30:T592,render = raymarch(` ${rotateX()} ${rotateY()} ${rotateZ()} ${sdCappedCone()} ${opSmoothUnion()} vec2 sceneSDF(vec3 p) { p = rotateY(u_time) * p; float s = sin(u_time * 2.) / 2. + 0.5; float t = smoothstep(0., 2., s); float l = 0.5; float r = 0.35; float r2 = r - s/2.; vec3 q = abs(p); float d = sdCappedCone(q + vec3(0, -l, 0.), l, r, r2); float a90 = radians(90.); float a45 = radians(45.); mat3 rotX = rotateX(a90); d = min(d, sdCappedCone(rotX * q + vec3(0, -l, 0.), l, r, r2)); d = min(d, sdCappedCone(rotX * rotateY(a90) * q + vec3(0, -l, 0.), l, r, r2)); d = opSmoothUnion(d, sdCappedCone(rotateX(a45) * q + vec3(0, -l, 0.), l, r, r2), 0.1); d = opSmoothUnion(d, sdCappedCone(rotateX(radians(60.)) * rotateY(a45)* q + vec3(0, -l, 0.), l, r, r2), 0.1); return vec2(d, 1.0); } `, { computeColor: ` ${phong()} vec3 computeColor(vec3 p, vec3 eye) { vec3 K_a = vec3(0.75); K_a = vec3(0.97, 0.22, 0.5) * step(0.1, mod(length(p), 0.2)); // Use the surface normal as the ambient color of the material //vec3 K_a = (estimateNormal(p) + vec3(1.0)) / 2.0; vec3 K_d = K_a; vec3 K_s = vec3(1.0, 1.0, 1.0); float shininess = 40.0; return phongIllumination(K_a, K_d, K_s, shininess, p, eye); }` , eye: `vec3(8., 5. * sin(u_time / 2.), 7.) * .5` , background: `vec3(0.97, 0.22, 0.5)` , raymarchingSteps: 250 , play: true })31:T413,viewof sdf = Inputs.select([ 'sdBox(p, vec3(1.0))', 'sdRoundBox(p, vec3(1.0), 0.3)', 'sdBoundingBox(p, vec3(1.0), 0.1)', 'sdSphere(p, 1.0)', 'sdTorus(p, vec2(2.0, 0.2))', 'sdCappedTorus(p, vec2(1.0, 0.0), 2.0, 0.3)', 'sdLink(p, 1.0, 0.8, 0.2)', 'sdCylinder(p, vec3(0., 0., 0.5))', 'sdCappedCylinder(p, 1.3, 0.5)', 'sdCappedCylinder2(p, vec3(-1.), vec3(1.), 0.8)', 'sdRoundedCylinder(p, 0.5, 0.3, 1.3)', 'sdCone(p, vec2(sin(1.3), cos(1.3)))', 'sdCappedCone(p, 1.0, 1.0, 0.3)', 'sdRoundCone(p, 0.5, 0.3, 1.5)', 'sdPlane(p, vec4(0.1))', 'sdHexPrism(p, vec2(1.0, 0.1))', 'sdTriPrism(p, vec2(1.0, 0.1))', 'sdCapsule(p, vec3(-1.), vec3(1.), 0.8)', 'sdVerticalCapsule(p, 1.0, 0.3)', 'sdSolidAngle(p, vec2(sin(0.5), cos(0.5)), 1.0)', 'sdEllipsoid(p, vec3(0.5, 0.2, 1.0))', 'sdOctahedron(p, 1.0)', 'sdOctahedron2(p, 1.3)', 'sdPyramid(p, 1.3)', 'udTriangle(p, vec3(-0.5), vec3(0.5, vec2(-0.5)), vec3(0., vec2(0.5)))', 'udQuad(p, vec3(-0.5), vec3(0.5, vec2(-0.5)), vec3(0.5), vec3(-0.5, vec2(0.5)))' ])32:T47a,await visibility(), raymarch(` ${rotateY()} ${sdSphere()} ${sdBox()} ${opUnion()} ${opSubtraction()} ${opIntersection()} ${opSmoothUnion()} ${opSmoothSubtraction()} ${opSmoothIntersection()} vec2 sceneSDF(vec3 p) { p = rotateY(u_time / 2.) * p; vec3 v = p + vec3(3., 0., 1.2); float u = opUnion(sdSphere(v - vec3(0., 0.5, 0.), 0.7), sdBox(v, vec3(1., 0.3, 1.))); v.x -= 3.; float s = opSubtraction(sdSphere(v - vec3(0., 0.5, 0.), 0.7), sdBox(v, vec3(1., 0.3, 1.))); v.x -= 3.; float i = opIntersection(sdSphere(v - vec3(0., 0.5, 0.), 0.7), sdBox(v, vec3(1., 0.3, 1.))); float a = opUnion(i, opUnion(s, u)); v = p + vec3(3., 0., -1.2); float su = opSmoothUnion(sdSphere(v - vec3(0., 0.5, 0.), 0.7), sdBox(v, vec3(1., 0.3, 1.)), sin(u_time)/4. + 0.26); v.x -= 3.; float ss = opSmoothSubtraction(sdSphere(v - vec3(0., 0.5, 0.), 0.7), sdBox(v, vec3(1., 0.3, 1.)), sin(u_time)/4. + 0.26); v.x -= 3.; float si = opSmoothIntersection(sdSphere(v - vec3(0., 0.5, 0.), 0.7), sdBox(v, vec3(1., 0.3, 1.)), sin(u_time)/4. + 0.26); float b = opUnion(si, opUnion(ss, su)); return vec2(opUnion(a, b), 1.0); } `, { play: false })33:T44c,sdBezier = () => ` float sdBezier(in vec2 pos, in vec2 A, in vec2 B, in vec2 C) { vec2 a = B - A; vec2 b = A - 2.0*B + C; vec2 c = a * 2.0; vec2 d = A - pos; float kk = 1.0 / dot(b,b); float kx = kk * dot(a,b); float ky = kk * (2.0*dot(a,a)+dot(d,b)) / 3.0; float kz = kk * dot(d,a); float res = 0.0; float p = ky - kx*kx; float p3 = p*p*p; float q = kx*(2.0*kx*kx - 3.0*ky) + kz; float h = q*q + 4.0*p3; if(h >= 0.0) { h = sqrt(h); vec2 x = (vec2(h, -h) - q) / 2.0; vec2 uv = sign(x)*pow(abs(x), vec2(1.0/3.0)); float t = uv.x + uv.y - kx; t = clamp(t, 0.0, 1.0); vec2 qos = d + (c + b*t)*t; res = dot(qos,qos); } else { float z = sqrt(-p); float v = acos(q/(p*z*2.0)) / 3.0; float m = cos(v); float n = sin(v)*1.732050808; vec3 t = vec3(m + m, -n - m, n - m) * z - kx; t = clamp(t, 0.0, 1.0); vec2 qos = d + (c + b*t.x)*t.x; res = dot(qos,qos); qos = d + (c + b*t.y)*t.y; res = min(res,dot(qos,qos)); qos = d + (c + b*t.z)*t.z; res = min(res,dot(qos,qos)); } return sqrt(res); }`34:[] 2e:{"title":"IQ SDF","cells":[{"id":379,"value":"md`\n# IQ SDF\nSigned Distance Functions from [Inigo Quilez](http://iquilezles.org/)([@iquilezles](https://twitter.com/iquilezles))`","pinned":false,"hidden":false,"mode":"ojs"},{"id":2786,"value":"iqSDF = ({sdSphere, sdBox, sdRoundBox, sdBoundingBox, sdTorus, sdCappedTorus, sdLink, sdCylinder, sdCone, sdCone2, sdCone3, sdPlane, sdHexPrism, sdTriPrism, sdCapsule, sdVerticalCapsule, sdCappedCylinder, sdCappedCylinder2, sdRoundedCylinder, sdCappedCone, sdSolidAngle, sdRoundCone, sdEllipsoid, sdOctahedron, sdOctahedron2, sdPyramid, udTriangle, udQuad, dot2, opElongate, opElongate2, opRound, opOnion, opExtrusion, opRevolution, length2, length6, length8, opUnion, opSubtraction, opIntersection, opSmoothUnion, opSmoothSubtraction, opSmoothIntersection, opBlend, opTranslate, rotateX, rotateY, rotateZ, opSymX, opSymY, opSymZ, opSymXY, opSymXZ, opSymYZ, opSymXYZ, opRep, opRepLim, opTwist, opCheapBend, sdCircle, sdLine, sdRect, sdEquilateralTriangle, sdTriangleIsocele, sdUnevenCapsule, sdTriangle, sdPentagon, sdHexagon, sdOctogon, sdHexagram, sdStar, sdTrapezoid, sdPie, sdArc, sdHorseshoe, sdVesica, sdCross, sdEllipse, sdParabola, sdBezier, sdRhombus, sdPolygon, ndot})","pinned":false,"hidden":false,"mode":"ojs"},{"id":388,"value":"$30","pinned":false,"hidden":false,"mode":"ojs"},{"id":1646,"value":"md`🎬Click