
	Floating point ceiling.
__forceinline float	floor (float val)
	Floating point flooring.
__forceinline float	round (float val)
	Floating point rounding.
__forceinline bool	fless (scalar f0, scalar f1, scalar tol)
	A fuzzy floating point less-then check.
__forceinline bool	fgreater (scalar f0, scalar f1, scalar tol)
	A fuzzy floating point greater-then check.
__forceinline scalar	saturate (scalar val)
	Saturate a value (clamps between 0.0f and 1.0f)
__forceinline double	saturate (double val)
	Saturate a value (clamps between 0.0f and 1.0f)
__forceinline float	lerp (float x, float y, float l)
	Linearly interpolate between 2 values: ret = x + l * (y - x)
__forceinline scalar	angulardistance (scalar from, scalar to)
	Get angular distance.
__forceinline bool	isdenormal (scalar s)
	Returns true if the input scalar is denormalized (#DEN)
__forceinline float	undenormalize (scalar s)
	Returns 0 if scalar is denormal.
__forceinline bool	nearequal (scalar a, scalar b, scalar epsilon)
	test of nearly equal given a tolerance (epsilon)
__forceinline scalar	cot (scalar x)
__forceinline scalar	smoothstep (scalar edge0, scalar edge1, scalar x)
__forceinline int	irand (int min, int max)
	Return a pseudo integer random number between min and max.
__forceinline int	mostsignificant (unsigned int val)
	Returns the position of the most significant bit of the number.
__forceinline unsigned int	align (unsigned int alignant, unsigned int alignment)
__forceinline uintptr_t	alignptr (uintptr_t alignant, uintptr_t alignment)
__forceinline unsigned int	align_down (unsigned int alignant, unsigned int alignment)
__forceinline uintptr_t	align_downptr (uintptr_t alignant, uintptr_t alignment)
__forceinline unsigned int	divandroundup (unsigned int dividend, unsigned int divider)
	Integer division with rounding.
__forceinline unsigned int	roundtopow2 (unsigned int val)
	Rounds up to next power of 2.
__forceinline uint64	randxor (randxorstate &state)
__forceinline uint32_t	pointerhash (void *ptr)
	cheap pointer hash using modulo with a mersenne prime
float	normtofloat (uint16_t value)
	convert normalized uint16_t to float
float	normtofloat (int16_t value)
	convert normalized int16_t to float
float	normtofloat (uint8_t value)
	convert normalized uint8_t to float
float	normtofloat (int8_t value)
	convert normalized int8_t to float
__forceinline __m128	fmadd (__m128 a, __m128 b, __m128 c)
	Fused multiply-add operation, (a * b) + c.
__forceinline __m128	less (__m128 a, __m128 b)
	Constructs a vector of results where each element corresponds to a[i] < b[i] with either 0 or 1.
__forceinline __m128	greater (__m128 a, __m128 b)
	Constructs a vector of results where each element corresponds to a[i] > b[i] with either 0 or 1.
__forceinline __m128	recip (__m128 a)
__forceinline __m128	mul (__m128 a, __m128 b)
__forceinline __m128	div (__m128 a, __m128 b)
template<int x, int y, int z, int w>
__forceinline __m128	swizzle (__m128 v)
transform	operator* (const transform &a, const transform &b)
transform	lerp (const transform &a, const transform &b, float t)
point	operator* (const transform &a, const point &b)
	transforms a position (applies scale, rotation and offset)
vector	operator* (const transform &a, const vector &b)
	transforms a vector (ignores position)
__forceinline vec2	lerp (const vec2 &v0, const vec2 &v1, scalar s)
__forceinline vec3	operator- (const vec3 &lhs)
__forceinline vec3	operator* (const vec3 &lhs, scalar t)
__forceinline vec3	operator* (const vec3 &lhs, const vec3 &rhs)
__forceinline vec3	operator+ (const vec3 &lhs, const vec3 &rhs)
__forceinline vec3	operator- (const vec3 &lhs, const vec3 &rhs)
__forceinline scalar	length (const vec3 &v)
__forceinline scalar	lengthsq (const vec3 &v)
__forceinline vec3	reciprocal (const vec3 &v)
__forceinline vec3	reciprocalapprox (const vec3 &v)
__forceinline vec3	multiply (const vec3 &v0, const vec3 &v1)
__forceinline vec3	multiplyadd (const vec3 &v0, const vec3 &v1, const vec3 &v2)
__forceinline vec3	divide (const vec3 &v0, const vec3 &v1)
__forceinline vec3	abs (const vec3 &v)
__forceinline vec3	cross (const vec3 &v0, const vec3 &v1)
__forceinline scalar	dot (const vec3 &v0, const vec3 &v1)
__forceinline vec3	barycentric (const vec3 &v0, const vec3 &v1, const vec3 &v2, scalar f, scalar g)
	calculates Result = v0 + f * (v1 - v0) + g * (v2 - v0)
__forceinline vec3	catmullrom (const vec3 &v0, const vec3 &v1, const vec3 &v2, const vec3 &v3, scalar s)
__forceinline vec3	hermite (const vec3 &v1, const vec3 &t1, const vec3 &v2, const vec3 &t2, scalar s)
__forceinline scalar	angle (const vec3 &v0, const vec3 &v1)
__forceinline vec3	lerp (const vec3 &v0, const vec3 &v1, scalar s)
__forceinline vec3	maximize (const vec3 &v0, const vec3 &v1)
__forceinline vec3	minimize (const vec3 &v0, const vec3 &v1)
__forceinline vec3	clamp (const vec3 &clamp, const vec3 &min, const vec3 &max)
__forceinline vec3	normalize (const vec3 &v)
__forceinline vec3	normalizeapprox (const vec3 &v)
__forceinline vec3	reflect (const vec3 &normal, const vec3 &incident)
__forceinline bool	less_any (const vec3 &v0, const vec3 &v1)
__forceinline bool	less_all (const vec3 &v0, const vec3 &v1)
__forceinline bool	lessequal_any (const vec3 &v0, const vec3 &v1)
__forceinline bool	lessequal_all (const vec3 &v0, const vec3 &v1)
__forceinline bool	greater_any (const vec3 &v0, const vec3 &v1)
__forceinline bool	greater_all (const vec3 &v0, const vec3 &v1)
__forceinline bool	greaterequal_any (const vec3 &v0, const vec3 &v1)
__forceinline bool	greaterequal_all (const vec3 &v0, const vec3 &v1)
__forceinline bool	equal_any (const vec3 &v0, const vec3 &v1)
__forceinline bool	nearequal (const vec3 &v0, const vec3 &v1, float epsilon)
__forceinline bool	nearequal (const vec3 &v0, const vec3 &v1, const vec3 &epsilon)
__forceinline vec3	less (const vec3 &v0, const vec3 &v1)
__forceinline vec3	greater (const vec3 &v0, const vec3 &v1)
__forceinline vec3	equal (const vec3 &v0, const vec3 &v1)
__forceinline vec3	splat (const vec3 &v, uint element)
__forceinline vec3	splat_x (const vec3 &v)
__forceinline vec3	splat_y (const vec3 &v)
__forceinline vec3	splat_z (const vec3 &v)
__forceinline vec3	permute (const vec3 &v0, const vec3 &v1, unsigned int i0, unsigned int i1, unsigned int i2)
__forceinline vec3	select (const vec3 &v0, const vec3 &v1, const uint i0, const uint i1, const uint i2)
__forceinline vec3	select (const vec3 &v0, const vec3 &v1, const vec3 &control)
__forceinline vec3	floor (const vec3 &v)
__forceinline vec3	ceiling (const vec3 &v)
__forceinline vec4	operator- (const vec4 &lhs)
__forceinline vec4	operator* (const vec4 &lhs, scalar t)
__forceinline vec4	operator* (const vec4 &lhs, const vec4 &rhs)
__forceinline vec4	operator+ (const vec4 &lhs, const vec4 &rhs)
__forceinline vec4	operator- (const vec4 &lhs, const vec4 &rhs)
__forceinline scalar	length (const vec4 &v)
__forceinline scalar	length3 (const vec4 &v)
__forceinline scalar	lengthsq (const vec4 &v)
__forceinline scalar	lengthsq3 (const vec4 &v)
__forceinline vec4	reciprocal (const vec4 &v)
__forceinline vec4	reciprocalapprox (const vec4 &v)
__forceinline vec4	multiply (const vec4 &v0, const vec4 &v1)
__forceinline vec4	multiplyadd (const vec4 &v0, const vec4 &v1, const vec4 &v2)
__forceinline vec4	divide (const vec4 &v0, const vec4 &v1)
__forceinline vec4	abs (const vec4 &v)
__forceinline vec4	cross3 (const vec4 &v0, const vec4 &v1)
__forceinline scalar	dot (const vec4 &v0, const vec4 &v1)
__forceinline scalar	dot3 (const vec4 &v0, const vec4 &v1)
__forceinline vec4	barycentric (const vec4 &v0, const vec4 &v1, const vec4 &v2, scalar f, scalar g)
	calculates Result = v0 + f * (v1 - v0) + g * (v2 - v0)
__forceinline vec4	catmullrom (const vec4 &v0, const vec4 &v1, const vec4 &v2, const vec4 &v3, scalar s)
__forceinline vec4	hermite (const vec4 &v1, const vec4 &t1, const vec4 &v2, const vec4 &t2, scalar s)
__forceinline scalar	angle (const vec4 &v0, const vec4 &v1)
__forceinline vec4	lerp (const vec4 &v0, const vec4 &v1, scalar s)
__forceinline vec4	maximize (const vec4 &v0, const vec4 &v1)
__forceinline vec4	minimize (const vec4 &v0, const vec4 &v1)
__forceinline vec4	clamp (const vec4 &clamp, const vec4 &min, const vec4 &max)
__forceinline vec4	normalize (const vec4 &v)
__forceinline vec4	normalizeapprox (const vec4 &v)
__forceinline vec4	normalize3 (const vec4 &v)
__forceinline vec4	normalize3approx (const vec4 &v)
__forceinline vec4	reflect (const vec4 &normal, const vec4 &incident)
__forceinline vec4	perspective_div (const vec4 &v)
__forceinline bool	less_any (const vec4 &v0, const vec4 &v1)
__forceinline bool	less_all (const vec4 &v0, const vec4 &v1)
__forceinline bool	lessequal_any (const vec4 &v0, const vec4 &v1)
__forceinline bool	lessequal_all (const vec4 &v0, const vec4 &v1)
__forceinline bool	greater_any (const vec4 &v0, const vec4 &v1)
__forceinline bool	greater_all (const vec4 &v0, const vec4 &v1)
__forceinline bool	greaterequal_any (const vec4 &v0, const vec4 &v1)
__forceinline bool	greaterequal_all (const vec4 &v0, const vec4 &v1)
__forceinline bool	equal_any (const vec4 &v0, const vec4 &v1)
__forceinline bool	nearequal (const vec4 &v0, const vec4 &v1, const float epsilon)
__forceinline bool	nearequal (const vec4 &v0, const vec4 &v1, const vec4 &epsilon)
__forceinline vec4	less (const vec4 &v0, const vec4 &v1)
__forceinline vec4	greater (const vec4 &v0, const vec4 &v1)
__forceinline vec4	equal (const vec4 &v0, const vec4 &v1)
__forceinline bool	less3_any (const vec4 &v0, const vec4 &v1)
__forceinline bool	less3_all (const vec4 &v0, const vec4 &v1)
__forceinline bool	lessequal3_any (const vec4 &v0, const vec4 &v1)
__forceinline bool	lessequal3_all (const vec4 &v0, const vec4 &v1)
__forceinline bool	greater3_any (const vec4 &v0, const vec4 &v1)
__forceinline bool	greater3_all (const vec4 &v0, const vec4 &v1)
__forceinline bool	greaterequal3_any (const vec4 &v0, const vec4 &v1)
__forceinline bool	greaterequal3_all (const vec4 &v0, const vec4 &v1)
__forceinline bool	equal3_any (const vec4 &v0, const vec4 &v1)
__forceinline bool	equal3_all (const vec4 &v0, const vec4 &v1)
__forceinline bool	nearequal3 (const vec4 &v0, const vec4 &v1, const vec4 &epsilon)
__forceinline vec4	splat (const vec4 &v, uint element)
__forceinline vec4	splat_x (const vec4 &v)
__forceinline vec4	splat_y (const vec4 &v)
__forceinline vec4	splat_z (const vec4 &v)
__forceinline vec4	splat_w (const vec4 &v)
__forceinline vec4	permute (const vec4 &v0, const vec4 &v1, unsigned int i0, unsigned int i1, unsigned int i2, unsigned int i3)
__forceinline vec4	select (const vec4 &v0, const vec4 &v1, const uint i0, const uint i1, const uint i2, const uint i3)
__forceinline vec4	select (const vec4 &v0, const vec4 &v1, const vec4 &control)
__forceinline vec4	floor (const vec4 &v)
__forceinline vec4	ceil (const vec4 &v)
__forceinline vec3	xyz (const vec4 &v)
__forceinline vector	operator- (const vector &rhs)
__forceinline vector	operator+ (const vector &lhs, const vector &rhs)
__forceinline vector	operator- (const vector &lhs, const vector &rhs)
__forceinline vector	operator* (const vector &lhs, scalar s)
__forceinline vector	operator* (const vector &lhs, const vector &rhs)
__forceinline vector	normalize (const vector &v)
__forceinline vector	normalizeapprox (const vector &v)
__forceinline scalar	dot (const vector &v0, const vector &v1)
__forceinline vector	cross (const vector &v0, const vector &v1)
__forceinline scalar	length (const vector &v)
__forceinline scalar	lengthsq (const vector &v)

