# Book of Shaders [🏠 Home](../README.md) > [Book of Shaders](./book-of-shaders.md) **Documents:** 117 | **Avg Quality:** 95% --- ## Contents - **Appendix** (1 entries) - **Chapter 00** (1 entries) - **Chapter 01** (1 entries) - **Chapter 02** (1 entries) - **Chapter 03** (1 entries) - **Chapter 04** (1 entries) - **Chapter 05** (1 entries) - **Chapter 06** (1 entries) - **Chapter 07** (1 entries) - **Chapter 08** (1 entries) - **Chapter 09** (1 entries) - **Chapter 10** (1 entries) - **Chapter 11** (1 entries) - **Chapter 12** (1 entries) - **Chapter 13** (1 entries) - **Chapter 14** (1 entries) - **Chapter 15** (1 entries) - **Chapter 16** (1 entries) - **Chapter 17** (1 entries) - **Chapter 18** (1 entries) - **Examples** (1 entries) - **Glossary Index** (1 entries) - **Abs** (1 entry) - **Acos** (1 entry) - **All** (1 entry) - **Any** (1 entry) - **Asin** (1 entry) - **Atan** (1 entry) - **Attribute** (1 entry) - **Bool** (1 entry) - **Bvec2** (1 entry) - **Bvec3** (1 entry) - **Bvec4** (1 entry) - **Ceil** (1 entry) - **Clamp** (1 entry) - **Const** (1 entry) - **Cos** (1 entry) - **Cross** (1 entry) - **Degrees** (1 entry) - **Dfdx** (1 entry) - **Dfdy** (1 entry) - **Distance** (1 entry) - **Dot** (1 entry) - **Equal** (1 entry) - **Exp** (1 entry) - **Exp2** (1 entry) - **Faceforward** (1 entry) - **Float** (1 entry) - **Floor** (1 entry) - **Fract** (1 entry) - **Gl_Es** (1 entry) - **Gl_Fragcolor** (1 entry) - **Gl_Fragcoord** (1 entry) - **Gl_Frontfacing** (1 entry) - **Gl_Maxcombinedtextureimageunits** (1 entry) - **Gl_Maxdrawbuffers** (1 entry) - **Gl_Maxfragmentuniformvectors** (1 entry) - **Gl_Maxtextureimageunits** (1 entry) - **Gl_Maxvaryingvectors** (1 entry) - **Gl_Maxvertexattribs** (1 entry) - **Gl_Maxvertextextureimageunits** (1 entry) - **Gl_Pointcoord** (1 entry) - **Gl_Pointsize** (1 entry) - **Gl_Position** (1 entry) - **Greaterthan** (1 entry) - **Greaterthanequal** (1 entry) - **Highp** (1 entry) - **In** (1 entry) - **Inout** (1 entry) - **Int** (1 entry) - **Inversesqrt** (1 entry) - **Ivec2** (1 entry) - **Ivec3** (1 entry) - **Ivec4** (1 entry) - **Length** (1 entry) - **Lessthan** (1 entry) - **Lessthanequal** (1 entry) - **Log** (1 entry) - **Log2** (1 entry) - **Lowp** (1 entry) - **Main** (1 entry) - **Mat2** (1 entry) - **Mat3** (1 entry) - **Mat4** (1 entry) - **Matrixcompmult** (1 entry) - **Max** (1 entry) - **Mediump** (1 entry) - **Min** (1 entry) - **Mix** (1 entry) - **Mod** (1 entry) - **Normalize** (1 entry) - **Not** (1 entry) - **Notequal** (1 entry) - **Out** (1 entry) - **Pow** (1 entry) - **Precision** (1 entry) - **Radians** (1 entry) - **Reflect** (1 entry) - **Refract** (1 entry) - **Return** (1 entry) - **Sampler2D** (1 entry) - **Samplercube** (1 entry) - **Sign** (1 entry) - **Sin** (1 entry) - **Smoothstep** (1 entry) - **Sqrt** (1 entry) - **Step** (1 entry) - **Struct** (1 entry) - **Tan** (1 entry) - **Texture2D** (1 entry) - **Texturecube** (1 entry) - **Uniform** (1 entry) - **Varying** (1 entry) - **Vec2** (1 entry) - **Vec3** (1 entry) - **Vec4** (1 entry) - **Void** (1 entry) --- ### Appendix **Appendix** _# Appendix 1. [How can I navigate this book off-line?](00/) 2. [How to run the examples on a Raspberry Pi?](01/) 3. [How to print this book?](02/) 4. [How can I collaborate with this book?](03/) 5. [An introduction for those coming from JS](04/) by [Nicolas Barradeau](http://www.barradeau.com/)..._ 🔗 [View Source](https://thebookofshaders.com/appendix/) ### Chapter 00 **Chapter 00** _# Introduction