to play/pause`","pinned":false,"hidden":false,"mode":"ojs"},{"id":2235,"value":"md`\nRead Inigo Quilez' articles for a more background:\n- http://iquilezles.org/www/articles/distfunctions/distfunctions.htm\n- http://iquilezles.org/www/articles/distfunctions2d/distfunctions2d.htm\n- [Raymarching - Primitives by Inigo Quilez on Shadertoy](https://www.shadertoy.com/view/Xds3zN)\n\nRendering made with the \\`raymarch\\` utility:`","pinned":false,"hidden":false,"mode":"ojs"},{"id":1624,"value":"import { raymarch, phong } from '@makio135/hello-raymarching'","pinned":false,"hidden":false,"mode":"ojs"},{"id":646,"value":"md`___\n### Primitives`","pinned":false,"hidden":false,"mode":"ojs"},{"id":192,"value":"md`**The region where an SDF is negative represents the interior of the surface.**`","pinned":false,"hidden":false,"mode":"ojs"},{"id":1817,"value":"await visibility(), raymarch(`\n#define PI 3.1415926\n\n${rotateY()}\n${sdSphere()}\n${sdBox()}\n${sdRoundBox()}\n${sdBoundingBox()}\n${sdTorus()}\n${sdCappedTorus()}\n${sdLink()}\n${sdCylinder()}\n${sdCone()}\n${sdPlane()}\n${sdHexPrism()}\n${sdTriPrism()}\n${sdCapsule()}\n${sdVerticalCapsule()}\n${sdCappedCylinder()}\n${sdCappedCylinder2()}\n${sdRoundedCylinder()}\n${sdCappedCone()}\n${sdSolidAngle()}\n${sdRoundCone()}\n${sdEllipsoid()}\n${sdOctahedron()}\n${sdOctahedron2()}\n${sdPyramid()}\n${udTriangle()}\n${udQuad()}\n\nvec2 sceneSDF(vec3 p) {\n p = rotateY(u_time) * p;\n return vec2(${sdf}, 0.1);\n}\n`, { play: true })","pinned":false,"hidden":false,"mode":"ojs"},{"id":1818,"value":"$31","pinned":false,"hidden":false,"mode":"ojs"},{"id":2061,"value":"md`🎬Click to play/pause\n___`","pinned":false,"hidden":false,"mode":"ojs"},{"id":373,"value":"sdSphere = () => `\nfloat sdSphere(vec3 p, float radius) {\n return length(p) - radius;\n}`","pinned":false,"hidden":false,"mode":"ojs"},{"id":375,"value":"sdBox = () => `\nfloat sdBox(vec3 p, vec3 b) {\n vec3 d = abs(p) - b;\n return length(max(d, 0.0))\n + min(max(d.x, max(d.y, d.z)), 0.0); // remove this line for an only partially signed sdf \n}`\n","pinned":false,"hidden":false,"mode":"ojs"},{"id":399,"value":"sdRoundBox = () => `\nfloat sdRoundBox(vec3 p, vec3 b, float r){\n vec3 d = abs(p) - b;\n return length(max(d, 0.0)) - r\n + min(max(d.x, max(d.y, d.z)), 0.0); // remove this line for an only partially signed sdf \n}`\n","pinned":false,"hidden":false,"mode":"ojs"},{"id":2794,"value":"sdBoundingBox = () => `\nfloat sdBoundingBox(vec3 p, vec3 b, float e) {\n p = abs(p) - b;\n vec3 q = abs(p + e) - e;\n return min(min(\n length(max(vec3(p.x, q.y, q.z), 0.)) + min(max(p.x, max(q.y, q.z)),0.),\n length(max(vec3(q.x, p.y, q.z), 0.)) + min(max(q.x, max(p.y, q.z)),0.)),\n length(max(vec3(q.x, q.y, p.z), 0.)) + min(max(q.x, max(q.y, p.z)),0.));\n}`","pinned":false,"hidden":false,"mode":"ojs"},{"id":403,"value":"sdTorus = () => `float sdTorus(vec3 p, vec2 t){\n vec2 q = vec2(length(p.xz) - t.x, p.y);\n return length(q) - t.y;\n}`","pinned":false,"hidden":false,"mode":"ojs"},{"id":416,"value":"sdCappedTorus = () => `\nfloat sdCappedTorus(in vec3 p, in vec2 sc, in float ra, in float rb) {\n p.x = abs(p.x);\n float k = (sc.y * p.x > sc.x * p.y) ? dot(p.xy, sc) : length(p.xy);\n return sqrt(dot(p, p) + ra * ra - 2.0 * ra * k) - rb;\n}`","pinned":false,"hidden":false,"mode":"ojs"},{"id":418,"value":"sdLink = () => `\nfloat sdLink(in vec3 p, in float le, in float r1, in float r2) {\n vec3 q = vec3(p.x, max(abs(p.y) - le, 0.0), p.z);\n return length(vec2(length(q.xy) - r1, q.z)) - r2;\n}`","pinned":false,"hidden":false,"mode":"ojs"},{"id":424,"value":"sdCylinder = () => `\nfloat sdCylinder(vec3 p, vec3 c) {\n return length(p.xz - c.xy) - c.z;\n}`","pinned":false,"hidden":false,"mode":"ojs"},{"id":426,"value":"sdCone = () => `\n// Cone - bound (not exact!)\nfloat sdCone(in vec3 p, in vec2 c) {\n // c is the sin/cos of the angle\n float q = length(p.xy);\n return dot(c, vec2(q, p.z));\n}`","pinned":false,"hidden":false,"mode":"ojs"},{"id":2807,"value":"sdCone2 = () => `\n// Cone - exact\nfloat sdCone( in vec3 p, in vec2 c, float h ) {\n // c is the sin/cos of the angle, h is height\n // Alternatively pass q instead of (c,h),\n // which is the point at the base in 2D\n vec2 q = h*vec2(c.x/c.y,-1.0);\n\n vec2 w = vec2( length(p.xz), p.y );\n vec2 a = w - q*clamp( dot(w,q)/dot(q,q), 0.0, 1.0 );\n vec2 b = w - q*vec2( clamp( w.x/q.x, 0.0, 1.0 ), 1.0 );\n float k = sign( q.y );\n float d = min(dot( a, a ),dot(b, b));\n float s = max( k*(w.x*q.y-w.y*q.x),k*(w.y-q.y) );\n return sqrt(d)*sign(s);\n}`","pinned":false,"hidden":false,"mode":"ojs"},{"id":2810,"value":"sdCone3 = () => `\n// Infinite Cone - exact\nfloat sdCone( vec3 p, vec2 c ) {\n // c is the sin/cos of the angle\n vec2 q = vec2( length(p.xz), -p.y );\n float d = length(q-c*max(dot(q,c), 0.0));\n return d * ((q.x*c.y-q.y*c.x<0.0)?