Variables
static const __m128i	maskX = _mm_setr_epi32( -1,0,0,0 )
static const __m128i	maskY = _mm_setr_epi32( 0,-1,0,0 )
static const __m128i	maskZ = _mm_setr_epi32( 0,0,-1,0 )
static const __m128i	maskW = _mm_setr_epi32( 0,0,0,-1 )
static const __m128	_id_x = _mm_setr_ps(1.0f, 0.0f, 0.0f, 0.0f)
static const __m128	_id_y = _mm_setr_ps(0.0f, 1.0f, 0.0f, 0.0f)
static const __m128	_id_z = _mm_setr_ps(0.0f, 0.0f, 1.0f, 0.0f)
static const __m128	_id_w = _mm_setr_ps(0.0f, 0.0f, 0.0f, 1.0f)
static const __m128	_minus1 = _mm_setr_ps(-1.0f, -1.0f, -1.0f, -1.0f)
static const __m128	_plus1 = _mm_setr_ps(1.0f, 1.0f, 1.0f, 1.0f)
static const __m128	_zero = _mm_setr_ps(0.0f, 0.0f, 0.0f, 0.0f)
static const __m128i	_sign = _mm_setr_epi32(0x80000000, 0x80000000, 0x80000000, 0x80000000)
static const __m128	_mask_xyz = _mm_castsi128_ps(_mm_setr_epi32( 0xFFFFFFFF, 0xFFFFFFFF, 0xFFFFFFFF, 0 ))
static const unsigned int	PERMUTE_0X = 0
static const unsigned int	PERMUTE_0Y = 1
static const unsigned int	PERMUTE_0Z = 2
static const unsigned int	PERMUTE_0W = 3
static const unsigned int	PERMUTE_1X = 4
static const unsigned int	PERMUTE_1Y = 5
static const unsigned int	PERMUTE_1Z = 6
static const unsigned int	PERMUTE_1W = 7

