Shader program. More...

Classes
struct	Ray

Public Member Functions
mat3	_referenceFrameFromZAxis (vec3 n)
	BUGGY More...

float	computeSampleRate (vec2 texCoord, vec2 samplerSize)
	Computes 2^mipLevel, avoiding the expensive log2 call needed for the actual MIP level. More...

float	computeToksvigGlossyExponent (float rawGlossyExponent, float rawNormalLength)
	http://blog.selfshadow.com/2011/07/22/specular-showdown/ More...

vec3	cosPowHemiRandom (vec2 r, const float k)
	Returns cos^k distributed random values distributed on the hemisphere about +z. More...

uint	expandBits (uint v)
	Expands a 10-bit integer into 30 bits by inserting 2 zeros after each bit. More...

uint	extractEvenBits (uint x)

vec3	hammersleyCosHemi (uint i, const uint N)
	Generate the ith 2D Hammersley point out of N on the cosine-weighted unit hemisphere with Z = up. More...

vec3	hammersleyHemi (uint i, const uint N)
	Generate the ith 2D Hammersley point out of N on the cosine-weighted unit hemisphere with Z = up. More...

vec2	hammersleySquare (uint i, const uint N)
	Generate the ith 2D Hammersley point out of N on the unit square [0, 1]^2 More...

vec3	hemisphereRandom (vec2 r)

vec3	HSVtoRGB (vec3 c)

mat4x4	identity4x4 ()

int	indexOfMaxComponent (vec3 v)
	Returns the index of the largest element. More...

int	indexOfMaxComponent (vec2 v)
	Returns the index of the largest element. More...

int	indexOfMaxComponent (float v)
	Returns zero. More...

float	infIfNegative (float x)

uint	interleaveBits (uvec3 inputval)
	Calculates a 30-bit Morton code for the given 3D point located within the unit cube [0,1]. More...

bool	isFinite (float x)

gentype	lengthSquared ($(vectype) v)

float	max3 (float a, float b, float c)

float	max4 (float a, float b, float c, float d)

float	maxComponent (vec2 a)

float	maxComponent (vec3 a)

float	maxComponent (vec4 a)

float	mean (float a)

float	mean (vec2 a)

float	mean (vec3 a)

float	mean (vec4 a)

float	meanComponent (vec4 a)

float	meanComponent (vec3 a)

float	meanComponent (vec2 a)

float	meanComponent (float a)

float	min3 (float a, float b, float c)

float	min4 (float a, float b, float c, float d)

float	minComponent (vec2 a)

float	minComponent (vec3 a)

float	minComponent (vec4 a)

float	mipMapLevel (in vec2 texture_coordinate, in vec2 textureSize)
	Computes the MIP-map level for a texture coordinate. More...

float	norm1 (vec3 v)

float	norm2 (vec3 v)

float	norm4 (vec2 v)
	L^4 norm. More...

float	norm8 (vec2 v)
	L^8 norm. More...

float	normInf (vec3 v)

float	packGlossyExponent (in float blinnPhongExponent)

mat4x4	pitch4x4 (float a)
	Constructs a 4x4 Y->Z rotation matrix, assuming R * v multiplication. More...

gentype	pow16 ($(gentype) x)
	Compute x^8. More...

gentype	pow2 ($(gentype) x)

gentype	pow3 ($(gentype) x)

gentype	pow4 ($(gentype) x)
	Compute x^4. More...

gentype	pow5 ($(gentype) x)
	Computes x⁵ More...

gentype	pow6 ($(gentype) x)
	Compute x^6. More...

gentype	pow64 ($(gentype) v)
	Compute v^64. More...

gentype	pow7 ($(gentype) x)

gentype	pow8 ($(gentype) x)
	Compute x^8. More...

mat3	referenceFrameFromZAxis (vec3 z)
	Given a z-axis, construct an orthonormal tangent space. More...

float	RGBtoCIELuminance (vec3 linearRGB)
	CIE luminance (Y) of linearRGB value (not sRGB!) More...

vec3	RGBtoHSV (vec3 c)

mat4x4	roll4x4 (float a)
	Constructs a 4x4 X->Y rotation matrix, assuming R * v multiplication. More...