-1.0:1.0);\n}`","pinned":false,"hidden":false,"mode":"ojs"},{"id":428,"value":"sdPlane = () => `\nfloat sdPlane(vec3 p, vec4 n) {\n // n must be normalized\n return dot(p, n.xyz) + n.w;\n}`","pinned":false,"hidden":false,"mode":"ojs"},{"id":519,"value":"sdHexPrism = () => `\nfloat sdHexPrism(vec3 p, vec2 h) {\n const vec3 k = vec3(-0.8660254, 0.5, 0.57735);\n p = abs(p);\n p.xy -= 2.0 * min(dot(k.xy, p.xy), 0.0) * k.xy;\n vec2 d = vec2(\n length(p.xy - vec2(clamp(p.x, -k.z * h.x, k.z * h.x), h.x)) * sign(p.y - h.x),\n p.z - h.y);\n return min(max(d.x, d.y), 0.0) + length(max(d, 0.0));\n}`","pinned":false,"hidden":false,"mode":"ojs"},{"id":527,"value":"sdTriPrism = () => `\nfloat sdTriPrism(vec3 p, vec2 h) {\n vec3 q = abs(p);\n return max(q.z - h.y, max(q.x * 0.866025 + p.y * 0.5, -p.y) - h.x * 0.5);\n}`","pinned":false,"hidden":false,"mode":"ojs"},{"id":534,"value":"sdCapsule = () => `\nfloat sdCapsule(vec3 p, vec3 a, vec3 b, float r) {\n vec3 pa = p - a, ba = b - a;\n float h = clamp(dot(pa, ba) / dot(ba, ba), 0.0, 1.0);\n return length(pa - ba * h) - r;\n}`","pinned":false,"hidden":false,"mode":"ojs"},{"id":536,"value":"sdVerticalCapsule = () => `\nfloat sdVerticalCapsule(vec3 p, float h, float r) {\n p.y -= clamp(p.y, 0.0, h);\n return length(p) - r;\n}`","pinned":false,"hidden":false,"mode":"ojs"},{"id":538,"value":"sdCappedCylinder = () => `\nfloat sdCappedCylinder(vec3 p, float h, float r) {\n vec2 d = abs(vec2(length(p.xz), p.y)) - vec2(r, h);\n return min(max(d.x, d.y), 0.0) + length(max(d, 0.0));\n}`","pinned":false,"hidden":false,"mode":"ojs"},{"id":540,"value":"sdCappedCylinder2 = () => `\nfloat sdCappedCylinder2(vec3 p, vec3 a, vec3 b, float r) {\n vec3 ba = b - a;\n vec3 pa = p - a;\n float baba = dot(ba, ba);\n float paba = dot(pa, ba);\n float x = length(pa * baba - ba * paba) - r * baba;\n float y = abs(paba - baba * 0.5) - baba * 0.5;\n float x2 = x * x;\n float y2 = y * y * baba;\n float d = (max(x, y) < 0.0) ? -min(x2, y2) : (((x > 0.0) ? x2 : 0.0) + ((y > 0.0) ? y2 : 0.0));\n return sign(d) * sqrt(abs(d)) / baba;\n}`","pinned":false,"hidden":false,"mode":"ojs"},{"id":543,"value":"sdRoundedCylinder = () => `\nfloat sdRoundedCylinder(vec3 p, float ra, float rb, float h) {\n vec2 d = vec2(length(p.xz) - 2.0 * ra + rb, abs(p.y) - h);\n return min(max(d.x, d.y), 0.0) + length(max(d, 0.0)) - rb;\n}`","pinned":false,"hidden":false,"mode":"ojs"},{"id":546,"value":"sdCappedCone = () => `\n${dot2()}\n\nfloat sdCappedCone(in vec3 p, in float h, in float r1, in float r2) {\n vec2 q = vec2(length(p.xz), p.y);\n\n vec2 k1 = vec2(r2, h);\n vec2 k2 = vec2(r2 - r1, 2.0 * h);\n vec2 ca = vec2(q.x - min(q.x,(q.y < 0.0) ? r1 : r2), abs(q.y) - h);\n vec2 cb = q - k1 + k2 * clamp(dot(k1 - q, k2) / dot2(k2), 0.0, 1.0);\n float s = (cb.x < 0.0 && ca.y < 0.0) ? -1.0 : 1.0;\n return s*sqrt(min(dot2(ca), dot2(cb)));\n}`","pinned":false,"hidden":false,"mode":"ojs"},{"id":548,"value":"sdSolidAngle = () => `\nfloat sdSolidAngle(vec3 p, vec2 c, float ra) {\n // c is the sin/cos of the angle\n vec2 q = vec2(length(p.xz), p.y);\n float l = length(q) - ra;\n float m = length(q - c * clamp(dot(q, c), 0.0, ra));\n return max(l, m * sign(c.y * q.x - c.x * q.y));\n}`","pinned":false,"hidden":false,"mode":"ojs"},{"id":550,"value":"sdRoundCone = () => `\nfloat sdRoundCone(in vec3 p, in float r1, float r2, float h) {\n vec2 q = vec2(length(p.xz), p.y);\n\n float b = (r1 - r2) / h;\n float a = sqrt(1.0 - b * b);\n float k = dot(q, vec2(-b, a));\n\n if(k < 0.0) return length(q) - r1;\n if(k > a * h) return length(q - vec2(0.0, h)) - r2;\n\n return dot(q, vec2(a, b)) - r1;\n}`","pinned":false,"hidden":false,"mode":"ojs"},{"id":552,"value":"sdEllipsoid = () => `\nfloat sdEllipsoid( in vec3 p, in vec3 r) {\n float k0 = length(p / r);\n float k1 = length(p / (r * r));\n return k0 * (k0 - 1.0) / k1;\n}`","pinned":false,"hidden":false,"mode":"ojs"},{"id":555,"value":"sdOctahedron = () => `\nfloat sdOctahedron(in vec3 p, in float s) {\n p = abs(p);\n float m = p.x + p.y + p.z - s;\n vec3 q;\n if(3.0 * p.x < m) q = p.xyz;\n else if(3.0 * p.y < m) q = p.yzx;\n else if(3.0 * p.z < m) q = p.zxy;\n else return m * 0.57735027;\n\n float k = clamp(0.5 * (q.z - q.y + s), 0.0, s); \n return length(vec3(q.x, q.y - s + k, q.z - k)); \n}`","pinned":false,"hidden":false,"mode":"ojs"},{"id":559,"value":"sdOctahedron2 = () => `\n// bound (not exact)\nfloat sdOctahedron2(in vec3 p, in float s) {\n p = abs(p);\n return (p.x + p.y + p.z - s) * 0.57735027;\n}`","pinned":false,"hidden":false,"mode":"ojs"},{"id":2803,"value":"sdPyramid = () => `\nfloat sdPyramid( vec3 p, float h) {\n float m2 = h*h + 0.25;\n \n p.xz = abs(p.xz);\n p.xz = (p.z>p.x) ? p.zx : p.xz;\n p.xz -= 0.5;\n\n vec3 q = vec3( p.z, h*p.y - 0.5*p.x, h*p.x + 0.5*p.y);\n \n float s = max(-q.x,0.0);\n float t = clamp( (q.y-0.5*p.z)/(m2+0.25), 0.0, 1.0 );\n \n float a = m2*(q.x+s)*(q.x+s) + q.y*q.y;\n float b = m2*(q.x+0.5*t)*(q.x+0.5*t) + (q.y-m2*t)*(q.y-m2*t);\n \n float d2 = min(q.y,-q.x*m2-q.y*0.5) > 0.0 ? 0.0 : min(a,b);\n \n return sqrt( (d2+q.z*q.z)/m2 ) * sign(max(q.z,-p.y));\n}`","pinned":false,"hidden":false,"mode":"ojs"},{"id":561,"value":"udTriangle = () => `\n${dot2()}\n\nfloat udTriangle( vec3 p, vec3 a, vec3 b, vec3 c) {\n vec3 ba = b - a; \n vec3 pa = p - a;\n vec3 cb = c - b;\n vec3 pb = p - b;\n vec3 ac = a - c;\n vec3 pc = p - c;\n vec3 nor = cross(ba, ac);\n\n return sqrt(\n (sign(dot(cross(ba, nor), pa)) +\n sign(dot(cross(cb, nor), pb)) +\n sign(dot(cross(ac, nor), pc)) < 2.0) ?\n min(min(\n dot2(ba * clamp(dot(ba, pa) / dot(ba, ba), 0.0, 1.0) - pa),\n dot2(cb * clamp(dot(cb, pb) / dot(cb, cb), 0.0, 1.0) - pb)),\n dot2(ac * clamp(dot(ac, pc) / dot(ac, ac), 0.0, 1.0) - pc)) :\n dot(nor, pa) * dot(nor, pa) / dot(nor, nor));\n}`","pinned":false,"hidden":false,"mode":"ojs"},{"id":565,"value":"udQuad = () => `\n${dot2()}\n\nfloat udQuad( vec3 p, vec3 a, vec3 b, vec3 c, vec3 d) {\n vec3 ba = b - a; vec3 pa = p - a;\n vec3 cb = c - b; vec3 pb = p - b;\n vec3 dc = d - c; vec3 pc = p - c;\n vec3 ad = a - d; vec3 pd = p - d;\n vec3 nor = cross(ba, ad);\n\n return sqrt(\n (sign(dot(cross(ba, nor), pa)) +\n sign(dot(cross(cb, nor), pb)) +\n sign(dot(cross(dc, nor), pc)) +\n sign(dot(cross(ad, nor), pd)) < 3.0) ?