Typedef Documentation

float32

typedef float Math::float32

float64

typedef double Math::float64

floatRectangle

typedef rectangle<float> Math::floatRectangle

intRectangle

typedef rectangle<int> Math::intRectangle

scalar

typedef float Math::scalar

Function Documentation

abs() [1/5]

__forceinline vec3 Math::abs

(

const vec3 &

v

)

abs() [2/5]

__forceinline vec4 Math::abs

(

const vec4 &

v

)

abs() [3/5]

__forceinline double Math::abs

(

double

a

)

abs() [4/5]

__forceinline int Math::abs

(

int

a

)

abs() [5/5]

__forceinline scalar Math::abs

(

scalar

a

)

acos()

__forceinline scalar Math::acos

(

scalar

x

)

affine() [1/3]

mat4 Math::affine	(	const vec3 &	scale,
		const quat &	rotation,
		const vec3 &	translation )

affine() [2/3]

mat4 Math::affine	(	const vec3 &	scale,
		const vec3 &	rotation,
		const vec3 &	translation )

affine() [3/3]

mat4 Math::affine	(	const vec3 &	scale,
		const vec3 &	rotationCenter,
		const quat &	rotation,
		const vec3 &	translation )

affinetransformation()

mat4 Math::affinetransformation	(	scalar	scale,
		const vec3 &	rotationCenter,
		const quat &	rotation,
		const vec3 &	translation )

align()

__forceinline unsigned int Math::align	(	unsigned int	alignant,
		unsigned int	alignment )

align_down()

__forceinline unsigned int Math::align_down	(	unsigned int	alignant,
		unsigned int	alignment )

align_downptr()

__forceinline uintptr_t Math::align_downptr	(	uintptr_t	alignant,
		uintptr_t	alignment )

alignptr()

__forceinline uintptr_t Math::alignptr	(	uintptr_t	alignant,
		uintptr_t	alignment )

angle() [1/2]

__forceinline scalar Math::angle	(	const vec3 &	v0,
		const vec3 &	v1 )

angle() [2/2]

__forceinline scalar Math::angle	(	const vec4 &	v0,
		const vec4 &	v1 )

angulardistance()

__forceinline scalar Math::angulardistance	(	scalar	from,
		scalar	to )

Get angular distance.

aseuler()

vec3 Math::aseuler

(

const mat4 &

m

)

asin()

__forceinline scalar Math::asin

(

scalar

x

)

atan()

__forceinline scalar Math::atan

(

scalar

x

)

barycentric() [1/3]

__forceinline quat Math::barycentric	(	const quat &	q0,
		const quat &	q1,
		const quat &	q2,
		scalar	f,
		scalar	g )

barycentric() [2/3]

__forceinline vec3 Math::barycentric	(	const vec3 &	v0,
		const vec3 &	v1,
		const vec3 &	v2,
		scalar	f,
		scalar	g )

calculates Result = v0 + f * (v1 - v0) + g * (v2 - v0)

barycentric() [3/3]

__forceinline vec4 Math::barycentric	(	const vec4 &	v0,
		const vec4 &	v1,
		const vec4 &	v2,
		scalar	f,
		scalar	g )

calculates Result = v0 + f * (v1 - v0) + g * (v2 - v0)

catmullrom() [1/2]

__forceinline vec3 Math::catmullrom	(	const vec3 &	v0,
		const vec3 &	v1,
		const vec3 &	v2,
		const vec3 &	v3,
		scalar	s )

catmullrom() [2/2]

__forceinline vec4 Math::catmullrom	(	const vec4 &	v0,
		const vec4 &	v1,
		const vec4 &	v2,
		const vec4 &	v3,
		scalar	s )

ceil() [1/2]

__forceinline vec4 Math::ceil

(

const vec4 &

v

)

ceil() [2/2]

__forceinline float Math::ceil

(

float

val

)

Floating point ceiling.

ceiling()

__forceinline vec3 Math::ceiling

(

const vec3 &

v

)

clamp() [1/5]

__forceinline vec3 Math::clamp	(	const vec3 &	clamp,
		const vec3 &	min,
		const vec3 &	max )

clamp() [2/5]

__forceinline vec4 Math::clamp	(	const vec4 &	clamp,
		const vec4 &	min,
		const vec4 &	max )

clamp() [3/5]

__forceinline float Math::clamp	(	float	val,
		float	minVal,
		float	maxVal )

Float clamping.

clamp() [4/5]

__forceinline int32_t Math::clamp	(	int32_t	val,
		int32_t	minVal,
		int32_t	maxVal )

int clamping.

clamp() [5/5]

__forceinline int64_t Math::clamp	(	int64_t	val,
		int64_t	minVal,
		int64_t	maxVal )

int clamping.

clip()

ClipStatus::Type Math::clip ( const plane & plane, const line & l, line & outClippedLine )

inline

conjugate()

__forceinline quat Math::conjugate

(

const quat &

q

)

cos()

__forceinline scalar Math::cos

(

scalar

x

)

cot()

__forceinline scalar Math::cot

(

scalar

x

)

cross() [1/2]

__forceinline vec3 Math::cross	(	const vec3 &	v0,
		const vec3 &	v1 )

cross() [2/2]

__forceinline vector Math::cross	(	const vector &	v0,
		const vector &	v1 )

cross3()

__forceinline vec4 Math::cross3	(	const vec4 &	v0,
		const vec4 &	v1 )

decompose()

void Math::decompose	(	const mat4 &	mat,
		vec3 &	outScale,
		quat &	outRotation,
		vec3 &	outTranslation )

deg2rad()

