precision mediump float; uniform vec2 u_resolution; uniform float u_time; uniform sampler2D texture_sampler; uniform sampler2D texts; //////////////////////////////////////////////////////////////// // // HG_SDF // // GLSL LIBRARY FOR BUILDING SIGNED DISTANCE BOUNDS // // version 2021-07-28 // // Check https://mercury.sexy/hg_sdf for updates // and usage examples. Send feedback to spheretracing@mercury.sexy. // // Brought to you by MERCURY https://mercury.sexy/ // // // // Released dual-licensed under // Creative Commons Attribution-NonCommercial (CC BY-NC) // or // MIT License // at your choice. // // SPDX-License-Identifier: MIT OR CC-BY-NC-4.0 // // ///// //////////////////////////////////////////////////////////////// // // HELPER FUNCTIONS/MACROS // //////////////////////////////////////////////////////////////// const float PI = 3.14159265; const float TAU = (2.*PI); const float PHI = sqrt(5.)*0.5 + 0.5; // 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.))); } // 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 = clamp( dot(p - a, ab) / dot(ab, ab), 0., 1. ); 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; } //////////////////////////////////////////////////////////////// // // 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)); } //#endSection End of library // https://stackoverflow.com/questions/4200224/random-noise-functions-for-glsl // golden_noise float noise(in vec2 xy, in float seed){ return fract(tan(distance(xy*PHI, xy)*seed)*xy.x); } mat2 Rot(float a) { float s=sin(a), c=cos(a); return mat2(c, -s, s, c); } vec3 applyFog(in vec3 color, in float distance) { float fogAmount = 1.0 - exp(-distance * 0.01); vec3 fogColor = vec3(0.17, 0.16, 0.24); return mix( color, fogColor, fogAmount ); } float opExtrusion( in vec3 p, in float sdf, in float h ) { vec2 w = vec2( sdf, abs(p.z) - h); return min(max(w.x,w.y),0.0) + length(max(w,0.0)); } float sdCog2d(vec2 pos) { float r = length(pos)*2.; float a = atan(pos.y,pos.x); float f = 1. - smoothstep(-0.2, .8, sin(a * 12.))*0.14; f = smoothstep(f,f + 2.,r); return f; } float sdCog(vec3 pos, float angle) { pos.xy *= Rot(angle); float d1 = opExtrusion(pos, sdCog2d(pos.xy), 0.15); float d2 = fCapsule(pos - vec3(0.,0., -0.5), vec3(0., 0.0, 0.), vec3(0., 0., 1.), 0.2); return 0.8 * fOpDifferenceRound(d1,d2,0.1)-0.02;} // Scene vec2 mapScene(in vec3 p) { float d = 1e10; float dGround = p.y + 1.5; d = min(d, dGround); float c1 = sdCog(p+vec3(1., 0., 0.), u_time); d = min(d, c1); float c2 = sdCog(p+vec3(0.5, -.87, 0.), -u_time); d = min(d, c2); float c3 = sdCog(p+vec3(0.5, .87, 0.), -u_time); d = min(d, c3); float mat = 0.; if ( d == c1) mat = 1.; if ( d == c2) mat = 2.; if ( d == c3) mat = 3.; return vec2(d, mat); } vec2 castRay(vec3 ro, vec3 rd) { float t = 0.0; float mat = 0.; for(int i=0; i < 100; i++) { vec3 p = ro + rd * t; vec2 res = mapScene(p); t += res.x; mat = res.y; if (t > 20. || res.x < abs(0.001*t) ) break; } if (t > 20.) t = -1.0; return vec2(t, mat); } float castShadow(vec3 ro, vec3 rd) { float res = 1.0; float t = 0.001; for(int i = 0; i < 100; i++) { vec3 pos = ro + t* rd; float h = mapScene(pos).x; res = min(res, 10.0*h/t); if (abs(h) < (0.001*t) ) break; t += h; if (t > 20.) break; } return clamp(res,0., 1.); } vec3 calcNormal(vec3 pos) { vec2 e = vec2(.001, 0.); vec3 n = vec3( mapScene(pos+e.xyy).x - mapScene(pos-e.xyy).x, mapScene(pos+e.yxy).x - mapScene(pos-e.yxy).x, mapScene(pos+e.yyx).x - mapScene(pos-e.yyx).x ); return normalize(n); } vec3 fresnel( vec3 F0, vec3 h, vec3 l ) { return F0 + ( 1.0 - F0 ) * pow( clamp( 1.0 - dot( h, l ), 0.0, 1.0 ), 5.0 ); } vec3 shading(vec3 v, vec3 n, vec3 dir, float material) { float shininess = 1.; vec3 final = vec3( 0.0 ); vec3 ref = reflect( dir, n ); vec3 Ks = vec3( 0.5 ); vec3 Kd = vec3( 1.0 ); vec3 outMaterial = vec3(0.1686, 0.1686, 0.1686); if (material == 0.) { outMaterial = vec3(0.1608, 0.1255, 0.1255); shininess = 1.; } else if (material == 1.) { outMaterial = vec3(0.2039, 0.2431, 0.3137); shininess = 16.; } else if (material == 2.) { outMaterial = vec3(0.0941, 0.102, 0.1137); shininess = 16.; } else if (material == 3.) { outMaterial = vec3(0.1569, 0.1922, 0.2549); shininess = 16.; } // light 0 { vec3 light_pos = vec3( -2.,.3, 10. ); vec3 light_color = vec3(0.71, 0.51, 0.72) * 5.; vec3 vl = normalize( light_pos - v ); vec3 diffuse = Kd * vec3( max( 0.0, dot( vl, n ) ) ); vec3 specular = vec3( max( 0.0, dot( vl, ref ) ) ); vec3 F = fresnel( Ks, normalize( vl - dir ), vl ); specular = pow( specular, vec3( shininess ) ); final += outMaterial * specular * light_color * mix( diffuse, specular, F ); } // light 1 { vec3 light_pos = vec3( 5.0, 5.0, -20.0 ); vec3 light_color = vec3(0.14, 0.36, 0.83)* 7.; vec3 vl = normalize( light_pos - v ); vec3 diffuse = Kd * vec3( max( 0.0, dot( vl, n ) ) ); vec3 specular = vec3( max( 0.0, dot( vl, ref ) ) ); vec3 F = fresnel( Ks, normalize( vl - dir ), vl ); specular = pow( specular, vec3( shininess ) ); final += outMaterial * specular * light_color * mix( diffuse, specular, F ); } { vec3 SUN_DIR = vec3(0. , .4, 1.); float sun_dif = clamp(dot(n, SUN_DIR), 0., 1.); float shadow = castShadow(v + n*0.02, SUN_DIR); final += outMaterial * vec3(1.1,1.2, 1.5) * sun_dif * sun_dif * shadow; } { vec3 SUN_DIR = vec3(0. , .6, -1.); float sun_dif = clamp(dot(n, SUN_DIR), 0., 1.); final += outMaterial * vec3(0.0353, 0.2667, 0.4784) * sun_dif; } // final += texture( iChannel0, ref ).rgb * fresnel( Ks, n, -dir ); // vec3 col = vec3(0.4)* ref.x; //vec3 col = vec3(0.0588, 0.0588, 0.1216);// - vec3(0.149, 0.0863, 0.2314) * v.x; //final += col * fresnel( vec3(.5), ref, -dir ); return final; } vec3 postProcess(vec3 pos, vec3 col) { float random = noise(gl_FragCoord.xy, 0.01+u_time); float random2 = noise(gl_FragCoord.xy, .2+u_time); col += clamp(vec3(0.5*random, 0.5*random2, 0.*random), 0.02, 1.)*0.05; // dither / noise col = pow( col, vec3(1.0/1.3) ); // gamma return col; } void main() { vec2 p = (2.0 * gl_FragCoord.xy - u_resolution.xy) / u_resolution.y; float angle = -0.4 +u_time*0.4; // camera vec3 ta = vec3(0.0, 0., 1.0); vec3 ro = ta + vec3(4.*sin(angle), cos(angle), 4.*cos(angle)); // *cos(angle)) vec3 ww = normalize(ta-ro); vec3 uu = normalize(cross(ww, vec3(0.,1.0, 0.))); // vec3 = pitch, yaw, pan vec3 vv = normalize(cross(uu,ww)); vec3 rd = normalize(p.x * uu + p.y*vv + ww * 1.8); // camera // global light vec3 col = vec3(0.1451, 0.1098, 0.1608) - vec3(0.9725, 0.5176, 0.0) *rd.y; vec2 t = castRay(ro, rd); vec3 pos = ro + rd * t.x; if (t.x > 0.) { vec3 nor = calcNormal(pos); col = shading(pos, nor, rd , t.y); // apply fog col = applyFog(col, t.x); } col = postProcess(pos, col); gl_FragColor = vec4( col , 1.0 ); }