vec3	schlickFresnel (in vec3 F0, in float cos_i, float smoothness)
	Compute Schlick's approximation of the Fresnel coefficient. More...

float	signNotZero (in float k)

vec2	signNotZero (in vec2 v)

gentype	smootherstep ($(gentype) edge0, $(gentype) edge1, $(gentype) x)
	Perlin's smootherstep that is analogous to smoothstep() but has zero 1st and 2nd order derivatives at t=0 and t=1, from Texturing and Modeling, Third Edition: A Procedural Approach (see http://en.wikipedia.org/wiki/Smoothstep) More...

gentype	smootherstep (float edge0, float edge1, $(gentype) x)

float	smoothnessToBlinnPhongExponent (in float g3dSmoothness)
	Matches UniversalBSDF::smoothnessToBlinnPhongExponent. More...

vec3	sphereRandom (vec2 r)

vec3	sphericalFibonacci (float i, float n)
	Generate a spherical fibonacci point http://lgdv.cs.fau.de/publications/publication/Pub.2015.tech.IMMD.IMMD9.spheri/ To generate a nearly uniform point distribution on the unit sphere of size N, do for (float i = 0.0; i < N; i += 1.0) { float3 point = sphericalFibonacci(i,N); }. More...

gentype	square ($(gentype) x)

float	sum (float a)

float	sum (vec2 a)

float	sum (vec3 a)

float	sum (vec4 a)

void	swap (inout $(gentype) a, inout $(gentype) b)

vec4	textureLodBicubic (sampler2D tex, vec2 uv, int lod)
	Implementation of Sigg and Hadwiger's Fast Third-Order Texture Filtering More...

vec4	textureLodSmooth (sampler2D tex, vec2 uv, int lod)
	A bicubic magnification filter, primarily useful for magnifying LOD 0 without bilinear magnification artifacts. More...

mat4x4	translate4x4 (vec3 t)
	Constructs a 4x4 translation matrix, assuming T * v multiplication. More...

gentype	unitSmootherstep ($(gentype) x)
	Avoids the clamping and division for smootherstep(0, 1, x) when x is known to be on the range [0, 1]. More...

gentype	unitSmoothstep ($(gentype) x)
	Avoids the clamping and division for smoothstep(0, 1, x) when x is known to be on the range [0, 1]. More...

mat4x4	yaw4x4 (float a)
	Constructs a 4x4 Z->X rotation matrix, assuming R * v multiplication. More...

Public Attributes
const float	centimeters = 0.01

const float	inf
	32-bit floating-point infinity More...

const float	inv8Pi = 1.0 / (8.0 * pi)

const float	invPi = 1.0 / pi
	1 / pi More...

const float	meters = 1.0

const float	millimeters = 0.001

const float	pi = 3.1415927
	Ratio of unit circle perimeter to its diameter. More...

Detailed Description

Shader program.

Member Function Documentation

◆ _referenceFrameFromZAxis()

mat3 glsl::g3dmath_glsl::_referenceFrameFromZAxis ( vec3 n )

inline

BUGGY

Given a z-axis (n), construct an orthonormal tangent space. Assumes z is a unit vector.

From http://jcgt.org/published/0006/01/01/ listing 3

Parameters

n	The unit z-axis (3rd column of the output)

Returns: The matrix

◆ computeSampleRate()

float glsl::g3dmath_glsl::computeSampleRate	(	vec2	texCoord,
		vec2	samplerSize
	)

inline

Computes 2^mipLevel, avoiding the expensive log2 call needed for the actual MIP level.

◆ computeToksvigGlossyExponent()

float glsl::g3dmath_glsl::computeToksvigGlossyExponent	(	float	rawGlossyExponent,
		float	rawNormalLength
	)

inline

http://blog.selfshadow.com/2011/07/22/specular-showdown/

◆ cosPowHemiRandom()

vec3 glsl::g3dmath_glsl::cosPowHemiRandom	(	vec2	r,
		const float	k
	)

inline

Returns cos^k distributed random values distributed on the hemisphere about +z.

Parameters

r	Two uniform random numbers on [0,1] See also cosHemiRandom texture.