__forceinline constexpr scalar Math::deg2rad ( scalar d )

constexpr

determinant()

__forceinline scalar Math::determinant

(

const mat4 &

m

)

div()

__forceinline __m128 Math::div	(	__m128	a,
		__m128	b )

divandroundup()

__forceinline unsigned int Math::divandroundup	(	unsigned int	dividend,
		unsigned int	divider )

Integer division with rounding.

divide() [1/2]

__forceinline vec3 Math::divide	(	const vec3 &	v0,
		const vec3 &	v1 )

divide() [2/2]

__forceinline vec4 Math::divide	(	const vec4 &	v0,
		const vec4 &	v1 )

dot() [1/8]

__forceinline scalar Math::dot	(	const plane &	p,
		const vec4 &	v1 )

dot() [2/8]

__forceinline scalar Math::dot	(	const point &	p,
		const vector &	v )

dot() [3/8]

__forceinline scalar Math::dot	(	const point &	p0,
		const point &	p1 )

dot() [4/8]

__forceinline scalar Math::dot	(	const quat &	q0,
		const quat &	q1 )

dot() [5/8]

__forceinline scalar Math::dot	(	const vec3 &	v0,
		const vec3 &	v1 )

dot() [6/8]

__forceinline scalar Math::dot	(	const vec4 &	v0,
		const vec4 &	v1 )

dot() [7/8]

__forceinline scalar Math::dot	(	const vector &	v,
		const point &	p )

dot() [8/8]

__forceinline scalar Math::dot	(	const vector &	v0,
		const vector &	v1 )

dot3()

__forceinline scalar Math::dot3	(	const vec4 &	v0,
		const vec4 &	v1 )

equal() [1/3]

__forceinline point Math::equal	(	const point &	v0,
		const point &	v1 )

equal() [2/3]

__forceinline vec3 Math::equal	(	const vec3 &	v0,
		const vec3 &	v1 )

equal() [3/3]

__forceinline vec4 Math::equal	(	const vec4 &	v0,
		const vec4 &	v1 )

equal3_all()

__forceinline bool Math::equal3_all	(	const vec4 &	v0,
		const vec4 &	v1 )

equal3_any()

__forceinline bool Math::equal3_any	(	const vec4 &	v0,
		const vec4 &	v1 )

equal_any() [1/3]

__forceinline bool Math::equal_any	(	const point &	v0,
		const point &	v1 )

equal_any() [2/3]

__forceinline bool Math::equal_any	(	const vec3 &	v0,
		const vec3 &	v1 )

equal_any() [3/3]

__forceinline bool Math::equal_any	(	const vec4 &	v0,
		const vec4 &	v1 )

exp()

__forceinline scalar Math::exp

(

scalar

x

)

exp2()

__forceinline scalar Math::exp2

(

scalar

x

)

fchop()

__forceinline int Math::fchop

(

scalar

f

)

Chop float to int.

Todo

type cast to int is slow!

fequal()

__forceinline bool Math::fequal	(	scalar	f0,
		scalar	f1,
		scalar	tol )

A fuzzy floating point equality check.

fgreater()

__forceinline bool Math::fgreater	(	scalar	f0,
		scalar	f1,
		scalar	tol )

A fuzzy floating point greater-then check.

fless()

__forceinline bool Math::fless	(	scalar	f0,
		scalar	f1,
		scalar	tol )

A fuzzy floating point less-then check.

floor() [1/3]

__forceinline vec3 Math::floor

(

const vec3 &

v

)

floor() [2/3]

__forceinline vec4 Math::floor

(

const vec4 &

v

)

floor() [3/3]

__forceinline float Math::floor

(

float

val

)

Floating point flooring.

fmadd()

__forceinline __m128 Math::fmadd	(	__m128	a,
		__m128	b,
		__m128	c )

Fused multiply-add operation, (a * b) + c.

fmod()

__forceinline scalar Math::fmod	(	scalar	x,
		scalar	y )

frnd()

__forceinline int Math::frnd

(

scalar

f

)

Round float to integer.

from_euler()

quat Math::from_euler

(

const vec3 &

v

)

fromeuler()

mat4 Math::fromeuler

(

const vec3 &

v

)

get_normal()

vector Math::get_normal ( const plane & plane )

inline

get_point()

point Math::get_point ( const plane & plane )

inline

greater() [1/4]

__forceinline __m128 Math::greater	(	__m128	a,
		__m128	b )

Constructs a vector of results where each element corresponds to a[i] > b[i] with either 0 or 1.

greater() [2/4]

__forceinline point Math::greater	(	const point &	v0,
		const point &	v1 )

greater() [3/4]

__forceinline vec3 Math::greater	(	const vec3 &	v0,
		const vec3 &	v1 )

greater() [4/4]

__forceinline vec4 Math::greater	(	const vec4 &	v0,
		const vec4 &	v1 )

greater3_all()

__forceinline bool Math::greater3_all	(	const vec4 &	v0,
		const vec4 &	v1 )

greater3_any()

__forceinline bool Math::greater3_any	(	const vec4 &	v0,
		const vec4 &	v1 )

greater_all() [1/3]

__forceinline bool Math::greater_all	(	const point &	v0,
		const point &	v1 )

greater_all() [2/3]

__forceinline bool Math::greater_all	(	const vec3 &	v0,
		const vec3 &	v1 )

greater_all() [3/3]

__forceinline bool Math::greater_all	(	const vec4 &	v0,
		const vec4 &	v1 )

greater_any() [1/3]

__forceinline bool Math::greater_any	(	const point &	v0,
		const point &	v1 )

greater_any() [2/3]

__forceinline bool Math::greater_any	(	const vec3 &	v0,
		const vec3 &	v1 )

greater_any() [3/3]

__forceinline bool Math::greater_any	(	const vec4 &	v0,
		const vec4 &	v1 )

greaterequal3_all()

__forceinline bool Math::greaterequal3_all	(	const vec4 &	v0,
		const vec4 &	v1 )

greaterequal3_any()

__forceinline bool Math::greaterequal3_any	(	const vec4 &	v0,
		const vec4 &	v1 )

greaterequal_all() [1/3]

__forceinline bool Math::greaterequal_all	(	const point &	v0,
		const point &	v1 )

greaterequal_all() [2/3]

__forceinline bool Math::greaterequal_all	(	const vec3 &	v0,
		const vec3 &	v1 )

greaterequal_all() [3/3]

__forceinline bool Math::greaterequal_all	(	const vec4 &	v0,
		const vec4 &	v1 )

greaterequal_any() [1/3]

__forceinline bool Math::greaterequal_any	(	const point &	v0,
		const point &	v1 )

greaterequal_any() [2/3]

__forceinline bool Math::greaterequal_any	(	const vec3 &	v0,
		const vec3 &	v1 )

greaterequal_any() [3/3]

__forceinline bool Math::greaterequal_any	(	const vec4 &	v0,
		const vec4 &	v1 )

hermite() [1/2]

