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create mode 100644 10/index.html create mode 100644 10/truchet.frag create mode 100644 11/1d-noise.frag create mode 100644 11/2d-noise.frag create mode 100644 11/3d-noise.frag create mode 100644 11/README.md create mode 100644 11/index.html create mode 100644 11/noise.frag create mode 100644 12/1d-fbm.frag create mode 100644 12/README.md create mode 100644 12/index.html create mode 100644 12/noise.frag create mode 100644 13/05.jpg create mode 100644 13/09.jpg create mode 100644 13/10.jpg create mode 100644 13/README.md create mode 100644 13/index.html create mode 100644 13/kanagawa.jpg create mode 100644 13/texture-noise.frag create mode 100644 13/texture.frag diff --git a/06/PhotoshopMathFP.glsl b/06/PhotoshopMathFP.glsl new file mode 100644 index 0000000..24e5886 --- /dev/null +++ b/06/PhotoshopMathFP.glsl @@ -0,0 +1,260 @@ +/* +** Copyright (c) 2012, Romain Dura romain@shazbits.com +** +** Permission to use, copy, modify, and/or distribute this software for any +** purpose with or without fee is hereby granted, provided that the above +** copyright notice and this permission notice appear in all copies. +** +** THE SOFTWARE IS PROVIDED "AS IS" AND THE AUTHOR DISCLAIMS ALL WARRANTIES +** WITH REGARD TO THIS SOFTWARE INCLUDING ALL IMPLIED WARRANTIES OF +** MERCHANTABILITY AND FITNESS. IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR ANY +** SPECIAL, DIRECT, INDIRECT, OR CONSEQUENTIAL DAMAGES OR ANY DAMAGES +** WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR PROFITS, WHETHER IN AN +** ACTION OF CONTRACT, NEGLIGENCE OR OTHER TORTIOUS ACTION, ARISING OUT OF OR +** IN CONNECTION WITH THE USE OR PERFORMANCE OF THIS SOFTWARE. +*/ + +/* +** Photoshop & misc math +** Blending modes, RGB/HSL/Contrast/Desaturate, levels control +** +** Romain Dura | Romz +** Blog: http://mouaif.wordpress.com +** Post: http://mouaif.wordpress.com/?p=94 +*/ + + + +/* +** Desaturation +*/ + +vec4 Desaturate(vec3 color, float Desaturation) +{ + vec3 grayXfer = vec3(0.3, 0.59, 0.11); + vec3 gray = vec3(dot(grayXfer, color)); + return vec4(mix(color, gray, Desaturation), 1.0); +} + + +/* +** Hue, saturation, luminance +*/ + +vec3 RGBToHSL(vec3 color) +{ + vec3 hsl; // init to 0 to avoid warnings ? (and reverse if + remove first part) + + float fmin = min(min(color.r, color.g), color.b); //Min. value of RGB + float fmax = max(max(color.r, color.g), color.b); //Max. value of RGB + float delta = fmax - fmin; //Delta RGB value + + hsl.z = (fmax + fmin) / 2.0; // Luminance + + if (delta == 0.0) //This is a gray, no chroma... + { + hsl.x = 0.0; // Hue + hsl.y = 0.0; // Saturation + } + else //Chromatic data... + { + if (hsl.z < 0.5) + hsl.y = delta / (fmax + fmin); // Saturation + else + hsl.y = delta / (2.0 - fmax - fmin); // Saturation + + float deltaR = (((fmax - color.r) / 6.0) + (delta / 2.0)) / delta; + float deltaG = (((fmax - color.g) / 6.0) + (delta / 2.0)) / delta; + float deltaB = (((fmax - color.b) / 6.0) + (delta / 2.0)) / delta; + + if (color.r == fmax ) + hsl.x = deltaB - deltaG; // Hue + else if (color.g == fmax) + hsl.x = (1.0 / 3.0) + deltaR - deltaB; // Hue + else if (color.b == fmax) + hsl.x = (2.0 / 3.0) + deltaG - deltaR; // Hue + + if (hsl.x < 0.0) + hsl.x += 1.0; // Hue + else if (hsl.x > 1.0) + hsl.x -= 1.0; // Hue + } + + return hsl; +} + +float HueToRGB(float f1, float f2, float hue) +{ + if (hue < 0.0) + hue += 1.0; + else if (hue > 1.0) + hue -= 1.0; + float res; + if ((6.0 * hue) < 1.0) + res = f1 + (f2 - f1) * 6.0 * hue; + else if ((2.0 * hue) < 1.0) + res = f2; + else if ((3.0 * hue) < 2.0) + res = f1 + (f2 - f1) * ((2.0 / 3.0) - hue) * 6.0; + else + res = f1; + return res; +} + +vec3 HSLToRGB(vec3 hsl) +{ + vec3 rgb; + + if (hsl.y == 0.0) + rgb = vec3(hsl.z); // Luminance + else + { + float f2; + + if (hsl.z < 0.5) + f2 = hsl.z * (1.0 + hsl.y); + else + f2 = (hsl.z + hsl.y) - (hsl.y * hsl.z); + + float f1 = 2.0 * hsl.z - f2; + + rgb.r = HueToRGB(f1, f2, hsl.x + (1.0/3.0)); + rgb.g = HueToRGB(f1, f2, hsl.x); + rgb.b= HueToRGB(f1, f2, hsl.x - (1.0/3.0)); + } + + return rgb; +} + + +/* +** Contrast, saturation, brightness +** Code of this function is from TGM's shader pack +** http://irrlicht.sourceforge.net/phpBB2/viewtopic.php?t=21057 +*/ + +// For all settings: 1.0 = 100% 0.5=50% 1.5 = 150% +vec3 ContrastSaturationBrightness(vec3 color, float brt, float sat, float con) +{ + // Increase or decrease theese values to adjust r, g and b color channels seperately + const float AvgLumR = 0.5; + const float AvgLumG = 0.5; + const float AvgLumB = 0.5; + + const vec3 LumCoeff = vec3(0.2125, 0.7154, 0.0721); + + vec3 AvgLumin = vec3(AvgLumR, AvgLumG, AvgLumB); + vec3 brtColor = color * brt; + vec3 intensity = vec3(dot(brtColor, LumCoeff)); + vec3 satColor = mix(intensity, brtColor, sat); + vec3 conColor = mix(AvgLumin, satColor, con); + return conColor; +} + + +/* +** Float blending modes +** Adapted from here: http://www.nathanm.com/photoshop-blending-math/ +** But I modified the HardMix (wrong condition), Overlay, SoftLight, ColorDodge, ColorBurn, VividLight, PinLight (inverted layers) ones to have correct results +*/ + +#define BlendLinearDodgef BlendAddf +#define BlendLinearBurnf BlendSubstractf +#define BlendAddf(base, blend) min(base + blend, 1.0) +#define BlendSubstractf(base, blend) max(base + blend - 1.0, 0.0) +#define BlendLightenf(base, blend) max(blend, base) +#define BlendDarkenf(base, blend) min(blend, base) +#define BlendLinearLightf(base, blend) (blend < 0.5 ? BlendLinearBurnf(base, (2.0 * blend)) : BlendLinearDodgef(base, (2.0 * (blend - 0.5)))) +#define BlendScreenf(base, blend) (1.0 - ((1.0 - base) * (1.0 - blend))) +#define BlendOverlayf(base, blend) (base < 0.5 ? (2.0 * base * blend) : (1.0 - 2.0 * (1.0 - base) * (1.0 - blend))) +#define BlendSoftLightf(base, blend) ((blend < 0.5) ? (2.0 * base * blend + base * base * (1.0 - 2.0 * blend)) : (sqrt(base) * (2.0 * blend - 1.0) + 2.0 * base * (1.0 - blend))) +#define BlendColorDodgef(base, blend) ((blend == 1.0) ? blend : min(base / (1.0 - blend), 1.0)) +#define BlendColorBurnf(base, blend) ((blend == 0.0) ? blend : max((1.0 - ((1.0 - base) / blend)), 0.0)) +#define BlendVividLightf(base, blend) ((blend < 0.5) ? BlendColorBurnf(base, (2.0 * blend)) : BlendColorDodgef(base, (2.0 * (blend - 0.5)))) +#define BlendPinLightf(base, blend) ((blend < 0.5) ? BlendDarkenf(base, (2.0 * blend)) : BlendLightenf(base, (2.0 *(blend - 0.5)))) +#define BlendHardMixf(base, blend) ((BlendVividLightf(base, blend) < 0.5) ? 0.0 : 1.0) +#define BlendReflectf(base, blend) ((blend == 1.0) ? blend : min(base * base / (1.0 - blend), 1.0)) + + +/* +** Vector3 blending modes +*/ + +// Component wise blending +#define Blend(base, blend, funcf) vec3(funcf(base.r, blend.r), funcf(base.g, blend.g), funcf(base.b, blend.b)) + +#define BlendNormal(base, blend) (blend) +#define BlendLighten BlendLightenf +#define BlendDarken BlendDarkenf +#define BlendMultiply(base, blend) (base * blend) +#define BlendAverage(base, blend) ((base + blend) / 2.0) +#define BlendAdd(base, blend) min(base + blend, vec3(1.0)) +#define BlendSubstract(base, blend) max(base + blend - vec3(1.0), vec3(0.0)) +#define BlendDifference(base, blend) abs(base - blend) +#define BlendNegation(base, blend) (vec3(1.0) - abs(vec3(1.0) - base - blend)) +#define BlendExclusion(base, blend) (base + blend - 2.0 * base * blend) +#define BlendScreen(base, blend) Blend(base, blend, BlendScreenf) +#define BlendOverlay(base, blend) Blend(base, blend, BlendOverlayf) +#define BlendSoftLight(base, blend) Blend(base, blend, BlendSoftLightf) +#define BlendHardLight(base, blend) BlendOverlay(blend, base) +#define BlendColorDodge(base, blend) Blend(base, blend, BlendColorDodgef) +#define BlendColorBurn(base, blend) Blend(base, blend, BlendColorBurnf) +#define BlendLinearDodge BlendAdd +#define BlendLinearBurn BlendSubstract +// Linear Light is another contrast-increasing mode +// If the blend color is darker than midgray, Linear Light darkens the image by decreasing the brightness. If the blend color is lighter than midgray, the result is a brighter image due to increased brightness. +#define BlendLinearLight(base, blend) Blend(base, blend, BlendLinearLightf) +#define BlendVividLight(base, blend) Blend(base, blend, BlendVividLightf) +#define BlendPinLight(base, blend) Blend(base, blend, BlendPinLightf) +#define BlendHardMix(base, blend) Blend(base, blend, BlendHardMixf) +#define BlendReflect(base, blend) Blend(base, blend, BlendReflectf) +#define BlendGlow(base, blend) BlendReflect(blend, base) +#define BlendPhoenix(base, blend) (min(base, blend) - max(base, blend) + vec3(1.0)) +#define BlendOpacity(base, blend, F, O) (F(base, blend) * O + blend * (1.0 - O)) + + +// Hue Blend mode creates the result color by combining the luminance and saturation of the base color with the hue of the blend color. +vec3 BlendHue(vec3 base, vec3 blend) +{ + vec3 baseHSL = RGBToHSL(base); + return HSLToRGB(vec3(RGBToHSL(blend).r, baseHSL.g, baseHSL.b)); +} + +// Saturation Blend mode creates the result color by combining the luminance and hue of the base color with the saturation of the blend color. +vec3 BlendSaturation(vec3 base, vec3 blend) +{ + vec3 baseHSL = RGBToHSL(base); + return HSLToRGB(vec3(baseHSL.r, RGBToHSL(blend).g, baseHSL.b)); +} + +// Color Mode keeps the brightness of the base color and applies both the hue and saturation of the blend color. +vec3 BlendColor(vec3 base, vec3 blend) +{ + vec3 blendHSL = RGBToHSL(blend); + return HSLToRGB(vec3(blendHSL.r, blendHSL.g, RGBToHSL(base).b)); +} + +// Luminosity Blend mode creates the result color by combining the hue and saturation of the base color with the luminance of the blend color. +vec3 BlendLuminosity(vec3 base, vec3 blend) +{ + vec3 baseHSL = RGBToHSL(base); + return HSLToRGB(vec3(baseHSL.r, baseHSL.g, RGBToHSL(blend).b)); +} + + +/* +** Gamma correction +** Details: http://blog.mouaif.org/2009/01/22/photoshop-gamma-correction-shader/ +*/ + +#define GammaCorrection(color, gamma) pow(color, 1.0 / gamma) + +/* +** Levels control (input (+gamma), output) +** Details: http://blog.mouaif.org/2009/01/28/levels-control-shader/ +*/ + +#define LevelsControlInputRange(color, minInput, maxInput) min(max(color - vec3(minInput), vec3(0.0)) / (vec3(maxInput) - vec3(minInput)), vec3(1.0)) +#define LevelsControlInput(color, minInput, gamma, maxInput) GammaCorrection(LevelsControlInputRange(color, minInput, maxInput), gamma) +#define LevelsControlOutputRange(color, minOutput, maxOutput) mix(vec3(minOutput), vec3(maxOutput), color) +#define LevelsControl(color, minInput, gamma, maxInput, minOutput, maxOutput) LevelsControlOutputRange(LevelsControlInput(color, minInput, gamma, maxInput), minOutput, maxOutput) diff --git a/06/README.md b/06/README.md new file mode 100644 index 0000000..de8f521 --- /dev/null +++ b/06/README.md @@ -0,0 +1,131 @@ +## Color + +![Paul Klee - Color Chart (1931)](klee.jpg) + +What are graphics without colors? right? First, lets learn more about the variable types you will probably use to store colors, that's a three dimensional vector (```vec3```) or fourth dimensional (```vec4```) if you are using an alpha channel. + +### Vectors properties + +We didn’t talk to much about vectors, but if you are familiar with object oriented programming paradigms you had notice that we have been accessing the data inside the vectors like any regular C ```struct```. + +```glsl +vec3 red = vec3(1.0,0.0,0.0); +red.x = 1.0; +red.y = 0.0; +red.z = 0.0; +``` + +There are other ways to access the same information, which for colors will make your code more readable. The values on ```.x```, ```.y``` and ```.z``` are overloaded to ```.r```, ```.g``` and ```.b```. Also there is an extra nomenclature you can use: ```.s```, ```.t``` and ```.p```. This don’t affect the values and is completely interchangeable. Use it on your own convenience to write clear code. + +On ```vec4``` there is an extra value for the alpha that also have different ways to access to it. Also, because vectors are essentially arrays of value you can access to the data just by using the index position of the component you want to modify or set. + +That gives a big spectrum of ways to access the same information. All the following calls per line are homologous. + +```glsl +vec4 vector; +vector[0] = vector.r = vector.x = vector.s; +vector[1] = vector.g = vector.y = vector.t; +vector[2] = vector.b = vector.z = vector.p; +vector[3] = vector.a = vector.w = vector.q; +``` + +Another great feature of vectors on GLSL is that this properties can be call combined and in different orders, making easy for example to cast and mix values. + +```glsl +vec3 yellow, magenta, blue; + +yellow.rg = vec2(1.0); +yellow[2] = 0.0; + +magenta = yellow.rbg; +blue.b = magenta.z; +``` + +#### For your toolbox + +If you have a background on design or new media, you are probably used to picking colors with number, which could be very counterintuitive. Lucky you, there are a lot of smart programs that make this job easy. Research for one that fits your needs and then train it to delivery colors in ```vec3``` or ```vec4``` format. For example here are the templates I use on [Spectrum](http://www.eigenlogik.com/spectrum/mac): + +``` + vec3({{rn}},{{gn}},{{bn}}) + vec4({{rn}},{{gn}},{{bn}},1.0) +``` + +### Mix function + +This GLSL native function will let you mix two variables by percentages. The percentage is define with a floating number between 0.0 and 1.0 while the variables can be any variable type including vectors. Actually all the functions have seen until now works with ```float```, ```vec2```, ```vec3``` and ```vec4```. + +Check the following code at line 18 and see how we are using the absolute values of a sin wave over time to mix ```colorA``` and ```colorB```. + +
+ + +### Playing with gradients + +But the ```mix``` function have more to offer. If in the third argument we pass a ```vec3``` instead of a single ```float``` we will be hable to control the transition bettween colors by individual channel. + +Take a look to the following example. + +
+ +Similarly to the examples on the previus chapter we are hooking the transition to the normalized *x* coordinate and visualizing it with a line. You can see how all channels goes a long together. + +Now, uncoment line number 24 and see what happens. Then try the lines 25 and 26. Remember that the lines visualize the amount ```colorA``` and ```colorB``` to mix per channel. + +You probably recognice the three shaping functions we are using in lines 25 to 26. Play with them! Is time for you to explore and show of your skills learned on the previus chapter and make interesting gradient. Try the following excersices: + +![William Turner - The Fighting Temeraire (1838)](turner.jpg) + +* Compose a gradient that resemblance a William Turner sunset + +* Animate a transition between a sunrise and sunset using ```u_time```. + +* Can you make rainbow just using what we have learn until now? + +* Using ```step()``` function create a procedural flag. + +### HSB + +Is hard to bring the subject of color with out speaking about color space. As you probably know there are different ways to organize color beside by red, green and blue channel. + +[HSB](http://en.wikipedia.org/wiki/HSL_and_HSV) stands for Hue, Saturation and Brightness (or Value) and is a more intuitive and useful organization of colors. Take a moment to read the ```rgb2hsv()``` and ```hsv2rgb()``` functions on the following code. + +
+ +By mapping the position on the x axis to the Hue and the brightness to the length we can obtain a bigger and clear spectrum of visible colors than before. This spacial translation of of color was relatively easy because both pairs of variables (the x and y and the hue and brightness) have a identical range from 0.0 to 1.0. + +Let’s stop for a second and look deeply to the functions, we will see that both of them receive and returns ```vec3``` variables. Also we will notice the arguments are define as ```in```. This is call variable [qualifier](http://www.shaderific.com/glsl-qualifiers/#inputqualifier) and in this case specify this variable as read only. In future examples we will see that also possible to define them variables as ```out``` or ```inout```. + +```glsl +int newFunction(in vec4 aVec4, // read-only + out vec3 aVec3, // write-only + inout int aInt); // read-write +``` + +Back to HSB, this color space is particularly clear and intuitive for understanding of color composition, while give as extraordinary good control to set our color values. Reason why is the default choose for color pickers user interface. + +HSB was originally designed to be represented on polar coordinates (based on the angle and radius) instead of cartesian coordinates (based on x and y). To map our HSB function to polar coordinates we need to obtain the angle and distance from the center of the viewport to the fragment coordinate. For that we will use the ```atan(y,x)``` (which is the GLSL version of ```atan2(y,x)```) and the ```length()``` function. This last one could sound tricky but ```vec2```, ```vec3``` and ```vec4``` are nothing but regular vectors in two, three and four dimensions. There is no reason why we couldn’t do typical vectorial and trigonometrical operations, in fact the flexibility of treating colors and vectors and vectors and colors is the main game of Shaders. + +There are more geometric functions beside [```length```](http://www.shaderific.com/glsl-functions/#length) like: [```distance()```](http://www.shaderific.com/glsl-functions/#distance), [```dot()```](http://www.shaderific.com/glsl-functions/#dotproduct), [```cross```](http://www.shaderific.com/glsl-functions/#crossproduct), [```normalize()```](http://www.shaderific.com/glsl-functions/#normalize), [```faceforward()```](http://www.shaderific.com/glsl-functions/#faceforward), [```reflect()```](http://www.shaderific.com/glsl-functions/#reflect) and [```refract()```](http://www.shaderific.com/glsl-functions/#refract). Also GLSL have special vector relational functions such as: [```lessThan()```](http://www.shaderific.com/glsl-functions/#lessthancomparison), [```lessThanEqual()```](http://www.shaderific.com/glsl-functions/#lessthanorequalcomparison), [```greaterThan()```](http://www.shaderific.com/glsl-functions/#greaterthancomparison) and [```greaterThanEqual()```](http://www.shaderific.com/glsl-functions/#greaterthanorequalcomparison). + +Once we obtain the angle and the length we need to “normalize” their values to the docile range between 0.0 to 1.0 we are used to. On line 42, ```atan(x,y)``` will return an angle in radians between -PI and PI (-3.14 to 3.14), so we need to divide this number by ```TWO_PI``` (defined on the top of the code) to get values between -0.5 to 0.5 which by a simple addition we can accommodate to the desired range of 0.0 to 1.0. The radius in other hand will return a maximum of 0.5 (because we are calculatin the distance form the center of the viewport) so we need to extend this range to it double (by multiplying by two) to get a maximum of 1.0. + +
