2b:null 2c:["$","title",null,{"children":"IQ SDF | David | Observable"}] 31: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 })32: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)))' ])33: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 })34: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); }`35:[] 2f:{"id":"75115372ed5e1f0d","slug":null,"title":"IQ SDF","thumbnail":"5eb5a184a8f8e2a458da044d30d5aa2c40054aa75360f7d3c5c03fe7eb35b5ac","access_level":"public","create_time":"$D2024-10-30T16:34:48.429Z","update_time":"$D2024-10-30T16:34:48.429Z","view_time":null,"first_public_time":"$D2024-10-30T16:34:48.429Z","has_unpublished_edits":null,"fork":{"id":"06d2e2ffbaf6cd9e","slug":"iq-sdf","title":"IQ SDF","owner":{"id":"33d0c3f28420ec9c","login":"makio135","name":"Lionel Radisson"}},"stars":0,"starred":false,"owner":{"type":"team","id":"cd42f0d98191a7df","login":"dvd101x","name":"David","avatar_url":"https://avatars-next.observableusercontent.com/665b28399b8c69493837e25bfd6b1e60e5c83f5f646e274cf39b5146449e30c6","tier":"starter_2024"},"version":2832,"publish_version":null,"role":null,"authored":false,"authors":[{"type":"individual","id":"c454621e13d910d3","login":"dvd101x","name":"David","avatar_url":"https://avatars-next.observableusercontent.com/665b28399b8c69493837e25bfd6b1e60e5c83f5f646e274cf39b5146449e30c6","tier":null}],"members":[{"type":"individual","id":"c454621e13d910d3","login":"dvd101x","name":"David","avatar_url":"https://avatars-next.observableusercontent.com/665b28399b8c69493837e25bfd6b1e60e5c83f5f646e274cf39b5146449e30c6","tier":null,"role":"editor"},{"type":"team","id":"cd42f0d98191a7df","login":"dvd101x","name":"David","avatar_url":"https://avatars-next.observableusercontent.com/665b28399b8c69493837e25bfd6b1e60e5c83f5f646e274cf39b5146449e30c6","tier":"starter_2024","role":"editor"}],"comments":[],"custom_thumbnail":false,"trashed":false,"lapsed":null,"subscribed":null,"forks":0,"collection":null,"type":"notebook","body":{"titling":"auto","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","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"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","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":388,"value":"$31","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":1646,"value":"md`🎬Click to play/pause`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":2235,"value":"md`\nRead Inigo Quilez' articles for a more background:\n- http://iquilezles.org/www/articles/distfunctions/distfunctions.htm\n- http://iquilezles.org/www/articles/distfunctions2d/distfunctions2d.htm\n- [Raymarching - Primitives by Inigo Quilez on Shadertoy](https://www.shadertoy.com/view/Xds3zN)\n\nRendering made with the \\`raymarch\\` utility:`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":1624,"value":"import { raymarch, phong } from '@makio135/hello-raymarching'","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":646,"value":"md`___\n### Primitives`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":192,"value":"md`**The region where an SDF is negative represents the interior of the surface.**`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":1817,"value":"await visibility(), raymarch(`\n#define PI 3.1415926\n\n${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(${sdf}, 0.1);\n}\n`, { play: true })","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":1818,"value":"$32","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":2061,"value":"md`🎬Click to play/pause\n___`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":373,"value":"sdSphere = () => `\nfloat sdSphere(vec3 p, float radius) {\n return length(p) - radius;\n}`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":375,"value":"sdBox = () => `\nfloat sdBox(vec3 p, vec3 b) {\n vec3 d = abs(p) - b;\n return length(max(d, 0.0))\n + min(max(d.x, max(d.y, d.z)), 0.0); // remove this line for an only partially signed sdf \n}`\n","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":399,"value":"sdRoundBox = () => `\nfloat sdRoundBox(vec3 p, vec3 b, float r){\n vec3 d = abs(p) - b;\n return length(max(d, 0.0)) - r\n + min(max(d.x, max(d.y, d.z)), 0.0); // remove this line for an only partially signed sdf \n}`\n","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":2794,"value":"sdBoundingBox = () => `\nfloat sdBoundingBox(vec3 p, vec3 b, float e) {\n p = abs(p) - b;\n vec3 q = abs(p + e) - e;\n return min(min(\n length(max(vec3(p.x, q.y, q.z), 0.)) + min(max(p.x, max(q.y, q.z)),0.),\n length(max(vec3(q.x, p.y, q.z), 0.)) + min(max(q.x, max(p.y, q.z)),0.)),\n length(max(vec3(q.x, q.y, p.z), 0.)) + min(max(q.x, max(q.y, p.z)),0.));\n}`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":403,"value":"sdTorus = () => `float sdTorus(vec3 p, vec2 t){\n vec2 q = vec2(length(p.xz) - t.x, p.y);\n return length(q) - t.y;\n}`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":416,"value":"sdCappedTorus = () => `\nfloat sdCappedTorus(in vec3 p, in vec2 sc, in float ra, in float rb) {\n p.x = abs(p.x);\n float k = (sc.y * p.x > sc.x * p.y) ? dot(p.xy, sc) : length(p.xy);\n return sqrt(dot(p, p) + ra * ra - 2.0 * ra * k) - rb;\n}`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":418,"value":"sdLink = () => `\nfloat sdLink(in vec3 p, in float le, in float r1, in float r2) {\n vec3 q = vec3(p.x, max(abs(p.y) - le, 0.0), p.z);\n return length(vec2(length(q.xy) - r1, q.z)) - r2;\n}`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":424,"value":"sdCylinder = () => `\nfloat sdCylinder(vec3 p, vec3 c) {\n return length(p.xz - c.xy) - c.z;\n}`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":426,"value":"sdCone = () => `\n// Cone - bound (not exact!)\nfloat sdCone(in vec3 p, in vec2 c) {\n // c is the sin/cos of the angle\n float q = length(p.xy);\n return dot(c, vec2(q, p.z));\n}`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":2807,"value":"sdCone2 = () => `\n// Cone - exact\nfloat sdCone( in vec3 p, in vec2 c, float h ) {\n // c is the sin/cos of the angle, h is height\n // Alternatively pass q instead of (c,h),\n // which is the point at the base in 2D\n vec2 q = h*vec2(c.x/c.y,-1.0);\n\n vec2 w = vec2( length(p.xz), p.y );\n vec2 a = w - q*clamp( dot(w,q)/dot(q,q), 0.0, 1.0 );\n vec2 b = w - q*vec2( clamp( w.x/q.x, 0.0, 1.0 ), 1.0 );\n float k = sign( q.y );\n float d = min(dot( a, a ),dot(b, b));\n float s = max( k*(w.x*q.y-w.y*q.x),k*(w.y-q.y) );\n return sqrt(d)*sign(s);\n}`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":2810,"value":"sdCone3 = () => `\n// Infinite Cone - exact\nfloat sdCone( vec3 p, vec2 c ) {\n // c is the sin/cos of the angle\n vec2 q = vec2( length(p.xz), -p.y );\n float d = length(q-c*max(dot(q,c), 0.0));\n return d * ((q.x*c.y-q.y*c.x<0.0)?-1.0:1.0);\n}`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":428,"value":"sdPlane = () => `\nfloat sdPlane(vec3 p, vec4 n) {\n // n must be normalized\n return dot(p, n.xyz) + n.w;\n}`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":519,"value":"sdHexPrism = () => `\nfloat sdHexPrism(vec3 p, vec2 h) {\n const vec3 k = vec3(-0.8660254, 0.5, 0.57735);\n p = abs(p);\n p.xy -= 2.0 * min(dot(k.xy, p.xy), 0.0) * k.xy;\n vec2 d = vec2(\n length(p.xy - vec2(clamp(p.x, -k.z * h.x, k.z * h.x), h.x)) * sign(p.y - h.x),\n p.z - h.y);\n return min(max(d.x, d.y), 0.0) + length(max(d, 0.0));\n}`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":527,"value":"sdTriPrism = () => `\nfloat sdTriPrism(vec3 p, vec2 h) {\n vec3 q = abs(p);\n return max(q.z - h.y, max(q.x * 0.866025 + p.y * 0.5, -p.y) - h.x * 0.5);\n}`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":534,"value":"sdCapsule = () => `\nfloat sdCapsule(vec3 p, vec3 a, vec3 b, float r) {\n vec3 pa = p - a, ba = b - a;\n float h = clamp(dot(pa, ba) / dot(ba, ba), 0.0, 1.0);\n return length(pa - ba * h) - r;\n}`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":536,"value":"sdVerticalCapsule = () => `\nfloat sdVerticalCapsule(vec3 p, float h, float r) {\n p.y -= clamp(p.y, 0.0, h);\n return length(p) - r;\n}`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":538,"value":"sdCappedCylinder = () => `\nfloat sdCappedCylinder(vec3 p, float h, float r) {\n vec2 d = abs(vec2(length(p.xz), p.y)) - vec2(r, h);\n return min(max(d.x, d.y), 0.0) + length(max(d, 0.0));\n}`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":540,"value":"sdCappedCylinder2 = () => `\nfloat sdCappedCylinder2(vec3 p, vec3 a, vec3 b, float r) {\n vec3 ba = b - a;\n vec3 pa = p - a;\n float baba = dot(ba, ba);\n float paba = dot(pa, ba);\n float x = length(pa * baba - ba * paba) - r * baba;\n float y = abs(paba - baba * 0.5) - baba * 0.5;\n float x2 = x * x;\n float y2 = y * y * baba;\n float d = (max(x, y) < 0.0) ? -min(x2, y2) : (((x > 0.0) ? x2 : 0.0) + ((y > 0.0) ? y2 : 0.0));\n return sign(d) * sqrt(abs(d)) / baba;\n}`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":543,"value":"sdRoundedCylinder = () => `\nfloat sdRoundedCylinder(vec3 p, float ra, float rb, float h) {\n vec2 d = vec2(length(p.xz) - 2.0 * ra + rb, abs(p.y) - h);\n return min(max(d.x, d.y), 0.0) + length(max(d, 0.0)) - rb;\n}`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":546,"value":"sdCappedCone = () => `\n${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","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"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","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"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","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"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","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"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","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"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","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"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","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":561,"value":"udTriangle = () => `\n${dot2()}\n\nfloat udTriangle( vec3 p, vec3 a, vec3 b, vec3 c) {\n vec3 ba = b - a; \n vec3 pa = p - a;\n vec3 cb = c - b;\n vec3 pb = p - b;\n vec3 ac = a - c;\n vec3 pc = p - c;\n vec3 nor = cross(ba, ac);\n\n return sqrt(\n (sign(dot(cross(ba, nor), pa)) +\n sign(dot(cross(cb, nor), pb)) +\n sign(dot(cross(ac, nor), pc)) < 2.0) ?\n min(min(\n dot2(ba * clamp(dot(ba, pa) / dot(ba, ba), 0.0, 1.0) - pa),\n dot2(cb * clamp(dot(cb, pb) / dot(cb, cb), 0.0, 1.0) - pb)),\n dot2(ac * clamp(dot(ac, pc) / dot(ac, ac), 0.0, 1.0) - pc)) :\n dot(nor, pa) * dot(nor, pa) / dot(nor, nor));\n}`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":565,"value":"udQuad = () => `\n${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","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"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","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":570,"value":"md`___\n### Primitive alterations`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":888,"value":"md`#### Elongation\nhttps://www.shadertoy.com/view/Ml3fWj`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"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","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":2264,"value":"md`🎬Click to play/pause`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"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","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"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","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":893,"value":"md`#### Rounding\nhttps://www.shadertoy.com/view/Mt3BDj`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"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","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":2261,"value":"md`🎬Click to play/pause`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":589,"value":"opRound = () => `\nfloat opRound(float sdf, float rad) {\n return sdf - rad;\n}`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":899,"value":"md`#### Onion\nhttps://www.shadertoy.com/view/MlcBDj`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":2092,"value":"await visibility(), raymarch(`\n${opOnion()}\n${rotateX()}\n${sdTorus()}\n\nvec2 sceneSDF(vec3 p) {\n float d = opOnion(opOnion(opOnion(sdTorus(p.xzy, vec2(1.5, 0.2)), 0.08), 0.04), 0.02);\n d = max(d, p.y + sin(u_time) * 1.8);\n return vec2(d, 1.0);\n}\n`, { play: false })","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":2258,"value":"md`🎬Click to play/pause`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":587,"value":"opOnion = () => `\nfloat opOnion(in float sdf, in float thickness) {\n return abs(sdf) - thickness;\n}`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":901,"value":"md`#### Revolution