The images above were made in different ways. The first one was made by Van Gogh's hand applying layer over layer of paint. It took him hours...._ 🔗 [View Source](https://thebookofshaders.com/00/) ### Chapter 01 **Chapter 01** _# Getting started ## What is a fragment shader? In the previous chapter we described shaders as the equivalent of the Gutenberg press for graphics. Why? And more importantly: what's a shader? ![From Letter-by-Letter, Right: William Blades (1891). To Page-by-page, Left: Rolt-Wheeler (1920).](print...._ 🔗 [View Source](https://thebookofshaders.com/01/) ### Chapter 02 **Chapter 02** _## Hello World Usually the "Hello world!" example is the first step to learning a new language. It's a simple one-line program that outputs an enthusiastic welcoming message and declares opportunities ahead. In GPU-land rendering text is an overcomplicated task for a first step, instead we'll choo..._ 🔗 [View Source](https://thebookofshaders.com/02/) ### Chapter 03 **Chapter 03** _## Uniforms So far we have seen how the GPU manages large numbers of parallel threads, each one responsible for assigning the color to a fraction of the total image. Although each parallel thread is blind to the others, we need to be able to send some inputs from the CPU to all the threads. Because..._ 🔗 [View Source](https://thebookofshaders.com/03/) ### Chapter 04 **Chapter 04** _## Running your shader As part of the construction of this book and my art practice I made an ecosystem of tools to create, display, share and curate shaders. These tools work consistently across Linux, MacOS, Windows and [Raspberry Pi](https://www.raspberrypi.org/) and browsers without the need of..._ 🔗 [View Source](https://thebookofshaders.com/04/) ### Chapter 05 **Chapter 05** _# Algorithmic drawing ## Shaping functions This chapter could be named "Mr. Miyagi's fence lesson." Previously, we mapped the normalized position of *x* and *y* to the *red* and *green* channels. Essentially we made a function that takes a two dimensional vector (x and y) and returns a four dimensi..._ 🔗 [View Source](https://thebookofshaders.com/05/) ### Chapter 06 **Chapter 06** _![Paul Klee - Color Chart (1931)](klee.jpg) ## Colors We haven't had much of a chance to talk about GLSL vector types. Before going further it's important to learn more about these variables and the subject of colors is a great way to find out more about them. If you are familiar with object orie..._ 🔗 [View Source](https://thebookofshaders.com/06/) ### Chapter 07 **Chapter 07** _![Alice Hubbard, Providence, United States, ca. 1892. Photo: Zindman/Freemont.](froebel.jpg) ## Shapes Finally! We have been building skills for this moment! You have learned most of the GLSL foundations, types and functions. You have practiced your shaping equations over and over. Now is the time..._ 🔗 [View Source](https://thebookofshaders.com/07/) ### Chapter 08 **Chapter 08** _## 2D Matrices

### Translate In the previous chapter we learned how to make some shapes - the trick to moving those shapes is to move the coordinate system itself. We can achieve that by sim..._ 🔗 [View Source](https://thebookofshaders.com/08/) ### Chapter 09 **Chapter 09** _## Patterns Since shader programs are executed by pixel-by-pixel no matter how much you repeat a shape the number of calculations stays constant. This means that fragment shaders are particulary suitable for tile patterns. [ ![Nina Warmerdam - The IMPRINT Project (2013)](warmerdam.jpg) ](../edit.p..._ 🔗 [View Source](https://thebookofshaders.com/09/) ### Chapter 10 **Chapter 10** _# Generative designs It is not a surprise that after so much repetition and order the author is forced to bring some chaos. ## Random [![Ryoji Ikeda - test pattern (2008) ](ryoji-ikeda.jpg) ](http://www.ryojiikeda.com/project/testpattern/#testpattern_live_set) Randomness is a maximal expression ..._ 🔗 [View Source](https://thebookofshaders.com/10/) ### Chapter 11 **Chapter 11** _ ![NASA / WMAP science team](mcb.jpg) ## Noise It's time for a break! We've been playing with random functions that look like TV white noise, our head is still spinning thinking about shaders, and our eyes are tired. Time to go out for a walk! We feel the air on our skin, the sun in our face. The..._ 🔗 [View Source](https://thebookofshaders.com/11/) ### Chapter 12 **Chapter 12** _![](dragonfly.jpg) ## Cellular Noise In 1996, sixteen years after Perlin's original Noise and five years before his Simplex Noise, [Steven Worley wrote a paper called “A Cellular Texture Basis Function”](http://www.rhythmiccanvas.com/research/papers/worley.pdf). In it, he describes a procedural t..._ 🔗 [View Source](https://thebookofshaders.com/12/) ### Chapter 13 **Chapter 13** _![Due East over Shadequarter Mountain - Matthew Rangel (2005) ](rangel.jpg) ## Fractal Brownian Motion Noise tends to mean different things to different people. Musicians will think of it in terms of disturbing sounds, communicators as interference and astrophysicists as cosmic microwave backgroun..._ 🔗 [View Source](https://thebookofshaders.com/13/) ### Chapter 14 **Chapter 14** _## Fractals Coming soon ... In the meantime, you can check out some examples with fractals on the [shadertoy.com](https://www.shadertoy.com/results?query=fractals) platform: [Basic Fractal](https://www.shadertoy.com/view/Mss3Wf) [Mandelbrot - distance](https://www.shadertoy.com/view/lsX3W4) [Mand..._ 🔗 [View Source](https://thebookofshaders.com/14/) ### Chapter 15 **Chapter 15** _# Image processing ## Textures ![](01.jpg) Graphic cards (GPUs) have special memory types for images. Usually on CPUs images are stored as arrays of bytes but GPUs store images as ```sampler2D``` which is more like a table (or matrix) of floating point vectors. More interestingly, the values of t..._ 🔗 [View Source](https://thebookofshaders.com/15/) ### Chapter 16 **Chapter 16** _## Image operations Below you will see some examples with images where you can play around and uncomment some lines to see the corresponding results. ### Invert

### Add, Subtract, Multiply and others ![](02.jpg) Created by kynd(@kyndinfo) and Patricio Gonzalez Vivo(@patriciogv)

This is a collection of examples extracted from the chapte..._ 🔗 [View Source](https://thebookofshaders.com/examples/) ### Glossary Index **Glossary Index** _# Glossary ## By theme * TYPES [void](./?search=void) [bool](./?search=bool) [int](./?search=int) [float](./?search=float) [bvec2](./?search=bvec2) [bvec3](./?search=bvec3) [bvec4](./?search=bvec4) [ivec2](./?search=ivec2) [ivec3](./?search=ivec3) [ivec4](./?search=ivec4) [vec2](./?search=vec2) [..._ 🔗 [View Source](https://thebookofshaders.com/glossary/) ### Abs ## Abs Return the absolute value of the parameter. ### Declaration ```glsl float abs(float x) vec2 abs(vec2 x) vec3 abs(vec3 x) vec4 abs(vec4 x) ``` ### Parameters ```x``` specifies the value of which to return the absolute. ### Description ```abs()``` returns the absolute value of ```x```.

