glsl 内置数学函数

https://www.shaderific.com/glsl-functions

OPENGL ES SHADING LANGUAGE BUILT-IN FUNCTIONS

This is a reference for the built-in functions of the OpenGL ES Shading Language that is described in the OpenGL ES Shading Language specification. For more information please visit: www.opengl.org/registry.

ANGLE & TRIGONOMETRY FUNCTIONS

Radians

float radians(float degrees)  
vec2 radians(vec2 degrees)  
vec3 radians(vec3 degrees)  
vec4 radians(vec4 degrees)

The radians function converts degrees to radians. The input parameter can be a floating scalar or a float vector. In case of a float vector all components are converted from degrees to radians separately.

Degrees

float degrees(float radians)  
vec2 degrees(vec2 radians)  
vec3 degrees(vec3 radians)  
vec4 degrees(vec4 radians)

The degrees function converts radians to degrees. The input parameter can be a floating scalar or a float vector. In case of a float vector every component is converted from radians to degrees separately.

Sine

float sin(float angle)  
vec2 sin(vec2 angle)  
vec3 sin(vec3 angle)  
vec4 sin(vec4 angle)

The sin function returns the sine of an angle in radians. The input parameter can be a floating scalar or a float vector. In case of a float vector the sine is calculated separately for every component.

Cosine

float cos(float angle)  
vec2 cos(vec2 angle)  
vec3 cos(vec3 angle)  
vec4 cos(vec4 angle)

The cos function returns the cosine of an angle in radians. The input parameter can be a floating scalar or a float vector. In case of a float vector the cosine is calculated separately for every component.

Tangent

float tan(float angle)  
vec2 tan(vec2 angle)  
vec3 tan(vec3 angle)  
vec4 tan(vec4 angle)

The tan function returns the tangent of an angle in radians. The input parameter can be a floating scalar or a float vector. In case of a float vector the tangent is calculated separately for every component.

Arcsine

float asin(float x)  
vec2 asin(vec2 x)  
vec3 asin(vec3 x)  
vec4 asin(vec4 x)

The asin function returns the arcsine of an angle in radians. It is the inverse function of sine. The input parameter can be a floating scalar or a float vector. In case of a float vector the arcsine is calculated separately for every component.

Arccosine

float acos(float x)  
vec2 acos(vec2 x)  
vec3 acos(vec3 x)  
vec4 acos(vec4 x)

The acos function returns the arccosine of an angle in radians. It is the inverse function of cosine. The input parameter can be a floating scalar or a float vector. In case of a float vector the arccosine is calculated separately for every component.

Arctangent

float atan(float y_over_x)  
vec2 atan(vec2 y_over_x)  
vec3 atan(vec3 y_over_x)  
vec4 atan(vec4 y_over_x)

The atan function returns the arctangent of an angle in radians. It is the inverse function of tangent. The input parameter can be a floating scalar or a float vector. In case of a float vector the arctangent is calculated separately for every component.

float atan(float y, float x)  
vec2 atan(vec2 y, vec2 x)  
vec3 atan(vec3 y, vec3 x)  
vec4 atan(vec4 y, vec4 x)

There is also a two-argument variation of the atan function (in other programming languages often called atan2). For a point with Cartesian coordinates (x, y) the function returns the angle θ of the same point with polar coordinates (r, θ).

EXPONENTIAL FUNCTIONS

Exponentiation

float pow(float x, float y)  
vec2 pow(vec2 x, vec2 y)  
vec3 pow(vec3 x, vec3 y)  
vec4 pow(vec4 x, vec4 y)

The power function returns x raised to the power of y. The input parameters can be floating scalars or float vectors. In case of float vectors the operation is done component-wise.

Exponential function

float exp(float x)  
vec2 exp(vec2 x)  
vec3 exp(vec3 x)  
vec4 exp(vec4 x)

The exp function returns the constant e raised to the power of x. The input parameter can be a floating scalar or a float vector. In case of a float vector the operation is done component-wise.

Natural logarithm

float log(float x)  
vec2 log(vec2 x)  
vec3 log(vec3 x)  
vec4 log(vec4 x)

The log function returns the power to which the constant e has to be raised to produce x. The input parameter can be a floating scalar or a float vector. In case of a float vector the operation is done component-wise.

