2c:null 2d:["$","title",null,{"children":"GLSL snippets | Lionel Radisson | Observable"}] 32:T11d5,md` ~~~ HG_SDF GLSL LIBRARY FOR BUILDING SIGNED DISTANCE BOUNDS version 2016-01-10 Check http://mercury.sexy/hg_sdf for updates and usage examples. Send feedback to spheretracing@mercury.sexy. Brought to you by MERCURY http://mercury.sexy Released as Creative Commons Attribution-NonCommercial (CC BY-NC) How to use this: 1. Build some system to #include glsl files in each other. Include this one at the very start. Or just paste everywhere. 2. Build a sphere tracer. See those papers: * "Sphere Tracing" http://graphics.cs.illinois.edu/sites/default/files/zeno.pdf * "Enhanced Sphere Tracing" http://lgdv.cs.fau.de/get/2234 The Raymnarching Toolbox Thread on pouet can be helpful as well http://www.pouet.net/topic.php?which=7931&page=1 and contains links to many more resources. 3. Use the tools in this library to build your distance bound f(). 4. ??? 5. Win a compo. (6. Buy us a beer or a good vodka or something, if you like.) Table of Contents: * Helper functions and macros * Collection of some primitive objects * Domain Manipulation operators * Object combination operators Why use this? The point of this lib is that everything is structured according to patterns that we ended up using when building geometry. It makes it more easy to write code that is reusable and that somebody else can actually understand. Especially code on Shadertoy (which seems to be what everybody else is looking at for "inspiration") tends to be really ugly. So we were forced to do something about the situation and release this lib ;) Everything in here can probably be done in some better way. Please experiment. We'd love some feedback, especially if you use it in a scene production. The main patterns for building geometry this way are: * Stay Lipschitz continuous. That means: don't have any distance gradient larger than 1. Try to be as close to 1 as possible - Distances are euclidean distances, don't fudge around. Underestimating distances will happen. That's why calling it a "distance bound" is more correct. Don't ever multiply distances by some value to "fix" a Lipschitz continuity violation. The invariant is: each fSomething() function returns a correct distance bound. * Use very few primitives and combine them as building blocks using combine opertors that preserve the invariant. * Multiply objects by repeating the domain (space). If you are using a loop inside your distance function, you are probably doing it wrong (or you are building boring fractals). * At right-angle intersections between objects, build a new local coordinate system from the two distances to combine them in interesting ways. * As usual, there are always times when it is best to not follow specific patterns. FAQ Q: Why is there no sphere tracing code in this lib? A: Because our system is way too complex and always changing. This is the constant part. Also we'd like everyone to explore for themselves. Q: This does not work when I paste it into Shadertoy!!!! A: Yes. It is GLSL, not GLSL ES. We like real OpenGL because it has way more features and is more likely to work compared to browser-based WebGL. We recommend you consider using OpenGL for your productions. Most of this can be ported easily though. Q: How do I material? A: We recommend something like this: Write a material ID, the distance and the local coordinate p into some global variables whenever an object's distance is smaller than the stored distance. Then, at the end, evaluate the material to get color, roughness, etc., and do the shading. Q: I found an error. Or I made some function that would fit in in this lib. Or I have some suggestion. A: Awesome! Drop us a mail at spheretracing@mercury.sexy. Q: Why is this not on