\n min(min(min(\n dot2(ba * clamp(dot(ba, pa) / dot2(ba), 0.0, 1.0) - pa),\n dot2(cb * clamp(dot(cb, pb) / dot2(cb), 0.0, 1.0) - pb)),\n dot2(dc * clamp(dot(dc, pc) / dot2(dc), 0.0, 1.0) - pc)),\n dot2(ad * clamp(dot(ad, pd) / dot2(ad), 0.0, 1.0) - pd)) :\n dot(nor, pa) * dot(nor, pa) / dot2(nor));\n}`","pinned":false,"hidden":false,"mode":"ojs"},{"id":725,"value":"dot2 = () => `\n#ifndef DOT2\n#define DOT2\nfloat dot2(in vec2 v) {\n return dot(v, v);\n}\n\nfloat dot2(in vec3 v) {\n return dot(v, v);\n}\n#endif`","pinned":false,"hidden":false,"mode":"ojs"},{"id":570,"value":"md`___\n### Primitive alterations`","pinned":false,"hidden":false,"mode":"ojs"},{"id":888,"value":"md`#### Elongation\nhttps://www.shadertoy.com/view/Ml3fWj`","pinned":false,"hidden":false,"mode":"ojs"},{"id":2025,"value":"await visibility(), raymarch(`\n${rotateY()}\n${opElongate()}\n${sdEllipsoid()}\n${opUnion()}\n\nvec2 sceneSDF(vec3 p) {\n p = rotateY(u_time + 0.8) * p;\n vec3 q = opElongate(p, vec3(0.8, 0., 0.5) * (sin(u_time * 2.)/2. + 0.5));\n float el = sdEllipsoid(q, vec3(0.2, 1.5, 0.5));\n return vec2(el, 1.0);\n}\n`, { play: false })","pinned":false,"hidden":false,"mode":"ojs"},{"id":2264,"value":"md`🎬Click to play/pause`","pinned":false,"hidden":false,"mode":"ojs"},{"id":568,"value":"opElongate = () => `\nvec3 opElongate(in vec3 p, in vec3 h){ \n vec3 q = abs(p) - h;\n return max(q, 0.0);\n}`","pinned":false,"hidden":false,"mode":"ojs"},{"id":576,"value":"opElongate2 = () => `\n// faster, but produces zero in the interior elongated box\nvec3 opElongate2(in vec3 p, in vec3 h){\n return p - clamp(p, -h, h));\n}`","pinned":false,"hidden":false,"mode":"ojs"},{"id":893,"value":"md`#### Rounding\nhttps://www.shadertoy.com/view/Mt3BDj`","pinned":false,"hidden":false,"mode":"ojs"},{"id":2073,"value":"await visibility(), raymarch(`\n${rotateY()}\n${sdHexPrism()}\n${opUnion()}\n${opRound()}\n\nvec2 sceneSDF(vec3 p) {\n mat3 rot = rotateY(u_time + 0.6);\n float d = sdHexPrism(rot * (p - vec3(-2., 0., 0.)), vec2(1.0, 0.2));\n float d2 = opRound(sdHexPrism(rot * (p - vec3(2., 0., 0.)), vec2(1.0, 0.2)), 0.2);\n return vec2(opUnion(d, d2), 1.0);\n}\n`, { play: false })","pinned":false,"hidden":false,"mode":"ojs"},{"id":2261,"value":"md`🎬Click to play/pause`","pinned":false,"hidden":false,"mode":"ojs"},{"id":589,"value":"opRound = () => `\nfloat opRound(float sdf, float rad) {\n return sdf - rad;\n}`","pinned":false,"hidden":false,"mode":"ojs"},{"id":899,"value":"md`#### Onion\nhttps://www.shadertoy.com/view/MlcBDj`","pinned":false,"hidden":false,"mode":"ojs"},{"id":2092,"value":"await visibility(), raymarch(`\n${opOnion()}\n${rotateX()}\n${sdTorus()}\n\nvec2 sceneSDF(vec3 p) {\n float d = opOnion(opOnion(opOnion(sdTorus(p.xzy, vec2(1.5, 0.2)), 0.08), 0.04), 0.02);\n d = max(d, p.y + sin(u_time) * 1.8);\n return vec2(d, 1.0);\n}\n`, { play: false })","pinned":false,"hidden":false,"mode":"ojs"},{"id":2258,"value":"md`🎬Click to play/pause`","pinned":false,"hidden":false,"mode":"ojs"},{"id":587,"value":"opOnion = () => `\nfloat opOnion(in float sdf, in float thickness) {\n return abs(sdf) - thickness;\n}`","pinned":false,"hidden":false,"mode":"ojs"},{"id":901,"value":"md`#### Revolution and extrusion from 2D\nhttps://www.shadertoy.com/view/4lyfzw`","pinned":false,"hidden":false,"mode":"ojs"},{"id":1441,"value":"await visibility(), raymarch(`\n${rotateY()}\n${opExtrusion()}\n${opRevolution()}\n\n// http://www.iquilezles.org/www/articles/distfunctions2d/distfunctions2d.htm\nfloat sdCross(in vec2 p, in vec2 b, float r) {\n p = abs(p); \n p = (p.y > p.x) ? p.yx : p.xy;\n vec2 q = p - b;\n float k = max(q.y, q.x);\n vec2 w = (k > 0.0) ? q : vec2(b.y - p.x, -k);\n return sign(k) * length(max(w, 0.0)) + r;\n}\n\nvec2 sceneSDF(vec3 p) {\n float d = 1e10;\n vec3 q = p + vec3(3., 0., 0.);\n d = min(d, opExtrusion(q, sdCross(q.xy, vec2(2., 0.5), 0.3), sin(u_time) + 1.01));\n q = p + vec3(-3., 0., 0.);\n d = min(d, sdCross(opRevolution(q, sin(u_time) / 2. + 0.5), vec2(2., 0.5), 0.3));\n return vec2(d, 1.0);\n}\n`, { play: false })","pinned":false,"hidden":false,"mode":"ojs"},{"id":1651,"value":"md`🎬Click to play/pause`","pinned":false,"hidden":false,"mode":"ojs"},{"id":578,"value":"opExtrusion = () => `\nfloat opExtrusion(in vec3 p, in float sdf, in float h) {\n vec2 w = vec2(sdf, abs(p.z) - h);\n return min(max(w.x, w.y), 0.0) + length(max(w, 0.0));\n}`","pinned":false,"hidden":false,"mode":"ojs"},{"id":797,"value":"opRevolution = () => `\nvec2 opRevolution(in vec3 p, float w) {\n return vec2(length(p.xz) - w, p.y);\n}`","pinned":false,"hidden":false,"mode":"ojs"},{"id":913,"value":"md`#### Change of Metric\nhttps://www.shadertoy.com/view/ltcfDj\n![](http://iquilezles.org/www/articles/distfunctions/gfx46.png)\n> NOT recommend since this technique produces a bound to the real SDF, which means the intersections with these kind of primitives are slower to find, and also produce wrong shadows when combined with algorithms that rely on accurate SDFs.`","pinned":false,"hidden":false,"mode":"ojs"},{"id":2242,"value":"await visibility(), raymarch(`\n${rotateY()}\n${length6()}\n${sdSphere().replace('length', 'length6')}\n\nvec2 sceneSDF(vec3 p) {\n p = rotateY(u_time / 2.) * p;\n float d = sdSphere(p, 1.0);\n return vec2(d, 1.0);\n}\n`, { play: false })","pinned":false,"hidden":false,"mode":"ojs"},{"id":2656,"value":"md`🎬Click to play/pause`","pinned":false,"hidden":false,"mode":"ojs"},{"id":792,"value":"length2 = () => `\nfloat length2(vec3 p) {\n p = p * p;\n return sqrt(p.x + p.y + p.z);\n}`","pinned":false,"hidden":false,"mode":"ojs"},{"id":794,"value":"length6 = () => `\nfloat length6(vec3 p) {\n p = p * p * p;\n p = p * p;\n return pow(p.x + p.y + p.z, 1.0 / 6.0);\n}`","pinned":false,"hidden":false,"mode":"ojs"},{"id":586,"value":"length8 = () => `\nfloat length8( vec3 p) {\n p = p * p;\n