Exponential function (base 2)

float exp2(float x)  
vec2 exp2(vec2 x)  
vec3 exp2(vec3 x)  
vec4 exp2(vec4 x)

The exp2 function returns 2 raised to the power of x. The input parameter can be a floating scalar or a float vector. In case of a float vector the operation is done component-wise.

Logarithm (base 2)

float log2(float x)  
vec2 log2(vec2 x)  
vec3 log2(vec3 x)  
vec4 log2(vec4 x)

The log2 function returns the power to which 2 has to be raised to produce x. The input parameter can be a floating scalar or a float vector. In case of a float vector the operation is done component-wise.

Square root

float sqrt(float x)  
vec2 sqrt(vec2 x)  
vec3 sqrt(vec3 x)  
vec4 sqrt(vec4 x)

The sqrt function returns the square root of x. The input parameter can be a floating scalar or a float vector. In case of a float vector the operation is done component-wise.

Inverse square root

float inversesqrt(float x)  
vec2 inversesqrt(vec2 x)  
vec3 inversesqrt(vec3 x)  
vec4 inversesqrt(vec4 x)

The inversesqrt function returns the inverse square root of x, i.e. the reciprocal of the square root. The input parameter can be a floating scalar or a float vector. In case of a float vector the operation is done component-wise.

COMMON FUNCTIONS

Absolute value

float abs(float x)  
vec2 abs(vec2 x)  
vec3 abs(vec3 x)  
vec4 abs(vec4 x)

The abs function returns the absolute value of x, i.e. x when x is positive or zero and -x for negative x. The input parameter can be a floating scalar or a float vector. In case of a float vector the operation is done component-wise.

Sign

float sign(float x)  
vec2 sign(vec2 x)  
vec3 sign(vec3 x)  
vec4 sign(vec4 x)

The sign function returns 1.0 when x is positive, 0.0 when x is zero and -1.0 when x is negative. The input parameter can be a floating scalar or a float vector. In case of a float vector the operation is done component-wise.

Floor

float floor(float x)  
vec2 floor(vec2 x)  
vec3 floor(vec3 x)  
vec4 floor(vec4 x)

The floor function returns the largest integer number that is smaller or equal to x. The input parameter can be a floating scalar or a float vector. In case of a float vector the operation is done component-wise.

Side note: The return value is of type floating scalar or float vector although the result of the operation is an integer.

Ceiling

float ceil(float x)  
vec2 ceil(vec2 x)  
vec3 ceil(vec3 x)  
vec4 ceil(vec4 x)

The ceiling function returns the smallest number that is larger or equal to x. The input parameter can be a floating scalar or a float vector. In case of a float vector the operation is done component-wise.

Side note: The return value is of type floating scalar or float vector although the result of the operation is an integer.

Fractional part

float fract(float x)  
vec2 fract(vec2 x)  
vec3 fract(vec3 x)  
vec4 fract(vec4 x)

The fract function returns the fractional part of x, i.e. x minus floor(x). The input parameter can be a floating scalar or a float vector. In case of a float vector the operation is done component-wise.

Modulo

float mod(float x, float y)  
vec2 mod(vec2 x, vec2 y)  
vec3 mod(vec3 x, vec3 y)  
vec4 mod(vec4 x, vec4 y)

The mod function returns x minus the product of y and floor(x/y). The input parameters can be floating scalars or float vectors. In case of float vectors the operation is done component-wise.

Side note: If x and y are integers the return value is the remainder of the division of x by y as expected.

float mod(float x, float y)  
vec2 mod(vec2 x, float y)  
vec3 mod(vec3 x, float y)  
vec4 mod(vec4 x, float y)

There is also a variation of the mod function where the second parameter is always a floating scalar.

Minimum

float min(float x, float y)  
vec2 min(vec2 x, vec2 y)  
vec3 min(vec3 x, vec3 y)  
vec4 min(vec4 x, vec4 y)

The min function returns the smaller of the two arguments. The input parameters can be floating scalars or float vectors. In case of float vectors the operation is done component-wise.

float min(float x, float y)  
vec2 min(vec2 x, float y)  
vec3 min(vec3 x, float y)  
vec4 min(vec4 x, float y)

There is also a variation of the min function where the second parameter is always a floating scalar.

Maximum

float max(float x, float y)  
vec2 max(vec2 x, vec2 y)  
vec3 max(vec3 x, vec3 y)  
vec4 max(vec4 x, vec4 y)

The max function returns the larger of the two arguments. The input parameters can be floating scalars or float vectors. In case of float vectors the operation is done component-wise.

float max(float x, float y)  
vec2 max(vec2 x, float y)  
vec3 max(vec3 x, float y)  
vec4 max(vec4 x, float y)

There is also a variation of the max function where the second parameter is always a floating scalar.