and extrusion from 2D\nhttps://www.shadertoy.com/view/4lyfzw`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":1441,"value":"await visibility(), raymarch(`\n${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","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":1651,"value":"md`🎬Click to play/pause`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"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","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"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","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"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","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":2242,"value":"await visibility(), raymarch(`\n${rotateY()}\n${length6()}\n${sdSphere().replace('length', 'length6')}\n\nvec2 sceneSDF(vec3 p) {\n p = rotateY(u_time / 2.) * p;\n float d = sdSphere(p, 1.0);\n return vec2(d, 1.0);\n}\n`, { play: false })","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":2656,"value":"md`🎬Click to play/pause`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":792,"value":"length2 = () => `\nfloat length2(vec3 p) {\n p = p * p;\n return sqrt(p.x + p.y + p.z);\n}`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":794,"value":"length6 = () => `\nfloat length6(vec3 p) {\n p = p * p * p;\n p = p * p;\n return pow(p.x + p.y + p.z, 1.0 / 6.0);\n}`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":586,"value":"length8 = () => `\nfloat length8( vec3 p) {\n p = p * p;\n p = p * p;\n p = p * p;\n return pow(p.x + p.y + p.z, 1.0 / 8.0);\n}`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":610,"value":"md`___\n### Primitive combinations`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":613,"value":"opUnion = () => `\nfloat opUnion(float d1, float d2) {\n return min(d1, d2);\n}\nvec2 opUnion(vec2 d1, vec2 d2) {\n return d1.x < d2.x ? d1 : d2;\n}`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":615,"value":"opSubtraction = () => `\n// subtract d1 from d2\nfloat opSubtraction(float d1, float d2) {\n return max(-d1, d2);\n}\nvec2 opSubtraction(vec2 d1, vec2 d2) {\n d1.x = -d1.x;\n return d1.x > d2.x ? d1 : d2;\n}`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":582,"value":"opIntersection = () => `\nfloat opIntersection(float d1, float d2) {\n return max(d1, d2);\n}\nvec2 opIntersection(vec2 d1, vec2 d2) {\n return d1.x > d2.x ? d1 : d2;\n}`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":617,"value":"opSmoothUnion = () => `\n// from http://www.iquilezles.org/www/articles/smin/smin.htm\nfloat opSmoothUnion(float a, float b, float k) {\n float h = max(k - abs(a - b), 0.0 ) / k;\n return min(a, b) - h * h * h * k * (1.0 / 6.0);\n}`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":619,"value":"opSmoothSubtraction = () => `\nfloat opSmoothSubtraction(float d1, float d2, float k) {\n float h = clamp(0.5 - 0.5 * (d2 + d1) / k, 0.0, 1.0);\n return mix(d2, -d1, h) + k * h * (1.0 - h);\n}`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":591,"value":"opSmoothIntersection = () => `\nfloat opSmoothIntersection(float d1, float d2, float k) {\n float h = clamp(0.5 - 0.5 * (d2 - d1) / k, 0.0, 1.0);\n return mix(d2, d1, h) + k * h * (1.0 - h);\n}`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":1410,"value":"$33","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":1654,"value":"md`🎬Click to play/pause`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":1090,"value":"opBlend = () => `\n// from https://www.alanzucconi.com/2016/07/01/signed-distance-functions/#part4\nfloat opBlend(float sdf1, float sdf2, float amount) {\n return amount * sdf1 + (1. - amount) * sdf2;\n}`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":1380,"value":"await visibility(), raymarch(`\n${rotateY()}\n${sdSphere()}\n${sdOctahedron()}\n${opBlend()}\n\nvec2 sceneSDF(vec3 p) {\n p = rotateY(u_time + 0.45) * p;\n\n float s = sdSphere(p, 2.0);\n float o = sdOctahedron(p, 2.0);\n float d = opBlend(s, o, sin(u_time - 0.55) / 2. + 0.5);\n return vec2(d, 1.0);\n}\n`, { play: false })","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":1657,"value":"md`🎬Click to play/pause`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":606,"value":"md`___\n### Positioning`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":1566,"value":"md`#### Translation\n~~~glsl\nvec3 q = position - translation;\n~~~\n`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":1805,"value":"opTranslate = () => `\nvec3 opTranslate(vec3 p, vec3 tr) {\n return p - tr;\n}`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":1563,"value":"md`#### Rotation`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":1543,"value":"rotateX = () => `\n// Rotation matrix around the X axis.