#define SHOW_POINTS 1 #define SHOW_SEGMENTS 1 #define SHOW_DUAL_POINTS 1 #define SHOW_DUAL 1 #define PI 3.14159265359 vec2 polar( float k , float t ) { return k*vec2(cos(t),sin(t)); } vec2 cmul( vec2 a, vec2 b ) { return vec2( a.x*b.x - a.y*b.y, a.x*b.y + a.y*b.x ); } vec2 cexp( vec2 z ) { return polar(exp(z.x) , z.y ); } vec2 clog( vec2 z ) { return vec2( log(length(z)) , atan(z.y , z.x) ); } vec2 cdiv( vec2 a, vec2 b ) { float d = dot(b,b); return vec2( dot(a,b), a.y*b.x - a.x*b.y ) / d; } vec2 cpow( vec2 z , float k ) { return polar(pow(length(z),k) , k*atan(z.y,z.x) ); } // segment.x is distance to closest point // segment.y is barycentric coefficient for closest point // segment.z is length of closest point on curve, on the curve, starting from A // segment.a is approximate length of curve vec4 segment( vec2 p, vec2 a, vec2 b ) { a -= p; b -= p; vec3 k = vec3( dot(a,a) , dot(b,b) , dot(a,b) ); float t = (k.x - k.z)/( k.x + k.y - 2.*k.z ); float len = length(b-a); if( t < 0. ){ return vec4( sqrt(k.x) , 0. , 0. , len ); } else if( t > 1. ){ return vec4( sqrt(k.y) , 1. , len , len ); } else { return vec4( length(a*(1.-t) + b*t) , t , t*len , len ); } } // https://www.shadertoy.com/view/4djSRW #define ITERATIONS 4 // *** Change these to suit your range of random numbers.. // *** Use this for integer stepped ranges, ie Value-Noise/Perlin noise functions. #define HASHSCALE1 .1031 #define HASHSCALE3 vec3(.1031, .1030, .0973) #define HASHSCALE4 vec4(1031, .1030, .0973, .1099) //---------------------------------------------------------------------------------------- /// 3 out, 2 in... vec3 hash32(vec2 p) { vec3 p3 = fract(vec3(p.xyx) * HASHSCALE3); p3 += dot(p3, p3.yxz+19.19); return fract((p3.xxy+p3.yzz)*p3.zyx); } vec3 hash3point(vec2 p) { //vec3 col = hash32(p); vec3 col = hash32(p*1.25672+vec2(.2,.8)) * hash32(vec2(p.y,p.x)/3.42464-vec2(.5,.0)) - hash32(vec2(3.0+p.y,1.2)) ; return pow( (abs(col)+max(col,0.0))/2.0 , vec3(.6,.5,.4) ); } float smoothFunction(float k) { return 1.0 / ( 1.0 + k*k ); } vec3 smoothFunction(vec3 k) { return 1.0 / ( 1.0 + k*k ); } float coeffDistPoint(vec2 uv,vec2 colPoint,float scale) { //float dist = length(uv - colPoint) * scale; //dist = pow(dist,0.25); //dist = 1.0 - smoothstep(0.0,1.0,dist); vec2 uv_ = (uv - colPoint)*scale*24.0; float dist = dot(uv_,uv_); return 1.0 / ( 1.0 + dist ); } void mixColorPoint(vec2 uv,inout vec3 col,vec2 colPoint,float scale) { col = mix( col , hash3point(colPoint) , coeffDistPoint(uv,colPoint,scale) ); } vec3 mixColorLine(vec2 uv,vec3 currentCol,vec3 colLine,vec2 lineA,vec2 lineB,float scale) { return