◆ expandBits()

uint glsl::g3dmath_glsl::expandBits ( uint v )

inline

Expands a 10-bit integer into 30 bits by inserting 2 zeros after each bit.

◆ extractEvenBits()

uint glsl::g3dmath_glsl::extractEvenBits ( uint x )

inline

◆ hammersleyCosHemi()

vec3 glsl::g3dmath_glsl::hammersleyCosHemi	(	uint	i,
		const uint	N
	)

inline

Generate the ith 2D Hammersley point out of N on the cosine-weighted unit hemisphere with Z = up.

Referenced Code: http://holger.dammertz.org/stuff/notes_HammersleyOnHemisphere.html

◆ hammersleyHemi()

vec3 glsl::g3dmath_glsl::hammersleyHemi	(	uint	i,
		const uint	N
	)

inline

Generate the ith 2D Hammersley point out of N on the cosine-weighted unit hemisphere with Z = up.

Referenced Code: http://holger.dammertz.org/stuff/notes_HammersleyOnHemisphere.html

◆ hammersleySquare()

vec2 glsl::g3dmath_glsl::hammersleySquare	(	uint	i,
		const uint	N
	)

inline

Generate the ith 2D Hammersley point out of N on the unit square [0, 1]^2

Referenced Code: http://holger.dammertz.org/stuff/notes_HammersleyOnHemisphere.html

◆ hemisphereRandom()

vec3 glsl::g3dmath_glsl::hemisphereRandom ( vec2 r )

inline

Parameters

r	Two uniform random numbers on [0,1]

Returns: uniformly distributed random sample on unit hemisphere about +z See also hemisphereRandom texture.

◆ HSVtoRGB()

vec3 glsl::g3dmath_glsl::HSVtoRGB ( vec3 c )

inline

Referenced Code: http://lolengine.net/blog/2013/07/27/rgb-to-hsv-in-glsl

◆ identity4x4()

mat4x4 glsl::g3dmath_glsl::identity4x4 ( )

inline

◆ indexOfMaxComponent() [1/3]

int glsl::g3dmath_glsl::indexOfMaxComponent ( vec3 v )

inline

Returns the index of the largest element.

◆ indexOfMaxComponent() [2/3]

int glsl::g3dmath_glsl::indexOfMaxComponent ( vec2 v )

inline

Returns the index of the largest element.

◆ indexOfMaxComponent() [3/3]

int glsl::g3dmath_glsl::indexOfMaxComponent ( float v )

inline

Returns zero.

◆ infIfNegative()

float glsl::g3dmath_glsl::infIfNegative ( float x )

inline

◆ interleaveBits()

uint glsl::g3dmath_glsl::interleaveBits ( uvec3 inputval )

inline

Calculates a 30-bit Morton code for the given 3D point located within the unit cube [0,1].

◆ isFinite()

bool glsl::g3dmath_glsl::isFinite ( float x )

inline

◆ lengthSquared()

gentype glsl::g3dmath_glsl::lengthSquared ( $(vectype) )

inline

◆ max3()

float glsl::g3dmath_glsl::max3	(	float	a,
		float	b,
		float	c
	)

inline

◆ max4()

float glsl::g3dmath_glsl::max4	(	float	a,
		float	b,
		float	c,
		float	d
	)

inline

◆ maxComponent() [1/3]

float glsl::g3dmath_glsl::maxComponent ( vec2 a )

inline

◆ maxComponent() [2/3]

float glsl::g3dmath_glsl::maxComponent ( vec3 a )

inline

◆ maxComponent() [3/3]

float glsl::g3dmath_glsl::maxComponent ( vec4 a )

inline

◆ mean() [1/4]

float glsl::g3dmath_glsl::mean ( float a )

inline

◆ mean() [2/4]

float glsl::g3dmath_glsl::mean ( vec2 a )

inline

◆ mean() [3/4]

float glsl::g3dmath_glsl::mean ( vec3 a )

inline

◆ mean() [4/4]

float glsl::g3dmath_glsl::mean ( vec4 a )

inline

◆ meanComponent() [1/4]

