2a:null 2b:["$","title",null,{"children":"Sinusoid as Cubic Bezier | Dmitry Baranovskiy | Observable"}] 31:[] 2e:{"id":"d630667f72f30871","slug":"sinusoid-as-cubic-bezier","title":"Sinusoid as Cubic Bezier","thumbnail":"656f07a9429a3b22c461bab078ca2df1d48ce90b8e661a491d047c9d0cc200bc","access_level":"public","create_time":"$D2022-01-31T06:38:34.022Z","update_time":"$D2022-11-22T01:04:58.454Z","view_time":null,"first_public_time":"$D2022-03-20T23:57:14.893Z","fork":false,"stars":1,"starred":false,"owner":{"type":"team","id":"e3672025b6b6f436","login":"dmitrybaranovskiy","name":"Dmitry Baranovskiy","avatar_url":"https://avatars-next.observableusercontent.com/c31e7f084a49a6e09f7724ab70028e1f8a03923326f084b8f9e86a014705daf0","tier":"starter_2024"},"version":112,"publish_version":null,"role":null,"authored":false,"authors":[{"type":"individual","id":"230ca2847200ccc9","login":"dmitrybaranovskiy","name":"Dmitry Baranovskiy","avatar_url":"https://avatars-next.observableusercontent.com/c31e7f084a49a6e09f7724ab70028e1f8a03923326f084b8f9e86a014705daf0","tier":null}],"members":[{"type":"individual","id":"230ca2847200ccc9","login":"dmitrybaranovskiy","name":"Dmitry Baranovskiy","avatar_url":"https://avatars-next.observableusercontent.com/c31e7f084a49a6e09f7724ab70028e1f8a03923326f084b8f9e86a014705daf0","tier":null,"role":"editor"}],"comments":[],"custom_thumbnail":false,"trashed":false,"subscribed":null,"forks":0,"collection":null,"type":"notebook","body":{"title":"Sinusoid as Cubic Bezier","cells":[{"id":0,"value":"# Sinusoid as Cubic Bezier","pinned":false,"hidden":false,"mode":"md"},{"id":19,"value":"","pinned":false,"hidden":false,"mode":"html"},{"id":3,"value":"viewof wl = Inputs.range([10, 1000], {\n value: 500,\n step: 1,\n label: \"Wavelength (w)\"\n})","pinned":false,"hidden":false,"mode":"ojs"},{"id":7,"value":"viewof ampl = Inputs.range([-5, 5], {\n value: 0.5,\n step: 0.01,\n label: \"Amplitude (A)\"\n})","pinned":false,"hidden":false,"mode":"ojs"},{"id":43,"value":"https://math.stackexchange.com/questions/4235124/getting-the-most-accurate-bezier-curve-that-plots-a-sine-wave","pinned":false,"hidden":false,"mode":"md"},{"id":55,"value":"a=\\frac{Aw}{2\\pi}\\approx${Math.round((ampl * wl) / (2 * Math.PI) * 1000)/1000}","pinned":false,"hidden":false,"mode":"tex"},{"id":61,"value":"v=2a\\sqrt{3}\\approx${Math.round(2*Math.sqrt(3) *(ampl * wl) / (2 * Math.PI) * 1000)/1000}","pinned":false,"hidden":false,"mode":"tex"},{"id":67,"value":"u=\\left(\\frac{8}{3}-\\sqrt{3}\\right)\\frac{w}{2}\\approx${Math.round(((8 / 3 - Math.sqrt(3)) * wl) / 2 * 1000) / 1000}","pinned":false,"hidden":false,"mode":"tex"},{"id":96,"value":"sin = getSinusoid(wl, ampl)","pinned":false,"hidden":false,"mode":"ojs"},{"id":31,"value":"getSinusoid = (wavelength, amplitude, dx = 0, dy = 0) => {\n const amp = (amplitude * wavelength) / (2 * Math.PI);\n const sq3 = 3 ** 0.5;\n const v = 2 * sq3 * amp;\n const u = ((8 / 3 - sq3) * wavelength) / 2;\n return [u + dx, dy - v, wavelength - u + dx, v + dy, wavelength + dx, dy];\n}","pinned":false,"hidden":false,"mode":"ojs"}],"files":"$W31","stdlib":"1","titling":"auto"}} 2f:"$2e:body"