2b:null 2c:["$","title",null,{"children":"Unit vector vs angular interpolation | Amit Patel | Observable"}] 31:[{"id":"715db1223e067f00500780077febc6cebbdd90c151d3d78317c802732252052ab0e367039872ab9c77d6ef99e5f55a0724b35ddc898a1c99cb14c31a379af80a","href":"https://static.observableusercontent.com/files/715db1223e067f00500780077febc6cebbdd90c151d3d78317c802732252052ab0e367039872ab9c77d6ef99e5f55a0724b35ddc898a1c99cb14c31a379af80a","name":"penguins.csv","type":"text/csv","lastModified":1670702200214.566,"size":13506}] 2f:{"id":"c9259cd74d8cf0f6","slug":"unit-vector-vs-angular-interpolation","title":"Unit vector vs angular interpolation","thumbnail":"1e23682a464714b2ca7f273c42f800724f1645e683b11c5167b2c86cd8e2303e","access_level":"public","create_time":"$D2022-12-10T19:56:40.214Z","update_time":"$D2022-12-10T20:33:03.775Z","view_time":null,"first_public_time":"$D2022-12-10T19:56:40.214Z","fork":{"id":"7dcef0ebff4028d9","slug":"input-chart","title":"Input + Chart","owner":{"id":"f35c755083683fe5","login":"observablehq","name":"Observable"}},"stars":1,"starred":false,"owner":{"type":"team","id":"468ec444dc0eb0ae","login":"redblobgames","name":"Amit Patel","avatar_url":"https://avatars-next.observableusercontent.com/e8ff190af9193a0b08dfdadf3fb2e93a0519966417f0c9a2063aae07a171e6b2","tier":"starter_2024"},"version":77,"publish_version":null,"role":null,"authored":false,"authors":[{"type":"individual","id":"c7764e85dbcadc6d","login":"redblobgames","name":"Amit Patel","avatar_url":"https://avatars-next.observableusercontent.com/e8ff190af9193a0b08dfdadf3fb2e93a0519966417f0c9a2063aae07a171e6b2","tier":null}],"members":[{"type":"individual","id":"c7764e85dbcadc6d","login":"redblobgames","name":"Amit Patel","avatar_url":"https://avatars-next.observableusercontent.com/e8ff190af9193a0b08dfdadf3fb2e93a0519966417f0c9a2063aae07a171e6b2","tier":null,"role":"editor"}],"comments":[],"custom_thumbnail":false,"trashed":false,"subscribed":null,"forks":1,"collection":null,"type":"notebook","body":{"title":"Unit vector vs angular interpolation","cells":[{"id":4,"value":"# Unit vector vs angular interpolation\n\nIf you have two unit vectors and want to interpolate between them, you can either convert to angles and interpolate the angles, or you can interpolate the vectors and normalize back to unit vectors. Here's a comparison. The vector + normalize approach is close at small angles.","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined"},{"id":5,"value":"viewof Angle = Inputs.range([1, 179], {step: 1, value: 20, label: \"Angle difference\"})","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":37,"value":"","pinned":false,"hidden":false,"mode":"html","author":"$undefined","summary":"$undefined"},{"id":6,"value":"viewof N = Inputs.range([3, 200], {step: 1, value: 20, label: \"Steps\"})","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":48,"value":"function lineAtAngle(deg) {\n let [x, y] = angleToUnitVector(deg)\n return svg``\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":7,"value":"function angleToUnitVector(angleDeg) { return [Math.cos(degToRad(angleDeg)), Math.sin(degToRad(angleDeg))] }","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":23,"value":"function degToRad(deg) { return deg/180*Math.PI }","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":25,"value":"startAngle = 90 - Angle/2","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":28,"value":"endAngle = 90 + Angle/2","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":30,"value":"startVec = angleToUnitVector(startAngle)","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":32,"value":"endVec = angleToUnitVector(endAngle)","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":51,"value":"interpolatedVecs = Array.from({length: N}, (_, i) => {\n let t = i/N\n let x = lerp(startVec[0], endVec[0], t)\n let y = lerp(startVec[1], endVec[1], t)\n let d = Math.hypot(x, y)\n return [x/d, y/d]\n})","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":60,"value":"interpolatedAngles = Array.from({length: N}, (_, i) => {\n return lerp(startAngle, endAngle, i/N)\n})","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":53,"value":"function lerp(a, b, t) { return a*(1-t) + b*t }","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"}],"files":"$W31","stdlib":"1","titling":"auto"}} 30:"$2f:body"