p = p * p;\n p = p * p;\n return pow(p.x + p.y + p.z, 1.0 / 8.0);\n}`","pinned":false,"hidden":false,"mode":"ojs"},{"id":610,"value":"md`___\n### Primitive combinations`","pinned":false,"hidden":false,"mode":"ojs"},{"id":613,"value":"opUnion = () => `\nfloat opUnion(float d1, float d2) {\n return min(d1, d2);\n}\nvec2 opUnion(vec2 d1, vec2 d2) {\n return d1.x < d2.x ? d1 : d2;\n}`","pinned":false,"hidden":false,"mode":"ojs"},{"id":615,"value":"opSubtraction = () => `\n// subtract d1 from d2\nfloat opSubtraction(float d1, float d2) {\n return max(-d1, d2);\n}\nvec2 opSubtraction(vec2 d1, vec2 d2) {\n d1.x = -d1.x;\n return d1.x > d2.x ? d1 : d2;\n}`","pinned":false,"hidden":false,"mode":"ojs"},{"id":582,"value":"opIntersection = () => `\nfloat opIntersection(float d1, float d2) {\n return max(d1, d2);\n}\nvec2 opIntersection(vec2 d1, vec2 d2) {\n return d1.x > d2.x ? d1 : d2;\n}`","pinned":false,"hidden":false,"mode":"ojs"},{"id":617,"value":"opSmoothUnion = () => `\n// from http://www.iquilezles.org/www/articles/smin/smin.htm\nfloat opSmoothUnion(float a, float b, float k) {\n float h = max(k - abs(a - b), 0.0 ) / k;\n return min(a, b) - h * h * h * k * (1.0 / 6.0);\n}`","pinned":false,"hidden":false,"mode":"ojs"},{"id":619,"value":"opSmoothSubtraction = () => `\nfloat opSmoothSubtraction(float d1, float d2, float k) {\n float h = clamp(0.5 - 0.5 * (d2 + d1) / k, 0.0, 1.0);\n return mix(d2, -d1, h) + k * h * (1.0 - h);\n}`","pinned":false,"hidden":false,"mode":"ojs"},{"id":591,"value":"opSmoothIntersection = () => `\nfloat opSmoothIntersection(float d1, float d2, float k) {\n float h = clamp(0.5 - 0.5 * (d2 - d1) / k, 0.0, 1.0);\n return mix(d2, d1, h) + k * h * (1.0 - h);\n}`","pinned":false,"hidden":false,"mode":"ojs"},{"id":1410,"value":"$32","pinned":false,"hidden":false,"mode":"ojs"},{"id":1654,"value":"md`🎬Click to play/pause`","pinned":false,"hidden":false,"mode":"ojs"},{"id":1090,"value":"opBlend = () => `\n// from https://www.alanzucconi.com/2016/07/01/signed-distance-functions/#part4\nfloat opBlend(float sdf1, float sdf2, float amount) {\n return amount * sdf1 + (1. - amount) * sdf2;\n}`","pinned":false,"hidden":false,"mode":"ojs"},{"id":1380,"value":"await visibility(), raymarch(`\n${rotateY()}\n${sdSphere()}\n${sdOctahedron()}\n${opBlend()}\n\nvec2 sceneSDF(vec3 p) {\n p = rotateY(u_time + 0.45) * p;\n\n float s = sdSphere(p, 2.0);\n float o = sdOctahedron(p, 2.0);\n float d = opBlend(s, o, sin(u_time - 0.55) / 2. + 0.5);\n return vec2(d, 1.0);\n}\n`, { play: false })","pinned":false,"hidden":false,"mode":"ojs"},{"id":1657,"value":"md`🎬Click to play/pause`","pinned":false,"hidden":false,"mode":"ojs"},{"id":606,"value":"md`___\n### Positioning`","pinned":false,"hidden":false,"mode":"ojs"},{"id":1566,"value":"md`#### Translation\n~~~glsl\nvec3 q = position - translation;\n~~~\n`","pinned":false,"hidden":false,"mode":"ojs"},{"id":1805,"value":"opTranslate = () => `\nvec3 opTranslate(vec3 p, vec3 tr) {\n return p - tr;\n}`","pinned":false,"hidden":false,"mode":"ojs"},{"id":1563,"value":"md`#### Rotation`","pinned":false,"hidden":false,"mode":"ojs"},{"id":1543,"value":"rotateX = () => `\n// Rotation matrix around the X axis.\nmat3 rotateX(float theta) {\n float c = cos(theta);\n float s = sin(theta);\n return mat3(\n vec3(1, 0, 0),\n vec3(0, c, -s),\n vec3(0, s, c)\n );\n}`","pinned":false,"hidden":false,"mode":"ojs"},{"id":1546,"value":"rotateY = () => `\n// Rotation matrix around the Y axis.\nmat3 rotateY(float theta) {\n float c = cos(theta);\n float s = sin(theta);\n return mat3(\n vec3(c, 0, s),\n vec3(0, 1, 0),\n vec3(-s, 0, c)\n );\n}`","pinned":false,"hidden":false,"mode":"ojs"},{"id":1549,"value":"rotateZ = () => `\n// Rotation matrix around the Z axis.\nmat3 rotateZ(float theta) {\n float c = cos(theta);\n float s = sin(theta);\n return mat3(\n vec3(c, -s, 0),\n vec3(s, c, 0),\n vec3(0, 0, 1)\n );\n}`","pinned":false,"hidden":false,"mode":"ojs"},{"id":1555,"value":"md`#### Scaling\nFor uniform scaling, we can use:\n~~~glsl\nfloat dist = some3D_SDF(position / scalingFactor) * scalingFactor;\n~~~\n\nFor non-uniform scaling:\n~~~glsl\nfloat dist = some3D_SDF(position / vec3(s_x, s_y, s_z)) * min(s_x, min(s_y, s_z));\n~~~\n\n`","pinned":false,"hidden":false,"mode":"ojs"},{"id":1333,"value":"md`#### Symmetry - bound and exact`","pinned":false,"hidden":false,"mode":"ojs"},{"id":1586,"value":"await visibility(), raymarch(`\n${rotateY()}\n${opSymXZ()}\n${sdBox()}\n\nvec2 sceneSDF(vec3 p) {\n p = rotateY(u_time + 0.7) * p;\n \n p = opSymXZ(p); // symmetry along XZ axis\n float l = cos(u_time * 2.) + 1.;\n return vec2(sdBox(p - vec3(l, 0., l), vec3(1.0)), 1.);\n}\n`, {play: false })","pinned":false,"hidden":false,"mode":"ojs"},{"id":2638,"value":"md`🎬Click to play/pause`","pinned":false,"hidden":false,"mode":"ojs"},{"id":630,"value":"opSymX = () => `\nvec3 opSymX(vec3 p) {\n p.x = abs(p.x);\n return p;\n}`","pinned":false,"hidden":false,"mode":"ojs"},{"id":1999,"value":"opSymY = () => `\nvec3 opSymY(vec3 p) {\n p.y = abs(p.y);\n return p;\n}`","pinned":false,"hidden":false,"mode":"ojs"},{"id":2000,"value":"opSymZ = () => `\nvec3 opSymZ(vec3 p) {\n p.z = abs(p.z);\n return p;\n}`","pinned":false,"hidden":false,"mode":"ojs"},{"id":635,"value":"opSymXY = () => `\nvec3 opSymXY(vec3 p) {\n p.xy = abs(p.xy);\n return p;\n}`","pinned":false,"hidden":false,"mode":"ojs"},{"id":2008,"value":"opSymXZ = () => `\nvec3 opSymXZ(vec3 p) {\n p.xz = abs(p.xz);\n return p;\n}`","pinned":false,"hidden":false,"mode":"ojs"},{"id":2010,"value":"opSymYZ = () => `\nvec3 opSymYZ(vec3 p) {\n p.yz = abs(p.yz);\n return p;\n}`","pinned":false,"hidden":false,"mode":"ojs"},{"id":2015,"value":"opSymXYZ = () => `\nvec3 opSymXYZ(vec3 p) {\n p = abs(p);\n return p;\n}`","pinned":false,"hidden":false,"mode":"ojs"},{"id":1350,"value":"md`#### Infinite Repetition`","pinned":false,"hidden":false,"mode":"ojs"},{"id":1718,"value":"await visibility(), raymarch(`\n${rotateX()}\n${rotateY()}\n${sdHexPrism()}\n${opRep()}\n\nvec2 sceneSDF(vec3 p) {\n p = rotateY(1. + u_time / 8.) * p;\n vec3 c = vec3(2.);\n vec3 q = opRep(p, c);\n float d = sdHexPrism(rotateX(u_time + 1.8) * q, vec2(0.5, 0.1));\n return vec2(d, 1.0);\n}\n`, { play: false})","pinned":false,"hidden":false,"mode":"ojs"},{"id":2641,"value":"md`🎬Click to play/pause`","pinned":false,"hidden":false,"mode":"ojs"},{"id":1768,"value":"opRep = () => `\n// Create infinite copies of an object\nvec3 opRep(in vec3 p, in vec3 s) {\n // s defines the space between repetitions of repetitions on each axis\n return mod(p + s * 0.5, s) - s * 0.5;\n}`","pinned":false,"hidden":false,"mode":"ojs"},{"id":1354,"value":"md`#### Finite Repetition`","pinned":false,"hidden":false,"mode":"ojs"},{"id":1760,"value":"await visibility(), raymarch(`\n${rotateX()}\n${rotateY()}\n${sdTriPrism()}\n${opRepLim()}\n\nvec2 sceneSDF(vec3 p) {\n p = rotateY(1. + u_time / 8.) * p;\n vec3 c = vec3(2.);\n float l = 6.;\n vec3 q = opRepLim(p, vec3(1.2), vec3(1., 1, 1.));\n float d = sdTriPrism(rotateX(u_time + 1.8) * q, vec2(0.5, 0.1));\n return vec2(d, 1.0);\n}\n`, { play: false })","pinned":false,"hidden":false,"mode":"ojs"},{"id":2644,"value":"md`🎬Click to play/pause`","pinned":false,"hidden":false,"mode":"ojs"},{"id":1764,"value":"opRepLim = () => `\n#ifndef ROUND_VEC3\n#define ROUND_VEC3\nvec3 round(vec3 p) {\n for(int i = 0; i < 3; i++) {\n p[i] = fract(p[i]) < 0.5 ? floor(p[i]) : ceil(p[i]); \n }\n return p;\n}\n#endif\n\nvec3 opRepLim(in vec3 p, in vec3 s, in vec3 lim) {\n // s defines the space between repetitions of repetitions on each axis\n // lim defines the number of repetitions on each axis\n vec3 q = p / s;\n return p - s * clamp(vec3(round(q)), -lim, lim);\n}`","pinned":false,"hidden":false,"mode":"ojs"},{"id":595,"value":"md`___\n### Deformations and distortions`","pinned":false,"hidden":false,"mode":"ojs"},{"id":1357,"value":"md`#### Displacement`","pinned":false,"hidden":false,"mode":"ojs"},{"id":1963,"value":"await visibility(), raymarch(`\n${sdTorus()}\n${rotateY()}\n\nfloat displace(vec3 p, float k) {\n return sin(20. * p.x) * sin(20. * p.y) * sin(20. * p.z) * k;\n}\n\nvec2 sceneSDF(vec3 p) {\n p = rotateY(u_time / 4. + 0.6) * p;\n float d = sdTorus(p.xzy, vec2(1.5, 0.5));\n d += displace(p, cos(u_time / 2.) * 0.05);\n return vec2(d, 1.0);\n}\n`, { play: false, raymarchingSteps: 200, antiAliasing: 2 })","pinned":false,"hidden":false,"mode":"ojs"},{"id":2646,"value":"md`🎬Click to play/pause`","pinned":false,"hidden":false,"mode":"ojs"},{"id":599,"value":"md`~~~glsl\nfloat d1 = primitive(p);\nfloat d2 = displacement(p);\nreturn d1 + d2;\n~~~`","pinned":false,"hidden":false,"mode":"ojs"},{"id":1358,"value":"md`#### Twist`","pinned":false,"hidden":false,"mode":"ojs"},{"id":1943,"value":"await visibility(), raymarch(`\n${sdBox()}\n${opTwist()}\n\nvec2 sceneSDF(vec3 p) {\n p = opTwist(p, cos(u_time));\n float d = sdBox(p, vec3(1.0, 1.0, 2.0));\n return vec2(d, 1.0);\n}\n`, { play: false })","pinned":false,"hidden":false,"mode":"ojs"},{"id":2649,"value":"md`🎬Click to play/pause`","pinned":false,"hidden":false,"mode":"ojs"},{"id":601,"value":"opTwist = () => `\nvec3 opTwist(in vec3 p, float k) {\n float c = cos(k * p.y);\n float s = sin(k * p.y);\n mat2 m = mat2(c, -s, s, c);\n vec3 q = vec3(m * p.xz, p.y);\n return q;\n}`","pinned":false,"hidden":false,"mode":"ojs"},{"id":1360,"value":"md`#### Bend`","pinned":false,"hidden":false,"mode":"ojs"},{"id":1957,"value":"await visibility(), raymarch(`\n${sdBox()}\n${opCheapBend()}\n\nvec2 sceneSDF(vec3 p) {\n p = opCheapBend(p, cos(u_time));\n float d = sdBox(p, vec3(1.5, 0.2, 1.5));\n return vec2(d, 1.0);\n}\n`, { play: false })","pinned":false,"hidden":false,"mode":"ojs"},{"id":2652,"value":"md`🎬Click to play/pause`","pinned":false,"hidden":false,"mode":"ojs"},{"id":594,"value":"opCheapBend = () => `\nvec3 opCheapBend(in vec3 p, float k) {\n float c = cos(k * p.x);\n float s = sin(k * p.x);\n mat2 m = mat2(c, -s, s, c);\n vec3 q = vec3(m * p.xy, p.z);\n return q;\n}`","pinned":false,"hidden":false,"mode":"ojs"},{"id":2267,"value":"md`___\n## 2D SDF`","pinned":false,"hidden":false,"mode":"ojs"},{"id":2395,"value":"await visibility(), fragment(`\nprecision mediump float;\n\nuniform vec2 u_resolution;\n\n${dot2()}\n${sdCircle()}\n${sdLine()}\n${sdRect()}\n${sdEquilateralTriangle()}\n${sdTriangleIsocele()}\n${sdUnevenCapsule()}\n${sdTriangle()}\n${sdPentagon()}\n${sdHexagon()}\n${sdOctogon()}\n${sdHexagram()}\n${sdStar()}\n${sdTrapezoid()}\n${sdPie()}\n${sdArc()}\n${sdHorseshoe()}\n${sdVesica()}\n${sdCross()}\n${sdEllipse()}\n${sdParabola()}\n${sdBezier()}\n${sdRhombus()}\n/*${sdPolygon(5)}*/\n\nvoid main() {\n vec2 p = (gl_FragCoord.xy - u_resolution / 2.) / u_resolution.y;\n float d = smoothstep(0., 0.005, ${sdf2d});\n gl_FragColor = vec4(vec3(d), 1.0);\n}\n`)","pinned":false,"hidden":false,"mode":"ojs"},{"id":2408,"value":"viewof sdf2d = Inputs.select([\n 'sdCircle(p, 0.2)',\n 'sdLine(p, vec2(-0.5, -0.3), vec2(0.5, 0.3))',\n 'sdRect(p, vec2(0.6, 0.3))',\n 'sdEquilateralTriangle(p * 2.)',\n 'sdTriangleIsocele(p, vec2(0.2, 0.6))',\n 'sdUnevenCapsule(p, 0.05, 0.1, 0.3)',\n 'sdTriangle(p, vec2(-0.4), vec2(0., 0.4), vec2(0.3, 0.))',\n 'sdPentagon(p, 0.4)',\n 'sdHexagon(p, 0.4)',\n 'sdOctogon(p, 0.4)',\n 'sdHexagram(p, 0.2)',\n 'sdStar(p, 0.35, 7, 0.9)',\n 'sdTrapezoid(p, 0.35, 0.3, 0.2)',\n 'sdPie(p, vec2(sin(radians(45.)), cos(radians(45.))), 