### See Also [sign()](/glossary/?search=si... [📖 View Full Entry](https://thebookofshaders.com/glossary/?search=abs) ### Acos ## Acos Return the arccosine of the parameter ### Declaration ```glsl float acos(float x) vec2 acos(vec2 x) vec3 acos(vec3 x) vec4 acos(vec4 x) ``` ### Parameters ```x``` specifies the value whose arccosine to return. ### Description ```acos()``` returns the angle whose trigonometric cosine is ```x```.

### See Also [cos()](/glossar... [📖 View Full Entry](https://thebookofshaders.com/glossary/?search=acos) ### All ## All Check whether all elements of a boolean vector are true ### Declaration ```glsl bool any(bvec2 x) bool any(bvec3 x) bool any(bvec4 x) ``` ### Parameters ```x``` specifies the vector to be tested for truth. ### Description ```all()``` returns true if all elements of ```x``` are ```true``` and ```false``` otherwise. It is functionally equivalent to: ```glsl bool all(bvec x){ // ... [📖 View Full Entry](https://thebookofshaders.com/glossary/?search=all) ### Any ## Any Check whether any element of a boolean vector is true ### Declaration ```glsl bool all(bvec2 x) bool all(bvec3 x) bool all(bvec4 x) ``` ### Parameters ```x``` specifies the vector to be tested for truth. ### Description ```any()``` returns true if any element of ```x``` is ```true``` and ```false``` otherwise. It is functionally equivalent to: ```glsl bool any(bvec x) { // bvec ... [📖 View Full Entry](https://thebookofshaders.com/glossary/?search=any) ### Asin ## Asin Return the arcsine of the parameter ### Declaration ```glsl float asin(float x) vec2 asin(vec2 x) vec3 asin(vec3 x) vec4 asin(vec4 x) ``` ### Parameters ```x``` specifies the value whose arcsine to return. ### Description ```asin()``` returns the angle whose trigonometric sine is ```x```.

### See Also [cos](/glossary/?searc... [📖 View Full Entry](https://thebookofshaders.com/glossary/?search=asin) ### Atan ## Atan Return the arc-tangent of the parameters ### Declaration ```glsl float atan(float y, float x) vec2 atan(vec2 y, vec2 x) vec3 atan(vec3 y, vec3 x) vec4 atan(vec4 y, vec4 x) float atan(float y_over_x) vec2 atan(vec2 y_over_x) vec3 atan(vec3 y_over_x) vec4 atan(vec4 y_over_x) ``` ### Parameters ```y``` specifies the numerator of the fraction whose arctangent to return. ```x```... [📖 View Full Entry](https://thebookofshaders.com/glossary/?search=atan) ### Attribute ## Attribute Vertex attribute data. ### Example ```glsl attribute vec4 v_color; ``` ### Description ```attribute``` read-only variables containing data shared from WebGL/OpenGL environment to the vertex shader. Because the vertex shader is executed one time for each vertex, attributes are specify per vertex data typically with information such as: space position, color, normal direction and tex... [📖 View Full Entry](https://thebookofshaders.com/glossary/?search=attribute) ### Bool ## Bool Boolean variable type ### Declaration ```glsl bool aBool = true; bool bBool = bool(aInt); bool cBool = bool(aFloat); ``` ### Description ```bool``` data type is either true or false. ### See Also [void](/glossary/?search=void), [bool](/glossary/?search=bool), [int](/glossary/?search=int), [float](/glossary/?search=float), [bvec2](/glossary/?search=bvec2), [bvec3](/glossary/?search=bvec3... [📖 View Full Entry](https://thebookofshaders.com/glossary/?search=bool) ### Bvec2 ## Bvec2 2 dimensional boolean vector ### Declaration ```glsl bvec2 aBvec2 = bvec2(true, true); bvec2 bBvec2 = bvec2(true); bvec2 cBvec2 = bvec2(aBvec3); bvec2 dBvec2 = bvec2(aBvec3.x, aBvec3.y); ``` ### Description ```bvec2``` is a boolean vector with two components. It can be initialized by: - Providing a scalar value for each component. - Providing one scalar value. This value is used for a... [📖 View Full Entry](https://thebookofshaders.com/glossary/?search=bvec2) ### Bvec3 ## Bvec3 3 dimensional boolean vector ### Declaration ```glsl vec3 aBvec3 = bvec3(true, true, true); vec3 bBvec3 = bvec3(true); vec3 cBvec3 = bvec3(aBvec4); vec3 dBvec3 = bvec3(aBvec4.x, aBvec4.y, aBvec4.z); vec3 eBvec3 = bvec3(aBvec2, aBool); vec3 fBvec3 = bvec3(aBvec2.x, aBvec2.y, aBool); ``` ### Description ```bvec3``` is a boolean vector with three components. It can be initialized by: - ... [📖 View Full Entry](https://thebookofshaders.com/glossary/?search=bvec3) ### Bvec4 ## Bvec4 4 dimensional boolean vector ### Declaration ```glsl vec4 aBvec4 = bvec4(true, true, true, true); vec4 bBvec4 = bvec4(true); vec4 cBvec4 = bvec4(aBvec2, aBool, aBvec3); vec4 dBvec4 = bvec4(aBvec2.x, aBvec2.y, aBool, aBvec3.x); ``` ### Description ```bvec4``` is a boolean vector with four components. It can be initialized by: - Providing a scalar value for each component. - Providing o... [📖 View Full Entry](https://thebookofshaders.com/glossary/?search=bvec4) ### Ceil ## Ceil Find the nearest integer that is greater than or equal to the parameter ### Declaration ```glsl float ceil(float x) vec2 ceil(vec2 x) vec3 ceil(vec3 x) vec4 ceil(vec4 x) ``` ### Parameters ```x``` specifies the value to evaluate. ### Description ```ceil()``` returns a value equal to the nearest integer that is greater than or equal to ```x```.