float glsl::g3dmath_glsl::meanComponent ( vec4 a )

inline

◆ meanComponent() [2/4]

float glsl::g3dmath_glsl::meanComponent ( vec3 a )

inline

◆ meanComponent() [3/4]

float glsl::g3dmath_glsl::meanComponent ( vec2 a )

inline

◆ meanComponent() [4/4]

float glsl::g3dmath_glsl::meanComponent ( float a )

inline

◆ min3()

float glsl::g3dmath_glsl::min3	(	float	a,
		float	b,
		float	c
	)

inline

◆ min4()

float glsl::g3dmath_glsl::min4	(	float	a,
		float	b,
		float	c,
		float	d
	)

inline

◆ minComponent() [1/3]

float glsl::g3dmath_glsl::minComponent ( vec2 a )

inline

◆ minComponent() [2/3]

float glsl::g3dmath_glsl::minComponent ( vec3 a )

inline

◆ minComponent() [3/3]

float glsl::g3dmath_glsl::minComponent ( vec4 a )

inline

◆ mipMapLevel()

float glsl::g3dmath_glsl::mipMapLevel	(	in vec2	texture_coordinate,
		in vec2	textureSize
	)

inline

Computes the MIP-map level for a texture coordinate.

Referenced Code: The OpenGL Graphics System: A Specification 4.2: chapter 3.9.11, equation 3.21

◆ norm1()

float glsl::g3dmath_glsl::norm1 ( vec3 v )

inline

◆ norm2()

float glsl::g3dmath_glsl::norm2 ( vec3 v )

inline

◆ norm4()

float glsl::g3dmath_glsl::norm4 ( vec2 v )

inline

L^4 norm.

◆ norm8()

float glsl::g3dmath_glsl::norm8 ( vec2 v )

inline

L^8 norm.

◆ normInf()

float glsl::g3dmath_glsl::normInf ( vec3 v )

inline

◆ packGlossyExponent()

float glsl::g3dmath_glsl::packGlossyExponent ( in float blinnPhongExponent )

inline

◆ pitch4x4()

mat4x4 glsl::g3dmath_glsl::pitch4x4 ( float a )

inline

Constructs a 4x4 Y->Z rotation matrix, assuming R * v multiplication.

a is in radians.

◆ pow16()

gentype glsl::g3dmath_glsl::pow16 ( $(gentype) )

inline

Compute x^8.

◆ pow2()

gentype glsl::g3dmath_glsl::pow2 ( $(gentype) )

inline

◆ pow3()

gentype glsl::g3dmath_glsl::pow3 ( $(gentype) )

inline

◆ pow4()

gentype glsl::g3dmath_glsl::pow4 ( $(gentype) )

inline

Compute x^4.

◆ pow5()

gentype glsl::g3dmath_glsl::pow5 ( $(gentype) )

inline

Computes x⁵

◆ pow6()

gentype glsl::g3dmath_glsl::pow6 ( $(gentype) )

inline

Compute x^6.

◆ pow64()

gentype glsl::g3dmath_glsl::pow64 ( $(gentype) )

inline

Compute v^64.

◆ pow7()

gentype glsl::g3dmath_glsl::pow7 ( $(gentype) )

inline

◆ pow8()

gentype glsl::g3dmath_glsl::pow8 ( $(gentype) )

inline

Compute x^8.

◆ referenceFrameFromZAxis()

mat3 glsl::g3dmath_glsl::referenceFrameFromZAxis ( vec3 z )

inline

Given a z-axis, construct an orthonormal tangent space.

Assumes z is a unit vector.

Deprecated:

◆ RGBtoCIELuminance()

float glsl::g3dmath_glsl::RGBtoCIELuminance ( vec3 linearRGB )

inline

CIE luminance (Y) of linearRGB value (not sRGB!)

◆ RGBtoHSV()

vec3 glsl::g3dmath_glsl::RGBtoHSV ( vec3 c )

inline

Referenced Code: http://lolengine.net/blog/2013/07/27/rgb-to-hsv-in-glsl

◆ roll4x4()

mat4x4 glsl::g3dmath_glsl::roll4x4 ( float a )

inline

Constructs a 4x4 X->Y rotation matrix, assuming R * v multiplication.

a is in radians.

