{"version":9,"randomSeed":"5f3498dc4049539aef3a7ce0d51a2f31","graph":{"viewport":{"xmin":-1.2500000000000018,"ymin":-1.1181867052944447,"xmax":1.2499999999999982,"ymax":1.1181867052944447}},"expressions":{"list":[{"type":"folder","id":"45","title":"library of useful functions"},{"type":"text","id":"46","folderId":"45","text":"project, R^3 -> R^2"},{"type":"text","id":"48","folderId":"45","text":"dot product, R^2 -> R^2 -> R"},{"type":"expression","id":"80","folderId":"45","color":"#2d70b3","latex":"M\\left(u,v\\right)=u.x\\cdot v.x+u.y\\cdot v.y"},{"type":"text","id":"50","folderId":"45","text":"cross product, R^3 -> R^3"},{"type":"expression","id":"51","folderId":"45","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":"52","folderId":"45","text":"normalise vector, R^2 -> R^2"},{"type":"expression","id":"53","folderId":"45","color":"#6042a6","latex":"N\\left(v\\right)=\\frac{v}{\\operatorname{distance}\\left(\\left(0,0\\right),v\\right)}"},{"type":"text","id":"54","folderId":"45","text":"insert element as replacement, R^n -> N -> {R, R^2} -> R^n"},{"type":"expression","id":"55","folderId":"45","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":"56","folderId":"45","text":"rotate around each axis, R^3 -> R^3"},{"type":"expression","id":"57","folderId":"45","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":"58","folderId":"45","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":"59","folderId":"45","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":"folder","id":"66","title":"setup"},{"type":"expression","id":"1","folderId":"66","color":"#c74440","latex":"R=1","slider":{"hardMin":true,"hardMax":true,"min":"0"}},{"type":"expression","id":"25","folderId":"66","color":"#2d70b3","latex":"P_{0}=\\left(0.556,0.508\\right)"},{"type":"expression","id":"28","folderId":"66","color":"#000000","latex":"D_{0}=\\left(-0.8740288088753306,0.4858741002111256\\right)","hidden":true},{"type":"expression","id":"29","folderId":"66","color":"#c74440","latex":"D_{0}\\to N\\left(D_{0}\\right)"},{"type":"folder","id":"70","title":"state"},{"type":"expression","id":"61","folderId":"70","color":"#2d70b3","latex":"P=\\left(0.556,0.508\\right)"},{"type":"expression","id":"62","folderId":"70","color":"#388c46","latex":"D=\\left(-0.8740288088753306,0.4858741002111256\\right)","hidden":true},{"type":"expression","id":"84","folderId":"70","color":"#c74440","latex":"D_{un}=\\left(0.008,-0.847\\right)"},{"type":"folder","id":"75","title":"line-circle intersection"},{"type":"expression","id":"81","folderId":"75","color":"#388c46","latex":"I_{dp}\\left(p,d,c,h\\right)=-M\\left(p-c,d\\right)+\\left[1,-1\\right]\\sqrt{h}"},{"type":"expression","id":"79","folderId":"75","color":"#c74440","latex":"I_{d}\\left(p,d,c,r\\right)=I_{dp}\\left(p,d,c,M\\left(p-c,d\\right)^{2}-M\\left(p-c,p-c\\right)+r^{2}\\right)"},{"type":"expression","id":"82","folderId":"75","color":"#6042a6","latex":"I_{p}\\left(p,d,c,r\\right)=p+d\\cdot I_{d}\\left(p,d,c,r\\right)"},{"type":"folder","id":"87","title":"reflection"},{"type":"expression","id":"88","folderId":"87","color":"#6042a6","latex":"R_{d}\\left(p,d\\right)=2\\cdot\\frac{M\\left(d,\\left(-p.y,p.x\\right)\\right)}{M\\left(\\left(-p.y,p.x\\right),\\left(-p.y,p.x\\right)\\right)}\\cdot\\left(-p.y,p.x\\right)-d"},{"type":"folder","id":"68","title":"display","collapsed":true},{"type":"expression","id":"27","folderId":"68","color":"#6042a6","latex":"x^{2}+y^{2}=R^{2}"},{"type":"expression","id":"95","folderId":"68","color":"#c74440","latex":"P_{1}=P+I_{d}\\left(P,D,\\left(0,0\\right),R\\right)\\left[1\\right]\\cdot D"},{"type":"expression","id":"96","folderId":"68","color":"#2d70b3","latex":"D_{1}=R_{d}\\left(I_{p}\\left(P,D,\\left(0,0\\right),R\\right)\\left[1\\right],D\\right)"},{"type":"expression","id":"97","folderId":"68","color":"#388c46","latex":"L=\\left[\\right]","lines":true},{"type":"expression","id":"72","folderId":"68","color":"#000000","latex":"\\operatorname{polygon}\\left(P,P_{1}\\right)"},{"type":"expression","id":"89","folderId":"68","color":"#000000","latex":"P_{2}=R_{d}\\left(I_{p}\\left(P,D,\\left(0,0\\right),R\\right)\\left[1\\right],D\\right)"},{"type":"expression","id":"90","color":"#c74440","latex":"S=\\left(P\\to P_{1},D\\to D_{1},L\\to\\operatorname{join}\\left(L,P\\right)\\right)"},{"type":"expression","id":"71","color":"#6042a6","latex":"Z=\\left(P\\to P_{0},D\\to D_{0},L\\to\\left[\\right]\\right)"}],"ticker":{"handlerLatex":"S","minStepLatex":"100","open":true}}}