+ +As you can see, our game here is all about transforming and mapping ranges to what we want. + +By this time will not be a problem to try the following excersises + +* Modify the polar example to get a spinning color wheel, just like the waiting mouse icon. + +* Use a shaping function together with the conversion function from HSB to RGB to expand a particular hue value and shrink the rest. + + +![William Home Lizars - Red, blue and yellow spectra, with the solar spectrum (1834)](spectrums.jpg) + +* If you look closely to the color wheel used on color pickers (see the image below) use a different spectrum acording to RYB color space. For example, the oposite color of red should be green (which is his opposite), but in our example is cyan. 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+vec3 colorB = vec3(1.000,0.833,0.224); + +void main() { + vec3 color = vec3(0.0); + + float pct = abs(sin(u_time)); + + // Mix use the last value (0-1) to + // mix the to colors + color = mix(colorA, colorB, pct); + + gl_FragColor = vec4(color,1.0); +} \ No newline at end of file diff --git a/06/spectrums.jpg b/06/spectrums.jpg new file mode 100644 index 0000000000000000000000000000000000000000..c7a61353b3d3aba89dac6725392fae52fce48b99 GIT binary patch literal 46432 zcmb5UbzD?m)Hix4rMpqdA%>y58|fIjm6VoJL`nptyF)sLE+r(ChM^lJlrHIz^d9^@ z&-;Ep_x^Ry-m}iy`|LjJyVlx!&fmGeKLJ7&MP)?*1qA?5zySRH0muOl&@mohpg(wk z@!;XZ2bkD|*w|QD*rfObxP%m>l#~>t0oq>%q(nBHY!>UZVpy% z2rC=weIqCjA3ns!#3sSUCSj!}r)K^Cef{kOh%nK%P+QPY7ywiv6f`1~zuf>0IMn|x z;D0X^R5WnB55b32|L;fOr0yU7{SM%wp#Z3aXoO(SU6Ak=0N|h!7w7lne{*>TGI{!{ zYQu8usy5OyvRZ&jDxN}02q6q0Bz@ospu#eSX4HmdS@jfHF>3()NKR=0BPBO52_QEi zu88r2V99Eg)>*{noc=s;>Bj{@~R15Vh>Q`{ED6$qpk_#&X z2BTZ+6Qe?nqk|H6X2;bUBGEp+zN0QIXj|l;IT^wr0Dy`jLk|5)n2#c@k_6Nck^<6N 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b/07/README.md @@ -0,0 +1,126 @@ +## Shapes + +We have been building skill for this moment! We learn most of GLSL foundations, types and functions, together with the knowledge of how to use mathematical equations for shaping values. Now is time to put all that together. In this chapter we are going to learn how to draw simple shapes in a parallel procedural way. + +### Rectangle + +Think on the double gradient of *x* and *y* maped on the *red* and *green* color channels we did on the uniforms chapter. That's our field, our space and territory. How we can use it to draw a rectangle? + +* Sketch a peace of code that use ```if``` statements over that spacial field between 0.0 and 1.0 in *x* and *y*. + +Once you finish that excersise take a look to the following code and imagine what happen on it. + +```glsl +#ifdef GL_ES +precision mediump float; +#endif + +uniform vec2 u_resolution; +uniform float u_time; + +void main(){ + vec2 st = gl_FragCoord.xy/u_resolution.xy; + vec3 color = vec3(0.0); + + float left = step(0.1,st.x); + float bottom = step(0.1,st.y); + + color = vec3( left * bottom ); + + gl_FragColor = vec4(color,1.0); +} +``` + +Here we are using ```step()``` to turn everything bellow 0.1 to to 0.0. That will make a line on the left and bottom of the canvas. + +![](rect.jpg) + +Looking closely to the previous code, we repeat the structure for each side. That means we can save some lines of code by passing directly two values and treating them in the same way with the same function. Look closely the following code. + +

+ +To repeat this on the top and left sides we need to invert the ```st``` gradient. That way the ```vec2(0.0,0.0)``` will be on the top left corner. + +#### Exercise + +* Implement the same code using ```smoothstep()``` instead of ```step()```. Try different values to get different results, go from blurred edges to elegant antialiased borders. + +* Do another implementation that use ```mod()```, ```ceil()```, ```floor()``` or ```fract()```. + +* Choose the implementation you like the most and make it function you ca reuse in the future. Try to leave it flexible and efficient. + +* Make another function to draw just the outline of the a rectagle. + +* Make a composition of rectangles and colors that resemble a [Mark Rothko](http://en.wikipedia.org/wiki/Mark_Rothko) painting. + +![Mark Rothko - Three (1950)](rothko.jpg) + +### Circles + +Circles requeire another approach. Rectangles were relative easy because of how the cartesian space works. For cicles, we can take advantage again of the polar coordinate system just like we did in the previus chapter. This time we +just need to calculate the distance to the center. All the points in the circunsference of a circle will have the same distance to the center so we can use this to trace the limits of this shape. + +There are several ways to calculate that. The easiest one is just using ```distance()``` functions, which internally get the ```length()``` of the difference between two points (in our case the fragment coordinate and the center of the canvas). The ```length()``` function is nothing but a shortcut of the [hypotenuse equation](http://en.wikipedia.org/wiki/Hypotenuse) that use square root (```sqrt()```) internally. + +![](hypotenuse.png) + +Take a look to the following code paying attention to what we do with the space coordinates. + +
+ +The closer to the center we get the lower (darker) the values becomes. Values don't get to high because from the center ( ```vec2(0.5, 0.5)``` ) the maximum distance barely goes over 0.5. Think this pattern or gradiant as a map and think: + +* What you can infer from it? + +* How we can use it to draw circle? + +* Comment and uncomment lines to try the different ways to get the same result. + +* Modify the above code in order to contain the circular gradient inside the canvas. + +### Distance field + +Go back to the example above. Imagine this as an altitude map. The gradient show us the pattern of something shape similar to a cone view from above. Imagie your self on the top of that cone, you hold to tip of a ruled tape while you drop the rest. Because you are in the center of the canvas, the ruler will mark "0.5" in the extreme. This will be constant in all your directions. Buy choosing where to cut horizontally the cone you will get a bigger or smaller circular surface. + +![](distance-field.jpg) + +This way of undersanding gradients as spacial information can be combined, once again with the shaping functions we have seen to get interesting results. This technique is known as “distant field” and is use in diferent ways from font outlines to 3D graphics. + +Try the following excersises: + +* Use ```set()``` to turn everything above 0.5 to white and everything bellow to 0.0 + +* Inverse the colors of the background and foreground. + +* Using ```smoothstep()``` experiment trying different values to get nice antialiased borders on your circle. + +* Once you are happy with your exercises result make a function of it that you can re-use in the future. + +* Can you animate your circle to grow and shrink simulating a beating heart? + +* Use your function to mask a color with it. + +* Make three compositions using just circles. Then animate them. + + +#### For your tool box + +* This is another way to create a circular distance field by using ```dot()``` product. This last one is slyly less expensive (in terms of computational power) than ```sqrt()```. + +
+ +### More about shapes and distance fields + +Distance fields can be use to draw almost everything. Obviously the complex the shape is, the more complicated the equation will be. + +
+ +A really convenient feature of DF is the ability to smooth edges. Because the “topological” nature of them, sharp edges get blended together producing softer edges the more away you are from the center you sample. This is particularly useful on fonts rendering. + +Take a look to the following code and note how the space is remaped in this topographical. Like concentric rings of a Zen garde the distance field values get smooth and rounders the further away they are from the center. + +
+ +If you play with the code you will discover that inside the triangle there is a negative area. Which in oposition makes shapes extremely sharp to the extreme. Because the values are under zero we can not see the diference but by changing ```fract()``` by ```sin()``` in line 42 you can see the triangle go shrink until disapear. This signed propertyis particular of **Signed Distance Fields**. + +Before going on deeper on Distance Field, let's learn more about moving, rotating and scaling our rectangles, circes and triangles. On the *Next* chapter we learn this and impruve our compositions. diff --git a/07/circle-making.frag b/07/circle-making.frag new file mode 100644 index 0000000..8dc8508 --- /dev/null +++ b/07/circle-making.frag @@ -0,0 +1,29 @@ +// Author @patriciogv - 2015 +// http://patriciogonzalezvivo.com +#ifdef GL_ES +precision mediump float; +#endif + +#define PI 3.14159265359 + +uniform vec2 u_resolution; +uniform float u_time; + +void main(){ + vec2 st = gl_FragCoord.xy/u_resolution; + + // a. The DISTANCE to the center whick is the + float pct = distance(st,vec2(0.5)); + + // b. The LENGTH to the vector to the center + // vec2 tC = vec2(0.5)-st; + // float pct = length(tC); + + // c. The SQUARE ROOT of the vector + // vec2 tC = vec2(0.5)-st; + // float pct = sqrt(tC.x*tC.x+tC.y*tC.y); + + vec3 color = vec3(pct); + + gl_FragColor = vec4( color, 1.0 ); +} \ No newline at end of file diff --git a/07/circle.frag b/07/circle.frag new file mode 100644 index 0000000..aa2ecf0 --- /dev/null +++ b/07/circle.frag @@ -0,0 +1,23 @@ +// Author @patriciogv - 2015 +// http://patriciogonzalezvivo.com +#ifdef GL_ES +precision mediump float; +#endif + +uniform vec2 u_resolution; +uniform float u_time; + +float circle(in vec2 _st, in float _radius){ + vec2 l = _st-vec2(0.5); + return 1.-smoothstep(_radius-(_radius*0.01), + _radius+(_radius*0.01), + dot(l,l)*4.0); +} + +void main(){ + vec2 st = gl_FragCoord.xy/u_resolution.xy; + + vec3 color = vec3(circle(st,0.9)); + + gl_FragColor = vec4( color, 1.0 ); +} \ No newline at end of file diff --git a/07/distance-field.jpg b/07/distance-field.jpg new file mode 100644 index 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    +
    + + + + + + + + \ No newline at end of file diff --git a/07/line.frag b/07/line.frag new file mode 100644 index 0000000..a387572 --- /dev/null +++ b/07/line.frag @@ -0,0 +1,39 @@ +#ifdef GL_ES +precision mediump float; +#endif + +uniform vec2 u_resolution; +uniform float u_time; + +float line( vec2 _st, + vec2 _p1, vec2 _p2, + float _width, float _spread){ + + _width = 1.0 / _width; + vec2 p2p1 = _p1 - _p2; + vec2 p1p2 = -(p2p1); + vec2 p2p = _st - _p2; + vec2 p1p = _st - _p1; + vec2 pp1 = -(p1p); + vec2 pd = normalize(vec2(p2p1.y, -p2p1.x)); + float proj = dot(pd, pp1); + float pr1 = dot(p2p1, p2p); + float pr2 = dot(p1p2, p1p); + + if(pr1 > 0.0 && pr2 > 0.0) { + return pow(1.0 / abs(proj * _width), _spread); + } else { + return 0.0; + } +} + +void main(){ + vec2 st = gl_FragCoord.xy/u_resolution.xy; + + vec3 color = vec3( line(st, + vec2(0.1), + vec2(0.9), + 0.005, 3.0) ); + + gl_FragColor = vec4(color,1.0); +} \ No newline at end of file diff --git a/07/rect-making-00.frag b/07/rect-making-00.frag new file mode 100644 index 0000000..f43b657 --- /dev/null +++ b/07/rect-making-00.frag @@ -0,0 +1,20 @@ +// Author @patriciogv - 2015 +// http://patriciogonzalezvivo.com +#ifdef GL_ES +precision mediump float; +#endif + +uniform vec2 u_resolution; +uniform float u_time; + +void main(){ + vec2 st = gl_FragCoord.xy/u_resolution.xy; + vec3 color = vec3(0.0); + + float left = step(0.1,st.x); + float bottom = step(0.1,st.y); + + color = vec3( left * bottom ); + + gl_FragColor = vec4(color,1.0); +} diff --git a/07/rect-making-01.frag b/07/rect-making-01.frag