◆ schlickFresnel()

vec3 glsl::g3dmath_glsl::schlickFresnel	(	in vec3	F0,
		in float	cos_i,
		float	smoothness
	)

inline

Compute Schlick's approximation of the Fresnel coefficient.

The original goes to 1.0 at glancing angles, which makes objects appear to glow, so we scale it down to 0.9.

We never put a Fresnel term on perfectly diffuse surfaces, so, if F0 is exactly black, then we keep the result black.

◆ signNotZero() [1/2]

float glsl::g3dmath_glsl::signNotZero ( in float k )

inline

◆ signNotZero() [2/2]

vec2 glsl::g3dmath_glsl::signNotZero ( in vec2 v )

inline

◆ smootherstep() [1/2]

gentype glsl::g3dmath_glsl::smootherstep	(	$(gentype),
		$(gentype),
		$(gentype)
	)

inline

Perlin's smootherstep that is analogous to smoothstep() but has zero 1st and 2nd order derivatives at t=0 and t=1, from Texturing and Modeling, Third Edition: A Procedural Approach (see http://en.wikipedia.org/wiki/Smoothstep)

◆ smootherstep() [2/2]

gentype glsl::g3dmath_glsl::smootherstep	(	float	edge0,
		float	edge1,
			$(gentype)
	)

inline

◆ smoothnessToBlinnPhongExponent()

float glsl::g3dmath_glsl::smoothnessToBlinnPhongExponent ( in float g3dSmoothness )

inline

Matches UniversalBSDF::smoothnessToBlinnPhongExponent.

Maps smoothness [0, 1] to Blinn-Phong exponent [0, infinity].

◆ sphereRandom()

vec3 glsl::g3dmath_glsl::sphereRandom ( vec2 r )

inline

Parameters

r	Two uniform random numbers on [0,1]

Returns: uniformly distributed random sample on unit sphere

http://mathworld.wolfram.com/SpherePointPicking.html

See also g3d_sphereRandom texture and sphericalFibonacci()

◆ sphericalFibonacci()

vec3 glsl::g3dmath_glsl::sphericalFibonacci	(	float	i,
		float	n
	)

inline

Generate a spherical fibonacci point http://lgdv.cs.fau.de/publications/publication/Pub.2015.tech.IMMD.IMMD9.spheri/ To generate a nearly uniform point distribution on the unit sphere of size N, do for (float i = 0.0; i < N; i += 1.0) { float3 point = sphericalFibonacci(i,N); }.

The points go from z = +1 down to z = -1 in a spiral. To generate samples on the +z hemisphere, just stop before i > N/2.

◆ square()

gentype glsl::g3dmath_glsl::square ( $(gentype) )

inline

◆ sum() [1/4]

float glsl::g3dmath_glsl::sum ( float a )

inline

◆ sum() [2/4]

float glsl::g3dmath_glsl::sum ( vec2 a )

inline

◆ sum() [3/4]

float glsl::g3dmath_glsl::sum ( vec3 a )

inline

◆ sum() [4/4]

float glsl::g3dmath_glsl::sum ( vec4 a )

inline

◆ swap()

void glsl::g3dmath_glsl::swap	(	inout $(gentype)	a,
		inout $(gentype)	b
	)

inline

◆ textureLodBicubic()

vec4 glsl::g3dmath_glsl::textureLodBicubic	(	sampler2D	tex,
		vec2	uv,
		int	lod
	)

inline

Implementation of Sigg and Hadwiger's Fast Third-Order Texture Filtering

http://http.developer.nvidia.com/GPUGems2/gpugems2_chapter20.html

Referenced Code: http://vec3.ca/bicubic-filtering-in-fewer-taps/

Referenced Code: http://pastebin.com/raw.php?i=YLLSBRFq

◆ textureLodSmooth()

vec4 glsl::g3dmath_glsl::textureLodSmooth	(	sampler2D	tex,
		vec2	uv,
		int	lod
	)

inline

A bicubic magnification filter, primarily useful for magnifying LOD 0 without bilinear magnification artifacts.