### See Also [a... [📖 View Full Entry](https://thebookofshaders.com/glossary/?search=cos) ### Cross ## Cross Calculate the cross product of two vectors ### Declaration ```glsl vec3 cross(vec3 x, vec3 y) ``` ### Parameters ```x``` specifies the first of two vectors ```y``` specifies the second of two vectors ### Description ```cross()``` returns the cross product of two vectors, ```x``` and ```y```. The input parameters can only be 3-component floating vectors. The cross product is equivalent... [📖 View Full Entry](https://thebookofshaders.com/glossary/?search=cross) ### Degrees ## Degrees Convert a quantity in radians to degrees ### Declaration ```glsl float degrees(float radians) vec2 degrees(vec2 radians) vec3 degrees(vec3 radians) vec4 degrees(vec4 radians) ``` ### Parameters ```radians``` specifies the quantity, in radians, to be converted to degrees. ### Description ```degrees()``` converts a quantity, specified in radians into degrees. That is, the return ... [📖 View Full Entry](https://thebookofshaders.com/glossary/?search=degrees) ### Dfdx ## DFdx Return the partial derivative of an argument with respect to x ### Declaration ```glsl genType dFdx(float x); ``` ### Parameters ```p``` specifies the expression of which to take the partial derivative. ### Description Available only in the fragment shader, ```dFdx``` return the partial derivative of expression ```p``` in ```x```. Derivatives are calculated using local differencing. Exp... [📖 View Full Entry](https://thebookofshaders.com/glossary/?search=dFdx) ### Dfdy ## DFdy Return the partial derivative of an argument with respect to y ### Declaration ```glsl genType dFdy(float y); ``` ### Parameters ```p``` specifies the expression of which to take the partial derivative. ### Description Available only in the fragment shader, ```dFdy``` return the partial derivative of expression ```p``` in ```y```. Derivatives are calculated using local differencing. Exp... [📖 View Full Entry](https://thebookofshaders.com/glossary/?search=dFdy) ### Distance ## Distance Calculate the distance between two points ### Declaration ```glsl float distance(float p0, float p1) float distance(vec2 p0, vec2 p1) float distance(vec3 p0, vec3 p1) float distance(vec4 p0, vec4 p1) ``` ### Parameters ```p0``` specifies the first of two points ```p1``` specifies the second of two points ### Description ```distance()``` returns the distance between the two po... [📖 View Full Entry](https://thebookofshaders.com/glossary/?search=distance) ### Dot ## Dot Calculate the dot product of two vectors ### Declaration ```glsl float dot(float x, float y) float dot(vec2 x, vec2 y) float dot(vec3 x, vec3 y) float dot(vec4 x, vec4 y) ``` ### Parameters ```x``` specifies the first of two vectors ```y``` specifies the second of two vectors ### Description ```dot()``` returns the dot product of two vectors, ```x``` and ```y```. i.e., ```x[0]⋅y[0... [📖 View Full Entry](https://thebookofshaders.com/glossary/?search=dot) ### Equal ## Equal Perform a component-wise equal-to comparison of two vectors ### Declaration ```glsl 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) ``` ### Parameters ```x``` specifies the first vector to be used in the comparison operation. ```y``` specifies the sec... [📖 View Full Entry](https://thebookofshaders.com/glossary/?search=equal) ### Exp ## Exp Return the natural exponentiation of the parameter ### Declaration ```glsl float exp(float x) vec2 exp(vec2 x) vec3 exp(vec3 x) vec4 exp(vec4 x) ``` ### Parameters ```x``` specifies the value to exponentiate. ### Description ```exp()``` returns the natural exponentiation of ```x```.

### See Also [log](/glossary/?search=log),... [📖 View Full Entry](https://thebookofshaders.com/glossary/?search=exp) ### Exp2 ## Exp2 Return 2 raised to the power of the parameter ### Declaration ```glsl float exp2(float x) vec2 exp2(vec2 x) vec3 exp2(vec3 x) vec4 exp2(vec4 x) ``` ### Parameters ```x``` specifies the value of the power to which 2 will be raised. ### Description ```exp2()``` returns 2 raised to the power of ```x```.