0.5)',\n 'sdArc(p, vec2(sin(radians(45.)), cos(radians(45.))), vec2(sin(radians(115.)), cos(radians(115.))), 0.2, 0.015)',\n 'sdHorseshoe(p, vec2(sin(radians(15.)), cos(radians(15.))), 0.3, vec2(0.2, 0.05))',\n 'sdVesica(p, 0.3, 0.1)',\n 'sdCross(p, vec2(0.4, 0.1), 0.05)',\n 'sdEllipse(p, vec2(0.1, 0.3))',\n 'sdParabola(p, 0.9)',\n 'sdBezier(p, vec2(-0.8, 0.3), vec2(-0.3, -0.5), vec2(0.5))',\n 'sdRhombus(p, vec2(0.2, 0.4))'\n].reverse())","pinned":false,"hidden":false,"mode":"ojs"},{"id":2276,"value":"sdCircle = () => `\nfloat sdCircle(vec2 p, float r){\n return length(p) - r;\n}`","pinned":false,"hidden":false,"mode":"ojs"},{"id":2282,"value":"sdLine = () => `\nfloat sdLine(in vec2 p, in vec2 a, in vec2 b){\n vec2 pa = p - a;\n vec2 ba = b - a;\n float h = clamp(dot(pa, ba) / dot(ba, ba), 0.0, 1.0);\n return length(pa - ba * h);\n}`","pinned":false,"hidden":false,"mode":"ojs"},{"id":2286,"value":"sdRect = () => `\nfloat sdRect(in vec2 p, in vec2 b) {\n vec2 d = abs(p) - b;\n return length(max(d, vec2(0))) + min(max(d.x, d.y), 0.0);\n}`","pinned":false,"hidden":false,"mode":"ojs"},{"id":2296,"value":"sdEquilateralTriangle = () => `\nfloat sdEquilateralTriangle(in vec2 p) {\n const float k = sqrt(3.0);\n p.x = abs(p.x) - 1.0;\n p.y = p.y + 1.0 / k;\n if(p.x + k * p.y > 0.0) p = vec2(p.x - k * p.y, - k * p.x - p.y) / 2.0;\n p.x -= clamp(p.x, -2.0, 0.0);\n return -length(p) * sign(p.y);\n}`","pinned":false,"hidden":false,"mode":"ojs"},{"id":2305,"value":"sdTriangleIsocele = () => `\nfloat sdTriangleIsocele(in vec2 p, in vec2 q) {\n p.x = abs(p.x);\n vec2 a = p - q*clamp( dot(p,q)/dot(q,q), 0.0, 1.0 );\n vec2 b = p - q*vec2( clamp( p.x/q.x, 0.0, 1.0 ), 1.0 );\n float s = -sign( q.y );\n vec2 d = min( vec2( dot(a,a), s*(p.x*q.y-p.y*q.x) ),\n vec2( dot(b,b), s*(p.y-q.y) ));\n return -sqrt(d.x)*sign(d.y);\n}`","pinned":false,"hidden":false,"mode":"ojs"},{"id":2309,"value":"sdUnevenCapsule = () => `\nfloat sdUnevenCapsule(vec2 p, float r1, float r2, float h) {\n p.x = abs(p.x);\n float b = (r1 - r2) / h;\n float a = sqrt(1.0 - b * b);\n float k = dot(p, vec2(-b, a));\n if(k < 0.0) return length(p) - r1;\n if(k > a * h) return length(p - vec2(0.0, h)) - r2;\n return dot(p, vec2(a, b) ) - r1;\n}`","pinned":false,"hidden":false,"mode":"ojs"},{"id":2313,"value":"sdTriangle = () => `\nfloat sdTriangle(in vec2 p, in vec2 p0, in vec2 p1, in vec2 p2) {\n vec2 e0 = p1 - p0, e1 = p2-p1, e2 = p0-p2;\n vec2 v0 = p - p0, v1 = p -p1, v2 = p -p2;\n vec2 pq0 = v0 - e0 * clamp(dot(v0, e0) / dot(e0, e0), 0.0, 1.0);\n vec2 pq1 = v1 - e1 * clamp(dot(v1, e1) / dot(e1, e1), 0.0, 1.0);\n vec2 pq2 = v2 - e2 * clamp(dot(v2, e2) / dot(e2, e2), 0.0, 1.0);\n float s = sign(e0.x * e2.y - e0.y * e2.x);\n vec2 d = min(min(vec2(dot(pq0, pq0), s * (v0.x * e0.y - v0.y * e0.x)),\n vec2(dot(pq1, pq1), s * (v1.x * e1.y - v1.y * e1.x))),\n vec2(dot(pq2, pq2), s * (v2.x * e2.y - v2.y * e2.x)));\n return -sqrt(d.x) * sign(d.y);\n}`","pinned":false,"hidden":false,"mode":"ojs"},{"id":2318,"value":"sdPentagon = () => `\nfloat sdPentagon(in vec2 p, in float r) {\n const vec3 k = vec3(0.809016994, 0.587785252, 0.726542528);\n p.x = abs(p.x);\n p -= 2.0 * min(dot(vec2(-k.x, k.y), p), 0.0) * vec2(-k.x, k.y);\n p -= 2.0 * min(dot(vec2(k.x, k.y), p), 0.0) * vec2(k.x, k.y);\n p -= vec2(clamp(p.x, -r * k.z,r * k.z), r);\n return length(p) * sign(p.y);\n}`","pinned":false,"hidden":false,"mode":"ojs"},{"id":2322,"value":"sdHexagon = () => `\nfloat sdHexagon(in vec2 p, in float r) {\n const vec3 k = vec3(-0.866025404, 0.5, 0.577350269);\n p = abs(p);\n p -= 2.0 * min(dot(k.xy, p), 0.0) * k.xy;\n p -= vec2(clamp(p.x, -k.z * r, k.z * r), r);\n return length(p) * sign(p.y);\n}`","pinned":false,"hidden":false,"mode":"ojs"},{"id":2326,"value":"sdOctogon = () => `\nfloat sdOctogon(in vec2 p, in float r) {\n const vec3 k = vec3(-0.9238795325, 0.3826834323, 0.4142135623 );\n p = abs(p);\n p -= 2.0 * min(dot(vec2( k.x, k.y), p), 0.0) * vec2( k.x, k.y);\n p -= 2.0 * min(dot(vec2(-k.x, k.y), p), 0.0) * vec2(-k.x, k.y);\n p -= vec2(clamp(p.x, -k.z * r, k.z * r), r);\n return length(p) * sign(p.y);\n}`","pinned":false,"hidden":false,"mode":"ojs"},{"id":2330,"value":"sdHexagram = () => `\nfloat sdHexagram(in vec2 p, in float r){\n const vec4 k = vec4(-0.5, 0.8660254038, 0.5773502692, 1.7320508076);\n p = abs(p);\n p -= 2.0 * min(dot(k.xy, p), 0.0) * k.xy;\n p -= 2.0 * min(dot(k.yx, p), 0.0) * k.yx;\n p -= vec2(clamp(p.x, r * k.z, r * k.w), r);\n return length(p) * sign(p.y);\n}`","pinned":false,"hidden":false,"mode":"ojs"},{"id":2334,"value":"sdStar = () => `\nfloat sdStar(in vec2 p, in float r, in int n, in float m) {\n // next 4 lines can be precomputed for a given shape\n float an = 3.141593/float(n);\n float en = 6.283185/m;\n vec2 acs = vec2(cos(an),sin(an));\n vec2 ecs = vec2(cos(en),sin(en)); // ecs=vec2(0,1) for regular polygon,\n\n float bn = mod(atan(p.x,p.y),2.0*an) - an;\n p = length(p)*vec2(cos(bn),abs(sin(bn)));\n p -= r*acs;\n p += ecs*clamp(-dot(p,ecs), 0.0, r*acs.y/ecs.y);\n return length(p)*sign(p.x);\n}`","pinned":false,"hidden":false,"mode":"ojs"},{"id":2338,"value":"sdTrapezoid = () => `\nfloat sdTrapezoid(in vec2 p, in float r1, float r2, float he) {\n vec2 k1 = vec2(r2,he);\n vec2 k2 = vec2(r2-r1,2.0*he);\n p.x = abs(p.x);\n vec2 ca = vec2(p.x-min(p.x,(p.y<0.0)?r1:r2), abs(p.y)-he);\n vec2 cb = p - k1 + k2*clamp(dot(k1-p,k2)/dot2(k2), 0.0, 1.0);\n float s = (cb.x<0.0 && ca.y<0.0) ? -1.0 : 1.0;\n return s*sqrt(min(dot2(ca),dot2(cb)));\n}`","pinned":false,"hidden":false,"mode":"ojs"},{"id":2342,"value":"sdPie = () => `\nfloat sdPie(in vec2 p, in vec2 c, in float r) {\n p.x = abs(p.x);\n float l = length(p) - r;\n float