julia.sttf

{"links":[{"end":"RenderOutput","filter":"Linear","slot":0,"start":"Image","wrapMode":"Repeat"}],"metadata":{"Author":"iq","Description":"The normal is computed analytically from the gradient of the Green function instead of estimating it numerically. The ambient occlusion is faked by using the orbit traps. I made this one in 2007: [url]https://www.youtube.com/watch?v=9AX8gNyrSWc[/url]","Name":"Julia - Quaternion 1","ShaderToyURL":"https://www.shadertoy.com/view/MsfGRr"},"nodes":[{"class":"RenderOutput","name":"RenderOutput"},{"class":"GLSLShader","name":"Image","source":"// Copyright Inigo Quilez, 2013 - https://iquilezles.org/\n// I am the sole copyright owner of this Work.\n// You cannot host, display, distribute or share this Work in any form,\n// including physical and digital. You cannot use this Work in any\n// commercial or non-commercial product, website or project. You cannot\n// sell this Work and you cannot mint an NFTs of it.\n// I share this Work for educational purposes, and you can link to it,\n// through an URL, proper attribution and unmodified screenshot, as part\n// of your educational material. If these conditions are too restrictive\n// please contact me and we'll definitely work it out.\n\n// A port of my 2007 demo Kindernoiser: https://www.youtube.com/watch?v=9AX8gNyrSWc (http://www.pouet.net/prod.php?which=32549)\n//\n// Info here:\n//    https://iquilezles.org/articles/juliasets3d\n//\n//\n// Related shaders\n//\n// Julia - Quaternion 1 : https://www.shadertoy.com/view/MsfGRr\n// Julia - Quaternion 2 : https://www.shadertoy.com/view/lsl3W2\n// Julia - Quaternion 3 : https://www.shadertoy.com/view/3tsyzl\n\n// antialias level (1, 2, 3...)\n#if HW_PERFORMANCE==1\n#define AA 1\n#else\n#define AA 2  // Set AA to 1 if your machine is too slow\n#endif\n\n\n// Normals computation:\n// 0: numerical gradient of d\n// 1: numerical gradient of G\n// 2: analytic  gradient of G\n// 3: analytic  gradient of G optimized\n#define METHOD 3\n\nvec4 qsqr( in vec4 a ) // square a quaterion\n{\n    return vec4( a.x*a.x - a.y*a.y - a.z*a.z - a.w*a.w,\n                 2.0*a.x*a.y,\n                 2.0*a.x*a.z,\n                 2.0*a.x*a.w );\n}\nvec4 qmul( in vec4 a, in vec4 b)\n{\n    return vec4(\n        a.x * b.x - a.y * b.y - a.z * b.z - a.w * b.w,\n        a.y * b.x + a.x * b.y + a.z * b.w - a.w * b.z, \n        a.z * b.x + a.x * b.z + a.w * b.y - a.y * b.w,\n        a.w * b.x + a.x * b.w + a.y * b.z - a.z * b.y );\n\n}\nvec4 qconj( in vec4 a )\n{\n    return vec4( a.x, -a.yzw );\n}\nfloat qlength2( in vec4 q )\n{\n    return dot(q,q);\n}\n\nconst int numIterations = 11;\n\nfloat map( in vec3 p, out vec4 oTrap, in vec4 c )\n{\n    vec4 z = vec4(p,0.0);\n    float md2 = 1.0;\n    float mz2 = dot(z,z);\n\n    vec4 trap = vec4(abs(z.xyz),dot(z,z));\n\n    float n = 1.0;\n    for( int i=0; i<numIterations; i++ )\n    {\n        // dz -> 2·z·dz, meaning |dz| -> 2·|z|·|dz|\n        // Now we take the 2.0 out of the loop and do it at the end with an exp2\n        md2 *= 4.0*mz2;\n        // z  -> z^2 + c\n        z = qsqr(z) + c;  \n\n        trap = min( trap, vec4(abs(z.xyz),dot(z,z)) );\n\n        mz2 = qlength2(z);\n        if(mz2>4.0) break;\n        n += 1.0;\n    }\n    \n    oTrap = trap;\n\n    return 0.25*sqrt(mz2/md2)*log(mz2);  // d = 0.5·|z|·log|z|/|z'|\n}\n\n#if METHOD==0\nvec3 calcNormal( in vec3 p, in vec4 c )\n{\n#if 1\n    vec2 e = vec2(1.0,-1.0)*0.5773*0.001;\n    vec4 za=vec4(p+e.xyy,0.0); float mz2a=qlength2(za), md2a=1.0;\n    vec4 zb=vec4(p+e.yyx,0.0); float mz2b=qlength2(zb), md2b=1.0;\n    vec4 zc=vec4(p+e.yxy,0.0); float mz2c=qlength2(zc), md2c=1.0;\n    vec4 zd=vec4(p+e.xxx,0.0); float mz2d=qlength2(zd), md2d=1.0;\n  \tfor(int i=0; i<numIterations; i++)\n    {\n        md2a *= mz2a; za = qsqr(za)+c; mz2a = qlength2(za);\n        md2b *= mz2b; zb = qsqr(zb)+c; mz2b = qlength2(zb);\n        md2c *= mz2c; zc = qsqr(zc)+c; mz2c = qlength2(zc);\n        md2d *= mz2d; zd = qsqr(zd)+c; mz2d = qlength2(zd);\n    }\n    return normalize( e.xyy*sqrt(mz2a/md2a)*log2(mz2a) + \n\t\t\t\t\t  e.yyx*sqrt(mz2b/md2b)*log2(mz2b) + \n\t\t\t\t\t  e.yxy*sqrt(mz2c/md2c)*log2(mz2c) + \n\t\t\t\t\t  e.xxx*sqrt(mz2d/md2d)*log2(mz2d) );\n#else    \n    const vec2 e = vec2(0.001,0.0);\n    vec4 za=vec4(p+e.xyy,0.0); float mz2a=qlength2(za), md2a=1.0;\n    vec4 zb=vec4(p-e.xyy,0.0); float mz2b=qlength2(zb), md2b=1.0;\n    vec4 zc=vec4(p+e.yxy,0.0); float mz2c=qlength2(zc), md2c=1.0;\n    vec4 zd=vec4(p-e.yxy,0.0); float mz2d=qlength2(zd), md2d=1.0;\n    vec4 ze=vec4(p+e.yyx,0.0); float mz2e=qlength2(ze), md2e=1.0;\n    vec4 zf=vec4(p-e.yyx,0.0); float mz2f=qlength2(zf), md2f=1.0;\n  \tfor(int i=0; i<numIterations; i++)\n    {\n        md2a *= mz2a; za = qsqr(za) + c; mz2a = qlength2(za);\n        md2b *= mz2b; zb = qsqr(zb) + c; mz2b = qlength2(zb);\n        md2c *= mz2c; zc = qsqr(zc) + c; mz2c = qlength2(zc);\n        md2d *= mz2d; zd = qsqr(zd) + c; mz2d = qlength2(zd);\n        md2e *= mz2e; ze = qsqr(ze) + c; mz2e = qlength2(ze);\n        md2f *= mz2f; zf = qsqr(zf) + c; mz2f = qlength2(zf);\n    }\n    float da = sqrt(mz2a/md2a)*log2(mz2a);\n    float db = sqrt(mz2b/md2b)*log2(mz2b);\n    float dc = sqrt(mz2c/md2c)*log2(mz2c);\n    float dd = sqrt(mz2d/md2d)*log2(mz2d);\n    float de = sqrt(mz2e/md2e)*log2(mz2e);\n    float df = sqrt(mz2f/md2f)*log2(mz2f);\n    \n    return normalize( vec3(da-db,dc-dd,de-df) );\n#endif    \n}\n#endif\n\n#if METHOD==1\nvec3 calcNormal( in vec3 p, in vec4 c )\n{\n    const vec2 e = vec2(0.001,0.0);\n    vec4 za = vec4(p+e.xyy,0.0);\n    vec4 zb = vec4(p-e.xyy,0.0);\n    vec4 zc = vec4(p+e.yxy,0.0);\n    vec4 zd = vec4(p-e.yxy,0.0);\n    vec4 ze = vec4(p+e.yyx,0.0);\n    vec4 zf = vec4(p-e.yyx,0.0);\n\n  \tfor(int i=0; i<numIterations; i++)\n    {\n        za = qsqr(za) + c; \n        zb = qsqr(zb) + c; \n        zc = qsqr(zc) + c; \n        zd = qsqr(zd) + c; \n        ze = qsqr(ze) + c; \n        zf = qsqr(zf) + c; \n    }\n    return normalize( vec3(log2(qlength2(za))-log2(qlength2(zb)),\n                           log2(qlength2(zc))-log2(qlength2(zd)),\n                           log2(qlength2(ze))-log2(qlength2(zf))) );\n\n}\n#endif\n\n#if METHOD==2\nvec3 calcNormal( in vec3 p, in vec4 c )\n{\n    vec4 z = vec4(p,0.0);\n\n    // identity derivative\n    mat4x4 J = mat4x4(1,0,0,0,  \n                      0,1,0,0,  \n                      0,0,1,0,  \n                      0,0,0,1 );\n\n  \tfor(int i=0; i<numIterations; i++)\n    {\n        // chain rule of jacobians (removed the 2 factor)\n        J = J*mat4x4(z.x, -z.y, -z.z, -z.w, \n                     z.y,  z.x,  0.0,  0.0,\n                     z.z,  0.0,  z.x,  0.0, \n                     z.w,  0.0,  0.0,  z.x);\n\n        // z -> z2 + c\n        z = qsqr(z) + c; \n        \n        if(qlength2(z)>4.0) break;\n    }\n\n    return normalize( (J*z).xyz );\n}\n#endif\n\n#if METHOD==3\nvec3 calcNormal( in vec3 p, in vec4 c )\n{\n    vec4 z = vec4(p,0.0);\n\n    // identity derivative\n    vec4 J0 = vec4(1,0,0,0);\n    vec4 J1 = vec4(0,1,0,0);\n    vec4 J2 = vec4(0,0,1,0);\n    \n  \tfor(int i=0; i<numIterations; i++)\n    {\n        vec4 cz = qconj(z);\n        \n        // chain rule of jacobians (removed the 2 factor)\n        J0 = vec4( dot(J0,cz), dot(J0.xy,z.yx), dot(J0.xz,z.zx), dot(J0.xw,z.wx) );\n        J1 = vec4( dot(J1,cz), dot(J1.xy,z.yx), dot(J1.xz,z.zx), dot(J1.xw,z.wx) );\n        J2 = vec4( dot(J2,cz), dot(J2.xy,z.yx), dot(J2.xz,z.zx), dot(J2.xw,z.wx) );\n\n        // z -> z2 + c\n        z = qsqr(z) + c; \n        \n        if(qlength2(z)>4.0) break;\n    }\n    \n\tvec3 v = vec3( dot(J0,z), \n                   dot(J1,z), \n                   dot(J2,z) );\n\n    return normalize( v );\n}\n#endif\n\n\n\n\n\nfloat intersect( in vec3 ro, in vec3 rd, out vec4 res, in vec4 c )\n{\n    vec4 tmp;\n    float resT = -1.0;\n\tfloat maxd = 10.0;\n    float h = 1.0;\n    float t = 0.0;\n    for( int i=0; i<300; i++ )\n    {\n        if( h<0.0001||t>maxd ) break;\n\t    h = map( ro+rd*t, tmp, c );\n        t += h;\n    }\n    if( t<maxd ) { resT=t; res = tmp; }\n\n\treturn resT;\n}\n\nfloat softshadow( in vec3 ro, in vec3 rd, float mint, float k, in vec4 c )\n{\n    float res = 1.0;\n    float t = mint;\n    for( int i=0; i<64; i++ )\n    {\n        vec4 kk;\n        float h = map(ro + rd*t, kk, c);\n        res = min( res, k*h/t );\n        if( res<0.001 ) break;\n        t += clamp( h, 0.01, 0.5 );\n    }\n    return clamp(res,0.0,1.0);\n}\n\nvec3 render( in vec3 ro, in vec3 rd, in vec4 c )\n{\n\tconst vec3 sun = vec3(  0.577, 0.577,  0.577 );\n    \n\tvec4 tra;\n\tvec3 col;\n    float t = intersect( ro, rd, tra, c );\n    if( t < 0.0 )\n    {\n     \tcol = vec3(0.7,0.9,1.0)*(0.7+0.3*rd.y);\n\t\tcol += vec3(0.8,0.7,0.5)*pow( clamp(dot(rd,sun),0.0,1.0), 48.0 );\n\t}\n\telse\n\t{\n        vec3 mate = vec3(1.0,0.8,0.7)*0.3;\n\t\t//mate.x = 1.0-10.0*tra.x;\n        \n        vec3 pos = ro + t*rd;\n        vec3 nor = calcNormal( pos, c );\n        \n\t\tfloat occ = clamp(2.5*tra.w-0.15,0.0,1.0);\n\t\t\n\n        col = vec3(0.0);\n\n        // sky\n        {\n        float co = clamp( dot(-rd,nor), 0.0, 1.0 );\n        vec3 ref = reflect( rd, nor );\n        //float sha = softshadow( pos+0.0005*nor, ref, 0.001, 4.0, c );\n        float sha = occ;\n        sha *= smoothstep( -0.1, 0.1, ref.y );\n        float fre = 0.1 + 0.9*pow(1.0-co,5.0);\n            \n\t\tcol  = mate*0.3*vec3(0.8,0.9,1.0)*(0.6+0.4*nor.y)*occ;\n\t\tcol +=  2.0*0.3*vec3(0.8,0.9,1.0)*(0.6+0.4*nor.y)*sha*fre;\n        }\n\n        // sun\n        {\n        const vec3 lig = sun;\n        float dif = clamp( dot( lig, nor ), 0.0, 1.0 );\n        float sha = softshadow( pos, lig, 0.001, 64.0, c );\n        vec3 hal = normalize( -rd+lig );\n        float co = clamp( dot(hal,lig), 0.0, 1.0 );\n        float fre = 0.04 + 0.96*pow(1.0-co,5.0);\n        float spe = pow(clamp(dot(hal,nor), 0.0, 1.0 ), 32.0 );\n        col += mate*3.5*vec3(1.00,0.90,0.70)*dif*sha;\n        col +=  7.0*3.5*vec3(1.00,0.90,0.70)*spe*dif*sha*fre;\n        }\n\n        // extra fill\n        {\n        const vec3 lig = vec3( -0.707, 0.000, -0.707 );\n\t\tfloat dif = clamp(0.5+0.5*dot(lig,nor), 0.0, 1.0 );\n        col += mate* 1.5*vec3(0.14,0.14,0.14)*dif*occ;\n        }\n        \n        // fake SSS\n        {\n        float fre = clamp( 1.+dot(rd,nor), 0.0, 1.0 );\n        col += mate* mate*0.6*fre*fre*(0.2+0.8*occ);\n        }\n    }\n\n\treturn pow( col, vec3(0.4545) );\n}\n\nvoid mainImage( out vec4 fragColor, in vec2 fragCoord )\n{\n    // anim\n    float time = iTime*.15;\n    vec4 c = 0.45*cos( vec4(0.5,3.9,1.4,1.1) + time*vec4(1.2,1.7,1.3,2.5) ) - vec4(0.3,0.0,0.0,0.0);\n\n    // camera\n\tfloat r = 1.5+0.15*cos(0.0+0.29*time);\n\tvec3 ro = vec3(           r*cos(0.3+0.37*time), \n\t\t\t\t\t0.3 + 0.8*r*cos(1.0+0.33*time), \n\t\t\t\t\t          r*cos(2.2+0.31*time) );\n\tvec3 ta = vec3(0.0,0.0,0.0);\n    float cr = 0.1*cos(0.1*time);\n    \n    \n    // render\n    vec3 col = vec3(0.0);\n    for( int j=0; j<AA; j++ )\n    for( int i=0; i<AA; i++ )\n    {\n        vec2 p = (-iResolution.xy + 2.0*(fragCoord + vec2(float(i),float(j))/float(AA))) / iResolution.y;\n\n        vec3 cw = normalize(ta-ro);\n        vec3 cp = vec3(sin(cr), cos(cr),0.0);\n        vec3 cu = normalize(cross(cw,cp));\n        vec3 cv = normalize(cross(cu,cw));\n        vec3 rd = normalize( p.x*cu + p.y*cv + 2.0*cw );\n\n        col += render( ro, rd, c );\n    }\n    col /= float(AA*AA);\n    \n    vec2 uv = fragCoord.xy / iResolution.xy;\n\tcol *= 0.7 + 0.3*pow(16.0*uv.x*uv.y*(1.0-uv.x)*(1.0-uv.y),0.25);\n    \n\tfragColor = vec4( col, 1.0 );\n}\n","type":"Image"}]}