\nmat3 rotateX(float theta) {\n float c = cos(theta);\n float s = sin(theta);\n return mat3(\n vec3(1, 0, 0),\n vec3(0, c, -s),\n vec3(0, s, c)\n );\n}`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":1546,"value":"rotateY = () => `\n// Rotation matrix around the Y axis.\nmat3 rotateY(float theta) {\n float c = cos(theta);\n float s = sin(theta);\n return mat3(\n vec3(c, 0, s),\n vec3(0, 1, 0),\n vec3(-s, 0, c)\n );\n}`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":1549,"value":"rotateZ = () => `\n// Rotation matrix around the Z axis.\nmat3 rotateZ(float theta) {\n float c = cos(theta);\n float s = sin(theta);\n return mat3(\n vec3(c, -s, 0),\n vec3(s, c, 0),\n vec3(0, 0, 1)\n );\n}`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":1555,"value":"md`#### Scaling\nFor uniform scaling, we can use:\n~~~glsl\nfloat dist = some3D_SDF(position / scalingFactor) * scalingFactor;\n~~~\n\nFor non-uniform scaling:\n~~~glsl\nfloat dist = some3D_SDF(position / vec3(s_x, s_y, s_z)) * min(s_x, min(s_y, s_z));\n~~~\n\n`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":1333,"value":"md`#### Symmetry - bound and exact`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":1586,"value":"await visibility(), raymarch(`\n${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","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":2638,"value":"md`🎬Click to play/pause`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":630,"value":"opSymX = () => `\nvec3 opSymX(vec3 p) {\n p.x = abs(p.x);\n return p;\n}`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":1999,"value":"opSymY = () => `\nvec3 opSymY(vec3 p) {\n p.y = abs(p.y);\n return p;\n}`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":2000,"value":"opSymZ = () => `\nvec3 opSymZ(vec3 p) {\n p.z = abs(p.z);\n return p;\n}`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":635,"value":"opSymXY = () => `\nvec3 opSymXY(vec3 p) {\n p.xy = abs(p.xy);\n return p;\n}`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":2008,"value":"opSymXZ = () => `\nvec3 opSymXZ(vec3 p) {\n p.xz = abs(p.xz);\n return p;\n}`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":2010,"value":"opSymYZ = () => `\nvec3 opSymYZ(vec3 p) {\n p.yz = abs(p.yz);\n return p;\n}`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":2015,"value":"opSymXYZ = () => `\nvec3 opSymXYZ(vec3 p) {\n p = abs(p);\n return p;\n}`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":1350,"value":"md`#### Infinite Repetition`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"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","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":2641,"value":"md`🎬Click to play/pause`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"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","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":1354,"value":"md`#### Finite Repetition`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"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","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":2644,"value":"md`🎬Click to play/pause`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"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","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":595,"value":"md`___\n### Deformations and distortions`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":1357,"value":"md`#### Displacement`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"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","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":2646,"value":"md`🎬Click to play/pause`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":599,"value":"md`~~~glsl\nfloat d1 = primitive(p);\nfloat