new file mode 100644 index 0000000..1956ed9 --- /dev/null +++ b/07/rect-making-01.frag @@ -0,0 +1,25 @@ +// Author @patriciogv - 2015 +// http://patriciogonzalezvivo.com +#ifdef GL_ES +precision mediump float; +#endif + +uniform vec2 u_resolution; +uniform float u_time; + +void main(){ + vec2 st = gl_FragCoord.xy/u_resolution.xy; + vec3 color = vec3(0.0); + + // Right & Bottom + vec2 rgBt = step(vec2(0.1),st); + float pct = rgBt.x * rgBt.y; + + // Left & top +// vec2 lfTp = step(vec2(0.1),1.0-st); +// pct *= lfTp.x * lfTp.y; + + color = vec3(pct); + + gl_FragColor = vec4(color,1.0); +} \ No newline at end of file diff --git a/07/rect.frag b/07/rect.frag new file mode 100644 index 0000000..2040315 --- /dev/null +++ b/07/rect.frag @@ -0,0 +1,27 @@ +// Author @patriciogv - 2015 +// http://patriciogonzalezvivo.com +#ifdef GL_ES +precision mediump float; +#endif + +uniform vec2 u_resolution; +uniform float u_time; + +float rect(in vec2 _st, in vec2 _size){ + _size = vec2(0.5) - _size*0.5; + vec2 uv = smoothstep(_size, + _size+vec2(0.001), + _st); + uv *= smoothstep(_size, + _size+vec2(0.001), + vec2(1.0)-_st); + return uv.x*uv.y; +} + +void main(){ + vec2 st = gl_FragCoord.xy/u_resolution.xy; + + vec3 color = vec3( rect(st, vec2(0.9)) ); + + gl_FragColor = vec4(color,1.0); +} \ No newline at end of file diff --git a/07/rect.jpg b/07/rect.jpg new file mode 100644 index 0000000000000000000000000000000000000000..14f63e97ebcacea58252929738038b60980971d1 GIT binary patch literal 117471 zcmeFZ1z43$w>N(8fK7LI2}ntIN|zwgDGegsy-5Y>RHRf=N;;)er4a-K>5$rhz((r7 zeV%ikH_mzA@5KB5&-t$F8({YDo_p@uv(~J8&6+i9xcPFk1Q4hxsVV^=5C~8~{Qx)1 zz!yb7M>_z})C4#H0Kfn+K==R{h0sxdE+B&6FdhnffrtPI>Jxx3 z;8+m*ztlms0OI@YSrSyelqZe=^k3>1p*{h5OBYucKvP+OpO=@x)7Hb$*7MhGuHWnY z{we3?_Slv|)!EYCmOEP5h~8Dzg#PLUD*c9U{RRo9XyaxRfg0#G9P{}u@@~k@3XY+wyu5|Bj+T zqALB?{vX-t^e@f`

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gl_FragCoord.xy/u_resolution.xy; + vec3 color = vec3(0.0); + + // Distance Field in 3 channels + float df = triangleDF(st, + vec2(0.40,0.45), + vec2(0.60,0.45), + vec2(0.5,0.60)); + color = vec3(df); + + // Make a shape of it + float size = fract(u_time*0.2); + float border = 0.025; + color.rb += smoothstep(size+border,size+1e-7,df)- + smoothstep(size+0.001,size+1e-7,df); + + gl_FragColor = vec4(color,1.0); +} \ No newline at end of file diff --git a/07/triangle.frag b/07/triangle.frag new file mode 100644 index 0000000..1c036df --- /dev/null +++ b/07/triangle.frag @@ -0,0 +1,46 @@ +// Author @patriciogv - 2015 +// http://patriciogonzalezvivo.com +#ifdef GL_ES +precision mediump float; +#endif + +#define PI 3.14159265358979323846 +#define TWO_PI 6.28318530717958647693 + +uniform vec2 u_resolution; +uniform float u_time; + +// Based on https://www.shadertoy.com/view/4sSSzG +float triangle (vec2 _st, + vec2 _p0, vec2 _p1, vec2 _p2, + float _smoothness){ + vec3 e0, e1, e2; + + e0.xy = 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Search for a specify quality on motion you are interested on (recording something from the *"real world"* first could be useful). It could be the come and go of the waves, a pendulum movement, a bouncing ball, a car accelerating, a bicycle stoping. + +### Rotations + +To rotate objects we also need to move the entire space system. For that we are going to use a [matrix](http://en.wikipedia.org/wiki/Matrix_%28mathematics%29). Matrixes are organized set of numbers in columns and rows, that are multiply by vectors following a precise set of rules, that modify the values of the vector in a particular way. + +![](matrixes.png) + +GLSL have native support for two, three and four dimensional matrixes: [```mat2```](http://www.shaderific.com/glsl-types/#2x2floatingpointmatrix) (2x2), [```mat3```](http://www.shaderific.com/glsl-types/#3x3floatingpointmatrix) (3x3) and [```mat4```](4x4floatingpointmatrix) (4x4) together with a matrix specific functions ( [```matrixCompMult()```](http://www.shaderific.com/glsl-functions/#componentwisematrixmultiplication) ) beside the multiplication (```*```) operator. + +Based on how matrixes behave is posible to construct matrixes that produces specific behaviur. For example we can use a matrix to translate a vector: + +![](3dtransmat.png) + +More interestingly, we can use a matrix to rotate the coordinate system. + +![](2drotmat.png) + +Take a look to the following code of a function that constructs a 2D rotation matrix. This function follows the above [formula](http://en.wikipedia.org/wiki/Rotation_matrix) that rotates the coordinates around the ```vec2(0.0)``` point. + +```glsl +mat2 rotate2d(float _angle){ + return mat2(cos(_angle),-sin(_angle), + sin(_angle),cos(_angle)); +} +``` + +According to the way we have been drawing shapes this is not exactly what we want. Our cross shape is draw in the center of the canvas which correspond to the position ```vec2(0.5)```. So before we rotate the space we need to move shape from the `center` to the ```vec2(0.0)``` coordinate, then rotate the space to finally move it back to the original place. + +
    + +Note that we need to multiply the rotation matrix for the position vector to return a rotated vector which in our example is just the original position variable that we are over writing. If you want to rotate different elements in different proportions you need to “preserve” the original coordinate system by assigning another vector. + +Try the following excersices: + +* Uncomment line 40 of above code and pay atention to what happens. + +* Comment the translations before and after the rotations on line 35 and 37 and observe the consecuences. + +* Use rotations to improve the animation you simulate in the translation exercise. + +### Scale + +So we saw how matrixes were use to translate and rotate object on space (more precise transform the coordinate system and by that rotate and move them). If you have use 3D modeling software or if you have use some push and pop matrix function in processing you will know that also matrixes can be use to scale the size of an object. + +![](3dscalemat.png) + +Following the previus formula we can understand how to make a 2D scaling matrix. + +```glsl +mat2 scale(vec2 _scale){ + return mat2(_scale.x,0.0, + 0.0,_scale.y); +} +``` + +
    + +Do the following excersises to understand deeply how it works + +* Uncommenting line 40 of above code to see the space coordinate being scale. + +* See what happens when you comment the translations before and after the scaling on line 35 and 37. + +* Try combining a rotation matrix together with a scale matrix. Be aware that the order matters. Multiply the matrix first and at the end the vectors. + +* Now that you know how to do draw different shapes, and move, rotate and scale them is time to make a nice composition. Design and construct a [fake UI or HUD (heads up display)](https://www.pinterest.com/patriciogonzv/huds/). Use the following ShaderToy example by [Ndel](https://www.shadertoy.com/user/ndel) as inspiration and reference. + + + +### Other uses for matrixes: color - YUV + +[YUV](http://en.wikipedia.org/wiki/YUV) is a color space use for analog encoding of photos and videos that use the range of human perception to reduce the bandwidth of chrominance components. + +The following code is an interesting opportunity to use [matrix](http://en.wikipedia.org/wiki/Matrix_(mathematics)) operations on GLSL to transform colors from one mode to the other one. + +
    + +As you can see we are treating colors as vectors by multiplying them to matrices. In that way we “move” the values arround. + diff --git a/08/cross-rotate.frag b/08/cross-rotate.frag new file mode 100644 index 0000000..84e9703 --- /dev/null +++ b/08/cross-rotate.frag @@ -0,0 +1,48 @@ +// Author @patriciogv - 2015 +// http://patriciogonzalezvivo.com +#ifdef GL_ES +precision mediump float; +#endif + +#define PI 3.14159265359 + +uniform vec2 u_resolution; +uniform float u_time; + +mat2 rotate2d(float _angle){ + return mat2(cos(_angle),-sin(_angle), + sin(_angle),cos(_angle)); +} + +float box(in vec2 _st, in vec2 _size){ + _size = vec2(0.5) - _size*0.5; + vec2 uv = smoothstep(_size, + _size+vec2(0.001), + _st); + uv *= smoothstep(_size, + _size+vec2(0.001), + vec2(1.0)-_st); + return uv.x*uv.y; +} + +float cross(in vec2 _st, float _size){ + return box(_st, vec2(_size,_size/4.)) + + box(_st, vec2(_size/4.,_size)); +} + +void main(){ + vec2 st = gl_FragCoord.xy/u_resolution.xy; + vec3 color = vec3(0.0); + + st -= vec2(0.5); + st = rotate2d( sin(u_time)*PI ) * st; + st += vec2(0.5); + + // Show the coordinates of the space on the background + // color = vec3(st.x,st.y,0.0); + + // Add the shape on the foreground + color += vec3(cross(st,0.4)); + + gl_FragColor = vec4(color,1.0); +} \ No newline at end of file diff --git a/08/cross-scale.frag b/08/cross-scale.frag new file mode 100644 index 0000000..c3dabe9 --- /dev/null +++ b/08/cross-scale.frag @@ -0,0 +1,48 @@ +// Author @patriciogv - 2015 +// http://patriciogonzalezvivo.com +#ifdef GL_ES +precision mediump float; +#endif + +#define PI 3.14159265359 + +uniform vec2 u_resolution; +uniform float u_time; + +mat2 scale(vec2 _scale){ + return mat2(_scale.x,0.0, + 0.0,_scale.y); +} + +float box(in vec2 _st, in vec2 _size){ + _size = vec2(0.5) - _size*0.5; + vec2 uv = smoothstep(_size, + _size+vec2(0.001), + _st); + uv *= smoothstep(_size, + _size+vec2(0.001), + vec2(1.0)-_st); + return uv.x*uv.y; +} + +float cross(in vec2 _st, float _size){ + return box(_st, vec2(_size,_size/4.)) + + box(_st, vec2(_size/4.,_size)); +} + +void main(){ + vec2 st = gl_FragCoord.xy/u_resolution.xy; + vec3 color = vec3(0.0); + + st -= vec2(0.5); + st = scale( vec2(sin(u_time)+1.0) ) * st; + st += vec2(0.5); + + // Show the coordinates of the space on the background + // color = vec3(st.x,st.y,0.0); + + // Add the shape on the foreground + color += vec3(cross(st,0.2)); + + gl_FragColor = vec4(color,1.0); +} \ No newline at end of file diff --git a/08/cross-translate.frag b/08/cross-translate.frag new file mode 100644 index 0000000..6cb39c2 --- /dev/null +++ b/08/cross-translate.frag @@ -0,0 +1,41 @@ +// Author @patriciogv - 2015 +// http://patriciogonzalezvivo.com +#ifdef GL_ES +precision mediump float; +#endif + +uniform vec2 u_resolution; +uniform float u_time; + +float box(in vec2 _st, in vec2 _size){ + _size = vec2(0.5) - _size*0.5; + vec2 uv = smoothstep(_size, + _size+vec2(0.001), + _st); + uv *= smoothstep(_size, + _size+vec2(0.001), + vec2(1.0)-_st); + return uv.x*uv.y; +} + +float cross(in vec2 _st, float _size){ + return box(_st, vec2(_size,_size/4.)) + + box(_st, vec2(_size/4.,_size)); +} + +void main(){ + vec2 st = gl_FragCoord.xy/u_resolution.xy; + vec3 color = vec3(0.0); + + // To move the cross we move the space + vec2 translate = vec2(cos(u_time),sin(u_time)); + st += translate*0.35; + + // Show the coordinates of the space on the background + // color = vec3(st.x,st.y,0.0); + + // Add the shape on the foreground + color += vec3(cross(st,0.25)); + + gl_FragColor = vec4(color,1.0); +} \ No newline at end of file diff --git a/08/cross.frag b/08/cross.frag new file mode 100644 index 0000000..3d4ee51 --- /dev/null +++ b/08/cross.frag @@ -0,0 +1,27 @@ +// Author @patriciogv - 2015 +// http://patriciogonzalezvivo.com +#ifdef GL_ES +precision mediump float; +#endif + +uniform vec2 u_resolution; +uniform float u_time; + +float box(vec2 _st, vec2 _size){ + _size = vec2(0.5) - _size*0.5; + vec2 uv = smoothstep(_size, + _size+vec2(0.0001), + _st); + uv *= smoothstep(_size, + _size+vec2(0.0001), + vec2(1.0)-_st); + return uv.x*uv.y; +} + +void main(){ + vec2 st = gl_FragCoord.xy/u_resolution.xy; + + vec3 color = vec3( box(st, vec2(0.4,0.1)) + box(st, vec2(0.1,0.4)) ); + + gl_FragColor = vec4(color,1.0); +} \ No newline at end of file diff --git a/08/index.html b/08/index.html new file mode 100644 index 0000000..0d6d2bb --- /dev/null +++ b/08/index.html @@ -0,0 +1,70 @@ + + + + + + + Matrix + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
    +
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+uniform vec2 u_resolution; +uniform float u_time; + +mat3 yuv2rgb = mat3(1.0, 0.0, 1.13983, + 1.0, -0.39465, -0.58060, + 1.0, 2.03211, 0.0); + +mat3 rgb2yuv = mat3(0.2126, 0.7152, 0.0722, + -0.09991, -0.33609, 0.43600, + 0.615, -0.5586, -0.05639); + +void main(){ + vec2 st = gl_FragCoord.xy/u_resolution; + vec3 color = vec3(0.0); + + st -= 0.5; + st *= 2.0; + color = yuv2rgb * vec3(0.5, st.x, st.y); + + gl_FragColor = vec4(color,1.0); +} \ No newline at end of file diff --git a/09/README.md b/09/README.md new file mode 100644 index 0000000..e71ecfd --- /dev/null +++ b/09/README.md @@ -0,0 +1,81 @@ +## Patterns + +Because in a shader programs are executed by pixel-by-pixel it doesn't really matters how much your repeat a shape. The number of calculations stays constant. That means that fragments shaders can be a particulary suitable tile patterns. + +![Nina Warmerdam - The IMPRINT Project (2013)](warmerdam.jpg) + +In the following chapter we are going to apply what we have learn so far an repeat it a long a canvas. Like the previous chapters our strategy is going to be based on multiplying the space coordenates (between 0.0 and 1.0) so the shapes we have been drawing in space between the values 0.0 and 1.0 will be repeated making a grid subscapes. + +*"The grid provide a framwrok withing which human intuition and ivention can operate and that it can subvert. Whitin the chaos of nature patterns provide a constrast and promise of order. From early paterns on pottery to geometric mosaics in Roman baths, people have long used grids to enhace their lives with decoration."* [*10 PRINT*, Mit Press, (2013)](http://10print.org/) + +First lets remember the [```fract()```](http://www.shaderific.com/glsl-functions/#fractionalpart) function, which is in esense the modulo of one (```mod(x,1.0)```), because return the fraction part of a number. On other words the number after the floating point. Our normalized coordinate system variable (```st```) already goes from 0.0 to 1.0 so it doesn't make sense to do something like: + +```glsl +void main(){ + vec2 st = gl_FragCoord.xy/u_resolution; + vec3 color = vec3(0.0); + st = fract(st); + color = vec3(st,0.0); + gl_FragColor = vec4(color,1.0); +} +``` + +But if we scale the normalized coordinate system up, let's say by three we will get three sequence of linear interpolations between 0-1, the first one between 0-1 and the second one for the floating points between 1-2 and the third one for the floating points after 2 and before 3. + +
    + +Now is time to draw something on each subspace in the same way we did on previus chapters, by uncomenting line 23. Because we are multiplying equally en x and y the aspect ratio of the space doesn't change and shapes on them will be as expected. + +Try some of the following excersices to get a deeper + +* Try different numbers to multiply the space. Try with floating point values and also with different values for x and y. + +* Make a re usable function of this tiling trick. + +* Dividing the space on 3 rows and 3 columns find a way to know in which column and row the thread is and use that to change the shape that is displaying. Try to compose a tic-tac-toe match. + +### Apply matrixes inside patterns + +Because each subdivision or cell is a smaller version of the normalized coordinate system we have been using before we can apply a matrix transformation to it in order to translate, rotate or scale the space inside. + +
    + +### Offset patterns + +So let's say we want to imitate how brick walls looks like. Pay attention to it, is immediately evident the presence of a half bridge offset on x every other row. How we can do that? + +![](brick.jpg) + +As a first step we need to know if the row of our thread is an even or un-even number, because we can use that to determine if we need to offset the x is necessary. + +For that we are going to use ```fract()``` again but with the coordinates at the double of space. Take a look to the folowing formula and how it looks like. + +
    + +By multiplying *x* by a half the space coordinate duplicate it size (which is the oposite of what we have been doing where we multiply the ```st``` and the space got shrinked). Let's say we are in position 1.0 (not even) we divide by two will be 0.5, while if the position was 2.0 (even) we devide by two the result will be 1.0. For values over 2.0, ```fract()``` will wrap them up and start again and again. This means the return value of this function will give numbers bellow 0.5 for not even numbers and above 0.5 for even. Isn't this super help full? + +Now we can apply some offset to not even rows to give some *brick* effect to our tiles. Check line number 10 and 11 of the following code: + +
    + +## Truchet Tiles + +Now that we had learn ways to know if our cell is on even or un even rows and columns is possible to reuse a single design element depending on their position. Conside the case of the [Truchet Tiles](http://en.wikipedia.org/wiki/Truchet_tiles) where a single design element can be presented in four diferent ways: + +![](truchet-00.png) + +By changing the patter acros tiles is possible to contruct infinite set of complex designs. + +![](truchet-01.png) + +Pay close attention to the function ```rotateTilePattern()``` and subdivide the space in four cells and assign one angle of rotation for each one. + +
    + +* Comment, uncomment and duplicate lines 51 to 54 for to compose new designs. + +## Making your own rules + +Making procedural patterns is a mental excercise for finding minimal an reusable elements. This practice is particulary old, we as a specie have been using grids and patterns to decorate textules, floors and borders of objects since a long time. The pleasure of repetition and variation, have mesmarize our imagination for a long time. Take your time to look [decorative patterns](https://www.pinterest.com/patriciogonzv/paterns/), see how artist and designers have challenge a long the history the fine edge between predictibility of order and the surprise of variation and chaos. 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z?O0h3Cq(`j(=gUgZ5s)qk1kYi2d-51JY&-xt3;OLQ6jqVrkAJ9X(V>&{(aiO;y?)7 zg&cGs@_7VMqL{2<+;}5OmOrx15pfi=squRpxM)zal0uAu->-kKw-i!b*SVyqr0hwj_;XFv c<+6(A-8S6D<-i@n6UK8;nX;iCR{L20+3XrQ%K!iX literal 0 HcmV?d00001 diff --git a/09/bricks.frag b/09/bricks.frag new file mode 100644 index 0000000..4c16354 --- /dev/null +++ b/09/bricks.frag @@ -0,0 +1,39 @@ +// Author @patriciogv - 2015 +// http://patriciogonzalezvivo.com +#ifdef GL_ES +precision mediump float; +#endif + +uniform vec2 u_resolution; +uniform float u_time; + +vec2 brickTile(vec2 _st, float _zoom){ + _st *= _zoom; + if (fract(_st.y * 0.5) > 0.5){ + _st.x += 0.5; + } + return fract(_st); +} + +float box(vec2 _st, vec2 _size){ + _size = vec2(0.5)-_size*0.5; + vec2 uv = smoothstep(_size,_size+vec2(1e-4),_st); + uv *= smoothstep(_size,_size+vec2(1e-4),vec2(1.0)-_st); + return uv.x*uv.y; +} + +void main(void){ + vec2 st = gl_FragCoord.xy/u_resolution.xy; + vec3 color = vec3(0.0); + + // Modern metric brick of 215mm x 102.5mm x 65mm + // http://www.jaharrison.me.uk/Brickwork/Sizes.html + // st /= vec2(2.15,0.65)/1.5; + + st = brickTile(st,5.0); + + color = vec3(box(st,vec2(0.95))); + // color = vec3(st,0.0); + + gl_FragColor = vec4(color,1.0); +} \ No newline at end of file diff --git a/09/checks.frag b/09/checks.frag new file mode 100644 index 0000000..d0a75f4 --- /dev/null +++ b/09/checks.frag @@ -0,0 +1,43 @@ +// Author @patriciogv - 2015 +// http://patriciogonzalezvivo.com +#ifdef GL_ES +precision mediump float; +#endif + +uniform vec2 u_resolution; +uniform float u_time; + +#define PI 3.14159265358979323846 + +vec2 rotate2D(vec2 _st, float _angle){ + _st -= 0.5; + _st = mat2(cos(_angle),-sin(_angle), + sin(_angle),cos(_angle)) * _st; + _st += 0.5; + return _st; +} + +vec2 tile(vec2 _st, float _zoom){ + _st *= _zoom; + return fract(_st); +} + +float box(vec2 _st, vec2 _size, float _smoothEdges){ + _size = vec2(0.5)-_size*0.5; + vec2 aa = vec2(_smoothEdges*0.5); + vec2 uv = smoothstep(_size,_size+aa,_st); + uv *= smoothstep(_size,_size+aa,vec2(1.0)-_st); + return uv.x*uv.y; +} + +void main(void){ + vec2 st = gl_FragCoord.xy/u_resolution.xy; + vec3 color = vec3(0.0); + + st = tile(st,4.); + st = rotate2D(st,PI*0.25); + color = vec3(box(st,vec2(0.7),0.01)); + // color = vec3(st,0.0); + + gl_FragColor = vec4(color,1.0); +} \ No newline at end of file diff --git a/09/diamondtiles.frag b/09/diamondtiles.frag new file mode 100644 index 0000000..eb2a405 --- /dev/null +++ b/09/diamondtiles.frag @@ -0,0 +1,59 @@ +// Author @patriciogv - 2015 +// http://patriciogonzalezvivo.com +#ifdef GL_ES +precision mediump float; +#endif + +#define PI 3.14159265358979323846 + +uniform vec2 u_resolution; +uniform float u_time; + +vec2 rotate2D(vec2 _st, float _angle){ + _st -= 0.5; + _st = mat2(cos(_angle),-sin(_angle), + sin(_angle),cos(_angle)) * _st; + _st += 0.5; + return _st; +} + +vec2 tile(vec2 _st, float _zoom){ + _st *= _zoom; + return fract(_st); +} + +float box(vec2 _st, vec2 _size, float _smoothEdges){ + _size = vec2(0.5)-_size*0.5; + vec2 aa = vec2(_smoothEdges*0.5); + vec2 uv = smoothstep(_size,_size+aa,_st); + uv *= smoothstep(_size,_size+aa,vec2(1.0)-_st); + return uv.x*uv.y; +} + +vec2 offset(vec2 _st, vec2 _offset){ + vec2 uv; + if(_st.x>0.5){ + uv.x = _st.x - 0.5; + } else { + uv.x = _st.x + 0.5; + } + if(_st.y>0.5){ + uv.y = _st.y - 0.5; + }else { + uv.y = _st.y + 0.5; + } + return uv; +} + +void main(void){ + vec2 st = gl_FragCoord.xy/u_resolution.xy; + st = tile(st,5.); + + vec2 offsetSt = offset(st,vec2(0.5)); + + st = rotate2D(st,PI*0.25); + + vec3 color = vec3( box(offsetSt,vec2(0.95),0.01) - box(st,vec2(0.3),0.01) + 2.