{"version":8,"graph":{"viewport":{"xmin":-3.8344947178109643,"ymin":-2.6164428658666496,"xmax":5.827854527525339,"ymax":4.078826879147242}},"randomSeed":"fc83bfd6cc150e0242db491b8cdec35d","expressions":{"list":[{"type":"text","id":"23","text":"Matrices are TL TR BL BR"},{"type":"expression","id":"24","color":"#2d70b3","latex":"m_{m}\\left(M,N\\right)=\\left[M\\left[1\\right]N\\left[1\\right]+M\\left[2\\right]N\\left[3\\right],M\\left[1\\right]N\\left[2\\right]+M\\left[2\\right]N\\left[4\\right],M\\left[3\\right]N\\left[1\\right]+M\\left[4\\right]N\\left[3\\right],M\\left[3\\right]N\\left[2\\right]+M\\left[4\\right]N\\left[4\\right]\\right]"},{"type":"expression","id":"25","color":"#388c46","latex":"m_{v}\\left(M,v\\right)=\\left(M\\left[1\\right]v.x+M\\left[2\\right]v.y,M\\left[3\\right]v.x+M\\left[4\\right]v.y\\right)"},{"type":"expression","id":"26","color":"#6042a6","latex":"A=\\left[0,1,-1,0\\right]"},{"type":"expression","id":"31","color":"#6042a6","latex":"C=\\left[0,-1,-1,0\\right]"},{"type":"expression","id":"44","color":"#000000","latex":"a=\\frac{5}{6}\\pi"},{"type":"expression","id":"45","color":"#c74440","latex":"E=\\left[\\cos\\left(a\\right),\\sin\\left(a\\right),-\\sin\\left(a\\right),\\cos\\left(a\\right)\\right]"},{"type":"expression","id":"55","color":"#c74440","latex":"p_{l}=\\left[\\left(-1,-1\\right),\\left(1,-1\\right),\\left(-1,0\\right),\\left(0,0\\right),\\left(1,0\\right),\\left(-1,1\\right),\\left(0,1\\right),\\left(1,1\\right)\\right]"},{"type":"text","id":"57","text":"BL -> TL, BR -> TR, TL -> BL, TR -> BR"},{"type":"expression","id":"54","color":"#000000","latex":"m_{v}\\left(m_{m}\\left(m_{m}\\left(A,C\\right),E\\right),p_{l}\\right)"},{"type":"expression","id":"59","color":"#6042a6","latex":"F=m_{m}\\left(m_{m}\\left(A,C\\right),E\\right)"},{"type":"expression","id":"60","color":"#000000","latex":"F\\left[1\\right]"},{"type":"expression","id":"61","color":"#c74440","latex":"F\\left[2\\right]"},{"type":"expression","id":"62","color":"#2d70b3","latex":"F\\left[3\\right]"},{"type":"expression","id":"63","color":"#388c46","latex":"F\\left[4\\right]"},{"type":"text","id":"40","text":"(A * B) * v = A * (B * v)"},{"type":"text","id":"42","text":"(A * B) * C = A * (B * C) = A * (B * (C * v))"}]}}