### See Also [log](/gl... [📖 View Full Entry](https://thebookofshaders.com/glossary/?search=exp2) ### Faceforward ## Faceforward Return a vector pointing in the same direction as another ### Declaration ```glsl 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) ``` ### Parameters ```N``` specifies the vector to orient. ```I``` specifies the incident vector. ```Nref``` spec... [📖 View Full Entry](https://thebookofshaders.com/glossary/?search=faceforward) ### Float ## Float Floating-point variable type ### Declaration ```glsl float aFloat = 1.0; float bFloat = float(aBool); float cFloat = float(aInt); ``` ### Description ```float``` is used for floating point values. ### See Also [void](/glossary/?search=void), [bool](/glossary/?search=bool), [int](/glossary/?search=int), [float](/glossary/?search=float), [bvec2](/glossary/?search=bvec2), [bvec3](/glossar... [📖 View Full Entry](https://thebookofshaders.com/glossary/?search=float) ### Floor ## Floor Find the nearest integer less than or equal to the parameter ### Declaration ```glsl float floor(float x) vec2 floor(vec2 x) vec3 floor(vec3 x) vec4 floor(vec4 x) ``` ### Parameters ```x``` specifies the value to evaluate. ### Description ```floor()``` returns a value equal to the nearest integer that is less than or equal to ```x```.

### S... [📖 View Full Entry](https://thebookofshaders.com/glossary/?search=fract) ### Gl_Es ## GL_ES ### Declaration / Example ### Parameters ### Description ### See Also ... [📖 View Full Entry](https://thebookofshaders.com/glossary/?search=GL_ES) ### Gl_Fragcolor ## Gl_FragColor ### Declaration / Example ### Parameters ### Description ### See Also ... [📖 View Full Entry](https://thebookofshaders.com/glossary/?search=gl_FragColor) ### Gl_Fragcoord ## Gl_FragCoord ### Declaration / Example ### Parameters ### Description ### See Also ... [📖 View Full Entry](https://thebookofshaders.com/glossary/?search=gl_FragCoord) ### Gl_Frontfacing ## Gl_FrontFacing ### Declaration / Example ### Parameters ### Description ### See Also ... [📖 View Full Entry](https://thebookofshaders.com/glossary/?search=gl_FrontFacing) ### Gl_Maxcombinedtextureimageunits ## Gl_MaxCombinedTextureImages ### Declaration / Example ### Parameters ### Description ### See Also ... [📖 View Full Entry](https://thebookofshaders.com/glossary/?search=gl_MaxCombinedTextureImageUnits) ### Gl_Maxdrawbuffers ## Gl_MaxDrawBuffers ### Declaration / Example ### Parameters ### Description ### See Also ... [📖 View Full Entry](https://thebookofshaders.com/glossary/?search=gl_MaxDrawBuffers) ### Gl_Maxfragmentuniformvectors ## Gl_MaxFragmentUniformVectors ### Declaration / Example ### Parameters ### Description ### See Also ... [📖 View Full Entry](https://thebookofshaders.com/glossary/?search=gl_MaxFragmentUniformVectors) ### Gl_Maxtextureimageunits ## Gl_MaxTextureImageUnits ### Declaration / Example ### Parameters ### Description ### See Also ... [📖 View Full Entry](https://thebookofshaders.com/glossary/?search=gl_MaxTextureImageUnits) ### Gl_Maxvaryingvectors ## Gl_MaxVaryingVectors ### Declaration / Example ### Parameters ### Description ### See Also ... [📖 View Full Entry](https://thebookofshaders.com/glossary/?search=gl_MaxVaryingVectors) ### Gl_Maxvertexattribs ## Gl_MaxVertexAttrbis ### Declaration / Example ### Parameters ### Description ### See Also ... [📖 View Full Entry](https://thebookofshaders.com/glossary/?search=gl_MaxVertexAttribs) ### Gl_Maxvertextextureimageunits ## Gl_MaxVertexTextureImageUnits ### Declaration / Example ### Parameters ### Description ### See Also ... [📖 View Full Entry](https://thebookofshaders.com/glossary/?search=gl_MaxVertexTextureImageUnits) ### Gl_Pointcoord ## Gl_PointCoord ### Declaration / Example ### Parameters ### Description ### See Also ... [📖 View Full Entry](https://thebookofshaders.com/glossary/?search=gl_PointCoord) ### Gl_Pointsize ## Gl_PointSize ### Declaration / Example ### Parameters ### Description ### See Also ... [📖 View Full Entry](https://thebookofshaders.com/glossary/?search=gl_PointSize) ### Gl_Position ## Gl_Position ### Declaration / Example ### Parameters ### Description ### See Also ... [📖 View Full Entry](https://thebookofshaders.com/glossary/?search=gl_Position) ### Greaterthan ## GreaterThan Perform a component-wise greater-than comparison of two vectors ### Declaration ```glsl 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) ``` ### Parameters ```x``` specifies the first vector to be used in the co... [📖 View Full Entry](https://thebookofshaders.com/glossary/?search=greaterThan) ### Greaterthanequal ## GreaterThanEqual Perform a component-wise greater-than-or-equal comparison of two vectors ### Declaration ```glsl 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) ``` ### Parameters ```x``` spe... [📖 View Full Entry](https://thebookofshaders.com/glossary/?search=greaterThanEqual) ### Highp ## Highp ### Declaration / Example ### Parameters ### Description ### See Also ... [📖 View Full Entry](https://thebookofshaders.com/glossary/?search=highp) ### In ## In ### Declaration / Example ### Parameters ### Description ### See Also ... [📖 View Full Entry](https://thebookofshaders.com/glossary/?search=in) ### Inout ## Inout ### Declaration / Example ### Parameters ### Description ### See Also ... [📖 View Full Entry](https://thebookofshaders.com/glossary/?search=inout) ### Int ## Int Integer data type ### Declaration ```glsl int aInt = 42; int bInt = int(aBool); int cInt = int(aFloat); ``` ### Description ```int``` is used for integer values. ### See Also [void](/glossary/?search=void), [bool](/glossary/?search=bool), [int](/glossary/?search=int), [float](/glossary/?search=float), [ivec2](/glossary/?search=ivec2), [ivec3](/glossary/?search=ivec3), [ivec4](/glossary/?... [📖 View Full Entry](https://thebookofshaders.com/glossary/?search=int) ### Inversesqrt ## Inversesqrt Return the inverse of the square root of the parameter ### Declaration ```glsl float inversesqrt(float x) vec2 inversesqrt(vec2 x) vec3 inversesqrt(vec3 x) vec4 inversesqrt(vec4 x) ``` ### Parameters ```x``` specifies the value of which to take the inverse of the square root. ### Description ```inversesqrt()``` returns the inverse of the square root of ```x```.