mix( currentCol , colLine , 1.0 - smoothstep(0.0,1.0,sqrt(sqrt( segment(uv,lineA,lineB).x * scale ))) ); } bool pointsOnSameSideOfLine(vec2 pointA,vec2 pointB,vec2 lineA, vec2 lineB) { vec2 n = lineB - lineA; n = vec2(n.y,-n.x); return dot(pointA-lineA,n) * dot(pointB-lineA,n) > 0.0; } float viewportMagnify = 1.0; vec2 screenToViewport(vec2 uv) { return (uv - iResolution.xy/2.0 ) / min(iResolution.x,iResolution.y) * viewportMagnify; } vec2 viewportToScreen(vec2 uv,vec2 base) { return (uv - base/4.0) / viewportMagnify * min(iResolution.x,iResolution.y) + iResolution.xy/2.0; //return (uv - iResolution.xy/2.0 ) / min(iResolution.x,iResolution.y) * viewportMagnify; } // there is three kind of points // in kisrhombille // named here A,B,C struct Equerre { vec2 A; // Right angle => 4 connections vec2 B; // Acute angle => 12 connections vec2 C; // Obtuse angle => 6 connections vec2 D; // on AB vec2 E; // on BC float r; float ID; }; // when decomposing an A,B,C triangle into thre subtriangles // A & B stays respectively A & B points // C becomes a B point // D created is a C point // E created is an A point float det22(vec2 a,vec2 b) { return a.x*b.y - a.y*b.x; } vec3 barycentricCoordinate(vec2 P,Equerre T) { vec2 PA = P - T.A; vec2 PB = P - T.B; vec2 PC = P - T.C; vec3 r = vec3( det22(PB,PC), det22(PC,PA), det22(PA,PB) ); return r / (r.x + r.y + r.z); } #define EQUERRE_COPY(T,Q) \ T.A = Q.A; \ T.B = Q.B; \ T.C = Q.C; #define EQUERRE_COMPUTE_DE(T) \ T.D = (2.0 * T.A + T.B)/3.0; \ T.E = (T.B + T.C)/2.0; #define EQUERRE_GET1(T,Q) \ T.A = Q.A; \ T.B = Q.C; \ T.C = Q.D; #define EQUERRE_GET2(T,Q) \ T.A = Q.E; \ T.B = Q.B; \ T.C = Q.D; #define EQUERRE_GET3(T,Q) \ T.A = Q.E; \ T.B = Q.C; \ T.C = Q.D; #define EQUERRE_GET_NEIGHBOUR_AB(T,Q) \ T.A = Q.A; \ T.B = Q.B; \ T.C = 2.0 * Q.A - Q.C; #define EQUERRE_GET_NEIGHBOUR_AC(T,Q) \ T.A = Q.A; \ T.B = 2.0 * Q.A - Q.B; \ T.C = Q.C; #define EQUERRE_GET_NEIGHBOUR_BC(T,Q) \ T.A = (3.0 * Q.C + Q.B)/2.0 - Q.A; \ T.B = Q.B; \ T.C = Q.C; #define EQUERRE_COND1(X,T) \ pointsOnSameSideOfLine(uv,T.A,T.D,T.C) #define EQUERRE_COND2(X,T) \ pointsOnSameSideOfLine(uv,T.B,T.D,T.E) #define EQUERRE_CENTER(T) ((T.A+T.B+T.C)/3.0) // Base Triangle Equerre Tri; float k = 1. - sqrt(3.)*.5; vec2 A,B,C,D,E,F,G,H; bool AB,BC,CD,DA; float logZoom = 0.; float angleShift = 0.; #define POINT_SPIRAL(n,m) (polar( pow(k,-(n + logZoom)/2.) , (n)/3.