__forceinline vec3 Math::hermite	(	const vec3 &	v1,
		const vec3 &	t1,
		const vec3 &	v2,
		const vec3 &	t2,
		scalar	s )

hermite() [2/2]

__forceinline vec4 Math::hermite	(	const vec4 &	v1,
		const vec4 &	t1,
		const vec4 &	v2,
		const vec4 &	t2,
		scalar	s )

identity()

__forceinline quat Math::identity

(

)

intersectline()

bool Math::intersectline ( const plane & plane, const point & startPoint, const point & endPoint, point & outIntersectPoint )

inline

intersectplane()

bool Math::intersectplane ( const plane & p1, const plane & p2, line & outLine )

inline

TODO: Test and make sure it produces correct intersection line.

inverse() [1/2]

__forceinline mat4 Math::inverse

(

const mat4 &

m

)

inverse() [2/2]

__forceinline quat Math::inverse

(

const quat &

q

)

irand()

__forceinline int Math::irand	(	int	min,
		int	max )

Return a pseudo integer random number between min and max.

isdenormal()

__forceinline bool Math::isdenormal

(

scalar

s

)

Returns true if the input scalar is denormalized (#DEN)

isidentity() [1/2]

__forceinline bool Math::isidentity

(

const mat4 &

m

)

isidentity() [2/2]

__forceinline bool Math::isidentity

(

const quat &

q

)

ispointinside()

bool Math::ispointinside	(	const vec4 &	p,
		const mat4 &	m )

length() [1/4]

__forceinline scalar Math::length

(

const quat &

q

)

length() [2/4]

__forceinline scalar Math::length

(

const vec3 &

v

)

length() [3/4]

__forceinline scalar Math::length

(

const vec4 &

v

)

length() [4/4]

__forceinline scalar Math::length

(

const vector &

v

)

length3()

__forceinline scalar Math::length3

(

const vec4 &

v

)

lengthsq() [1/4]

__forceinline scalar Math::lengthsq

(

const quat &

q

)

lengthsq() [2/4]

__forceinline scalar Math::lengthsq

(

const vec3 &

v

)

lengthsq() [3/4]

__forceinline scalar Math::lengthsq

(

const vec4 &

v

)

lengthsq() [4/4]

__forceinline scalar Math::lengthsq

(

const vector &

v

)

lengthsq3()

__forceinline scalar Math::lengthsq3

(

const vec4 &

v

)

lerp() [1/5]

transform Math::lerp ( const transform & a, const transform & b, float t )

inline

lerp() [2/5]

__forceinline vec2 Math::lerp	(	const vec2 &	v0,
		const vec2 &	v1,
		scalar	s )

lerp() [3/5]

__forceinline vec3 Math::lerp	(	const vec3 &	v0,
		const vec3 &	v1,
		scalar	s )

lerp() [4/5]

__forceinline vec4 Math::lerp	(	const vec4 &	v0,
		const vec4 &	v1,
		scalar	s )

lerp() [5/5]

__forceinline float Math::lerp	(	float	x,
		float	y,
		float	l )

Linearly interpolate between 2 values: ret = x + l * (y - x)

less() [1/4]

__forceinline __m128 Math::less	(	__m128	a,
		__m128	b )

Constructs a vector of results where each element corresponds to a[i] < b[i] with either 0 or 1.

less() [2/4]

__forceinline point Math::less	(	const point &	v0,
		const point &	v1 )

less() [3/4]

__forceinline vec3 Math::less	(	const vec3 &	v0,
		const vec3 &	v1 )

less() [4/4]

__forceinline vec4 Math::less	(	const vec4 &	v0,
		const vec4 &	v1 )

less3_all()

__forceinline bool Math::less3_all	(	const vec4 &	v0,
		const vec4 &	v1 )

less3_any()

__forceinline bool Math::less3_any	(	const vec4 &	v0,
		const vec4 &	v1 )

less_all() [1/3]

__forceinline bool Math::less_all	(	const point &	v0,
		const point &	v1 )

less_all() [2/3]

__forceinline bool Math::less_all	(	const vec3 &	v0,
		const vec3 &	v1 )

less_all() [3/3]

__forceinline bool Math::less_all	(	const vec4 &	v0,
		const vec4 &	v1 )

less_any() [1/3]

__forceinline bool Math::less_any	(	const point &	v0,
		const point &	v1 )

less_any() [2/3]

__forceinline bool Math::less_any	(	const vec3 &	v0,
		const vec3 &	v1 )

less_any() [3/3]

__forceinline bool Math::less_any	(	const vec4 &	v0,
		const vec4 &	v1 )

lessequal3_all()

__forceinline bool Math::lessequal3_all	(	const vec4 &	v0,
		const vec4 &	v1 )

lessequal3_any()

__forceinline bool Math::lessequal3_any	(	const vec4 &	v0,
		const vec4 &	v1 )

lessequal_all() [1/3]

__forceinline bool Math::lessequal_all	(	const point &	v0,
		const point &	v1 )

lessequal_all() [2/3]

__forceinline bool Math::lessequal_all	(	const vec3 &	v0,
		const vec3 &	v1 )

lessequal_all() [3/3]

__forceinline bool Math::lessequal_all	(	const vec4 &	v0,
		const vec4 &	v1 )

lessequal_any() [1/3]

__forceinline bool Math::lessequal_any	(	const point &	v0,
		const point &	v1 )

lessequal_any() [2/3]

__forceinline bool Math::lessequal_any	(	const vec3 &	v0,
		const vec3 &	v1 )

lessequal_any() [3/3]

__forceinline bool Math::lessequal_any	(	const vec4 &	v0,
		const vec4 &	v1 )

ln()

__forceinline quat Math::ln

(

const quat &

q

)

log()

__forceinline scalar Math::log

(

scalar

x

)

get logarithm of x

log2()

__forceinline scalar Math::log2

(

scalar

f

)

log2() function.

lookatlh()

__forceinline mat4 Math::lookatlh	(	const point &	eye,
		const point &	at,
		const vector &	up )

lookatrh()

__forceinline mat4 Math::lookatrh	(	const point &	eye,
		const point &	at,
		const vector &	up )

max() [1/3]

template<typename TYPE >

__forceinline TYPE Math::max	(	TYPE	a,
		TYPE	b )

max() [2/3]

template<typename TYPE0 , typename ... TYPEN>

__forceinline TYPE0 Math::max	(	TYPE0	first,
		TYPE0	second,
		TYPEN...	rest )

max() [3/3]

template<>

__forceinline unsigned int Math::max	(	unsigned int	a,
		unsigned int	b )

branchless max for uint32

maximize() [1/3]

__forceinline point Math::maximize	(	const point &	v0,
		const point &	v1 )

maximize() [2/3]

__forceinline vec3 Math::maximize	(	const vec3 &	v0,
		const vec3 &	v1 )

maximize() [3/3]

__forceinline vec4 Math::maximize	(	const vec4 &	v0,
		const vec4 &	v1 )

min() [1/4]

template<typename TYPE >

__forceinline TYPE Math::min	(	TYPE	a,
		TYPE	b )

min() [2/4]

template<typename TYPE0 , typename ... TYPEN>

__forceinline TYPE0 Math::min	(	TYPE0	first,
		TYPE0	second,
		TYPEN...	rest )

min() [3/4]

template<>

__forceinline uint16_t Math::min	(	uint16_t	a,
		uint16_t	b )

branchless min for uints

min() [4/4]

template<>

__forceinline unsigned int Math::min	(	unsigned int	a,
		unsigned int	b )

branchless min for uints

minimize() [1/3]

__forceinline point Math::minimize	(	const point &	v0,
		const point &	v1 )

minimize() [2/3]

__forceinline vec3 Math::minimize	(	const vec3 &	v0,
		const vec3 &	v1 )

minimize() [3/3]

__forceinline vec4 Math::minimize	(	const vec4 &	v0,
		const vec4 &	v1 )

modangle()

__forceinline scalar Math::modangle

(

scalar

a

)

Normalize an angular value into the range rad(0) to rad(360).