m = length(p-c*clamp(dot(p,c),0.0,r)); // c = sin/cos of the aperture\n return max(l,m*sign(c.y*p.x-c.x*p.y));\n}`","pinned":false,"hidden":false,"mode":"ojs"},{"id":2346,"value":"sdArc = () => `\nfloat sdArc(in vec2 p, in vec2 sca, in vec2 scb, in float ra, float rb) {\n p *= mat2(sca.x,sca.y,-sca.y,sca.x);\n p.x = abs(p.x);\n float k = (scb.y*p.x>scb.x*p.y) ? dot(p.xy,scb) : length(p.xy);\n return sqrt(dot(p,p) + ra*ra - 2.0*ra*k) - rb;\n}`","pinned":false,"hidden":false,"mode":"ojs"},{"id":2350,"value":"sdHorseshoe = () => `\nfloat sdHorseshoe(in vec2 p, in vec2 c, in float r, in vec2 w) {\n p.x = abs(p.x);\n float l = length(p);\n p = mat2(-c.x, c.y, \n c.y, c.x)*p;\n p = vec2((p.y>0.0)?p.x:l*sign(-c.x),\n (p.x>0.0)?p.y:l);\n p = vec2(p.x,abs(p.y-r))-w;\n return length(max(p,0.0)) + min(0.0,max(p.x,p.y));\n}`","pinned":false,"hidden":false,"mode":"ojs"},{"id":2354,"value":"sdVesica = () => `\nfloat sdVesica(vec2 p, float r, float d) {\n p = abs(p);\n float b = sqrt(r*r-d*d);\n return ((p.y-b)*d>p.x*b) ? length(p-vec2(0.0,b))\n : length(p-vec2(-d,0.0))-r;\n}`","pinned":false,"hidden":false,"mode":"ojs"},{"id":2358,"value":"sdCross = () => `\nfloat sdCross(in vec2 p, in vec2 b, float r) {\n p = abs(p); p = (p.y>p.x) ? p.yx : p.xy;\n vec2 q = p - b;\n float k = max(q.y,q.x);\n vec2 w = (k>0.0) ? q : vec2(b.y-p.x,-k);\n return sign(k)*length(max(w,0.0)) + r;\n}`","pinned":false,"hidden":false,"mode":"ojs"},{"id":2366,"value":"sdEllipse = () => `\nfloat sdEllipse(in vec2 p, in vec2 ab) {\n p = abs(p); if(p.x > p.y) {p=p.yx;ab=ab.yx;}\n float l = ab.y*ab.y - ab.x*ab.x;\n float m = ab.x*p.x/l; float m2 = m*m; \n float n = ab.y*p.y/l; float n2 = n*n; \n float c = (m2+n2-1.0)/3.0; float c3 = c*c*c;\n float q = c3 + m2*n2*2.0;\n float d = c3 + m2*n2;\n float g = m + m*n2;\n float co;\n if(d<0.0) {\n float h = acos(q/c3)/3.0;\n float s = cos(h);\n float t = sin(h)*sqrt(3.0);\n float rx = sqrt(-c*(s + t + 2.0) + m2);\n float ry = sqrt(-c*(s - t + 2.0) + m2);\n co = (ry+sign(l)*rx+abs(g)/(rx*ry)- m)/2.0;\n }\n else {\n float h = 2.0*m*n*sqrt(d);\n float s = sign(q+h)*pow(abs(q+h), 1.0/3.0);\n float u = sign(q-h)*pow(abs(q-h), 1.0/3.0);\n float rx = -s - u - c*4.0 + 2.0*m2;\n float ry = (s - u)*sqrt(3.0);\n float rm = sqrt(rx*rx + ry*ry);\n co = (ry/sqrt(rm-rx)+2.0*g/rm-m)/2.0;\n }\n vec2 r = ab * vec2(co, sqrt(1.0-co*co));\n return length(r-p) * sign(p.y-r.y);\n}`","pinned":false,"hidden":false,"mode":"ojs"},{"id":2370,"value":"sdParabola = () => `\nfloat sdParabola(in vec2 pos, in float k) { \n pos.x = abs(pos.x);\n \n float p = (1.0-2.0*k*pos.y)/(6.0*k*k);\n float q = -abs(pos.x)/(4.0*k*k);\n \n float h = q*q + p*p*p;\n float r = sqrt(abs(h));\n\n float x = (h>0.0) ? \n pow(-q+r,1.0/3.0) - pow(abs(-q-r),1.0/3.0)*sign(q+r) :\n 2.0*cos(atan(r,-q)/3.0)*sqrt(-p);\n \n return length(pos-vec2(x,k*x*x)) * sign(pos.x-x);\n}`","pinned":false,"hidden":false,"mode":"ojs"},{"id":2270,"value":"$33","pinned":false,"hidden":false,"mode":"ojs"},{"id":2292,"value":"sdRhombus = () => `\n${ndot()}\n\nfloat sdRhombus(in vec2 p, in vec2 b) {\n vec2 q = abs(p);\n float h = clamp((-2.0 * ndot(q, b) + ndot(b, b)) / dot(b, b), -1.0, 1.0);\n float d = length(q - 0.5 * b * vec2(1.0 - h, 1.0 + h));\n return d * sign(q.x * b.y + q.y * b.x - b.x * b.y);\n}`","pinned":false,"hidden":false,"mode":"ojs"},{"id":2362,"value":"sdPolygon = (N) => `\nconst int N = ${N};\nfloat sdPolygon( in vec2[N] v, in vec2 p ) {\n const int num = v.length();\n float d = dot(p-v[0],p-v[0]);\n float s = 1.0;\n for( int i=0, j=num-1; i=v[i].y, p.ye.y*w.x );\n if( all(cond) || all(not(cond)) ) s*=-1.0; \n }\n \n return s*sqrt(d);\n}`","pinned":false,"hidden":false,"mode":"ojs"},{"id":2568,"value":"ndot = () => `\n#ifndef NDOT\n#define NDOT\nfloat ndot(vec2 a, vec2 b ) {\n return a.x*b.x - a.y*b.y;\n}\n#endif`","pinned":false,"hidden":false,"mode":"ojs"},{"id":2435,"value":"md`___`","pinned":false,"hidden":false,"mode":"ojs"},{"id":2376,"value":"md`### Making shapes rounded`","pinned":false,"hidden":false,"mode":"ojs"},{"id":2378,"value":"md`~~~glsl\nsdShape(p) - radius\n~~~`","pinned":false,"hidden":false,"mode":"ojs"},{"id":2632,"value":"await visibility(), fragment(`\nprecision mediump float;\n\nuniform vec2 u_resolution;\nuniform vec2 u_mouse;\n\n${sdRhombus()}\n\nvoid main() {\n vec2 p = (gl_FragCoord.xy - u_resolution/2.) / u_resolution.y;\n float c = smoothstep(0., 0.005, sdRhombus(p, vec2(0.2, 0.3)) - u_mouse.x / u_resolution.x);\n gl_FragColor = vec4(vec3(c), 1.0);\n}\n`, { play: false })","pinned":false,"hidden":false,"mode":"ojs"},{"id":2672,"value":"md`🎬Click to play/pause and move mouse to interact`","pinned":false,"hidden":false,"mode":"ojs"},{"id":2380,"value":"md`### Making shapes annular`","pinned":false,"hidden":false,"mode":"ojs"},{"id":2375,"value":"md`~~~glsl\nabs(sdShape(p)) - radius\n~~~`","pinned":false,"hidden":false,"mode":"ojs"},{"id":2684,"value":"await visibility(), fragment(`\nprecision mediump float;\n\nuniform vec2 u_resolution;\nuniform vec2 u_mouse;\n\n${sdRhombus()}\n\nvoid main() {\n vec2 p = (gl_FragCoord.xy - u_resolution/2.) / u_resolution.y;\n float c = smoothstep(0., 0.005, abs(sdRhombus(p, vec2(0.2, 0.3))) - u_mouse.x / (u_resolution.x * 5.));\n gl_FragColor = vec4(vec3(c), 1.0);\n}\n`, { play: false })","pinned":false,"hidden":false,"mode":"ojs"},{"id":2691,"value":"md`🎬Click to play/pause and move mouse to interact`","pinned":false,"hidden":false,"mode":"ojs"},{"id":90,"value":"md`___\n## Imports`","pinned":false,"hidden":false,"mode":"ojs"},{"id":2392,"value":"import { fragment } from '@makio135/hello-fragment'","pinned":false,"hidden":false,"mode":"ojs"}],"files":"$W34","stdlib":"1","titling":"auto"}