### See Also [distance()]... [📖 View Full Entry](https://thebookofshaders.com/glossary/?search=length) ### Lessthan ## LessThan Perform a component-wise less-than comparison of two vectors ### Declaration ```glsl 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) ``` ### Parameters ```x``` specifies the first vector to be used in the comparison operation. `... [📖 View Full Entry](https://thebookofshaders.com/glossary/?search=lessThan) ### Lessthanequal ## LessThanEqual Perform a component-wise less-than-or-equal comparison of two vectors ### Declaration ```glsl 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) ``` ### Parameters ```x``` specifies the first vector ... [📖 View Full Entry](https://thebookofshaders.com/glossary/?search=lessThanEqual) ### Log ## Log Return the natural logarithm of the parameter ### Declaration ```glsl float log(float x) vec2 log(vec2 x) vec3 log(vec3 x) vec4 log(vec4 x) ``` ### Parameters ```x``` specifies the value of which to take the natural logarithm. ### Description ```log()``` returns the natural logarithm of ```x```.

### See Also [log2](/glossary... [📖 View Full Entry](https://thebookofshaders.com/glossary/?search=log) ### Log2 ## Log2 Return the base 2 logarithm of the parameter ### Declaration ```glsl float log2(float x) vec2 log2(vec2 x) vec3 log2(vec3 x) vec4 log2(vec4 x) ``` ### Parameters ```x``` specifies the value of which to take the base 2 logarithm. ### Description ```log2()``` returns the base 2 logarithm of ```x```.