github? A: Because we were too lazy. If we get bugged about it enough, we'll do it. Q: Your license sucks for me. A: Oh. What should we change it to? Q: I have trouble understanding what is going on with my distances. A: Some visualization of the distance field helps. Try drawing a plane that you can sweep through your scene with some color representation of the distance field at each point and/or iso lines at regular intervals. Visualizing the length of the gradient (or better: how much it deviates from being equal to 1) is immensely helpful for understanding which parts of the distance field are broken. ~~~`33:T4ff0,hg_sdf = () => ` //////////////////////////////////////////////////////////////// // // HELPER FUNCTIONS/MACROS // //////////////////////////////////////////////////////////////// #define PI 3.14159265 #define TAU (2.*PI) #define PHI (sqrt(5.)*0.5 + 0.5) // Clamp to [0,1] - this operation is free under certain circumstances. // For further information see // http://www.humus.name/Articles/Persson_LowLevelThinking.pdf and // http://www.humus.name/Articles/Persson_LowlevelShaderOptimization.pdf #define saturate(x) clamp(x, 0., 1.) // Sign function that doesn't return 0 float sgn(float x) { return (x<0.)?-1.:1.; } vec2 sgn(vec2 v) { return vec2((v.x<0.)?-1.:1., (v.y<0.)?-1.:1.); } float square (float x) { return x*x; } vec2 square (vec2 x) { return x*x; } vec3 square (vec3 x) { return x*x; } float lengthSqr(vec3 x) { return dot(x, x); } // Maximum/minumum elements of a vector float vmax(vec2 v) { return max(v.x, v.y); } float vmax(vec3 v) { return max(max(v.x, v.y), v.z); } float vmax(vec4 v) { return max(max(v.x, v.y), max(v.z, v.w)); } float vmin(vec2 v) { return min(v.x, v.y); } float vmin(vec3 v) { return min(min(v.x, v.y), v.z); } float vmin(vec4 v) { return min(min(v.x, v.y), min(v.z, v.w)); } //////////////////////////////////////////////////////////////// // // PRIMITIVE DISTANCE FUNCTIONS // //////////////////////////////////////////////////////////////// // // Conventions: // // Everything that is a distance function is called fSomething. // The first argument is always a point in 2 or 3-space called

. // Unless otherwise noted, (if the object has an intrinsic "up" // side or direction) the y axis is "up" and the object is // centered at the origin. // //////////////////////////////////////////////////////////////// float fSphere(vec3 p, float r) { return length(p) - r; } // Plane with normal n (n is normalized) at some distance from the origin float fPlane(vec3 p, vec3 n, float distanceFromOrigin) { return dot(p, n) + distanceFromOrigin; } // Cheap Box: distance to corners is overestimated float fBoxCheap(vec3 p, vec3 b) { //cheap box return vmax(abs(p) - b); } // Box: correct distance to corners float fBox(vec3 p, vec3 b) { vec3 d = abs(p) - b; return length(max(d, vec3(0))) + vmax(min(d, vec3(0))); } // Same as above, but in two dimensions (an endless box) float fBox2Cheap(vec2 p, vec2 b) { return vmax(abs(p)-b); } float fBox2(vec2 p, vec2 b) { vec2 d = abs(p) - b; return length(max(d, vec2(0))) + vmax(min(d, vec2(0))); } // Endless "corner" float fCorner (vec2 p) { return length(max(p, vec2(0))) + vmax(min(p, vec2(0))); } // Blobby ball object. You've probably seen it somewhere. This is not a correct distance bound, beware. float fBlob(vec3 p) { p = abs(p); if (p.x < max(p.y, p.z)) p = p.yzx; if (p.x < max(p.y, p.z)) p = p.yzx; float b = max(max(max( dot(p, normalize(vec3(1))), dot(p.xz, normalize(vec2(PHI+1., 1.)))), dot(p.yx, normalize(vec2(1., PHI)))), dot(p.xz, normalize(vec2(1., PHI)))); float l = length(p); return l - 1.5 - 0.2 * (1.5 / 2.)