*PI + m*PI/2. - angleShift )) // why nPI/3 and not nPI/6 ??????????????????????????? void ComputeSpiralPoints(float r) { A = POINT_SPIRAL(r,0.); B = POINT_SPIRAL(r,1.); C = POINT_SPIRAL(r,2.); D = POINT_SPIRAL(r,3.); E = POINT_SPIRAL(r+1.,3.); F = POINT_SPIRAL(r+1.,0.); G = POINT_SPIRAL(r+1.,1.); H = POINT_SPIRAL(r+1.,2.); } bool FindEquerre(float r,vec2 uv) { ComputeSpiralPoints(r); AB = !pointsOnSameSideOfLine(uv,C,A,B); BC = !pointsOnSameSideOfLine(uv,D,B,C); CD = !pointsOnSameSideOfLine(uv,A,C,D); DA = !pointsOnSameSideOfLine(uv,B,D,A); Tri.r = r; if(AB && !BC) { Tri.A = B; Tri.B = E; Tri.C = F; Tri.ID = r*4.+0.; } else if(BC && !CD) { Tri.A = C; Tri.B = F; Tri.C = G; Tri.ID = r*4.+1.; } else if(CD && !DA) { Tri.A = D; Tri.B = G; Tri.C = H; Tri.ID = r*4.+2.; } else if(DA && !AB) { Tri.A = A; Tri.B = H; Tri.C = E; Tri.ID = r*4.+3.; } else { //return AB || BC || CD || DA; return false; } return true; } vec2 deformation_pole = vec2(.3,.0); vec2 deformation( vec2 uv ) { float nbPoles = 5.; vec2 ret = vec2(1.,0.); for(float i = 0. ; i < nbPoles ; i += 1. ) { ret = cmul(ret,uv - polar(deformation_pole.x,2.*PI*i/nbPoles)); } return cdiv( ret/nbPoles , cpow(uv,2.) ); //uv = cdiv( uv + deformation_pole , uv - deformation_pole ); //uv = cdiv(vec2(1.,0.),uv); //return uv; //return clog( uv + deformation_pole ) - clog( uv - deformation_pole ); //return cexp( cdiv( uv + deformation_pole , clog( uv - deformation_pole ) ) ); } vec2 deformation_inverse(vec2 def ) { return cdiv(2.*deformation_pole,def - vec2(1.,0.)) + deformation_pole; } void mainImage( out vec4 fragColor, in vec2 fragCoord ) { fragColor = vec4(1.0); int nbIterations = 1 + int(floor(pow((1.0 - cos(iTime*3.14/13.0))/2.0,0.5)*7.1)); vec2 uv = screenToViewport(fragCoord.xy ); uv *= mat2(cos(iTime/6.+vec4(0.,1.6,-1.6,0.))); vec2 uv_s = deformation(uv); viewportMagnify =1.; //uv_s *= viewportMagnify; angleShift = cos(iTime/7.5)*8.; logZoom = sin(iTime/4.)*13.; float r = floor( -log(dot(uv_s,uv_s))/log(k) - logZoom ); if( !FindEquerre(r+1.,uv_s) ) { // inside circle FindEquerre(r,uv_s); } fragColor.rgb = hash3point(vec2(Tri.ID,Tri.ID*Tri.ID)); /*Tri.A = deformation_inverse(Tri.A); Tri.B = deformation_inverse(Tri.B); Tri.C = deformation_inverse(Tri.C); uv_s = uv;*/ float scale = 1./viewportMagnify/(1. + dot(uv_s,uv_s)*1.); // LOG correction vec3 EquerreColor = vec3(0.0,0.0,0.0); #if SHOW_SEGMENTS==1 #define OPERATION1(x,y) fragColor.rgb = mixColorLine(uv_s,fragColor.rgb,EquerreColor,x,y,scale); OPERATION1(Tri.A,Tri.B); OPERATION1(Tri.B,Tri.C); OPERATION1(Tri.C,Tri.A); #endif scale /= 3.; vec2 TriCenterMix = (Tri.A + Tri.B + Tri.C)/3.; #if SHOW_DUAL_POINTS==1 fragColor.rgb *= 3.*(.5 + coeffDistPoint(uv_s,TriCenterMix,scale)); #endif fragColor.rgb = tanh(fragColor.rgb *2./(1. + dot(uv_s,uv_s)/1e3 ) ); // LOG correction }