d2 = displacement(p);\nreturn d1 + d2;\n~~~`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":1358,"value":"md`#### Twist`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"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","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":2649,"value":"md`🎬Click to play/pause`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"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","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":1360,"value":"md`#### Bend`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"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","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":2652,"value":"md`🎬Click to play/pause`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"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","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":2267,"value":"md`___\n## 2D SDF`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"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, ${sdf2d});\n gl_FragColor = vec4(vec3(d), 1.0);\n}\n`)","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":2408,"value":"viewof sdf2d = Inputs.select([\n 'sdCircle(p, 0.2)',\n 'sdLine(p, vec2(-0.5, -0.3), vec2(0.5, 0.3))',\n 'sdRect(p, vec2(0.6, 0.3))',\n 'sdEquilateralTriangle(p * 2.)',\n 'sdTriangleIsocele(p, vec2(0.2, 0.6))',\n 'sdUnevenCapsule(p, 0.05, 0.1, 0.3)',\n 'sdTriangle(p, vec2(-0.4), vec2(0., 0.4), vec2(0.3, 0.))',\n 'sdPentagon(p, 0.4)',\n 'sdHexagon(p, 0.4)',\n 'sdOctogon(p, 0.4)',\n 'sdHexagram(p, 0.2)',\n 'sdStar(p, 0.35, 7, 0.9)',\n 'sdTrapezoid(p, 0.35, 0.3, 0.2)',\n 'sdPie(p, vec2(sin(radians(45.)), cos(radians(45.))), 0.5)',\n 'sdArc(p, vec2(sin(radians(45.)), cos(radians(45.))), vec2(sin(radians(115.)), cos(radians(115.))), 0.2, 0.015)',\n 'sdHorseshoe(p, vec2(sin(radians(15.)), cos(radians(15.))), 0.3, vec2(0.2, 0.05))',\n 'sdVesica(p, 0.3, 0.1)',\n 'sdCross(p, vec2(0.4, 0.1), 0.05)',\n 'sdEllipse(p, vec2(0.1, 0.3))',\n 'sdParabola(p, 0.9)',\n 'sdBezier(p, vec2(-0.8, 0.3), vec2(-0.3, -0.5), vec2(0.5))',\n 'sdRhombus(p, vec2(0.2, 0.4))'\n].reverse())","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":2276,"value":"sdCircle = () => `\nfloat sdCircle(vec2 p, float r){\n return length(p) - r;\n}`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":2282,"value":"sdLine = () => `\nfloat sdLine(in vec2 p, in vec2 a, in vec2 b){\n vec2 pa = p - a;\n vec2 ba = b - a;\n float h = clamp(dot(pa, ba) / dot(ba, ba), 0.0, 1.0);\n return length(pa - ba * h);\n}`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":2286,"value":"sdRect = () => `\nfloat sdRect(in vec2 p, in vec2 b) {\n vec2 d = abs(p) - b;\n return length(max(d, vec2(0))) + min(max(d.x, d.y), 0.0);\n}`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":2296,"value":"sdEquilateralTriangle = () => `\nfloat sdEquilateralTriangle(in vec2 p) {\n const float k = sqrt(3.0);\n p.x = abs(p.x) - 1.0;\n p.y = p.y + 1.0 / k;\n if(p.x + k * p.y > 0.0) p = vec2(p.x - k * p.y, - k * p.x - p.y) / 2.0;\n p.x -= clamp(p.x, -2.0, 0.0);\n return -length(p) * sign(p.y);\n}`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":2305,"value":"sdTriangleIsocele = () => `\nfloat sdTriangleIsocele(in vec2 p, in vec2 q) {\n p.x = abs(p.x);\n vec2 a = p - q*clamp( dot(p,q)/dot(q,q), 0.0, 1.0 );\n vec2 b = p - q*vec2( clamp( p.x/q.x, 0.0, 1.0 ), 1.0 );\n float s = -sign( q.y );\n vec2 d = min( vec2( dot(a,a), s*(p.x*q.y-p.y*q.x) ),\n vec2( dot(b,b), s*(p.y-q.y) ));\n return -sqrt(d.x)*sign(d.y);\n}`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":2309,"value":"sdUnevenCapsule = () => `\nfloat sdUnevenCapsule(vec2 p, float r1, float r2, float h) {\n p.x = abs(p.x);\n float b = (r1 - r2) / h;\n float a = sqrt(1.0 - b * b);\n float k = dot(p, vec2(-b, a));\n if(k < 0.0) return length(p) - r1;\n if(k > a * h) return length(p - vec2(0.0, h)) - r2;\n return dot(p, vec2(a, b) ) - r1;\n}`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":2313,"value":"sdTriangle = () => `\nfloat sdTriangle(in vec2 p, in vec2 p0, in vec2 p1, in vec2 p2) {\n vec2 e0 = p1 - p0, e1 = p2-p1, e2 = p0-p2;\n vec2 v0 = p - p0, v1 = p -p1, v2 = p -p2;\n vec2 pq0 = v0 - e0 * clamp(dot(v0, e0) / dot(e0, e0), 0.0, 1.0);\n vec2 