FIXME : seems that the xna version limits from -pi to pi, not 0 .. 2pi. will copy behaviour despite what description says

mostsignificant()

__forceinline int Math::mostsignificant

(

unsigned int

val

)

Returns the position of the most significant bit of the number.

mul()

__forceinline __m128 Math::mul	(	__m128	a,
		__m128	b )

multiply() [1/2]

__forceinline vec3 Math::multiply	(	const vec3 &	v0,
		const vec3 &	v1 )

multiply() [2/2]

__forceinline vec4 Math::multiply	(	const vec4 &	v0,
		const vec4 &	v1 )

multiplyadd() [1/2]

__forceinline vec3 Math::multiplyadd	(	const vec3 &	v0,
		const vec3 &	v1,
		const vec3 &	v2 )

multiplyadd() [2/2]

__forceinline vec4 Math::multiplyadd	(	const vec4 &	v0,
		const vec4 &	v1,
		const vec4 &	v2 )

nearequal() [1/6]

__forceinline bool Math::nearequal	(	const point &	v0,
		const point &	v1,
		float	epsilon )

nearequal() [2/6]

__forceinline bool Math::nearequal	(	const vec3 &	v0,
		const vec3 &	v1,
		const vec3 &	epsilon )

nearequal() [3/6]

__forceinline bool Math::nearequal	(	const vec3 &	v0,
		const vec3 &	v1,
		float	epsilon )

nearequal() [4/6]

__forceinline bool Math::nearequal	(	const vec4 &	v0,
		const vec4 &	v1,
		const float	epsilon )

nearequal() [5/6]

__forceinline bool Math::nearequal	(	const vec4 &	v0,
		const vec4 &	v1,
		const vec4 &	epsilon )

nearequal() [6/6]

__forceinline bool Math::nearequal	(	scalar	a,
		scalar	b,
		scalar	epsilon )

test of nearly equal given a tolerance (epsilon)

nearequal3()

__forceinline bool Math::nearequal3	(	const vec4 &	v0,
		const vec4 &	v1,
		const vec4 &	epsilon )

normalize() [1/5]

__forceinline plane Math::normalize

(

const plane &

p

)

normalize() [2/5]

__forceinline quat Math::normalize

(

const quat &

q

)

normalize() [3/5]

__forceinline vec3 Math::normalize

(

const vec3 &

v

)

normalize() [4/5]

__forceinline vec4 Math::normalize

(

const vec4 &

v

)

normalize() [5/5]

__forceinline vector Math::normalize

(

const vector &

v

)

normalize3()

__forceinline vec4 Math::normalize3

(

const vec4 &

v

)

normalize3approx()

__forceinline vec4 Math::normalize3approx

(

const vec4 &

v

)

normalizeapprox() [1/3]

__forceinline vec3 Math::normalizeapprox

(

const vec3 &

v

)

normalizeapprox() [2/3]

__forceinline vec4 Math::normalizeapprox

(

const vec4 &

v

)

normalizeapprox() [3/3]

__forceinline vector Math::normalizeapprox

(

const vector &

v

)

normtofloat() [1/4]

float Math::normtofloat ( int16_t value )

inline

convert normalized int16_t to float

normtofloat() [2/4]

float Math::normtofloat ( int8_t value )

inline

convert normalized int8_t to float

normtofloat() [3/4]

float Math::normtofloat ( uint16_t value )

inline

convert normalized uint16_t to float

normtofloat() [4/4]

float Math::normtofloat ( uint8_t value )

inline

convert normalized uint8_t to float

operator*() [1/19]

__forceinline plane Math::operator*	(	const mat4 &	m,
		const plane &	p )

operator*() [2/19]

__forceinline vec4 Math::operator*	(	const mat4 &	m,
		const point &	p )

operator*() [3/19]

__forceinline vec4 Math::operator*	(	const mat4 &	m,
		const vec3 &	v )

operator*() [4/19]

__forceinline vec4 Math::operator*	(	const mat4 &	m,
		const vec4 &	v )

operator*() [5/19]

__forceinline vector Math::operator*	(	const mat4 &	m,
		const vector &	v )

operator*() [6/19]

__forceinline mat4 Math::operator*	(	const mat4 &	m0,
		const mat4 &	m1 )

operator*() [7/19]

__forceinline quat Math::operator*	(	const quat &	q0,
		const quat &	q1 )

operator*() [8/19]

point Math::operator* ( const transform & a, const point & b )

inline

transforms a position (applies scale, rotation and offset)

operator*() [9/19]

transform Math::operator* ( const transform & a, const transform & b )

inline

operator*() [10/19]

vector Math::operator* ( const transform & a, const vector & b )

inline

transforms a vector (ignores position)

operator*() [11/19]

__forceinline vec3 Math::operator*	(	const vec3 &	lhs,
		const vec3 &	rhs )

operator*() [12/19]

__forceinline vec3 Math::operator*	(	const vec3 &	lhs,
		scalar	t )

operator*() [13/19]

__forceinline vec4 Math::operator*	(	const vec4 &	lhs,
		const vec4 &	rhs )

operator*() [14/19]

__forceinline vec4 Math::operator*	(	const vec4 &	lhs,
		scalar	t )

operator*() [15/19]

__forceinline vector Math::operator*	(	const vector &	lhs,
		const vector &	rhs )

operator*() [16/19]

__forceinline vector Math::operator*	(	const vector &	lhs,
		scalar	s )

operator*() [17/19]

float Math::operator* ( float one, half two )

inline

operator*() [18/19]

half Math::operator* ( half one, float two )

inline

operator*() [19/19]

half Math::operator* ( half one, half two )

inline

operator+() [1/7]

__forceinline point Math::operator+	(	const point &	lhs,
		const vector &	rhs )

operator+() [2/7]

__forceinline vec3 Math::operator+	(	const vec3 &	lhs,
		const vec3 &	rhs )

operator+() [3/7]

__forceinline vec4 Math::operator+	(	const vec4 &	lhs,
		const vec4 &	rhs )

operator+() [4/7]

__forceinline vector Math::operator+	(	const vector &	lhs,
		const vector &	rhs )

operator+() [5/7]

float Math::operator+ ( float one, half two )

inline

operator+() [6/7]

half Math::operator+ ( half one, float two )

inline

operator+() [7/7]

half Math::operator+ ( half one, half two )

inline

operator-() [1/11]

