{"version":9,"randomSeed":"4cb87e8212a7b70d1f695d594c32f96b","graph":{"viewport":{"xmin":-6.061690069361485,"ymin":-2.8493036414340853,"xmax":4.5633099306385185,"ymax":4.791258306574991}},"expressions":{"list":[{"type":"folder","id":"109","title":"initial data","collapsed":true},{"type":"expression","id":"1","folderId":"109","color":"#c74440","latex":"P=\\left[\\left(2,1\\right),\\left(-1,-1\\right),\\left(-2,4\\right),\\left(1,0\\right),\\left(-1,2\\right),\\left(0,1\\right),\\left(-2,1\\right),\\left(-3,0\\right),\\left(-2,-1\\right),\\left(1,-2\\right),\\left(-1,-2\\right),\\left(0,4\\right),\\left(-4,2\\right),\\left(-4,-1\\right),\\left(-3,2\\right),\\left(-3,4\\right),\\left(1,2\\right)\\right]","pointSize":"20"},{"type":"folder","id":"118","title":"solution data","collapsed":true},{"type":"expression","id":"119","folderId":"118","color":"#2d70b3","latex":"S=\\left[\\right]"},{"type":"expression","id":"128","folderId":"118","color":"#6042a6","latex":"R=\\left(S\\to\\left[\\right],i\\to1,j\\to1\\right)"},{"type":"expression","id":"129","folderId":"118","color":"#000000","latex":"\\operatorname{polygon}\\left(P\\left[S\\right]\\right)","fillOpacity":"0.2","lineWidth":"6"},{"type":"folder","id":"111","title":"selected points"},{"type":"expression","id":"95","folderId":"111","color":"#6042a6","latex":"P\\left[i\\right]","pointSize":"30"},{"type":"expression","id":"96","folderId":"111","color":"#388c46","latex":"P\\left[j\\right]","pointSize":"30"},{"type":"expression","id":"148","folderId":"111","color":"#000000","latex":"\\operatorname{polygon}\\left(P\\left[\\left\\{\\operatorname{length}\\left(S\\right)>0:S\\left[\\operatorname{length}\\left(S\\right)\\right],i\\right\\}\\right],P\\left[j\\right]\\right)","lineOpacity":"0.3","lineWidth":"6"},{"type":"expression","id":"93","folderId":"111","color":"#2d70b3","latex":"i=1","slider":{"hardMin":true,"min":"1","step":"1"}},{"type":"expression","id":"94","folderId":"111","color":"#388c46","latex":"j=5","slider":{"hardMin":true,"min":"1","step":"1"}},{"type":"folder","id":"113","title":"basic linear algebra","hidden":true,"collapsed":true},{"type":"expression","id":"101","folderId":"113","color":"#000000","latex":"m_{n}=P\\left[j\\right].y-P\\left[i\\right].y"},{"type":"expression","id":"102","folderId":"113","color":"#c74440","latex":"m_{d}=P\\left[j\\right].x-P\\left[i\\right].x"},{"type":"expression","id":"99","folderId":"113","color":"#388c46","latex":"m=\\frac{m_{n}}{m_{d}}"},{"type":"expression","id":"97","folderId":"113","color":"#c74440","latex":"y-P\\left[j\\right].y=m\\left(x-P\\left[j\\right].x\\right)"},{"type":"expression","id":"100","folderId":"113","color":"#6042a6","latex":"y-mx=P\\left[j\\right].y-mP\\left[j\\right].x"},{"type":"expression","id":"103","folderId":"113","color":"#2d70b3","latex":"m_{d}y-m_{n}x=m_{d}P\\left[j\\right].y-m_{n}P\\left[j\\right].x"},{"type":"expression","id":"105","folderId":"113","color":"#6042a6","latex":"m_{d}y-m_{n}x\\le m_{d}P\\left[j\\right].y-m_{n}P\\left[j\\right].x"},{"type":"folder","id":"115","title":"picking the right next point","collapsed":true},{"type":"text","id":"121","folderId":"115","text":"is point P[j] a good next choice?"},{"type":"expression","id":"116","folderId":"115","color":"#000000","latex":"G=\\left\\{\\operatorname{length}\\left(P\\left[m_{d}P.y-m_{n}P.x<m_{d}P\\left[j\\right].y-m_{n}P\\left[j\\right].x\\right]\\right)=0:1,0\\right\\}\\cdot\\left\\{i=j:0,1\\right\\}"},{"type":"text","id":"123","folderId":"115","text":"computation step"},{"type":"expression","id":"125","folderId":"115","color":"#c74440","latex":"A=\\left\\{G=1:\\left\\{S\\left[1\\right]=i:\\left(i\\to i\\right),\\left(S\\to\\operatorname{join}\\left(S,i\\right),i\\to j,j\\to1\\right)\\right\\},\\left(j\\to j+1\\right)\\right\\}"},{"type":"expression","id":"136","color":"#2d70b3","latex":"R"}],"ticker":{"handlerLatex":"A","minStepLatex":"100","open":true}}}