This just adjusts the rate at which we move between taps, not the number of taps.

Referenced Code: https://www.shadertoy.com/view/4df3Dn

◆ translate4x4()

mat4x4 glsl::g3dmath_glsl::translate4x4 ( vec3 t )

inline

Constructs a 4x4 translation matrix, assuming T * v multiplication.

◆ unitSmootherstep()

gentype glsl::g3dmath_glsl::unitSmootherstep ( $(gentype) )

inline

Avoids the clamping and division for smootherstep(0, 1, x) when x is known to be on the range [0, 1].

◆ unitSmoothstep()

gentype glsl::g3dmath_glsl::unitSmoothstep ( $(gentype) )

inline

Avoids the clamping and division for smoothstep(0, 1, x) when x is known to be on the range [0, 1].

◆ yaw4x4()

mat4x4 glsl::g3dmath_glsl::yaw4x4 ( float a )

inline

Constructs a 4x4 Z->X rotation matrix, assuming R * v multiplication.

a is in radians.

Member Data Documentation

◆ centimeters

const float glsl::g3dmath_glsl::centimeters = 0.01

◆ inf

const float glsl::g3dmath_glsl::inf

Initial value:

= 
    1.0 / 0.0

32-bit floating-point infinity

◆ inv8Pi

const float glsl::g3dmath_glsl::inv8Pi = 1.0 / (8.0 * pi)

◆ invPi

const float glsl::g3dmath_glsl::invPi = 1.0 / pi

1 / pi

◆ meters

const float glsl::g3dmath_glsl::meters = 1.0

◆ millimeters

const float glsl::g3dmath_glsl::millimeters = 0.001

◆ pi

const float glsl::g3dmath_glsl::pi = 3.1415927

Ratio of unit circle perimeter to its diameter.

Classes

Public Member Functions

Public Attributes

Detailed Description

Member Function Documentation

◆ _referenceFrameFromZAxis()

◆ computeSampleRate()

◆ computeToksvigGlossyExponent()

◆ cosPowHemiRandom()

◆ expandBits()

◆ extractEvenBits()

◆ hammersleyCosHemi()

◆ hammersleyHemi()

◆ hammersleySquare()

◆ hemisphereRandom()

◆ HSVtoRGB()

◆ identity4x4()

◆ indexOfMaxComponent() [1/3]

◆ indexOfMaxComponent() [2/3]

◆ indexOfMaxComponent() [3/3]

◆ infIfNegative()

◆ interleaveBits()

◆ isFinite()

◆ lengthSquared()

◆ max3()

◆ max4()

◆ maxComponent() [1/3]

◆ maxComponent() [2/3]

◆ maxComponent() [3/3]

◆ mean() [1/4]

◆ mean() [2/4]

◆ mean() [3/4]

◆ mean() [4/4]

◆ meanComponent() [1/4]

◆ meanComponent() [2/4]

◆ meanComponent() [3/4]

◆ meanComponent() [4/4]

◆ min3()

◆ min4()

◆ minComponent() [1/3]

◆ minComponent() [2/3]

◆ minComponent() [3/3]

◆ mipMapLevel()

◆ norm1()

◆ norm2()

◆ norm4()

◆ norm8()

◆ normInf()

◆ packGlossyExponent()

◆ pitch4x4()

◆ pow16()

◆ pow2()

◆ pow3()

◆ pow4()

◆ pow5()

◆ pow6()

◆ pow64()

◆ pow7()

◆ pow8()

◆ referenceFrameFromZAxis()

◆ RGBtoCIELuminance()

◆ RGBtoHSV()

◆ roll4x4()

◆ schlickFresnel()

◆ signNotZero() [1/2]

◆ signNotZero() [2/2]

◆ smootherstep() [1/2]

◆ smootherstep() [2/2]

◆ smoothnessToBlinnPhongExponent()

◆ sphereRandom()

◆ sphericalFibonacci()

◆ square()

◆ sum() [1/4]

◆ sum() [2/4]

◆ sum() [3/4]

◆ sum() [4/4]

◆ swap()

◆ textureLodBicubic()

◆ textureLodSmooth()

◆ translate4x4()