__forceinline vector Math::operator-	(	const point &	lhs,
		const point &	rhs )

operator-() [2/11]

__forceinline point Math::operator-	(	const point &	lhs,
		const vector &	rhs )

operator-() [3/11]

__forceinline vec3 Math::operator-

(

const vec3 &

lhs

)

operator-() [4/11]

__forceinline vec3 Math::operator-	(	const vec3 &	lhs,
		const vec3 &	rhs )

operator-() [5/11]

__forceinline vec4 Math::operator-

(

const vec4 &

lhs

)

operator-() [6/11]

__forceinline vec4 Math::operator-	(	const vec4 &	lhs,
		const vec4 &	rhs )

operator-() [7/11]

__forceinline vector Math::operator-	(	const vector &	lhs,
		const vector &	rhs )

operator-() [8/11]

__forceinline vector Math::operator-

(

const vector &

rhs

)

operator-() [9/11]

float Math::operator- ( float one, half two )

inline

operator-() [10/11]

half Math::operator- ( half one, float two )

inline

operator-() [11/11]

half Math::operator- ( half one, half two )

inline

operator/() [1/3]

float Math::operator/ ( float one, half two )

inline

operator/() [2/3]

half Math::operator/ ( half one, float two )

inline

operator/() [3/3]

half Math::operator/ ( half one, half two )

inline

ortholh()

__forceinline mat4 Math::ortholh	(	scalar	w,
		scalar	h,
		scalar	zn,
		scalar	zf )

orthooffcenterlh()

__forceinline mat4 Math::orthooffcenterlh	(	scalar	l,
		scalar	r,
		scalar	t,
		scalar	b,
		scalar	zn,
		scalar	zf )

orthooffcenterrh()

__forceinline mat4 Math::orthooffcenterrh	(	scalar	l,
		scalar	r,
		scalar	t,
		scalar	b,
		scalar	zn,
		scalar	zf )

orthorh()

__forceinline mat4 Math::orthorh	(	scalar	w,
		scalar	h,
		scalar	zn,
		scalar	zf )

permute() [1/2]

__forceinline vec3 Math::permute	(	const vec3 &	v0,
		const vec3 &	v1,
		unsigned int	i0,
		unsigned int	i1,
		unsigned int	i2 )

permute() [2/2]

__forceinline vec4 Math::permute	(	const vec4 &	v0,
		const vec4 &	v1,
		unsigned int	i0,
		unsigned int	i1,
		unsigned int	i2,
		unsigned int	i3 )

perspective_div()

__forceinline vec4 Math::perspective_div

(

const vec4 &

v

)

perspfovlh()

__forceinline mat4 Math::perspfovlh	(	scalar	fovy,
		scalar	aspect,
		scalar	zn,
		scalar	zf )

perspfovrh()

__forceinline mat4 Math::perspfovrh	(	scalar	fovy,
		scalar	aspect,
		scalar	zn,
		scalar	zf )

persplh()

__forceinline mat4 Math::persplh	(	scalar	w,
		scalar	h,
		scalar	zn,
		scalar	zf )

perspoffcenterlh()

__forceinline mat4 Math::perspoffcenterlh	(	scalar	l,
		scalar	r,
		scalar	b,
		scalar	t,
		scalar	zn,
		scalar	zf )

perspoffcenterrh()

__forceinline mat4 Math::perspoffcenterrh	(	scalar	l,
		scalar	r,
		scalar	b,
		scalar	t,
		scalar	zn,
		scalar	zf )

persprh()

__forceinline mat4 Math::persprh	(	scalar	w,
		scalar	h,
		scalar	zn,
		scalar	zf )

pointerhash()

__forceinline uint32_t Math::pointerhash

(

void *

ptr

)

cheap pointer hash using modulo with a mersenne prime

pow()

__forceinline scalar Math::pow	(	scalar	x,
		scalar	y )

quatExp()

__forceinline quat Math::quatExp

(

const quat &

q

)

quatUndenormalize()

__forceinline quat Math::quatUndenormalize

(

const quat &

q

)

quatyawpitchroll()

quat Math::quatyawpitchroll	(	scalar	y,
		scalar	x,
		scalar	z )

rad2deg()

__forceinline constexpr scalar Math::rad2deg ( scalar r )

constexpr

rand() [1/2]

__forceinline scalar Math::rand

(

)

Return a pseudo random number between 0 and 1.

rand() [2/2]

__forceinline scalar Math::rand	(	scalar	min,
		scalar	max )

Return a pseudo random number between min and max.

randxor()

__forceinline uint64 Math::randxor

(

randxorstate &

state

)

recip()

__forceinline __m128 Math::recip

(

__m128

a

)

reciprocal() [1/2]

__forceinline vec3 Math::reciprocal

(

const vec3 &

v

)

reciprocal() [2/2]

__forceinline vec4 Math::reciprocal

(

const vec4 &

v

)

reciprocalapprox() [1/2]

__forceinline vec3 Math::reciprocalapprox

(

const vec3 &

v

)

reciprocalapprox() [2/2]

__forceinline vec4 Math::reciprocalapprox

(

const vec4 &

v

)

reflect() [1/3]

__forceinline vec3 Math::reflect	(	const vec3 &	normal,
		const vec3 &	incident )

reflect() [2/3]

__forceinline vec4 Math::reflect	(	const vec4 &	normal,
		const vec4 &	incident )

reflect() [3/3]

mat4 Math::reflect

(

const vec4 &

p

)

based on this http://www.opengl.org/discussion_boards/showthread.php/169605-reflection-matrix-how-to-derive

rotate()

__forceinline vec3 Math::rotate	(	quat const &	q,
		vec3 const &	v )

Rotate a vector by a quaternion.

https://blog.molecular-matters.com/2013/05/24/a-faster-quaternion-vector-multiplication/

rotationaxis()

__forceinline mat4 Math::rotationaxis	(	const vec3 &	axis,
		scalar	angle )

rotationmatrix()

quat Math::rotationmatrix

(

const mat4 &

m

)

rotationquat()

mat4 Math::rotationquat

(

const quat &

q

)

TODO: rewrite using SSE.

rotationquataxis()

__forceinline quat Math::rotationquataxis	(	const vec3 &	axis,
		scalar	angle )

quat from rotation axis + angle.