*box(st,vec2(0.2),0.01) ); + + gl_FragColor = vec4(color,1.0); +} \ No newline at end of file diff --git a/09/geometricpatters.png b/09/geometricpatters.png new file mode 100644 index 0000000000000000000000000000000000000000..01bcb43b3f84a8e05dbf9149fe69d7a01811288c GIT binary patch literal 2682300 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      +
      +
      +
      + + + + + + + + \ No newline at end of file diff --git a/09/mirrortiles.frag b/09/mirrortiles.frag new file mode 100644 index 0000000..4a8c6dd --- /dev/null +++ b/09/mirrortiles.frag @@ -0,0 +1,36 @@ +// Author @patriciogv - 2015 +// http://patriciogonzalezvivo.com +#ifdef GL_ES +precision mediump float; +#endif + +#define PI 3.14159265358979323846 + +uniform vec2 u_resolution; +uniform float u_time; + +float fillX(vec2 _st, float _pct,float _antia){ + return smoothstep( _pct-_antia, _pct, _st.x); +} + +float fillY(vec2 _st, float _pct,float _antia){ + return smoothstep( _pct-_antia, _pct, _st.y); +} + +vec2 mirrorTile(vec2 _st, float _zoom){ + _st *= _zoom; + if (fract(_st.y * 0.5) > 0.5){ + _st.y = 1.0-_st.y; + } + return fract(_st); +} + +void main(){ + vec2 st = gl_FragCoord.xy/u_resolution.xy; + vec3 color = vec3(0.0); + + st = mirrorTile(st,5.0); + color = vec3(fillY(st,0.5+sin(st.x*PI*2.0)*0.45,0.02)); + + gl_FragColor = vec4( color, 1.0 ); +} \ No newline at end of file diff --git a/09/nuts.frag b/09/nuts.frag new file mode 100644 index 0000000..a9990e2 --- /dev/null +++ b/09/nuts.frag @@ -0,0 +1,49 @@ +// Author @patriciogv - 2015 +// http://patriciogonzalezvivo.com +#ifdef GL_ES +precision mediump float; +#endif + +#define PI 3.14159265358979323846 + +uniform vec2 u_resolution; +uniform float u_time; + +float rows = 10.0; + +vec2 brickTile(vec2 _st, float _zoom){ + _st *= _zoom; + if (fract(_st.y * 0.5) > 0.5){ + _st.x += 0.5; + } + return fract(_st); +} + +vec2 rotate2D(vec2 _st, float _angle){ + _st -= 0.5; + _st = mat2(cos(_angle),-sin(_angle), + sin(_angle),cos(_angle)) * _st; + _st += 0.5; + return _st; +} + +void main(){ + + vec2 st = gl_FragCoord.xy/u_resolution.xy; + st = brickTile(st,rows); + + float angle = PI*0.25*cos(u_time*0.5); + + if (fract( (gl_FragCoord.y/u_resolution.y) * 0.5 * rows) > 0.5){ + angle *= -1.0; + } + + st = rotate2D(st,angle); + + st *= 2.0; + float pct = (1.0+cos(PI*st.x))*0.5; + + vec3 color = vec3( 1.0-smoothstep( 0.5,0.6, pow(pct,st.y) ) * 1.0-smoothstep( 0.79,0.81, pow(pct,2.0-st.y ) ) ); + + gl_FragColor = vec4(color,1.0); +} \ No newline at end of file diff --git a/09/rotatedtiles.frag b/09/rotatedtiles.frag new file mode 100644 index 0000000..8004890 --- /dev/null +++ b/09/rotatedtiles.frag @@ -0,0 +1,91 @@ +// Author @patriciogv - 2015 +// http://patriciogonzalezvivo.com +#ifdef GL_ES +precision mediump float; +#endif + +#define PI 3.14159265358979323846 +#define TWO_PI 6.28318530717958647693 + +uniform vec2 u_resolution; +uniform float u_time; + +vec2 rotate2D (vec2 _st, float _angle) { + _st -= 0.5; + _st = mat2(cos(_angle),-sin(_angle), + sin(_angle),cos(_angle)) * _st; + _st += 0.5; + return _st; +} + +vec2 tile (vec2 _st, float _zoom) { + _st *= _zoom; + return fract(_st); +} + +vec2 rotateTile(vec2 _st){ + _st *= 2.0; + + float index = 0.0; + if (fract(_st.x * 0.5) > 0.5){ + index += 1.0; + } + if (fract(_st.y * 0.5) > 0.5){ + index += 2.0; + } + + _st = fract(_st); + + if(index == 1.0){ + _st = rotate2D(_st,PI*0.5); + } else if(index == 2.0){ + _st = rotate2D(_st,PI*-0.5); + } else if(index == 3.0){ + _st = rotate2D(_st,PI); + } + + return _st; +} + +// Based on https://www.shadertoy.com/view/4sSSzG +float triangle (vec2 _st, + vec2 _p0, vec2 _p1, vec2 _p2, + float _smoothness) { + vec3 e0, e1, e2; + + e0.xy = normalize(_p1 - _p0).yx * vec2(+1.0, -1.0); + e1.xy = normalize(_p2 - _p1).yx * vec2(+1.0, -1.0); + e2.xy = normalize(_p0 - _p2).yx * vec2(+1.0, -1.0); + + e0.z = dot(e0.xy, _p0) - _smoothness; + e1.z = dot(e1.xy, _p1) - _smoothness; + e2.z = dot(e2.xy, _p2) - _smoothness; + + float a = max(0.0, dot(e0.xy, _st) - e0.z); + float b = max(0.0, dot(e1.xy, _st) - e1.z); + float c = max(0.0, dot(e2.xy, _st) - e2.z); + + return smoothstep(_smoothness * 2.0, + 1e-7, + length(vec3(a, b, c))); +} + +void main (void) { + vec2 st = gl_FragCoord.xy/u_resolution.xy; + + st = tile(st,3.0); + st = rotateTile(st); + + float pattern = 0.0; + + st = rotate2D(st,-PI*u_time*0.25); + pattern = triangle(st, + vec2(0.30,-0.5), + vec2(0.70,0.-0.5), + vec2(0.5,1.0), + 0.01); + + vec3 color = vec3(pattern); + + gl_FragColor = vec4(color,1.0); +} \ No newline at end of file diff --git a/09/sidegrid.frag b/09/sidegrid.frag new file mode 100644 index 0000000..dab93af --- /dev/null +++ b/09/sidegrid.frag @@ -0,0 +1,36 @@ +// Author @patriciogv - 2015 +// http://patriciogonzalezvivo.com +#ifdef GL_ES +precision mediump float; +#endif + +#define PI 3.14159265358979323846 +#define TWO_PI 6.28318530717958647693 +#define PHI 1.618033988749894848204586834 + +uniform vec2 u_resolution; +uniform float u_time; + +vec2 tile(vec2 _st, float _zoom){ + _st *= _zoom; + return fract(_st); +} + +float X(vec2 _st, float _width){ + float pct0 = smoothstep(_st.x-_width,_st.x,_st.y); + pct0 *= 1.-smoothstep(_st.x,_st.x+_width,_st.y); + + float pct1 = smoothstep(_st.x-_width,_st.x,1.0-_st.y); + pct1 *= 1.-smoothstep(_st.x,_st.x+_width,1.0-_st.y); + + return 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_pct+0.01, _st.y); +} + +float random (in float _x) { + return fract(sin(_x)*1e4); +} + +void main() { + vec2 st = gl_FragCoord.xy/u_resolution.xy; + st.x *= u_resolution.x/u_resolution.y; + vec3 color = vec3(0.0); + + float y = random(st.x*0.001+u_time); + + // color = vec3(y); + float pct = plot(st,y); + color = (1.0-pct)*color+pct*vec3(0.0,1.0,0.0); + + gl_FragColor = vec4(color,1.0); +} \ No newline at end of file diff --git a/10/2d-random-mosaic.frag b/10/2d-random-mosaic.frag new file mode 100644 index 0000000..7714ef0 --- /dev/null +++ b/10/2d-random-mosaic.frag @@ -0,0 +1,30 @@ +// Author @patriciogv - 2015 +// http://patriciogonzalezvivo.com +#ifdef GL_ES +precision mediump float; +#endif + +uniform vec2 u_resolution; +uniform float u_time; + +float random (in vec2 _st) { + return fract(sin(dot(_st.xy, + vec2(12.9898,78.233)))* + 43758.5453123); +} + +void main() { + vec2 st = gl_FragCoord.xy/u_resolution.xy; + st *= 10.0; + + vec2 ivec = floor(st); // integer + vec2 fvec = fract(st); // fraction + + // Assign a random value base on the integer coord + vec3 color = vec3(random( ivec )); + + // Un comment to see the subdivided grid + // color = vec3(fvec,0.0); + + gl_FragColor = vec4(color,1.0); +} \ No newline at end of file diff --git a/10/2d-random-truchet.frag b/10/2d-random-truchet.frag new file mode 100644 index 0000000..bf8de2f --- /dev/null +++ b/10/2d-random-truchet.frag @@ -0,0 +1,57 @@ +// Author @patriciogv - 2015 +// http://patriciogonzalezvivo.com +#ifdef GL_ES +precision mediump float; +#endif + +#define PI 3.14159265358979323846 + +uniform vec2 u_resolution; +uniform float u_time; + +float random (in vec2 _st) { + return fract(sin(dot(_st.xy, + vec2(12.9898,78.233)))* + 43758.5453123); +} + +vec2 truchetPattern(in vec2 _st, in float _index){ + _index = fract(((_index-0.5)*2.0)); + if (_index > 0.75) { + _st = vec2(1.0) - _st; + } else if (_index > 0.5) { + _st = vec2(1.0-_st.x,_st.y); + } else if (_index > 0.25) { + _st = 1.0-vec2(1.0-_st.x,_st.y); + } + return _st; +} + +void main() { + vec2 st = gl_FragCoord.xy/u_resolution.xy; + st *= 10.0; + // st = (st-vec2(5.0))*(abs(sin(u_time*0.2))*5.); + // st.x += u_time*3.0; + + vec2 ivec = floor(st); // integer + vec2 fvec = fract(st); // fraction + + vec2 tile = truchetPattern(fvec, random( ivec )); + + float color = 0.0; + + // Maze + color = smoothstep(tile.x-0.3,tile.x,tile.y)- + smoothstep(tile.x,tile.x+0.3,tile.y); + + // Circles + // color = (step(length(tile),0.6) - + // step(length(tile),0.4) ) + + // (step(length(tile-vec2(1.)),0.6) - + // step(length(tile-vec2(1.)),0.4) ); + + // Truchet (2 triangles) + // color = step(tile.x,tile.y); + + gl_FragColor = vec4(vec3(color),1.0); +} \ No newline at end of file diff --git a/10/2d-random.frag b/10/2d-random.frag new file mode 100644 index 0000000..a4d7c48 --- /dev/null +++ b/10/2d-random.frag @@ -0,0 +1,22 @@ +// Author @patriciogv - 2015 +// http://patriciogonzalezvivo.com +#ifdef GL_ES +precision mediump float; +#endif + +uniform vec2 u_resolution; +uniform float u_time; + +float random (in vec2 _st) { + return fract(sin(dot(_st.xy, + vec2(12.9898,78.233)))* + 43758.5453123); +} + +void main() { + vec2 st = gl_FragCoord.xy/u_resolution.xy; + + float rnd = random( st ); + + gl_FragColor = vec4(vec3(rnd),1.0); +} \ No newline at end of file diff --git a/10/README.md b/10/README.md new file mode 100644 index 0000000..1c6e344 --- /dev/null +++ b/10/README.md @@ -0,0 +1,47 @@ +# Generative designs + +Is not a surprise that after so much repetition and order the author is force to bring some chaos. + +## Random + +Random is a maximal expression of entropy, but how to generate random inside such predictible, constant and rigid enviroment? + +Let's start for analizing the following function: + +

      + +As you can see, we are extracting only the fractional part of a sine wave. We have done this in the past. We can apreciate and understand how the ```sin()``` function that returns values between ```-1``` and ```1``` have been braked only and forced to be all positive values. We are going to use this effect for our purposes of achinving some random values by "breaking" this sine wave in smaller and smaller pieces. Why? by multiplying the ```sin(x)``` for bigger numbers. Go a head and click on the function and start adding some zeros. + +By the time you get to 100000 ( and the equation looks like this: ```y = fract(sin(x)*100000.0)``` ) you probably are not hable to distinguish the sine wave any more. The granulary of the fractions have corrupt the flow of the sine in random chaos. + +## 2D Random + +Now is time to apply this same principle on both *x* and *y* axis. For that we need a way to transform a two dimensional vector into a one dimensional float point value. There are different ways to do this, but the ```dot()``` function can be very particulary helpfull in this case, becuse of it avility to return a float values between 0 and 1 depending if two vectors are align. + +
      + +Take a look to line 11 and 12 and how we are comparing the ```in vec2 _st``` with a ___ vector ( ```vec2(12.9898,78.233)```). + +* Try changing the values on lines 12 and 13. See how the random pattern change and what we can learn from it. + +## Using the chaos + +Actually randomness in pure form can be too chaotic, letres try to balance it entropy with some order. + +Take close look to the following code. Specially on lines 20 and 21. + +
      + +After scaling the space ten times more (line 10), we separate the integers of the coordenates from the fractions. We are familiar with this last operation because we have been usign it to subdevide a space in smaller cells that consistantly go from 0 to 1. By obtaining the integer of the coordinate we isolate a common value for all the threads inside a cell, to then use that integer to obtain a random value. Because the random is deterministic will be constant for all the pixels on that cell as long the random function is the same for all the threads. + +Combining this two values will allow you to mix variation and order. + +Take a look to this GLSL port of the famouse ```10 PRINT CHR$(205.5+RND(1)); : GOTO 10``` maze generator. + +
      + +You can get an interesting variation by uncommenting the block of lines from 48 to 51. In case you want to animate it you can uncoment lines 33 and 34. + +Using random aesthetically can be problematic. It's simply too chaotic and not really to many things looks ```random()``` in real life. Usually estocastic values are some how related to the previus one. If you look to a rain pattern, or the wallstreet chart (which both quite random), they are nothing like the random pattern we made at the begining of this chapter. The reason? Well random values have no correlation between them what so ever. + +On the *Next* chapter we will learn about noise, the smooth and *natural looking* way of computational chaos. diff --git a/10/index.html b/10/index.html new file mode 100644 index 0000000..ccf1bcf --- /dev/null +++ b/10/index.html @@ -0,0 +1,72 @@ + + + + + + + Random + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
      +
      +
      + +
      + + + + + + + + + \ No newline at end of file diff --git a/10/truchet.frag b/10/truchet.frag new file mode 100644 index 0000000..0cf9d71 --- /dev/null +++ b/10/truchet.frag @@ -0,0 +1,59 @@ +// Author @patriciogv - 2015 +// http://patriciogonzalezvivo.com + +#ifdef GL_ES +precision mediump float; +#endif + +#define PI 3.14159265358979323846 + +uniform vec2 u_resolution; +uniform float u_time; + +vec2 rotate2D (vec2 _st, float _angle) { + _st -= 0.5; + _st = mat2(cos(_angle),-sin(_angle), + sin(_angle),cos(_angle)) * _st; + _st += 0.5; + return _st; +} + +vec2 tile (vec2 _st, float _zoom) { + _st *= _zoom; + return fract(_st); +} + +vec2 rotateTilePattern(vec2 _st){ + _st *= 2.0; + + float index = 0.0; + if (fract(_st.x * 0.5) > 0.5){ + index += 1.0; + } + if (fract(_st.y * 0.5) > 0.5){ + index += 2.0; + } + + _st = fract(_st); + + if(index == 1.0){ + _st = rotate2D(_st,PI*0.5); + } else if(index == 2.0){ + _st = rotate2D(_st,PI*-0.5); + } else if(index == 3.0){ + _st = rotate2D(_st,PI); + } + + return _st; +} + +void main (void) { + vec2 st = gl_FragCoord.xy/u_resolution.xy; + + st = tile(st,3.0); + st = rotateTilePattern(st); + // st = tile(st,3.0); + // st = rotate2D(st,-PI*u_time*0.25); + + gl_FragColor = vec4(vec3(step(st.x,st.y)),1.0); +} \ No newline at end of file diff --git a/11/1d-noise.frag b/11/1d-noise.frag new file mode 100644 index 0000000..9a1314c --- /dev/null +++ b/11/1d-noise.frag @@ -0,0 +1,40 @@ +#ifdef GL_ES +precision mediump float; +#endif + +uniform vec2 u_resolution; +uniform float u_time; + +float plot(vec2 _st, float _pct){ + return smoothstep( _pct-0.01, _pct, _st.y) - + smoothstep( _pct, _pct+0.01, _st.y); +} + +float random (in float _x) { + return fract(sin(_x)*1e4); +} + +// Based on Morgan McGuire @morgan3d +// https://www.shadertoy.com/view/4dS3Wd +float noise (in float _x) { + float i = floor(_x); + float f = fract(_x); + float u = f * f * (3.0 - 2.0 * f); + return mix(random(i), random(i + 1.0), u); +} + +void main() { + vec2 st = gl_FragCoord.xy/u_resolution.xy; + st.x *= u_resolution.x/u_resolution.y; + vec3 color = vec3(0.0); + + float y = 0.0; + // y = random(st.x*0.001+u_time); + y = noise(st.x*3.+u_time); + + // color = vec3(y); + float pct = plot(st,y); + color = (1.0-pct)*color+pct*vec3(0.0,1.0,0.0); + + gl_FragColor = vec4(color,1.0); +} \ No newline at end of file diff --git a/11/2d-noise.frag b/11/2d-noise.frag new file mode 100644 index 0000000..7360584 --- /dev/null +++ b/11/2d-noise.frag @@ -0,0 +1,62 @@ +#ifdef GL_ES +precision mediump float; +#endif + +uniform vec2 u_resolution; +uniform float u_time; + +float random (in vec2 _st) { + return fract(sin(dot(_st.xy, + vec2(12.9898,78.233)))* + 43758.5453123); +} + +// Based on Morgan McGuire @morgan3d +// https://www.shadertoy.com/view/4dS3Wd +float noise (in vec2 _st) { + vec2 i = floor(_st); + vec2 f = fract(_st); + + // Four corners in 2D of a tile + float a = random(i); + float b = random(i + vec2(1.0, 0.0)); + float c = random(i + vec2(0.0, 1.0)); + float d = random(i + vec2(1.0, 1.0)); + + vec2 u = f * f * (3.0 - 2.0 * f); + + return mix(a, b, u.x) + + (c - a)* u.y * (1.0 - u.x) + + (d - b) * u.x * u.y; +} + +#define NUM_OCTAVES 5 + +float fbm ( in vec2 _st) { + float v = 0.0; + float a = 0.5; + vec2 shift = vec2(100.0); + // Rotate to reduce axial bias + mat2 rot = mat2(cos(0.5),sin(0.5), + -sin(0.5),cos(0.50)); + for (int i = 0; i < NUM_OCTAVES; ++i) { + v += a * noise(_st); + _st = rot * _st * 2.0 + shift; + a *= 0.5; + } + return v; +} + +void main() { + vec2 st = gl_FragCoord.xy/u_resolution.xy; + vec3 color = vec3(0.0); + + vec2 pos = vec2(st*5.0+u_time); + + float noise = noise(pos); + float fbm = fbm(pos); + + color = vec3( mix(noise, fbm, abs(sin(u_time)))); + + gl_FragColor = vec4(color,1.0); +} \ No newline at end of file diff --git a/11/3d-noise.frag b/11/3d-noise.frag new file mode 100644 index 0000000..db542f9 --- /dev/null +++ b/11/3d-noise.frag @@ -0,0 +1,70 @@ +#ifdef GL_ES +precision mediump float; +#endif + +uniform vec2 u_resolution; +uniform float u_time; + +float random (in float _x) { + return fract(sin(_x)*1e4); +} + +// Based on Morgan McGuire @morgan3d +// https://www.shadertoy.com/view/4dS3Wd +float noise (in vec3 _p) { + const vec3 step = vec3(110.0, 241.0, 171.0); + + vec3 i = floor(_p); + vec3 f = fract(_p); + + // For performance, compute the base input to a + // 1D random from the integer part of the + // argument and the incremental change to the + // 1D based on the 3D -> 1D wrapping + float n = dot(i, step); + + vec3 u = f * f * (3.0 - 2.0 * f); + return mix( mix(mix(random(n + dot(step, vec3(0,0,0))), + random(n + dot(step, vec3(1,0,0))), + u.x), + mix(random(n + dot(step, vec3(0,1,0))), + random(n + dot(step, vec3(1,1,0))), + u.x), + u.y), + mix(mix(random(n + dot(step, vec3(0,0,1))), + random(n + dot(step, vec3(1,0,1))), + u.x), + mix(random(n + dot(step, vec3(0,1,1))), + random(n + dot(step, vec3(1,1,1))), + u.x), + u.y), + u.z); +} + +#define NUM_OCTAVES 5 + +float fbm ( in vec3 _p) { + float v = 0.0; + float a = 0.5; + vec3 shift = vec3(100); + for (int i = 0; i < NUM_OCTAVES; ++i) { + v += a * noise(_p); + _p = _p * 2.0 + shift; + a *= 0.5; + } + return v; +} + +void main() { + vec2 st = gl_FragCoord.xy/u_resolution.xy; + vec3 color = vec3(0.0); + + vec3 pos = vec3(st*5.0,u_time*0.1); + + float noise = noise(pos); + float fbm = fbm(pos); + + color = vec3( mix(noise, fbm, abs(sin(u_time)))); + + gl_FragColor = vec4(color,1.0); +} \ No newline at end of file diff --git a/11/README.md b/11/README.md new file mode 100644 index 0000000..6afbb3b --- /dev/null +++ b/11/README.md @@ -0,0 +1,6 @@ +## Noise + +Coming soon… + +
      + diff --git a/11/index.html b/11/index.html new file mode 100644 index 0000000..efcf64a --- /dev/null +++ b/11/index.html @@ -0,0 +1,70 @@ + + + + + + + Noise + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
      +
      +