* cos(min(sqrt(1.01 - b / l)*(PI / 0.25), PI)); } // Cylinder standing upright on the xz plane float fCylinder(vec3 p, float r, float height) { float d = length(p.xz) - r; d = max(d, abs(p.y) - height); return d; } // Capsule: A Cylinder with round caps on both sides float fCapsule(vec3 p, float r, float c) { return mix(length(p.xz) - r, length(vec3(p.x, abs(p.y) - c, p.z)) - r, step(c, abs(p.y))); } // Distance to line segment between and , used for fCapsule() version 2below float fLineSegment(vec3 p, vec3 a, vec3 b) { vec3 ab = b - a; float t = saturate(dot(p - a, ab) / dot(ab, ab)); return length((ab*t + a) - p); } // Capsule version 2: between two end points and with radius r float fCapsule(vec3 p, vec3 a, vec3 b, float r) { return fLineSegment(p, a, b) - r; } // Torus in the XZ-plane float fTorus(vec3 p, float smallRadius, float largeRadius) { return length(vec2(length(p.xz) - largeRadius, p.y)) - smallRadius; } // A circle line. Can also be used to make a torus by subtracting the smaller radius of the torus. float fCircle(vec3 p, float r) { float l = length(p.xz) - r; return length(vec2(p.y, l)); } // A circular disc with no thickness (i.e. a cylinder with no height). // Subtract some value to make a flat disc with rounded edge. float fDisc(vec3 p, float r) { float l = length(p.xz) - r; return l < 0. ? abs(p.y) : length(vec2(p.y, l)); } // Hexagonal prism, circumcircle variant float fHexagonCircumcircle(vec3 p, vec2 h) { vec3 q = abs(p); return max(q.y - h.y, max(q.x*sqrt(3.)*0.5 + q.z*0.5, q.z) - h.x); //this is mathematically equivalent to this line, but less efficient: //return max(q.y - h.y, max(dot(vec2(cos(PI/3.), sin(PI/3.)), q.zx), q.z) - h.x); } // Hexagonal prism, incircle variant float fHexagonIncircle(vec3 p, vec2 h) { return fHexagonCircumcircle(p, vec2(h.x*sqrt(3.)*0.5, h.y)); } // Cone with correct distances to tip and base circle. Y is up, 0 is in the middle of the base. float fCone(vec3 p, float radius, float height) { vec2 q = vec2(length(p.xz), p.y); vec2 tip = q - vec2(0., height); vec2 mantleDir = normalize(vec2(height, radius)); float mantle = dot(tip, mantleDir); float d = max(mantle, -q.y); float projected = dot(tip, vec2(mantleDir.y, -mantleDir.x)); // distance to tip if ((q.y > height) && (projected < 0.)) { d = max(d, length(tip)); } // distance to base ring if ((q.x > radius) && (projected > length(vec2(height, radius)))) { d = max(d, length(q - vec2(radius, 0.))); } return d; } // // "Generalized Distance Functions" by Akleman and Chen. // see the Paper at https://www.viz.tamu.edu/faculty/ergun/research/implicitmodeling/papers/sm99.pdf // // This set of constants is used to construct a large variety of geometric primitives. // Indices are shifted by 1 compared to the paper because we start counting at Zero. // Some of those are slow whenever a driver decides to not unroll the loop, // which seems to happen for fIcosahedron und fTruncatedIcosahedron on nvidia 350.12 at least. // Specialized implementations can well be faster in all cases. // vec3 GDFVectors[19]; void initGDFVectors() { GDFVectors[0] = normalize(vec3(1, 0, 0)); GDFVectors[1] = normalize(vec3(0, 1, 0)); GDFVectors[2] = normalize(vec3(0, 0, 1)); GDFVectors[3] = normalize(vec3(1, 1, 1 )); GDFVectors[4] = normalize(vec3(-1, 1, 1)); GDFVectors[5] = normalize(vec3(1, -1, 1)); GDFVectors[6] = normalize(vec3(1, 1, -1)); GDFVectors[7] = normalize(vec3(0., 1., PHI+1.)); GDFVectors[8] = normalize(vec3(0., -1., PHI+1.)); GDFVectors[9] = normalize(vec3(PHI+1., 0., 1.)); GDFVectors[10] = normalize(vec3(-PHI-1., 0., 1.)); GDFVectors[11] = normalize(vec3(1., PHI+1., 0.)); GDFVectors[12] = normalize(vec3(-1., PHI+1., 0.)); GDFVectors[13] = normalize(vec3(0., PHI, 1.)); GDFVectors[14] = normalize(vec3(0., -PHI, 1.)); GDFVectors[15] = normalize(vec3(1., 0., PHI)); GDFVectors[16] = normalize(vec3(-1., 0., PHI)); GDFVectors[17] = normalize(vec3(PHI, 1., 0.)); GDFVectors[18] = normalize(vec3(-PHI, 