30:[] 2e:{"title":"Vector Math","cells":[{"id":0,"value":"md`# Vector Math\n\nFunctions for doing linear algebra.\n\n~~~js\nimport { vecmath } from \"@harrystevens/vector-math@254\";\n~~~\n`","pinned":false,"hidden":false,"mode":"ojs"},{"id":18,"value":"vecmath = ({\n abs,\n add,\n sub,\n mult,\n div,\n limit,\n normalize,\n setMag,\n getMag,\n dot,\n project,\n ang,\n dist,\n trans,\n invalid\n});","pinned":true,"hidden":false,"mode":"ojs"},{"id":21,"value":"md`## Arithmetic`","pinned":false,"hidden":false,"mode":"ojs"},{"id":252,"value":"abs = v => {\n const out = [];\n for (let i = 0; i < v.length; i++){\n out[i] = Math.abs(v[i]);\n }\n return out;\n}","pinned":true,"hidden":false,"mode":"ojs"},{"id":9,"value":"// Add vector w to vector v\nadd = (v, w) => {\n let out = [];\n for (let i = 0; i < v.length; i++){\n out[i] = v[i] + w[i];\n }\n return out;\n}","pinned":true,"hidden":false,"mode":"ojs"},{"id":11,"value":"// Subtract vector w from vector v\nsub = (v, w) => {\n let out = [];\n for (let i = 0; i < v.length; i++){\n out[i] = v[i] - w[i];\n }\n return out;\n}","pinned":true,"hidden":false,"mode":"ojs"},{"id":13,"value":"// Multiply vector v by w, either a vector of equal length or a scalar\nmult = (v, w) => {\n let that = [];\n if (typeof w === \"number\"){\n for (let i = 0; i < v.length; i++){\n that[i] = w;\n }\n }\n else {\n that = w; \n }\n let out = [];\n for (let i = 0; i < v.length; i++){\n out[i] = v[i] * that[i];\n }\n return out;\n}","pinned":true,"hidden":false,"mode":"ojs"},{"id":15,"value":"// Divide vector v by w, either a vector of equal length or a scalar\ndiv = (v, w) => {\n let that = [];\n if (typeof w === \"number\"){\n for (let i = 0; i < v.length; i++){\n that[i] = w;\n }\n }\n else {\n that = w; \n }\n let out = [];\n for (let i = 0; i < v.length; i++){\n out[i] = v[i] / that[i];\n }\n \n return out;\n}","pinned":true,"hidden":false,"mode":"ojs"},{"id":73,"value":"// Limit the magnitude of this vector to the value used for the n parameter.\nlimit = (v, n) => {\n let out = v;\n \n const sq = Math.pow(getMag(v), 2);\n if (sq > n * n){\n out = div(out, Math.sqrt(sq));\n out = mult(out, n);\n }\n return out;\n}","pinned":true,"hidden":false,"mode":"ojs"},{"id":82,"value":"// Normalize the vector to length 1 (make it a unit vector).\nnormalize = v => {\n const m = getMag(v), l = v.length;\n return m ? mult(v, 1 / m) : v.map(d => 1 / l);\n}","pinned":true,"hidden":false,"mode":"ojs"},{"id":97,"value":"// Get the magnitude of a vector\ngetMag = v => {\n let l = v.length, sums = 0;\n \n for (let i = 0; i < l; i++){\n sums += v[i] * v[i];\n }\n \n return Math.sqrt(sums);\n}","pinned":true,"hidden":false,"mode":"ojs"},{"id":80,"value":"// Set the magnitude of this vector to the value used for the n parameter.\nsetMag = (v, n) => {\n return mult(normalize(v), n);\n}","pinned":true,"hidden":false,"mode":"ojs"},{"id":271,"value":"// Compute the dot product or inner product\ndot = (v1, v2) => {\n let o = 0;\n for (let i = 0, l = v1.length; i < l; i++){\n o += v1[i] * v2[i];\n }\n return o;\n}","pinned":true,"hidden":false,"mode":"ojs"},{"id":281,"value":"// Projects vector v1 onto vector v2\nproject = (v1, v2) => {\n return mult(v2, dot(v1, v2) / dot(v2, v2))\n}","pinned":true,"hidden":false,"mode":"ojs"},{"id":30,"value":"md`## Geometry`","pinned":false,"hidden":false,"mode":"ojs"},{"id":34,"value":"// Angle from vector v to vector w in radians\n// Only works for 2d vectors\nang = (v, w) => Math.atan2(w[1] - v[1], w[0] - v[0]);","pinned":true,"hidden":false,"mode":"ojs"},{"id":743,"value":"dist([2, 1], project([2, 1], [6, 8]))","pinned":true,"hidden":false,"mode":"ojs"},{"id":746,"value":"Math.pow(2 - 6/5, 2) + Math.pow(1 - 8/5, 2)","pinned":true,"hidden":false,"mode":"ojs"},{"id":39,"value":"// Distance from position of vector v to position of vector w in pixels\ndist = (v, w) => {\n let sum = 0;\n for (let i = 0, l = v.length; i < l; i++){\n sum += Math.pow(w[i] - v[i], 2);\n }\n return Math.sqrt(sum);\n}","pinned":true,"hidden":false,"mode":"ojs"},{"id":44,"value":"// Translate position of vector v by an angle in radians and a distance in pixels\ntrans = (v, ang, dist) => [v[0] + dist * Math.cos(ang), v[1] + dist * Math.sin(ang)];","pinned":true,"hidden":false,"mode":"ojs"},{"id":160,"value":"md`## Errors`","pinned":false,"hidden":false,"mode":"ojs"},{"id":163,"value":"invalid = v => {\n let out = false;\n for (let i = 0, l = v.length; i < l; i++){\n const d = v[i];\n if (typeof d !== \"number\" || !isFinite(d)) {\n out = true;\n break;\n }\n }\n return out;\n}","pinned":true,"hidden":false,"mode":"ojs"},{"id":336,"value":"md`## Math`","pinned":false,"hidden":false,"mode":"ojs"},{"id":339,"value":"sqrt = Math.sqrt","pinned":true,"hidden":false,"mode":"ojs"}],"files":"$W30","stdlib":"1","titling":"auto"}