{"version":10,"randomSeed":"b436c3a139d64eb36117e57c265e6c4a","graph":{"viewport":{"xmin":-10,"ymin":-6.503137939958592,"xmax":10,"ymax":6.503137939958592}},"expressions":{"list":[{"type":"text","id":"9","text":"project, R^3 -> R^2"},{"type":"expression","id":"2","color":"#2d70b3","latex":"P\\left(v\\right)=\\frac{\\left(v\\left[1\\right],v\\left[2\\right]\\right)}{v\\left[3\\right]}"},{"type":"text","id":"35","text":"project list, R^(3*n) -> R^3 -> R^2 -> (R^2)^n"},{"type":"expression","id":"36","color":"#2d70b3","latex":"P_{L}\\left(v,o,\\phi\\right)=\\left[P\\left(R_{x}\\left(R_{y}\\left(o+\\left[v\\left[3k-2\\right],v\\left[3k-1\\right],v\\left[3k\\right]\\right],\\phi.x\\right),\\phi.y\\right)\\right)\\operatorname{for}k=\\left[1...\\frac{\\operatorname{length}\\left(v\\right)}{3}\\right]\\right]"},{"type":"text","id":"11","text":"dot product, R^n -> R^n -> R"},{"type":"expression","id":"7","color":"#c74440","latex":"D\\left(u,v\\right)=\\sum_{k=1}^{\\min\\left(\\operatorname{length}\\left(u\\right),\\operatorname{length}\\left(v\\right)\\right)}u\\left[k\\right]v\\left[k\\right]"},{"type":"text","id":"13","text":"cross product, R^3 -> R^3"},{"type":"expression","id":"3","color":"#388c46","latex":"C\\left(u,v\\right)=\\left[u\\left[2\\right]v\\left[3\\right]-u\\left[3\\right]v\\left[2\\right],u\\left[3\\right]v\\left[1\\right]-u\\left[1\\right]v\\left[3\\right],u\\left[1\\right]v\\left[2\\right]-u\\left[2\\right]v\\left[1\\right]\\right]"},{"type":"text","id":"15","text":"normalise vector, R^n -> R^n"},{"type":"expression","id":"4","color":"#6042a6","latex":"N\\left(v\\right)=\\frac{v}{\\sqrt{D\\left(v,v\\right)}}"},{"type":"text","id":"17","text":"insert element as replacement, R^n -> N -> {R, R^2} -> R^n"},{"type":"expression","id":"18","color":"#2d70b3","latex":"I\\left(L,i,x\\right)=\\left\\{i=1:\\operatorname{join}\\left(x,L\\left[2...\\right]\\right),i=\\operatorname{length}\\left(L\\right):\\operatorname{join}\\left(L\\left[1...\\operatorname{length}\\left(L\\right)-1\\right],x\\right),\\operatorname{join}\\left(L\\left[1...i-1\\right],x,L\\left[i+1...\\right]\\right)\\right\\}"},{"type":"text","id":"30","text":"rotate around each axis, R^3 -> R^3"},{"type":"expression","id":"31","color":"#2d70b3","latex":"R_{x}\\left(v,\\theta\\right)=\\left[v\\left[1\\right],v\\left[2\\right]\\cos\\theta-v\\left[3\\right]\\sin\\theta,v\\left[2\\right]\\sin\\theta+v\\left[3\\right]\\cos\\theta\\right]"},{"type":"expression","id":"32","color":"#388c46","latex":"R_{y}\\left(v,\\theta\\right)=\\left[v\\left[1\\right]\\cos\\theta-v\\left[3\\right]\\sin\\theta,v\\left[2\\right],v\\left[1\\right]\\sin\\theta+v\\left[3\\right]\\cos\\theta\\right]"},{"type":"expression","id":"33","color":"#6042a6","latex":"R_{z}\\left(v,\\theta\\right)=\\left[v\\left[1\\right]\\cos\\theta-v\\left[2\\right]\\sin\\theta,v\\left[1\\right]\\sin\\theta+v\\left[2\\right]\\cos\\theta,v\\left[3\\right]\\right]"},{"type":"text","id":"38","text":"extract bit i of n, R -> Z -> N"},{"type":"expression","id":"39","color":"#2d70b3","latex":"B\\left(n,i\\right)=\\operatorname{floor}\\left(\\operatorname{mod}\\left(\\frac{n}{2^{i}},2\\right)\\right)"},{"type":"text","id":"41","text":"merge bit-list, N^n -> N"},{"type":"expression","id":"42","color":"#6042a6","latex":"B_{i}\\left(v\\right)=\\operatorname{total}\\left(2^{\\left[0...\\operatorname{length}\\left(v\\right)\\right]}v\\right)","hidden":true},{"type":"text","id":"45","text":"sum bits at given positions to get a bitmask, N^n -> N"},{"type":"expression","id":"46","color":"#2d70b3","latex":"M\\left(v\\right)=\\operatorname{total}\\left(2^{v-1}\\right)","hidden":true}]}}