1., 0.)); } // Version with variable exponent. // This is slow and does not produce correct distances, but allows for bulging of objects. float fOctahedron(vec3 p, float r, float e) { float d = 0.; for (int i = 3; i <= 6; ++i) d += pow(abs(dot(p, GDFVectors[i])), e); return pow(d, 1./e) - r; } float fDodecahedron(vec3 p, float r, float e) { float d = 0.; for (int i = 13; i <= 18; ++i) d += pow(abs(dot(p, GDFVectors[i])), e); return pow(d, 1./e) - r; } float fIcosahedron(vec3 p, float r, float e) { float d = 0.; for (int i = 3; i <= 12; ++i) d += pow(abs(dot(p, GDFVectors[i])), e); return pow(d, 1./e) - r; } float fTruncatedOctahedron(vec3 p, float r, float e) { float d = 0.; for (int i = 0; i <= 6; ++i) d += pow(abs(dot(p, GDFVectors[i])), e); return pow(d, 1./e) - r; } // Version with without exponent, creates objects with sharp edges and flat faces float fTruncatedIcosahedron(vec3 p, float r, float e) { float d = 0.; for (int i = 3; i <= 18; ++i) d += pow(abs(dot(p, GDFVectors[i])), e); return pow(d, 1./e) - r; } float fOctahedron(vec3 p, float r) { float d = 0.; for (int i = 3; i <= 6; ++i) d = max(d, abs(dot(p, GDFVectors[i]))); return d - r; } float fDodecahedron(vec3 p, float r) { float d = 0.; for (int i = 13; i <= 18; ++i) d = max(d, abs(dot(p, GDFVectors[i]))); return d - r; } float fIcosahedron(vec3 p, float r) { float d = 0.; for (int i = 3; i <= 12; ++i) d = max(d, abs(dot(p, GDFVectors[i]))); return d - r; } float fTruncatedOctahedron(vec3 p, float r) { float d = 0.; for (int i = 0; i <= 6; ++i) d = max(d, abs(dot(p, GDFVectors[i]))); return d - r; } float fTruncatedIcosahedron(vec3 p, float r) { float d = 0.; for (int i = 3; i <= 18; ++i) d = max(d, abs(dot(p, GDFVectors[i]))); return d - r; } //////////////////////////////////////////////////////////////// // // DOMAIN MANIPULATION OPERATORS // //////////////////////////////////////////////////////////////// // // Conventions: // // Everything that modifies the domain is named pSomething. // // Many operate only on a subset of the three dimensions. For those, // you must choose the dimensions that you want manipulated // by supplying e.g. or // // is always the first argument and modified in place. // // Many of the operators partition space into cells. An identifier // or cell index is returned, if possible. This return value is // intended to be optionally used e.g. as a random seed to change // parameters of the distance functions inside the cells. // // Unless stated otherwise, for cell index 0,

is unchanged and cells // are centered on the origin so objects don't have to be moved to fit. // // //////////////////////////////////////////////////////////////// // Rotate around a coordinate axis (i.e. in a plane perpendicular to that axis) by angle . // Read like this: R(p.xz, a) rotates "x towards z". // This is fast if is a compile-time constant and slower (but still practical) if not. void pR(inout vec2 p, float a) { p = cos(a)*p + sin(a)*vec2(p.y, -p.x); } // Shortcut for 45-degrees rotation void pR45(inout vec2 p) { p = (p + vec2(p.y, -p.x))*sqrt(0.5); } // Repeat space along one axis. Use like this to repeat along the x axis: // - using the return value is optional. float pMod1(inout float p, float size) { float halfsize = size*0.5; float c = floor((p + halfsize)/size); p = mod(p + halfsize, size) - halfsize; return c; } // Same, but mirror every second cell so they match at the boundaries float pModMirror1(inout float p, float size) { float halfsize = size*0.5; float c = floor((p + halfsize)/size); p = mod(p + halfsize,size) - halfsize; p *= mod(c, 2.0)*2. - 1.; return c; } // Repeat the domain only in positive direction. Everything in the negative half-space is unchanged. float pModSingle1(inout float p, float size) { float halfsize = size*0.5; float