### See Also [log](/gloss... [📖 View Full Entry](https://thebookofshaders.com/glossary/?search=log2) ### Lowp ## Lowp ### Declaration / Example ### Parameters ### Description ### See Also ... [📖 View Full Entry](https://thebookofshaders.com/glossary/?search=lowp) ### Main ## Main ### Declaration / Example ### Parameters ### Description ### See Also ... [📖 View Full Entry](https://thebookofshaders.com/glossary/?search=main) ### Mat2 ## Mat2 2x2 floating point matrix ### Declaration ```glsl mat2 aMat2 = mat2(1.0, 0.0, // 1. column 0.0, 1.0); // 2. column mat2 bMat2 = mat2(1.0); mat2 cMat2 = mat2(aVec2, bVec2); mat2 dMat2 = mat2(aVec3, aFloat); ``` ### Description ```mat2``` data type is compose for a 2x2 matrix of floating point. As you can see above, can be initialize in different ways: - Providing a val... [📖 View Full Entry](https://thebookofshaders.com/glossary/?search=mat2) ### Mat3 ## Mat3 3x3 floating point matrix ### Declaration ```glsl mat3 aMat3 = mat3(1.0, 0.0, 0.0, // 1. column 0.0, 1.0, 0.0, // 2. column 0.0, 0.0, 1.0); // 3. column mat3 bMat3 = mat3(1.0); mat3 cMat3 = mat3(aVec3, bVec3, cVec3); mat3 dMat3 = mat3(aVec4, aVec3, bVec4, aFloat); ``` ### Description ```mat3``` data type is compose for a 3x3 matrix of floating point... [📖 View Full Entry](https://thebookofshaders.com/glossary/?search=mat3) ### Mat4 ## Mat4 4x4 floating point matrix ### Declaration ```glsl mat4 aMat4 = mat4(1.0, 0.0, 0.0, 0.0, // 1. column 0.0, 1.0, 0.0, 0.0, // 2. column 0.0, 0.0, 1.0, 0.0, // 3. column 0.0, 0.0, 0.0, 1.0); // 4. column mat4 bMat4 = mat4(1.0); mat4 cMat4 = mat4(aVec4, bVec4, cVec4, dVec4); mat4 dMat4 = mat4(aVec4, aVec3, bVec4, cVec4, aFloat); ``` #... [📖 View Full Entry](https://thebookofshaders.com/glossary/?search=mat4) ### Matrixcompmult ## MatrixCompMult Perform a component-wise multiplication of two matrices ### Declaration ```glsl mat2 matrixCompMult(mat2 x, mat2 y) mat3 matrixCompMult(mat3 x, mat3 y) mat4 matrixCompMult(mat4 x, mat4 y) ``` ### Parameters ```x``` specifies the first matrix multiplicand. ```y``` specifies the second matrix multiplicand. ### Description ```matrixCompMult()``` performs a component-wise mul... [📖 View Full Entry](https://thebookofshaders.com/glossary/?search=matrixCompMult) ### Max ## Max Return the greater of two values ### Declaration ```glsl float max(float x, float y) vec2 max(vec2 x, vec2 y) vec3 max(vec3 x, vec3 y) vec4 max(vec4 x, vec4 y) vec2 max(vec2 x, float y) vec3 max(vec3 x, float y) vec4 max(vec4 x, float y) ``` ### Parameters ```x``` specifies the first value to compare. ```y``` specifies the second value to compare. ### Description ```max()``` ... [📖 View Full Entry](https://thebookofshaders.com/glossary/?search=max) ### Mediump ## Mediump ### Declaration / Example ### Parameters ### Description ### See Also ... [📖 View Full Entry](https://thebookofshaders.com/glossary/?search=mediump) ### Min ## Min Return the lesser of two values ### Declaration ```glsl float min(float x, float y) vec2 min(vec2 x, vec2 y) vec3 min(vec3 x, vec3 y) vec4 min(vec4 x, vec4 y) vec2 min(vec2 x, float y) vec3 min(vec3 x, float y) vec4 min(vec4 x, float y) ``` ### Parameters ```x``` specifies the first value to compare. ```y``` specifies the second value to compare. ### Description ```min()``` r... [📖 View Full Entry](https://thebookofshaders.com/glossary/?search=min) ### Mix ## Mix Constrain a value to lie between two further values ### Declaration ```glsl 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) vec2 mix(vec2 x, vec2 y, float a) vec3 mix(vec3 x, vec3 y, float a) vec4 mix(vec4 x, vec4 y, float a) ``` ### Parameters ```x``` specifies the start of the range in whi... [📖 View Full Entry](https://thebookofshaders.com/glossary/?search=mix) ### Mod ## Mod Compute value of one parameter modulo another ### Declaration ```glsl float mod(float x, float y) vec2 mod(vec2 x, vec2 y) vec3 mod(vec3 x, vec3 y) vec4 mod(vec4 x, vec4 y) vec2 mod(vec2 x, float y) vec3 mod(vec3 x, float y) vec4 mod(vec4 x, float y) ``` ### Parameters ```x``` specifies the value to evaluate. ```y``` specifies the value to obtain the modulo of. ### Description... [📖 View Full Entry](https://thebookofshaders.com/glossary/?search=mod) ### Normalize ## Normalize Calculate the unit vector in the same direction as the input vector ### Declaration ```glsl float normalize(float x) vec2 normalize(vec2 x) vec3 normalize(vec3 x) vec4 normalize(vec4 x) ``` ### Parameters ```x``` specifies the vector to normalize. ### Description ```normalize()``` returns a vector with the same direction as its parameter, ```x```, but with length 1. ### See ... [📖 View Full Entry](https://thebookofshaders.com/glossary/?search=normalize) ### Not ## Not Logically invert a boolean vector ### Declaration ```glsl bvec2 not(bvec2 x) bvec3 not(bvec3 x) bvec4 not(bvec4 x) ``` ### Parameters ```x``` specifies the vector to be inverted. ### Description ```not()``` logically inverts the boolean vector ```x```. It returns a new boolean vector for which each element ```i``` is computed as ```!x[i]```. ### See Also [any()](/glossary/?search=an... [📖 View Full Entry](https://thebookofshaders.com/glossary/?search=not) ### Notequal ## NotEqual Perform a component-wise not-equal-to comparison of two vectors ### Declaration ```glsl 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) ``` ### Parameters ```x``` specifies the first vector to be used in the comparison operation. ... [📖 View Full Entry](https://thebookofshaders.com/glossary/?search=notEqual) ### Out ## Out ### Declaration / Example ### Parameters ### Description ### See Also ... [📖 View Full Entry](https://thebookofshaders.com/glossary/?search=out) ### Pow ## Pow Return the value of the first parameter raised to the power of the second. ### Declaration ```glsl float pow(float x, float y) vec2 pow(vec2 x, vec2 y) vec3 pow(vec3 x, vec3 y) vec4 pow(vec4 x, vec4 y) ``` ### Parameters ```x``` specifies the value to raise to the power ```y```. ```y``` specifies the power to which to raise ```x```. ### Description ```pow()``` returns the value of... [📖 View Full Entry](https://thebookofshaders.com/glossary/?search=pow) ### Precision ## Precision ### Declaration / Example ### Parameters ### Description ### See Also ... [📖 View Full Entry](https://thebookofshaders.com/glossary/?search=precision) ### Radians ## Radians Convert a quantity in degrees to radians ### Declaration ```glsl float radians(float degrees) vec2 radians(vec2 degrees) vec3 radians(vec3 degrees) vec4 radians(vec4 degrees) ``` ### Parameters ```degrees``` specifies the quantity, in degrees, to be converted to radians. ### Description ```radians()``` converts a quantity, specified in degrees into radians. That is, the return ... [📖 View Full Entry](https://thebookofshaders.com/glossary/?search=radians) ### Reflect ## Reflect Calculate the reflection direction for an incident vector ### Declaration ```glsl float reflect(float I, float N) vec2 reflect(vec2 I, vec2 N) vec3 reflect(vec3 I, vec3 N) vec4 reflect(vec4 I, vec4 N) ``` ### Parameters ```I``` specifies the incident vector. ```N``` specifies the normal vector. ### Description For a given incident vector ```I``` and surface normal ```N``` refl... [📖 View Full Entry](https://thebookofshaders.com/glossary/?search=reflect) ### Refract ## Refract Calculate the refraction direction for an incident vector ### Declaration ```glsl 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) ``` ### Parameters ```I``` specifies the incident vector. ```N``` specifies the normal vector. ```eta``` specifies the ratio of indice... [📖 View Full Entry](https://thebookofshaders.com/glossary/?search=refract) ### Return ## Return ### Declaration / Example ### Parameters ### Description ### See Also ... [📖 View Full Entry](https://thebookofshaders.com/glossary/?search=return) ### Sampler2D ## Sampler2D ### Declaration / Example ### Parameters ### Description ### See Also ... [📖 View Full Entry](https://thebookofshaders.com/glossary/?search=sampler2D) ### Samplercube ## SamplerCube ### Declaration / Example ### Parameters ### Description ### See Also ... [📖 View Full Entry](https://thebookofshaders.com/glossary/?search=samplerCube) ### Sign ## Sign Extract the sign of the parameter ### Declaration ```glsl float sign(float x) vec2 sign(vec2 x) vec3 sign(vec3 x) vec4 sign(vec4 x) ``` ### Parameters ```x``` specifies the value from which to extract the sign. ### Description ```sign()``` returns -1.0 if x is less than 0.0, 0.0 if x is equal to 0.0, and +1.0 if x is greater than 0.0.