Clamp

float clamp(float x, float minVal, float maxVal)  
vec2 clamp(vec2 x, vec2 minVal, vec2 maxVal)  
vec3 clamp(vec3 x, vec3 minVal, vec3 maxVal)  
vec4 clamp(vec4 x, vec4 minVal, vec4 maxVal)

The clamp function returns x if it is larger than minVal and smaller than maxVal. In case x is smaller than minVal, minVal is returned. If x is larger than maxVal, maxVal is returned. The input parameters can be floating scalars or float vectors. In case of float vectors the operation is done component-wise.

float clamp(float x, float minVal, float maxVal)  
vec2 clamp(vec2 x, float minVal, float maxVal)  
vec3 clamp(vec3 x, float minVal, float maxVal)  
vec4 clamp(vec4 x, flfloat minVal, float maxVal)

There is also a variation of the clamp function where the second and third parameters are always a floating scalars.

Mix

float mix(float x, float y, float a)  
vec2 mix(vec2 x, vec2 y, vec2 a)  
vec3 mix(vec3 x, vec3 y, vec3 a)  
vec4 mix(vec4 x, vec4 y, vec4 a)

The mix function returns the linear blend of x and y, i.e. the product of x and (1 - a) plus the product of y and a. The input parameters can be floating scalars or float vectors. In case of float vectors the operation is done component-wise.

float mix(float x, float y, float a)  
vec2 mix(vec2 x, vec2 y, float a)  
vec3 mix(vec3 x, vec3 y, float a)  
vec4 mix(vec4 x, vec4 y, float a)

There is also a variation of the mix function where the third parameter is always a floating scalar.

Step

float step(float edge, float x)  
vec2 step(vec2 edge, vec2 x)  
vec3 step(vec3 edge, vec3 x)  
vec4 step(vec4 edge, vec4 x)

The step function returns 0.0 if x is smaller than edge and otherwise 1.0. The input parameters can be floating scalars or float vectors. In case of float vectors the operation is done component-wise.

float step(float edge, float x)  
vec2 step(float edge, vec2 x)  
vec3 step(float edge, vec3 x)  
vec4 step(float edge, vec4 x)

There is also a variation of the step function where the edge parameter is always a floating scalar.

Smoothstep

float smoothstep(float edge0, float edge1, float x)  
vec2 smoothstep(vec2 edge0, vec2 edge1, vec2 x)  
vec3 smoothstep(vec3 edge0, vec3 edge1, vec3 x)  
vec4 smoothstep(vec4 edge0, vec4 edge1, vec4 x)

The smoothstep function returns 0.0 if x is smaller than edge0 and 1.0 if x is larger than edge1. Otherwise the return value is interpolated between 0.0 and 1.0 using Hermite polynomials. The input parameters can be floating scalars or float vectors. In case of float vectors the operation is done component-wise.

float smoothstep(float edge0, float edge1, float x)  
vec2 smoothstep(float edge0, float edge1, vec2 x)  
vec3 smoothstep(float edge0, float edge1, vec3 x)  
vec4 smoothstep(float edge0, float edge1, vec4 x)

There is also a variation of the smoothstep function where the edge0 and edge1 parameters are always floating scalars.

GEOMETRIC FUNCTIONS

Length

float length(float x)  
float length(vec2 x)  
float length(vec3 x)  
float length(vec4 x)

The length function returns the length of a vector defined by the Euclidean norm, i.e. the square root of the sum of the squared components. The input parameter can be a floating scalar or a float vector. In case of a floating scalar the length function is trivial and returns the absolute value.

Distance

float distance(float p0, float p1)  
float distance(vec2 p0, vec2 p1)  
float distance(vec3 p0, vec3 p1)  
float distance(vec4 p0, vec4 p1)

The distance function returns the distance between two points. The distance of two points is the length of the vector d = p0 - p1, that starts at p1 and points to p0. The input parameters can be floating scalars or float vectors. In case of floating scalars the distance function is trivial and returns the absolute value of d.

