// License CC0: Saturday Torus // Inspired by: https://www.istockphoto.com/photo/black-and-white-stripes-projection-on-torus-gm488221403-39181884 #define PI 3.141592654 #define TAU (2.0*PI) #define TIME iTime #define TTIME (TAU*TIME) #define RESOLUTION iResolution #define ROT(a) mat2(cos(a), sin(a), -sin(a), cos(a)) #define PCOS(x) (0.5+0.5*cos(x)) // License: MIT, author: Inigo Quilez, found: https://iquilezles.org/articles/intersectors float rayTorus(vec3 ro, vec3 rd, vec2 tor) { float po = 1.0; float Ra2 = tor.x*tor.x; float ra2 = tor.y*tor.y; float m = dot(ro,ro); float n = dot(ro,rd); // bounding sphere { float h = n*n - m + (tor.x+tor.y)*(tor.x+tor.y); if(h<0.0) return -1.0; //float t = -n-sqrt(h); // could use this to compute intersections from ro+t*rd } // find quartic equation float k = (m - ra2 - Ra2)/2.0; float k3 = n; float k2 = n*n + Ra2*rd.z*rd.z + k; float k1 = k*n + Ra2*ro.z*rd.z; float k0 = k*k + Ra2*ro.z*ro.z - Ra2*ra2; #ifndef TORUS_REDUCE_PRECISION // prevent |c1| from being too close to zero if(abs(k3*(k3*k3 - k2) + k1) < 0.01) { po = -1.0; float tmp=k1; k1=k3; k3=tmp; k0 = 1.0/k0; k1 = k1*k0; k2 = k2*k0; k3 = k3*k0; } #endif float c2 = 2.0*k2 - 3.0*k3*k3; float c1 = k3*(k3*k3 - k2) + k1; float c0 = k3*(k3*(-3.0*k3*k3 + 4.0*k2) - 8.0*k1) + 4.0*k0; c2 /= 3.0; c1 *= 2.0; c0 /= 3.0; float Q = c2*c2 + c0; float R = 3.0*c0*c2 - c2*c2*c2 - c1*c1; float h = R*R - Q*Q*Q; float z = 0.0; if(h < 0.0) { // 4 intersections float sQ = sqrt(Q); z = 2.0*sQ*cos(acos(R/(sQ*Q)) / 3.0); } else { // 2 intersections float sQ = pow(sqrt(h) + abs(R), 1.0/3.0); z = sign(R)*abs(sQ + Q/sQ); } z = c2 - z; float d1 = z - 3.0*c2; float d2 = z*z - 3.0*c0; if(abs(d1) < 1.0e-4) { if(d2 < 0.0) return -1.0; d2 = sqrt(d2); } else { if(d1 < 0.0) return -1.0; d1 = sqrt(d1/2.0); d2 = c1/d1; } //---------------------------------- float result = 1e20; h = d1*d1 - z + d2; if(h > 0.0) { h = sqrt(h); float t1 = -d1 - h - k3; t1 = (po<0.0)?2.0/t1:t1; float t2 = -d1 + h - k3; t2 = (po<0.0)?2.0/t2:t2; if(t1 > 0.0) result=t1; if(t2 > 0.0) result=min(result,t2); } h = d1*d1 - z - d2; if(h > 0.0) { h = sqrt(h); float t1 = d1 - h - k3; t1 = (po<0.0)?2.0/t1:t1; float t2 = d1 + h - k3; t2 = (po<0.0)?2.0/t2:t2; if(t1 > 0.0) result=min(result,t1); if(t2 > 0.0) result=min(result,t2); } return result; } // License: MIT, author: Inigo Quilez, found: https://iquilezles.org/articles/intersectors vec3 torusNormal(vec3 pos, vec2 tor) { return normalize(pos*(dot(pos,pos)- tor.y*tor.y - tor.x*tor.x*vec3(1.0,1.0,-1.0))); } // License: Unknown, author: Unknown, found: don't remember float tanh_approx(float x) { // Found this somewhere on the interwebs // return tanh(x); float x2 = x*x; return clamp(x*(27.0 + x2)/(27.0+9.0*x2), -1.0, 1.0); } vec3 color(vec2 p, vec2 q) { const float rdd = 2.0; vec3 ro = 1.*vec3(0., 0.75, -0.2); vec3 la = vec3(0.0, 0.0, 0.2); vec3 up = vec3(0.3, 0.0, 1.0); vec3 lp1 = ro; lp1.xy *= ROT(0.85); lp1.xz *= ROT(-0.5); vec3 ww = normalize(la - ro); vec3 uu = normalize(cross(up, ww)); vec3 vv = normalize(cross(ww,uu)); vec3 rd = normalize(p.x*uu + p.y*vv + rdd*ww); const vec2 tor = 0.55*vec2(1.0, 0.75); float td = rayTorus(ro, rd, tor); vec3 tpos = ro + rd*td; vec3 tnor = -torusNormal(tpos, tor); vec3 tref = reflect(rd, tnor); vec3 ldif1 = lp1 - tpos; float ldd1 = dot(ldif1, ldif1); float ldl1 = sqrt(ldd1); vec3 ld1 = ldif1/ldl1; vec3 sro = tpos+0.05*tnor; float sd = rayTorus(sro, ld1, tor); vec3 spos = sro+ld1*sd; vec3 snor = -torusNormal(spos, tor); float dif1 = max(dot(tnor, ld1), 0.0); float spe1 = pow(max(dot(tref, ld1), 0.0), 10.0); float r = length(tpos.xy); float a = atan(tpos.y, tpos.x)-PI*tpos.z/(r+0.5*abs(tpos.z))-TTIME/45.0; float s = mix(0.05, 0.5, tanh_approx(2.0*abs(td-0.75))); vec3 bcol0 = vec3(0.3); vec3 bcol1 = vec3(0.025); vec3 tcol = mix(bcol0, bcol1, smoothstep(-s, s, sin(9.0*a))); vec3 col = vec3(0.0); if (td > -1.0) { col += tcol*mix(0.2, 1.0, dif1/ldd1)+0.25*spe1; col *= sqrt(abs(dot(rd, tnor))); } if (sd < ldl1) { col *= mix(1.0, 0.0, pow(abs(dot(ld1, snor)), 3.0*tanh_approx(sd))); } return col; } // License: MIT, author: Inigo Quilez, found: https://iquilezles.org/www/index.htm vec3 postProcess(vec3 col, vec2 q) { col = clamp(col, 0.0, 1.0); col = pow(col, 1.0/vec3(2.2)); col = col*0.6+0.4*col*col*(3.0-2.0*col); col = mix(col, vec3(dot(col, vec3(0.33))), -0.4); col *=0.5+0.5*pow(19.0*q.x*q.y*(1.0-q.x)*(1.0-q.y),0.7); return col; } void mainImage( out vec4 fragColor, in vec2 fragCoord ) { vec2 q = fragCoord/iResolution.xy; vec2 p = -1. + 2. * q; p.x *= RESOLUTION.x/RESOLUTION.y; vec3 col = color(p, q); col = postProcess(col, q); fragColor = vec4(col, 1.0); }

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