### See Also [acos]... [📖 View Full Entry](https://thebookofshaders.com/glossary/?search=sin) ### Smoothstep ## Smoothstep Perform Hermite interpolation between two values ### Declaration ```glsl 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) vec2 smoothstep(float edge0, float edge1, vec2 x) vec3 smoothstep(float edge0, float edge1, vec3 x) vec4 ... [📖 View Full Entry](https://thebookofshaders.com/glossary/?search=smoothstep) ### Sqrt ## Sqrt Return the square root of the parameter ### Declaration ```glsl float sqrt(float x) vec2 sqrt(vec2 x) vec3 sqrt(vec3 x) vec4 sqrt(vec4 x) ``` ### Parameters ```x``` specifies the value of which to take the square root. ### Description ```sqrt()``` returns the square root of ```x```.

### See Al... [📖 View Full Entry](https://thebookofshaders.com/glossary/?search=tan) ### Texture2D ## Texture2D Retrieves texels from a texture ### Declaration ```glsl vec4 texture2D(sampler2D sampler, vec2 coord) vec4 texture2D(sampler2D sampler, vec2 coord, float bias) ``` ### Parameters ```sampler``` specifies the sampler to which the texture from which texels will be retrieved is bound. ```coord``` specifies the texture coordinates at which texture will be sampled. ```bias``` specifie... [📖 View Full Entry](https://thebookofshaders.com/glossary/?search=texture2D) ### Texturecube ## TextureCube Retrieves texels from a texture ### Declaration ```glsl vec4 textureCube(samplerCube sampler, vec3 coord) vec4 textureCube(samplerCube sampler, vec3 coord, float bias) ``` ### Parameters ```sampler``` specifies the sampler to which the texture from which texels will be retrieved is bound. ```coord``` specifies the texture coordinates at which texture will be sampled. ```bias``... [📖 View Full Entry](https://thebookofshaders.com/glossary/?search=textureCube) ### Uniform ## Uniform Uniform variable qualifier. ### Example ```glsl uniform vec4 direction; ``` ### Description ```uniform``` variables contain read-only data shared from WebGL/OpenGL environment to a vertex or fragment shader. The value is per primitive, so is useful for variables which remain constant along a primitive, frame or scene. ### See Also [attribute](/glossary/?search=attribute), [const](/g... [📖 View Full Entry](https://thebookofshaders.com/glossary/?search=uniform) ### Varying ## Varying Varying variable qualifier. ### Example ```glsl varying vec3 position; ``` ### Description ```varying``` variables contain data shared from a vertex shader to a fragment shader. The variable must be written in the vertex shader and the read-only value in the fragment shader is then interpolated from the vertices which make up the fragment. ### See Also [attribute](/glossary/?search=... [📖 View Full Entry](https://thebookofshaders.com/glossary/?search=varying) ### Vec2 ## Vec2 2 dimensional floating point vector ### Declaration ```glsl vec2 aVec2 = vec2(1.0, 1.0); vec2 bVec2 = vec2(1.0); vec2 cVec2 = vec2(aVec3); vec2 dVec2 = vec2(aVec3.x, aVec3.y); ``` ### Description ```vec2``` is a floating point vector with two components. It can be initialized by: - Providing a scalar value for each component. - Providing one scalar value. This value is used for all com... [📖 View Full Entry](https://thebookofshaders.com/glossary/?search=vec2) ### Vec3 ## Vec3 3 dimensional floating point vector ### Declaration ```glsl vec3 aVec3 = vec3(1.0, 1.0, 1.0); vec3 bVec3 = vec3(1.0); vec3 cVec3 = vec3(aVec4); vec3 dVec3 = vec3(aVec4.x, aVec4.y, aVec4.z); vec3 eVec3 = vec3(aVec2, aFloat); vec3 fVec3 = vec3(aVec2.x, aVec2.y, aFloat); ``` ### Description ```vec3``` is a floating point vector with three components. It can be initialized by: - Providing... [📖 View Full Entry](https://thebookofshaders.com/glossary/?search=vec3) ### Vec4 ## Vec4 4 dimensional floating point vector ### Declaration ```glsl vec4 aVec4 = vec4(1.0, 1.0, 1.0, 1.0); vec4 bVec4 = vec4(1.0); vec4 cVec4 = vec4(aVec2, aFloat, aVec3); vec4 dVec4 = vec4(aBvec2.x, aBvec2.y, aFloat, aBvec3.x); ``` ### Description ```vec4``` is a floating point vector with four components. It can be initialized by: - Providing a scalar value for each component. - Providing on... [📖 View Full Entry](https://thebookofshaders.com/glossary/?search=vec4) ### Void ## Void ### Declaration ```glsl void main(void); int aFunction(void); void bFunction(float); ``` ### Description ```void``` is used when a function has no parameters or when a function does not return a value. ### See Also [void](/glossary/?search=void), [bool](/glossary/?search=bool), [int](/glossary/?search=int), [float](/glossary/?search=float) ... [📖 View Full Entry](https://thebookofshaders.com/glossary/?search=void)