Dot product

float dot(float x, float y)  
float dot(vec2 x, vec2 y)  
float dot(vec3 x, vec3 y)  
float dot(vec4 x, vec4 y)

The dot function returns the dot product of the two input parameters, i.e. the sum of the component-wise products. If x and y are the same the square root of the dot product is equivalent to the length of the vector. The input parameters can be floating scalars or float vectors. In case of floating scalars the dot function is trivial and returns the product of x and y.

Cross product

vec3 cross(vec3 x, vec3 y)

The cross function returns the cross product of the two input parameters, i.e. a vector that is perpendicular to the plane containing x and y and has a magnitude that is equal to the area of the parallelogram that x and y span. The input parameters can only be 3-component floating vectors. The cross product is equivalent to the product of the length of the vectors times the sinus of the(smaller) angle between x and y.

Normalize

float normalize(float x)  
vec2 normalize(vec2 x)  
vec3 normalize(vec3 x)  
vec4 normalize(vec4 x)

The normalize function returns a vector with length 1.0 that is parallel to x, i.e. x divided by its length. The input parameter can be a floating scalar or a float vector. In case of a floating scalar the normalize function is trivial and returns 1.0.

Faceforward

float faceforward(float N, float I, float Nref)  
vec2 faceforward(vec2 N, vec2 I, vec2 Nref)  
vec3 faceforward(vec3 N, vec3 I, vec3 Nref)  
vec4 faceforward(vec4 N, vec4 I, vec4 Nref)

The faceforward function returns a vector that points in the same direction as a reference vector. The function has three input parameters of the type floating scalar or float vector: N, the vector to orient, I, the incident vector, and Nref, the reference vector. If the dot product of I and Nref is smaller than zero the return value is N. Otherwise -N is returned.

Reflect

float reflect(float I, float N)  
vec2 reflect(vec2 I, vec2 N)  
vec3 reflect(vec3 I, vec3 N)  
vec4 reflect(vec4 I, vec4 N)

The reflect function returns a vector that points in the direction of reflection. The function has two input parameters of the type floating scalar or float vector: I, the incident vector, and N, the normal vector of the reflecting surface.

Side note: To obtain the desired result the vector N has to be normalized. The reflection vector always has the same length as the incident vector. From this it follows that the reflection vector is normalized if N and I are both normalized.

Refract

float refract(float I, float N, float eta)  
vec2 refract(vec2 I, vec2 N, float eta)  
vec3 refract(vec3 I, vec3 N, float eta)  
vec4 refract(vec4 I, vec4 N, float eta)

The refract function returns a vector that points in the direction of refraction. The function has two input parameters of the type floating scalar or float vector and one input parameter of the type floating scalar: I, the incident vector, N, the normal vector of the refracting surface, and eta, the ratio of indices of refraction.

Side note: To obtain the desired result the vectors I and N have to be normalized.

MATRIX FUNCTIONS

Component-wise matrix multiplication

mat2 matrixCompMult(mat2 x, mat2 y)  
mat3 matrixCompMult(mat3 x, mat3 y)  
mat4 matrixCompMult(mat4 x, mat4 y)

The matrixCompMult function returns a matrix resulting from a component-wise multiplication. The function has two input parameters of the type floating point matrix and returns a matrix of the same type. The indices of the returned matrix are calculated as follows: z[i][j] = x[i][j] * y[i][j]

Side note: This is NOT the matrix multiplication known from linear algebra. To obtain the "normal" matrix multiplication the ordinary multiplication operator symbol is used: z = x * y

VECTOR RELATIONAL FUNCTIONS

Less than comparison

bvec2 lessThan(vec2 x, vec2 y)  
bvec3 lessThan(vec3 x, vec3 y)    
bvec4 lessThan(vec4 x, vec4 y)  

bvec2 lessThan(ivec2 x, ivec2 y)  
bvec3 lessThan(ivec3 x, ivec3 y)  
bvec4 lessThan(ivec4 x, ivec4 y)

The lessThan function returns a boolean vector as result of a component-wise comparison in the form of x[i] < y[i]. The function has two input parameters of the type floating point vector or signed integer vector.

Less than or equal comparison

bvec2 lessThanEqual(vec2 x, vec2 y)  
bvec3 lessThanEqual(vec3 x, vec3 y)  
bvec4 lessThanEqual(vec4 x, vec4 y)  

bvec2 lessThanEqual(ivec2 x, ivec2 y)  
bvec3 lessThanEqual(ivec3 x, ivec3 y)  
bvec4 lessThanEqual(ivec4 x, ivec4 y)

The lessThanEqual function returns a boolean vector as result of a component-wise comparison in the form of x[i] <= data-preserve-html-node="true" y[i]. The function has two input parameters of the type floating point vector or signed integer vector.