Axis has to be normalized

rotationx()

__forceinline mat4 Math::rotationx

(

scalar

angle

)

rotationy()

__forceinline mat4 Math::rotationy

(

scalar

angle

)

rotationyawpitchroll()

__forceinline mat4 Math::rotationyawpitchroll	(	scalar	yaw,
		scalar	pitch,
		scalar	roll )

rotationz()

__forceinline mat4 Math::rotationz

(

scalar

angle

)

round()

__forceinline float Math::round

(

float

val

)

Floating point rounding.

roundtopow2()

__forceinline unsigned int Math::roundtopow2

(

unsigned int

val

)

Rounds up to next power of 2.

saturate() [1/2]

__forceinline double Math::saturate

(

double

val

)

Saturate a value (clamps between 0.0f and 1.0f)

saturate() [2/2]

__forceinline scalar Math::saturate

(

scalar

val

)

Saturate a value (clamps between 0.0f and 1.0f)

scaling() [1/3]

__forceinline mat4 Math::scaling

(

const vec3 &

s

)

scaling() [2/3]

__forceinline mat4 Math::scaling

(

scalar

scale

)

scaling() [3/3]

__forceinline mat4 Math::scaling	(	scalar	sx,
		scalar	sy,
		scalar	sz )

select() [1/4]

__forceinline vec3 Math::select	(	const vec3 &	v0,
		const vec3 &	v1,
		const uint	i0,
		const uint	i1,
		const uint	i2 )

select() [2/4]

__forceinline vec3 Math::select	(	const vec3 &	v0,
		const vec3 &	v1,
		const vec3 &	control )

select() [3/4]

__forceinline vec4 Math::select	(	const vec4 &	v0,
		const vec4 &	v1,
		const uint	i0,
		const uint	i1,
		const uint	i2,
		const uint	i3 )

select() [4/4]

__forceinline vec4 Math::select	(	const vec4 &	v0,
		const vec4 &	v1,
		const vec4 &	control )

sgn()

__forceinline scalar Math::sgn

(

scalar

a

)

sin()

__forceinline scalar Math::sin

(

scalar

x

)

skewsymmetric()

__forceinline mat4 Math::skewsymmetric

(

const vec3 &

v

)

slerp()

__forceinline quat Math::slerp	(	const quat &	q1,
		const quat &	q2,
		scalar	t )

quat slerp TODO: rewrite using sse/avx

smoothstep()

__forceinline scalar Math::smoothstep	(	scalar	edge0,
		scalar	edge1,
		scalar	x )

splat() [1/2]

__forceinline vec3 Math::splat	(	const vec3 &	v,
		uint	element )

splat() [2/2]

__forceinline vec4 Math::splat	(	const vec4 &	v,
		uint	element )

splat_w()

__forceinline vec4 Math::splat_w

(

const vec4 &

v

)

splat_x() [1/2]

__forceinline vec3 Math::splat_x

(

const vec3 &

v

)

splat_x() [2/2]

__forceinline vec4 Math::splat_x

(

const vec4 &

v

)

splat_y() [1/2]

__forceinline vec3 Math::splat_y

(

const vec3 &

v

)

splat_y() [2/2]

__forceinline vec4 Math::splat_y

(

const vec4 &

v

)

splat_z() [1/2]

__forceinline vec3 Math::splat_z

(

const vec3 &

v

)

splat_z() [2/2]

__forceinline vec4 Math::splat_z

(

const vec4 &

v

)

sqrt()

__forceinline scalar Math::sqrt

(

scalar

x

)

squad()

__forceinline quat Math::squad	(	const quat &	q1,
		const quat &	a,
		const quat &	b,
		const quat &	c,
		scalar	t )

squadsetup()

__forceinline void Math::squadsetup	(	const quat &	q0,
		const quat &	q1,
		const quat &	q2,
		const quat &	q3,
		quat &	aOut,
		quat &	bOut,
		quat &	cOut )

swizzle()

template<int x, int y, int z, int w>

__forceinline __m128 Math::swizzle

(

__m128

v

)

tan()

__forceinline scalar Math::tan

(

scalar

x

)

to_axisangle()

__forceinline void Math::to_axisangle	(	const quat &	q,
		vec4 &	outAxis,
		scalar &	outAngle )

to_euler()

vec3 Math::to_euler

(

const quat &

q

)

transformation()

mat4 Math::transformation	(	const vec3 &	scalingCenter,
		const quat &	scalingRotation,
		const vec3 &	scale,
		const vec3 &	rotationCenter,
		const quat &	rotation,
		const vec3 &	trans )

translation() [1/2]

__forceinline mat4 Math::translation

(

const vec3 &

t

)

translation() [2/2]

__forceinline mat4 Math::translation	(	scalar	x,
		scalar	y,
		scalar	z )

transpose()

__forceinline mat4 Math::transpose

(

const mat4 &

m

)

trs()

__forceinline mat4 Math::trs	(	const vec3 &	position,
		const quat &	rotation,
		const vec3 &	scale )

A short hand for creating a TRS (translation, rotation, scale) matrix from pos, rot and scale.

undenormalize()

__forceinline float Math::undenormalize

(

scalar

s

)

Returns 0 if scalar is denormal.

xyz() [1/2]

__forceinline vec3 Math::xyz

(

const point &

v

)

xyz() [2/2]

__forceinline vec3 Math::xyz

(

const vec4 &

v

)

Variable Documentation

_id_w

const __m128 Math::_id_w = _mm_setr_ps(0.0f, 0.0f, 0.0f, 1.0f)

static

_id_x

const __m128 Math::_id_x = _mm_setr_ps(1.0f, 0.0f, 0.0f, 0.0f)

static

_id_y

const __m128 Math::_id_y = _mm_setr_ps(0.0f, 1.0f, 0.0f, 0.0f)

static

_id_z

const __m128 Math::_id_z = _mm_setr_ps(0.0f, 0.0f, 1.0f, 0.0f)

static

_mask_xyz

const __m128 Math::_mask_xyz = _mm_castsi128_ps(_mm_setr_epi32( 0xFFFFFFFF, 0xFFFFFFFF, 0xFFFFFFFF, 0 ))

static

_minus1

const __m128 Math::_minus1 = _mm_setr_ps(-1.0f, -1.0f, -1.0f, -1.0f)

static

_plus1

const __m128 Math::_plus1 = _mm_setr_ps(1.0f, 1.0f, 1.0f, 1.0f)

static

_sign

const __m128i Math::_sign = _mm_setr_epi32(0x80000000, 0x80000000, 0x80000000, 0x80000000)

static

_zero

const __m128 Math::_zero = _mm_setr_ps(0.0f, 0.0f, 0.0f, 0.0f)

static

maskW

const __m128i Math::maskW = _mm_setr_epi32( 0,0,0,-1 )

static

maskX

const __m128i Math::maskX = _mm_setr_epi32( -1,0,0,0 )

static

maskY

const __m128i Math::maskY = _mm_setr_epi32( 0,-1,0,0 )

static

maskZ

const __m128i Math::maskZ = _mm_setr_epi32( 0,0,-1,0 )

static

PERMUTE_0W

const unsigned int Math::PERMUTE_0W = 3

static

PERMUTE_0X

const unsigned int Math::PERMUTE_0X = 0

static

PERMUTE_0Y

const unsigned int Math::PERMUTE_0Y = 1

static

PERMUTE_0Z

const unsigned int Math::PERMUTE_0Z = 2

static

PERMUTE_1W

const unsigned int Math::PERMUTE_1W = 7

static

PERMUTE_1X

const unsigned int Math::PERMUTE_1X = 4

static

PERMUTE_1Y

const unsigned int Math::PERMUTE_1Y = 5

static

PERMUTE_1Z

const unsigned int Math::PERMUTE_1Z = 6

static