      + + + + + + + + \ No newline at end of file diff --git a/11/noise.frag b/11/noise.frag new file mode 100644 index 0000000..5ed5a2d --- /dev/null +++ b/11/noise.frag @@ -0,0 +1,113 @@ +#ifdef GL_ES +precision mediump float; +#endif + +uniform vec2 u_resolution; +uniform float u_time; + +float random (in float _x) { + return fract(sin(_x)*1e4); +} + +float random (in vec2 _st) { + // return fract(sin(dot(_st.xy ,vec2(12.9898,78.233))) * 43758.5453123); + return fract( 1e4 * sin(17.0 * _st.x + _st.y * 0.1) * (0.1 + abs(sin(_st.y * 13.0 + _st.x)))); +} + +// Based on Morgan McGuire @morgan3d +// https://www.shadertoy.com/view/4dS3Wd +float noise (in float _x) { + float i = floor(_x); + float f = fract(_x); + float u = f * f * (3.0 - 2.0 * f); + return mix(random(i), random(i + 1.0), u); +} + +float noise (in vec2 _st){ + vec2 i = floor(_st); + vec2 f = fract(_st); + + // Four corners in 2D of a tile + float a = random(i); + float b = random(i + vec2(1.0, 0.0)); + float c = random(i + vec2(0.0, 1.0)); + float d = random(i + vec2(1.0, 1.0)); + + // Simple 2D lerp using smoothstep envelope between the values. + // return vec3(mix(mix(a, b, smoothstep(0.0, 1.0, f.x)), + // mix(c, d, smoothstep(0.0, 1.0, f.x)), + // smoothstep(0.0, 1.0, f.y))); + + // Same code, with the clamps in smoothstep and common subexpressions + // optimized away. + vec2 u = f * f * (3.0 - 2.0 * f); + return mix(a, b, u.x) + (c - a) * u.y * (1.0 - u.x) + (d - b) * u.x * u.y; +} + +float noise (in vec3 _p) { + const vec3 step = vec3(110.0, 241.0, 171.0); + + vec3 i = floor(_p); + vec3 f = fract(_p); + + // For performance, compute the base input to a 1D random from the integer part of the argument and the + // incremental change to the 1D based on the 3D -> 1D wrapping + float n = dot(i, step); + + vec3 u = f * f * (3.0 - 2.0 * f); + return mix(mix(mix( random(n + dot(step, vec3(0, 0, 0))), random(n + dot(step, vec3(1, 0, 0))), u.x), + mix( random(n + dot(step, vec3(0, 1, 0))), random(n + dot(step, vec3(1, 1, 0))), u.x), u.y), + mix(mix( random(n + dot(step, vec3(0, 0, 1))), random(n + dot(step, vec3(1, 0, 1))), u.x), + mix( random(n + dot(step, vec3(0, 1, 1))), random(n + dot(step, vec3(1, 1, 1))), u.x), u.y), u.z); +} + +#define NUM_OCTAVES 5 + +float fbm ( in float _x) { + float v = 0.0; + float a = 0.5; + float shift = float(100.0); + for (int i = 0; i < NUM_OCTAVES; ++i) { + v += a * noise(_x); + _x = _x * 2.0 + shift; + a *= 0.5; + } + return v; +} + + +float fbm ( in vec2 _st) { + float v = 0.0; + float a = 0.5; + vec2 shift = vec2(100.0); + // Rotate to reduce axial bias + mat2 rot = mat2(cos(0.5), sin(0.5), -sin(0.5), cos(0.50)); + for (int i = 0; i < NUM_OCTAVES; ++i) { + v += a * noise(_st); + _st = rot * _st * 2.0 + shift; + a *= 0.5; + } + return v; +} + + +float fbm ( in vec3 _p) { + float v = 0.0; + float a = 0.5; + vec3 shift = vec3(100); + for (int i = 0; i < NUM_OCTAVES; ++i) { + v += a * noise(_p); + _p = _p * 2.0 + shift; + a *= 0.5; + } + return v; +} + +void main() { + vec2 st = gl_FragCoord.xy/u_resolution.xy; + vec3 color = vec3(0.0); + + color = vec3( fbm(vec3(st*10.,u_time*0.1)) ); + + gl_FragColor = vec4(color,1.0); +} \ No newline at end of file diff --git a/12/1d-fbm.frag b/12/1d-fbm.frag new file mode 100644 index 0000000..53299e8 --- /dev/null +++ b/12/1d-fbm.frag @@ -0,0 +1,55 @@ +#ifdef GL_ES +precision mediump float; +#endif + +uniform vec2 u_resolution; +uniform float u_time; + +float plot(vec2 _st, float _pct){ + return smoothstep( _pct-0.01, _pct, _st.y) - + smoothstep( _pct, _pct+0.01, _st.y); +} + +float random (in float _x) { + return fract(sin(_x)*1e4); +} + +// Based on Morgan McGuire @morgan3d +// https://www.shadertoy.com/view/4dS3Wd +float noise (in float _x) { + float i = floor(_x); + float f = fract(_x); + float u = f * f * (3.0 - 2.0 * f); + return mix(random(i), random(i + 1.0), u); +} + +#define NUM_OCTAVES 5 + +float fbm ( in float _x) { + float v = 0.0; + float a = 0.5; + float shift = float(100.0); + for (int i = 0; i < NUM_OCTAVES; ++i) { + v += a * noise(_x); + _x = _x * 2.0 + shift; + a *= 0.5; + } + return v; +} + +void main() { + vec2 st = gl_FragCoord.xy/u_resolution.xy; + st.x *= u_resolution.x/u_resolution.y; + vec3 color = vec3(0.0); + + float y = 0.0; + // y = random(st.x*0.001+u_time); + // y = noise(st.x*3.+u_time); + y = fbm(st.x*3.0+u_time); + + // color = vec3(y); + float pct = plot(st,y); + color = (1.0-pct)*color+pct*vec3(0.0,1.0,0.0); + + gl_FragColor = vec4(color,1.0); +} \ No newline at end of file diff --git a/12/README.md b/12/README.md new file mode 100644 index 0000000..f73ea4f --- /dev/null +++ b/12/README.md @@ -0,0 +1,5 @@ +## Fractional Brownian Motion + +Coming soon… + +
      diff --git a/12/index.html b/12/index.html new file mode 100644 index 0000000..8da0af8 --- /dev/null +++ b/12/index.html @@ -0,0 +1,70 @@ + + + + + + + Fractional Brownian Motion + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
      +
      +
      + + + + + + + + \ No newline at end of file diff --git a/12/noise.frag b/12/noise.frag new file mode 100644 index 0000000..f69a593 --- /dev/null +++ b/12/noise.frag @@ -0,0 +1,113 @@ +#ifdef GL_ES +precision mediump float; +#endif + +uniform vec2 u_resolution; +uniform float u_time; + +// Based on Morgan +// https://www.shadertoy.com/view/4dS3Wd +float random (in float _x) { + return fract(sin(_x)*1e4); +} + +float random (in vec2 _st) { + // return fract(sin(dot(_st.xy ,vec2(12.9898,78.233))) * 43758.5453123); + return fract( 1e4 * sin(17.0 * _st.x + _st.y * 0.1) * (0.1 + abs(sin(_st.y * 13.0 + _st.x)))); +} + +float noise (in float _x) { + float i = floor(_x); + float f = fract(_x); + float u = f * f * (3.0 - 2.0 * f); + return mix(random(i), random(i + 1.0), u); +} + +float noise (in vec2 _st){ + vec2 i = floor(_st); + vec2 f = fract(_st); + + // Four corners in 2D of a tile + float a = random(i); + float b = random(i + vec2(1.0, 0.0)); + float c = random(i + vec2(0.0, 1.0)); + float d = random(i + vec2(1.0, 1.0)); + + // Simple 2D lerp using smoothstep envelope between the values. + // return vec3(mix(mix(a, b, smoothstep(0.0, 1.0, f.x)), + // mix(c, d, smoothstep(0.0, 1.0, f.x)), + // smoothstep(0.0, 1.0, f.y))); + + // Same code, with the clamps in smoothstep and common subexpressions + // optimized away. + vec2 u = f * f * (3.0 - 2.0 * f); + return mix(a, b, u.x) + (c - a) * u.y * (1.0 - u.x) + (d - b) * u.x * u.y; +} + +float noise (in vec3 _p) { + const vec3 step = vec3(110.0, 241.0, 171.0); + + vec3 i = floor(_p); + vec3 f = fract(_p); + + // For performance, compute the base input to a 1D random from the integer part of the argument and the + // incremental change to the 1D based on the 3D -> 1D wrapping + float n = dot(i, step); + + vec3 u = f * f * (3.0 - 2.0 * f); + return mix(mix(mix( random(n + dot(step, vec3(0, 0, 0))), random(n + dot(step, vec3(1, 0, 0))), u.x), + mix( random(n + dot(step, vec3(0, 1, 0))), random(n + dot(step, vec3(1, 1, 0))), u.x), u.y), + mix(mix( random(n + dot(step, vec3(0, 0, 1))), random(n + dot(step, vec3(1, 0, 1))), u.x), + mix( random(n + dot(step, vec3(0, 1, 1))), random(n + dot(step, vec3(1, 1, 1))), u.x), u.y), u.z); +} + +#define NUM_OCTAVES 5 + +float fbm ( in float _x) { + float v = 0.0; + float a = 0.5; + float shift = float(100.0); + for (int i = 0; i < NUM_OCTAVES; ++i) { + v += a * noise(_x); + _x = _x * 2.0 + shift; + a *= 0.5; + } + return v; +} + + +float fbm ( in vec2 _st) { + float v = 0.0; + float a = 0.5; + vec2 shift = vec2(100.0); + // Rotate to reduce axial bias + mat2 rot = mat2(cos(0.5), sin(0.5), -sin(0.5), cos(0.50)); + for (int i = 0; i < NUM_OCTAVES; ++i) { + v += a * noise(_st); + _st = rot * _st * 2.0 + shift; + a *= 0.5; + } + return v; +} + + +float fbm ( in vec3 _p) { + float v = 0.0; + float a = 0.5; + vec3 shift = vec3(100); + for (int i = 0; i < NUM_OCTAVES; ++i) { + v += a * noise(_p); + _p = _p * 2.0 + shift; + a *= 0.5; + } + return v; +} + +void main() { + vec2 st = gl_FragCoord.xy/u_resolution.xy; + vec3 color = vec3(0.0); + + color = vec3( fbm(vec3(st*10.,u_time*0.1)) ); + + gl_FragColor = vec4(color,1.0); +} \ No newline at end of file diff --git a/13/05.jpg b/13/05.jpg new file mode 100644 index 0000000000000000000000000000000000000000..af4999e1381fabe7ca983789d59c8ac3b2ece4d4 GIT binary patch literal 56527 zcmeFZc|4Wf_b_}Nj(MIFnI&Y-kTOr1WeiCi$9Rt6IOfoxL^2C0nvgl+n5QVEB$=l0Xy=O25^8$5%_QcnqHVR0cHm9w@5b#FB30`99-vtj)b3vgQu4# zkD*ed}<;|mECd*^!fN=A~$02D+ zDQQLUCwYuVN>1^Ztl}|AAcrI#g2=!VE-5W76%YTV2TbqYPh0HmLC`&-Upf&t-6Q@5 z!y-VwpKK)+rR8~~B^6~96lJ9FXi^yQ&$5z&Qv9|DtoSc`z;J)sg9!GUZv)Y9c@(>N zW+0pb7v7$P=ib2HJVZ?>uDymK1lwDHXbCaM=^~zPZy1VzsL9F6DaffQD5x2zD5)4& z=%}gbSPn2Tu`n?mV4x<1pO5{>zusXqR8%yyH1xEz^vtxhw9NP$E%SaBhW{A`drc4n zIiv>NBZl!oL<}%u2H4&RC?w@xD@+AwNdhATpfElV1CN7~kdl#8P*TDEH4z385&uf0 zhhT6RF%g`Igp8D&gqT_eBr*`gc^Rch)J{7v@%dbmCS^{zU#iY8z+&3$D02*Rxl4mg zFwtyjY#HGz%lhEymBX4z=1yAA9%AL#-dlV|u9QWzbo-5e(-um8bhSLCwP#{AyW)B8 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For this task, the graphics cards are equipped with special accelerated memory types which require the image to be uploaded before being used. Like vegetables in restaurant kitchens, the elements have to be chopped and ready before cooking starts. ****we need to talk about this paragraph and improve it **** + +## What is a texture? + +Coming soon… + +![fabric](05.jpg) + +

      + +## Playing + +
      \ No newline at end of file diff --git a/13/index.html b/13/index.html new file mode 100644 index 0000000..53e44a7 --- /dev/null +++ b/13/index.html @@ -0,0 +1,70 @@ + + + + + + + Textures + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
      +
      +
      +
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u_tex0Resolution; + +uniform vec2 u_resolution; +uniform float u_time; + +// Based on Morgan +// https://www.shadertoy.com/view/4dS3Wd +float random (in vec2 _st) { + return fract(sin(dot(_st.xy, + vec2(12.9898,78.233)))* + 43758.5453123); +} + +float noise (in vec2 _st) { + vec2 i = floor(_st); + vec2 f = fract(_st); + + // Four corners in 2D of a tile + float a = random(i); + float b = random(i + vec2(1.0, 0.0)); + float c = random(i + vec2(0.0, 1.0)); + float d = random(i + vec2(1.0, 1.0)); + + vec2 u = f * f * (3.0 - 2.0 * f); + + return mix(a, b, u.x) + + (c - a)* u.y * (1.0 - u.x) + + (d - b) * u.x * u.y; +} + +void main () { + vec2 st = gl_FragCoord.xy/u_resolution.xy; + + st *= 2.0; + + float angle = noise( st + u_time * 0.1 )*PI; + float radius = 0.2; + st += radius * vec2(cos(angle),sin(angle)); + + vec4 color = vec4(st.x,st.y,0.0,1.0); + color = texture2D(u_tex0,st); + + gl_FragColor = color; +} \ No newline at end of file diff --git a/13/texture.frag b/13/texture.frag new file mode 100644 index 0000000..555ad42 --- /dev/null +++ b/13/texture.frag @@ -0,0 +1,18 @@ +#ifdef GL_ES +precision mediump float; +#endif + +uniform sampler2D u_tex0; +uniform vec2 u_tex0Resolution; + +uniform vec2 u_resolution; +uniform float u_time; + +void main () { + vec2 st = gl_FragCoord.xy/u_resolution.xy; + vec4 color = vec4(st.x,st.y,0.0,1.0); + + color = texture2D(u_tex0,st); + + gl_FragColor = color; +} \ No newline at end of file

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