c = floor((p + halfsize)/size); if (p >= 0.) p = mod(p + halfsize, size) - halfsize; return c; } // Repeat only a few times: from indices to (similar to above, but more flexible) float pModInterval1(inout float p, float size, float start, float stop) { float halfsize = size*0.5; float c = floor((p + halfsize)/size); p = mod(p+halfsize, size) - halfsize; if (c > stop) { //yes, this might not be the best thing numerically. p += size*(c - stop); c = stop; } if (c = (repetitions/2.)) c = abs(c); return c; } // Repeat in two dimensions vec2 pMod2(inout vec2 p, vec2 size) { vec2 c = floor((p + size*0.5)/size); p = mod(p + size*0.5,size) - size*0.5; return c; } // Same, but mirror every second cell so all boundaries match vec2 pModMirror2(inout vec2 p, vec2 size) { vec2 halfsize = size*0.5; vec2 c = floor((p + halfsize)/size); p = mod(p + halfsize, size) - halfsize; p *= mod(c,vec2(2))*2. - vec2(1); return c; } // Same, but mirror every second cell at the diagonal as well vec2 pModGrid2(inout vec2 p, vec2 size) { vec2 c = floor((p + size*0.5)/size); p = mod(p + size*0.5, size) - size*0.5; p *= mod(c,vec2(2))*2. - vec2(1); p -= size/2.; if (p.x > p.y) p.xy = p.yx; return floor(c/2.); } // Repeat in three dimensions vec3 pMod3(inout vec3 p, vec3 size) { vec3 c = floor((p + size*0.5)/size); p = mod(p + size*0.5, size) - size*0.5; return c; } // Mirror at an axis-aligned plane which is at a specified distance from the origin. float pMirror (inout float p, float dist) { float s = sgn(p); p = abs(p)-dist; return s; } // Mirror in both dimensions and at the diagonal, yielding one eighth of the space. // translate by dist before mirroring. vec2 pMirrorOctant (inout vec2 p, vec2 dist) { vec2 s = sgn(p); pMirror(p.x, dist.x); pMirror(p.y, dist.y); if (p.y > p.x) p.xy = p.yx; return s; } // Reflect space at a plane float pReflect(inout vec3 p, vec3 planeNormal, float offset) { float t = dot(p, planeNormal)+offset; if (t < 0.) { p = p - (2.*t)*planeNormal; } return sgn(t); } //////////////////////////////////////////////////////////////// // // OBJECT COMBINATION OPERATORS // //////////////////////////////////////////////////////////////// // // We usually need the following boolean operators to combine two objects: // Union: OR(a,b) // Intersection: AND(a,b) // Difference: AND(a,!b) // (a and b being the distances to the objects). // // The trivial implementations are min(a,b) for union, max(a,b) for intersection // and max(a,-b) for difference. To combine objects in more interesting ways to // produce rounded edges, chamfers, stairs, etc. instead of plain sharp edges we // can use combination operators. It is common to use some kind of "smooth minimum" // instead of min(), but we don't like that because it does not preserve Lipschitz // continuity in many cases. // // Naming convention: since they return a distance, they are called fOpSomething. // The different flavours usually implement all the boolean operators above // and are called fOpUnionRound, fOpIntersectionRound, etc. // // The basic idea: Assume the object surfaces intersect at a right angle. The two // distances and constitute a new local two-dimensional coordinate system // with the actual intersection as the origin. In this coordinate system, we can // evaluate any 2D distance function we want in order to shape the edge. // // The operators below are just those that we found useful or interesting and should // be seen as examples. There are infinitely more possible operators. // // They are designed to actually produce correct distances or distance bounds, unlike // popular "smooth minimum" operators, on the condition that the gradients of the two // SDFs are at right angles. When they are off by more than 30 degrees or so, the // Lipschitz condition will no longer hold (i.e. you might get artifacts). The worst // case is parallel surfaces that are close to each other. // // Most have a float argument to specify the radius of the feature they represent. // This should be much smaller than the object size. // // Some of them have checks like "if ((-a < r) && (-b < r))" that restrict // their influence (and computation cost) to a certain area. You might // want to lift that restriction or enforce it. We have left it as comments // in some cases. // // usage example: // // float fTwoBoxes(vec3 p) { // float box0 = fBox(p, vec3(1)); // float box1 = fBox(p-vec3(1), vec3(1)); // return fOpUnionChamfer(box0, box1, 0.2); // } // //////////////////////////////////////////////////////////////// // The "Chamfer" flavour makes a 45-degree chamfered edge (the diagonal of a square of size ): float fOpUnionChamfer(float a, float b, float r) { return min(min(a, b), (a - r + b)*sqrt(0.5)); } // Intersection has to deal with what is normally the inside of the resulting object // when using union, which we normally don't care about too much. Thus, intersection // implementations sometimes differ from union implementations. float fOpIntersectionChamfer(float a, float b, float r) { return max(max(a, b), (a + r + b)*sqrt(0.5)); } // Difference can be built from Intersection or Union: float fOpDifferenceChamfer (float a, float b, float r) { return fOpIntersectionChamfer(a, -b, r); } // The "Round" variant uses a quarter-circle to join the two objects smoothly: float fOpUnionRound(float a, float b, float r) { vec2 u = max(vec2(r - a,r - b), vec2(0)); return max(r, min (a, b)) - length(u); } float fOpIntersectionRound(float a, float b, float r) { vec2 u = max(vec2(r + a,r + b), vec2(0)); return min(-r, max (a, b)) + length(u); } float fOpDifferenceRound (float a, float b, float r) { return fOpIntersectionRound(a, -b, r); } // The "Columns" flavour makes n-1 circular columns at a 45 degree angle: float fOpUnionColumns(float a, float b, float r, float n) { if ((a < r) && (b < r)) { vec2 p = vec2(a, b); float columnradius = r*sqrt(2.)/((n-1.)*2.+sqrt(2.)); pR45(p); p.x -= sqrt(2.)/2.*r; p.x += columnradius*sqrt(2.); if (mod(n,2.) == 1.) { p.y += columnradius; } // At this point, we have turned 45 degrees and moved at a point on the // diagonal that we want to place the columns on. // Now, repeat the domain along this direction and place a circle. pMod1(p.y, columnradius*2.); float result = length(p) - columnradius; result = min(result, p.x); result = min(result, a); return min(result, b); } else { return min(a, b); } } float fOpDifferenceColumns(float a, float b, float r, float n) { a = -a; float m = min(a, b); //avoid the expensive computation where not needed (produces discontinuity though) if ((a < r) && (b < r)) { vec2 p = vec2(a, b); float columnradius = r*sqrt(2.)/n/2.0; columnradius = r*sqrt(2.)/((n-1.)*2.+sqrt(2.)); pR45(p); p.y += columnradius; p.x -= sqrt(2.)/2.*r; p.x += -columnradius*sqrt(2.)/2.; if (mod(n,2.) == 1.) { p.y += columnradius; } pMod1(p.y,columnradius*2.); float result = -length(p) + columnradius; result = max(result, p.x); result = min(result, a); return -min(result, b); } else { return -m; } } float fOpIntersectionColumns(float a, float b, float r, float n) { return fOpDifferenceColumns(a,-b,r, n); } // The "Stairs" flavour produces n-1 steps of a staircase: // much less stupid version by paniq float fOpUnionStairs(float a, float b, float r, float n) { float s = r/n; float u = b-r; return min(min(a,b), 0.5 * (u + a + abs ((mod (u - a + s, 2. * s)) - s))); } // We can just call Union since stairs are symmetric. float fOpIntersectionStairs(float a, float b, float r, float n) { return -fOpUnionStairs(-a, -b, r, n); } float fOpDifferenceStairs(float a, float b, float r, float n) { return -fOpUnionStairs(-a, b, r, n); } // Similar to fOpUnionRound, but more lipschitz-y at acute angles // (and less so at 90 degrees). Useful when fudging around too much // by MediaMolecule, from Alex Evans' siggraph slides float fOpUnionSoft(float a, float b, float r) { float e = max(r - abs(a - b), 0.); return min(a, b) - e*e*0.25/r; } // produces a cylindical pipe that runs along the intersection. // No objects remain, only the pipe. This is not a boolean operator. float fOpPipe(float a, float b, float r) { return length(vec2(a, b)) - r; } // first object gets a v-shaped engraving where it intersect the second float fOpEngrave(float a, float b, float r) { return max(a, (a + r - abs(b))*sqrt(0.5)); } // first object gets a capenter-style groove cut out float fOpGroove(float a, float b, float ra, float rb) { return max(a, min(a + ra, rb - abs(b))); } // first object gets a capenter-style tongue attached float fOpTongue(float a, float b, float ra, float rb) { return min(a, max(a - ra, abs(b) - rb)); } `34:T220b,phototoshop = () => ` /* ** Desaturation */ vec3 desaturate(vec3 color, float desaturation) { vec3 grayXfer = vec3(0.3, 0.59, 0.11); vec3 gray = vec3(dot(grayXfer, color)); return vec3(mix(color, gray, desaturation)); } /* ** 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) `35:[] 30:{"id":"8fd96d201a644723","slug":"glsl-snippets","title":"GLSL 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https://observablehq.com/@makio135/motion-toolkit`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":376,"value":"glslSnippets = ({\n map,\n map01,\n modularDist,\n fsnoise,\n palette, \n hsv,\n rotate2D,\n rotate3D,\n opBlend,\n random,\n matcap,\n snoise2,\n snoise3,\n snoise4,\n cnoise2,\n cnoise3,\n cnoise4,\n pnoise2,\n pnoise3,\n pnoise4,\n easeBackInOut,\n easeBackIn,\n easeBackOut,\n easeBounceInOut,\n easeBounceIn,\n easeBounceOut,\n easeCircularInOut,\n easeCircularIn,\n easeCircularOut,\n easeCubicInOut,\n easeCubicIn,\n easeCubicOut,\n easeElasticInOut,\n easeElasticIn,\n easeElasticOut,\n easeExponentialInOut,\n easeExponentialIn,\n easeExponentialOut,\n easeLinear,\n easeQuadraticInOut,\n easeQuadraticIn,\n easeQuadraticOut,\n easeQuarticInOut,\n easeQuarticIn,\n easeQuarticOut,\n easeQuinticInOut,\n easeQuinticIn,\n easeQuinticOut,\n easeSineInOut,\n easeSineIn,\n easeSineOut,\n hg_sdf,\n phototoshop,\n})","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":4,"value":"map = () => `\nfloat map(float n, float start1, float stop1, float start2, float stop2) {\n return (n - start1) / (stop1 - start1) * (stop2 - start2) + start2;\n}`","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":64,"value":"map01 = () => `\nfloat map(float n, float start, float stop) {\n return (n - start) / (stop - start);\n}`","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":45,"value":"modularDist = () => `\nfloat modularDist(float value, float modValue) {\n return min(mod(value, modValue), abs(modValue - mod(value, modValue)));\n}`","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":5,"value":"fsnoise = () => `\n// from https://github.com/doxas/twigl\n// fract sin noise\nfloat fsnoise(vec2 c){\n return fract(sin(dot(c, vec2(12.9898, 78.233))) * 43758.5453);\n}\n\n// fsnoise for macOS\nfloat fsnoiseDigits(vec2 c){\n return fract(sin(dot(c, vec2(0.129898, 0.78233))) * 437.585453);\n}`","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":35,"value":"palette = (a, b, c, d) => {\n const vec3 = arr => `vec3(${arr.map(n => n.toFixed(2)).join(',')})`\n return `\n// https://iquilezles.org/www/articles/palettes/palettes.htm\nvec3 palette(float t){ \n return ${vec3(a)} + ${vec3(b)} * cos(2. * ${Math.PI} * (${vec3(c)} * t + ${vec3(d)}));\n}`}","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":9,"value":"hsv = () => `\n// from