{"version":8,"graph":{"viewport":{"xmin":-7.207432802300562,"ymin":-3.1484149479697194,"xmax":8.485865889046664,"ymax":7.725841949580996}},"randomSeed":"60070be1b5030f50d282112fabcd2825","expressions":{"list":[{"type":"text","id":"54","text":"Ray origin"},{"type":"expression","id":"9","color":"#6042a6","latex":"o=\\left[1.9,-1.5\\right]"},{"type":"text","id":"56","text":"Ray direction"},{"type":"expression","id":"10","color":"#000000","latex":"a_{0}=\\left[-0.8,0.6\\right]"},{"type":"expression","id":"11","color":"#c74440","latex":"a=\\frac{a_{0}}{\\sqrt{d_{ot}\\left(a_{0},a_{0}\\right)}}"},{"type":"text","id":"58","text":"Plane (line) normal"},{"type":"expression","id":"12","color":"#2d70b3","latex":"n_{0}=\\left[0.1,0.5\\right]"},{"type":"expression","id":"13","color":"#388c46","latex":"n=\\frac{n_{0}}{\\sqrt{d_{ot}\\left(n_{0},n_{0}\\right)}}"},{"type":"text","id":"68","text":"Plane distance from origin"},{"type":"expression","id":"14","color":"#6042a6","latex":"h=1.3","slider":{"playDirection":-1}},{"type":"expression","id":"2","color":"#2d70b3","latex":"d_{ot}\\left(u,v\\right)=u\\left[1\\right]v\\left[1\\right]+u\\left[2\\right]v\\left[2\\right]"},{"type":"text","id":"72","text":"Intersection distance along ray = (plane distance - ray origin . plane normal) / (ray direction . plane normal)"},{"type":"expression","id":"40","color":"#000000","latex":"c=\\frac{h-d_{ot}\\left(o,n\\right)}{d_{ot}\\left(a,n\\right)}"},{"type":"text","id":"60","text":"Show plane (line)"},{"type":"expression","id":"46","color":"#c74440","latex":"n\\left[1\\right]x+n\\left[2\\right]y=h"},{"type":"text","id":"62","text":"Show ray origin"},{"type":"expression","id":"48","color":"#388c46","latex":"\\left(o\\left[1\\right],o\\left[2\\right]\\right)"},{"type":"text","id":"64","text":"Show ray"},{"type":"expression","id":"49","color":"#6042a6","latex":"a\\left[2\\right]\\left(x-o\\left[1\\right]\\right)-a\\left[1\\right]\\left(y-o\\left[2\\right]\\right)=0"},{"type":"text","id":"66","text":"Show intersection"},{"type":"expression","id":"52","color":"#2d70b3","latex":"\\left(\\left(o+ac\\right)\\left[1\\right],\\left(o+ac\\right)\\left[2\\right]\\right)"}]}}