Greater than comparison

bvec2 greaterThan(vec2 x, vec2 y)  
bvec3 greaterThan(vec3 x, vec3 y)  
bvec4 greaterThan(vec4 x, vec4 y)  

bvec2 greaterThan(ivec2 x, ivec2 y)  
bvec3 greaterThan(ivec3 x, ivec3 y)  
bvec4 greaterThan(ivec4 x, ivec4 y)

The greaterThan function returns a boolean vector as result of a component-wise comparison in the form of x[i] > y[i]. The function has two input parameters of the type floating point vector or signed integer vector.

Greater than or equal comparison

bvec2 greaterThanEqual(vec2 x, vec2 y)  
bvec3 greaterThanEqual(vec3 x, vec3 y)  
bvec4 greaterThanEqual(vec4 x, vec4 y)  

bvec2 greaterThanEqual(ivec2 x, ivec2 y)  
bvec3 greaterThanEqual(ivec3 x, ivec3 y)  
bvec4 greaterThanEqual(ivec4 x, ivec4 y)

The greaterThanEqual function returns a boolean vector as result of a component-wise comparison in the form of x[i] >= y[i]. The function has two input parameters of the type floating point vector or signed integer vector.

Equal comparison

bvec2 equal(vec2 x, vec2 y)  
bvec3 equal(vec3 x, vec3 y)  
bvec4 equal(vec4 x, vec4 y)  

bvec2 equal(ivec2 x, ivec2 y)  
bvec3 equal(ivec3 x, ivec3 y)  
bvec4 equal(ivec4 x, ivec4 y)

The equal function returns a boolean vector as result of a component-wise comparison in the form of x[i] = y[i]. The function has two input parameters of the type floating point vector or signed integer vector.

Not equal comparison

bvec2 notEqual(vec2 x, vec2 y)  
bvec3 notEqual(vec3 x, vec3 y)  
bvec4 notEqual(vec4 x, vec4 y)  

bvec2 notEqual(ivec2 x, ivec2 y)  
bvec3 notEqual(ivec3 x, ivec3 y)  
bvec4 notEqual(ivec4 x, ivec4 y)

The notEqual function returns a boolean vector as result of a component-wise comparison in the form of x[i] != y[i]. The function has two input parameters of the type floating point vector or signed integer vector.

Any evaluation

bool any(bvec2 x)  
bool any(bvec3 x)  
bool any(bvec4 x)

The any function returns a boolean value as result of the evaluation whether any component of the input vector is TRUE. The function has one input parameters of the type boolean vector.

All evaluation

bool all(bvec2 x)  
bool all(bvec3 x)  
bool all(bvec4 x)

The all function returns a boolean value as result of the evaluation whether all components of the input vector are TRUE. The function has one input parameters of the type boolean vector.

Not evaluation

bvec2 not(bvec2 x)  
 bvec3 not(bvec3 x)  
 bvec4 not(bvec4 x)

The not function returns a boolean vector as result of a component-wise logical complement operation. The function has one input parameters of the type boolean vector.

TEXTURE LOOKUP FUNCTIONS

2D texture lookup

vec4 texture2D(sampler2D sampler, vec2 coord)  
vec4 texture2D(sampler2D sampler, vec2 coord, float bias)

The texture2D function returns a texel, i.e. the (color) value of the texture for the given coordinates. The function has one input parameter of the type sampler2D and one input parameter of the type vec2 : sampler, the uniform the texture is bound to, and coord, the 2-dimensional coordinates of the texel to look up.

There is an optional third input parameter of the type float: bias. After calculating the appropriate level of detail for a texture with mipmaps the bias is added before the actual texture lookup operation is executed.

Side note: On iOS devices texture lookup functionality is only available in the fragment shader.

Cubemap texture lookup

vec4 textureCube(samplerCube sampler, vec3 coord)  
vec4 textureCube(samplerCube sampler, vec3 coord, float bias)

The textureCube function returns a texel, i.e. the (color) value of the texture for the given coordinates. The function has one input parameter of the type samplerCube and one input parameter of the type vec3 : sampler, the uniform the texture is bound to, and coord, the 3-dimensional coordinates of the texel to look up.