https://github.com/doxas/twigl\nvec3 hsv(float h, float s, float v){\n vec4 t = vec4(1.0, 2.0 / 3.0, 1.0 / 3.0, 3.0);\n vec3 p = abs(fract(vec3(h) + t.xyz) * 6.0 - vec3(t.w));\n return v * mix(vec3(t.x), clamp(p - vec3(t.x), 0.0, 1.0), s);\n}`","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":11,"value":"rotate2D = () => `\n// from https://github.com/doxas/twigl\nmat2 rotate2D(float r){\n return mat2(cos(r), sin(r), -sin(r), cos(r));\n}`","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":8,"value":"rotate3D = () => `\n// from https://github.com/doxas/twigl\nmat3 rotate3D(float angle, vec3 axis){\n vec3 a = normalize(axis);\n float s = sin(angle);\n float c = cos(angle);\n float r = 1.0 - c;\n return mat3(\n a.x * a.x * r + c,\n a.y * a.x * r + a.z * s,\n a.z * a.x * r - a.y * s,\n a.x * a.y * r - a.z * s,\n a.y * a.y * r + c,\n a.z * a.y * r + a.x * s,\n a.x * a.z * r + a.y * s,\n a.y * a.z * r - a.x * s,\n a.z * a.z * r + c\n );\n}`","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":382,"value":"opBlend = () => `\n// from https://github.com/SebLague/Ray-Marching/blob/f7e44c15a212dec53b244b1f53cdaf318f6ec700/Assets/Scripts/SDF/Raymarching.compute#L82\nvec4 opBlend(float a, float b, vec3 colA, vec3 colB, float k) {\n float h = clamp(0.5 + 0.5 * (b - a) / k, 0.0, 1.0);\n float blendDst = lerp(b, a, h) - k * h * (1.0 - h);\n vec3 blendCol = lerp(colB, colA, h);\n return vec4(blendCol, blendDst);\n}`","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":397,"value":"random = () => `\nfloat random(float n) {\n return fract(sin(n * 128.3218756321));\n}`","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":128,"value":"md`___\n## GLSLify modules`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":132,"value":"import {include} from '@mbostock/pseudo-glslify'","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":386,"value":"md`### matcap\nFrom https://github.com/hughsk/matcap`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":413,"value":"matcap()","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":387,"value":"matcap = () => include('matcap/matcap.glsl')","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":142,"value":"md`### glsl-noise\nFrom https://www.npmjs.com/package/glsl-noise`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":160,"value":"snoise2 = () => include('glsl-noise/simplex/2d.glsl')","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":159,"value":"snoise3 = () => include('glsl-noise/simplex/3d.glsl')","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":158,"value":"snoise4 = () => include('glsl-noise/simplex/4d.glsl')","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":157,"value":"cnoise2 = () => include('glsl-noise/classic/2d.glsl')","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":156,"value":"cnoise3 = () => include('glsl-noise/classic/3d.glsl')","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":155,"value":"cnoise4 = () => include('glsl-noise/classic/4d.glsl')","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":154,"value":"pnoise2 = () => include('glsl-noise/periodic/2d.glsl')","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":153,"value":"pnoise3 = () => include('glsl-noise/periodic/3d.glsl')","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":152,"value":"pnoise4 = () => include('glsl-noise/periodic/4d.glsl')","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":145,"value":"md`### glsl-easings\nFrom https://github.com/glslify/glsl-easings`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":252,"value":"easeBackInOut = () => include('glsl-easings/back-in-out.glsl')","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":253,"value":"easeBackIn = () => 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