{"version":10,"randomSeed":"cf4f72aa1e693592a7949b4be92a4eb8","graph":{"viewport":{"xmin":-5.6428246050815725,"ymin":-6.4842412335844095,"xmax":6.3518043011684275,"ymax":5.201651077398193}},"expressions":{"list":[{"type":"expression","id":"1","color":"#c74440","latex":"P_{wp}=\\left[\\left(0,0\\right),\\left(3,0\\right),\\left(5.5,1\\right),\\left(6,3.5\\right),\\left(6,6\\right),\\left(1.5,6.5\\right),\\left(-0.5,3\\right),\\left(2,1.5\\right),\\left(3.5,3.5\\right),\\left(4.5,5.5\\right)\\right]","hidden":true},{"type":"expression","id":"15","color":"#6042a6","latex":"P=\\left[\\left(-3,-2\\right),\\left(1,1\\right),\\left(2,-1\\right),\\left(-2,2\\right),\\left(-1,3\\right),\\left(-1,-5\\right),\\left(3,-3\\right),\\left(3,1\\right)\\right]"},{"type":"text","id":"5","text":"see https://www.desmos.com/calculator/9eag7b4rgu for derivation"},{"type":"expression","id":"2","color":"#2d70b3","latex":"C_{CC}\\left(a,b,c\\right)=\\frac{\\left(\\left(b.x^{2}-a.x^{2}+b.y^{2}-a.y^{2}\\right)\\left(c.y-a.y\\right)-\\left(c.x^{2}-a.x^{2}+c.y^{2}-a.y^{2}\\right)\\left(b.y-a.y\\right),\\left(c.x^{2}-a.x^{2}+c.y^{2}-a.y^{2}\\right)\\left(b.x-a.x\\right)-\\left(b.x^{2}-a.x^{2}+b.y^{2}-a.y^{2}\\right)\\left(c.x-a.x\\right)\\right)}{2\\left(b.x\\cdot c.y-a.y\\cdot b.x-a.x\\cdot c.y-b.y\\cdot c.x+a.x\\cdot b.y+a.y\\cdot c.x\\right)}"},{"type":"expression","id":"3","color":"#388c46","latex":"R_{CC}\\left(a,b,c\\right)=\\operatorname{distance}\\left(a,C_{CC}\\left(a,b,c\\right)\\right)"},{"type":"expression","id":"7","color":"#c74440","latex":"V_{DT}\\left(i,j,k\\right)=\\prod_{u=1}^{\\operatorname{length}\\left(P\\right)}\\left\\{\\left(u-i\\right)\\left(u-j\\right)\\left(u-k\\right)=0:1,\\operatorname{distance}\\left(P\\left[u\\right],C_{CC}\\left(P\\left[i\\right],P\\left[j\\right],P\\left[k\\right]\\right)\\right)\\ge\\operatorname{distance}\\left(P\\left[i\\right],C_{CC}\\left(P\\left[i\\right],P\\left[j\\right],P\\left[k\\right]\\right)\\right):1\\right\\}"},{"type":"expression","id":"14","color":"#388c46","latex":"P_{i}=\\left[1...\\operatorname{length}\\left(P\\right)\\right]"},{"type":"expression","id":"11","color":"#000000","latex":"\\left[\\operatorname{polygon}\\left(\\left\\{V_{DT}\\left(A,B,C\\right)=1:P\\left[A,B,C\\right],\\left[\\left(0,0\\right)\\right]\\left[1,1,1\\right]\\right\\}\\right)\\operatorname{for}A=P_{i},B=P_{i},C=P_{i}\\right]","fillOpacity":"0.2"},{"type":"expression","id":"91","color":"#c74440","latex":"\\operatorname{distance}\\left(\\left[C_{CC}\\left(P\\left[A\\right],P\\left[B\\right],P\\left[C\\right]\\right)\\operatorname{for}A=P_{i},B=P_{i},C=P_{i}\\right],\\left(x,y\\right)\\right)=\\left[V_{DT}\\left(A,B,C\\right)R_{CC}\\left(P\\left[A\\right],P\\left[B\\right],P\\left[C\\right]\\right)\\operatorname{for}A=P_{i},B=P_{i},C=P_{i}\\right]"}]}}