pq1 = v1 - e1 * clamp(dot(v1, e1) / dot(e1, e1), 0.0, 1.0);\n vec2 pq2 = v2 - e2 * clamp(dot(v2, e2) / dot(e2, e2), 0.0, 1.0);\n float s = sign(e0.x * e2.y - e0.y * e2.x);\n vec2 d = min(min(vec2(dot(pq0, pq0), s * (v0.x * e0.y - v0.y * e0.x)),\n vec2(dot(pq1, pq1), s * (v1.x * e1.y - v1.y * e1.x))),\n vec2(dot(pq2, pq2), s * (v2.x * e2.y - v2.y * e2.x)));\n return -sqrt(d.x) * sign(d.y);\n}`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":2318,"value":"sdPentagon = () => `\nfloat sdPentagon(in vec2 p, in float r) {\n const vec3 k = vec3(0.809016994, 0.587785252, 0.726542528);\n p.x = abs(p.x);\n p -= 2.0 * min(dot(vec2(-k.x, k.y), p), 0.0) * vec2(-k.x, k.y);\n p -= 2.0 * min(dot(vec2(k.x, k.y), p), 0.0) * vec2(k.x, k.y);\n p -= vec2(clamp(p.x, -r * k.z,r * k.z), r);\n return length(p) * sign(p.y);\n}`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":2322,"value":"sdHexagon = () => `\nfloat sdHexagon(in vec2 p, in float r) {\n const vec3 k = vec3(-0.866025404, 0.5, 0.577350269);\n p = abs(p);\n p -= 2.0 * min(dot(k.xy, p), 0.0) * k.xy;\n p -= vec2(clamp(p.x, -k.z * r, k.z * r), r);\n return length(p) * sign(p.y);\n}`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":2326,"value":"sdOctogon = () => `\nfloat sdOctogon(in vec2 p, in float r) {\n const vec3 k = vec3(-0.9238795325, 0.3826834323, 0.4142135623 );\n p = abs(p);\n p -= 2.0 * min(dot(vec2( k.x, k.y), p), 0.0) * vec2( k.x, k.y);\n p -= 2.0 * min(dot(vec2(-k.x, k.y), p), 0.0) * vec2(-k.x, k.y);\n p -= vec2(clamp(p.x, -k.z * r, k.z * r), r);\n return length(p) * sign(p.y);\n}`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":2330,"value":"sdHexagram = () => `\nfloat sdHexagram(in vec2 p, in float r){\n const vec4 k = vec4(-0.5, 0.8660254038, 0.5773502692, 1.7320508076);\n p = abs(p);\n p -= 2.0 * min(dot(k.xy, p), 0.0) * k.xy;\n p -= 2.0 * min(dot(k.yx, p), 0.0) * k.yx;\n p -= vec2(clamp(p.x, r * k.z, r * k.w), r);\n return length(p) * sign(p.y);\n}`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":2334,"value":"sdStar = () => `\nfloat sdStar(in vec2 p, in float r, in int n, in float m) {\n // next 4 lines can be precomputed for a given shape\n float an = 3.141593/float(n);\n float en = 6.283185/m;\n vec2 acs = vec2(cos(an),sin(an));\n vec2 ecs = vec2(cos(en),sin(en)); // ecs=vec2(0,1) for regular polygon,\n\n float bn = mod(atan(p.x,p.y),2.0*an) - an;\n p = length(p)*vec2(cos(bn),abs(sin(bn)));\n p -= r*acs;\n p += ecs*clamp(-dot(p,ecs), 0.0, r*acs.y/ecs.y);\n return length(p)*sign(p.x);\n}`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":2338,"value":"sdTrapezoid = () => `\nfloat sdTrapezoid(in vec2 p, in float r1, float r2, float he) {\n vec2 k1 = vec2(r2,he);\n vec2 k2 = vec2(r2-r1,2.0*he);\n p.x = abs(p.x);\n vec2 ca = vec2(p.x-min(p.x,(p.y<0.0)?r1:r2), abs(p.y)-he);\n vec2 cb = p - k1 + k2*clamp(dot(k1-p,k2)/dot2(k2), 0.0, 1.0);\n float s = (cb.x<0.0 && ca.y<0.0) ? -1.0 : 1.0;\n return s*sqrt(min(dot2(ca),dot2(cb)));\n}`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":2342,"value":"sdPie = () => `\nfloat sdPie(in vec2 p, in vec2 c, in float r) {\n p.x = abs(p.x);\n float l = length(p) - r;\n float m = length(p-c*clamp(dot(p,c),0.0,r)); // c = sin/cos of the aperture\n return max(l,m*sign(c.y*p.x-c.x*p.y));\n}`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":2346,"value":"sdArc = () => `\nfloat sdArc(in vec2 p, in vec2 sca, in vec2 scb, in float ra, float rb) {\n p *= mat2(sca.x,sca.y,-sca.y,sca.x);\n p.x = abs(p.x);\n float k = (scb.y*p.x>scb.x*p.y) ? dot(p.xy,scb) : length(p.xy);\n return sqrt(dot(p,p) + ra*ra - 2.0*ra*k) - rb;\n}`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":2350,"value":"sdHorseshoe = () => `\nfloat sdHorseshoe(in vec2 p, in vec2 c, in float r, in vec2 w) {\n p.x = abs(p.x);\n float l = length(p);\n p = mat2(-c.x, c.y, \n c.y, c.x)*p;\n p = vec2((p.y>0.0)?p.x:l*sign(-c.x),\n (p.x>0.0)?p.y:l);\n p = vec2(p.x,abs(p.y-r))-w;\n return length(max(p,0.0)) + min(0.0,max(p.x,p.y));\n}`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":2354,"value":"sdVesica = () => `\nfloat sdVesica(vec2 p, float r, float d) {\n p = abs(p);\n float b = sqrt(r*r-d*d);\n return ((p.y-b)*d>p.x*b) ? length(p-vec2(0.0,b))\n : length(p-vec2(-d,0.0))-r;\n}`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":2358,"value":"sdCross = () => `\nfloat sdCross(in vec2 p, in vec2 b, float r) {\n p = abs(p); p = (p.y>p.x) ? p.yx : p.xy;\n vec2 q = p - b;\n float k = max(q.y,q.x);\n vec2 w = (k>0.0) ? q : vec2(b.y-p.x,-k);\n return sign(k)*length(max(w,0.0)) + r;\n}`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":2366,"value":"sdEllipse = () => `\nfloat sdEllipse(in vec2 p, in vec2 ab) {\n p = abs(p); if(p.x > p.y) {p=p.yx;ab=ab.yx;}\n float l = ab.y*ab.y - ab.x*ab.x;\n float m = ab.x*p.x/l; float m2 = m*m; \n float n = ab.y*p.y/l; float n2 = n*n; \n float c = (m2+n2-1.0)/3.0; float c3 = c*c*c;\n float q = c3 + m2*n2*2.0;\n float d = c3 + m2*n2;\n float g = m + m*n2;\n float co;\n if(d<0.0) {\n float h = acos(q/c3)/3.0;\n float s = cos(h);\n float t = sin(h)*sqrt(3.0);\n float rx = sqrt(-c*(s + t + 2.0) + m2);\n float ry = sqrt(-c*(s - t + 2.0) + m2);\n co = (ry+sign(l)*rx+abs(g)/(rx*ry)- m)/2.0;\n }\n else {\n float h = 2.0*m*n*sqrt(d);\n float s = sign(q+h)*pow(abs(q+h), 1.0/3.0);\n float u = sign(q-h)*pow(abs(q-h), 1.0/3.0);\n float rx = -s - u - c*4.0 + 2.0*m2;\n float ry = (s - u)*sqrt(3.0);\n float rm = sqrt(rx*rx + ry*ry);\n co = (ry/sqrt(rm-rx)+2.0*g/rm-m)/2.0;\n }\n vec2 r = ab * vec2(co, sqrt(1.0-co*co));\n return length(r-p) * sign(p.y-r.y);\n}`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":2370,"value":"sdParabola = () => `\nfloat sdParabola(in vec2 pos, in float k) { \n pos.x = abs(pos.x);\n \n float p = (1.0-2.0*k*pos.y)/(6.0*k*k);\n float q = -abs(pos.x)/(4.0*k*k);\n \n float h = q*q + p*p*p;\n float r = sqrt(abs(h));\n\n float x = (h>0.0) ? \n pow(-q+r,1.0/3.0) - pow(abs(-q-r),1.0/3.0)*sign(q+r) :\n 2.0*cos(atan(r,-q)/3.0)*sqrt(-p);\n \n return length(pos-vec2(x,k*x*x)) * sign(pos.x-x);\n}`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":2270,"value":"$34","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":2292,"value":"sdRhombus = () => `\n${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","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":2362,"value":"sdPolygon = (N) => `\nconst int N = ${N};\nfloat sdPolygon( in vec2[N] v, in vec2 p ) {\n const int num = v.length();\n float d = dot(p-v[0],p-v[0]);\n float s = 1.0;\n for( int i=0, j=num-1; i=v[i].y, p.ye.y*w.x );\n if( all(cond) || all(not(cond)) ) s*=-1.0; \n }\n \n return s*sqrt(d);\n}`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":2568,"value":"ndot = () => `\n#ifndef NDOT\n#define NDOT\nfloat ndot(vec2 a, vec2 b ) {\n return a.x*b.x - a.y*b.y;\n}\n#endif`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":2435,"value":"md`___`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":2376,"value":"md`### Making shapes rounded`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":2378,"value":"md`~~~glsl\nsdShape(p) - radius\n~~~`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":2632,"value":"await visibility(), fragment(`\nprecision mediump float;\n\nuniform vec2 u_resolution;\nuniform vec2 u_mouse;\n\n${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","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":2672,"value":"md`🎬Click to play/pause and move mouse to interact`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":2380,"value":"md`### Making shapes annular`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":2375,"value":"md`~~~glsl\nabs(sdShape(p)) - radius\n~~~`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":2684,"value":"await visibility(), fragment(`\nprecision mediump float;\n\nuniform vec2 u_resolution;\nuniform vec2 u_mouse;\n\n${sdRhombus()}\n\nvoid main() {\n vec2 p = (gl_FragCoord.xy - u_resolution/2.) / u_resolution.y;\n float c = smoothstep(0., 0.005, abs(sdRhombus(p, vec2(0.2, 0.3))) - u_mouse.x / (u_resolution.x * 5.));\n gl_FragColor = vec4(vec3(c), 1.0);\n}\n`, { play: false })","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":2691,"value":"md`🎬Click to play/pause and move mouse to interact`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":90,"value":"md`___\n## Imports`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":2392,"value":"import { fragment } from '@makio135/hello-fragment'","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"}],"files":"$W35","stdlib":"1"}} 30:"$2f:body"