{"version":9,"randomSeed":"9000104b89ab04e5bf6cdafb6f4d1d4c","graph":{"viewport":{"xmin":-0.1455539903269655,"ymin":0.26181391508917273,"xmax":0.15639442358979408,"ymax":0.5637623290059324},"showGrid":false,"showXAxis":false,"showYAxis":false},"expressions":{"list":[{"type":"folder","id":"26","title":"setup"},{"type":"expression","id":"65","folderId":"26","color":"#2d70b3","latex":"h_{b}=12"},{"type":"expression","id":"6","folderId":"26","color":"#c74440","latex":"h=h_{b}+\\sin\\left(a\\right)"},{"type":"expression","id":"4","folderId":"26","color":"#6042a6","latex":"Z=30"},{"type":"expression","id":"57","folderId":"26","color":"#c74440","latex":"a=2\\pi\\frac{\\left[0.5...n\\right]}{n}"},{"type":"expression","id":"63","folderId":"26","color":"#000000","latex":"R_{b}=3","slider":{"hardMin":true,"hardMax":true,"min":"0"}},{"type":"expression","id":"42","folderId":"26","color":"#2d70b3","latex":"R=R_{b}+\\cos\\left(a\\right)","hidden":true,"slider":{"hardMin":true,"hardMax":true,"min":"0"}},{"type":"expression","id":"61","folderId":"26","color":"#388c46","latex":"r=1"},{"type":"folder","id":"24","title":"projection","hidden":true,"collapsed":true},{"type":"expression","id":"1","folderId":"24","color":"#c74440","latex":"P\\left(x,y,z\\right)=\\frac{\\left(x,y\\right)}{z}"},{"type":"text","id":"30","folderId":"24","text":"circle projection, xz plane, centre (0, h, Z), radius 1"},{"type":"expression","id":"41","folderId":"24","color":"#c74440","latex":"P\\left(r\\cos\\left(t\\right),h,Z+r\\sin\\left(t\\right)\\right)","parametricDomain":{"min":"","max":"2\\pi"},"domain":{"min":"0","max":"2\\pi"}},{"type":"text","id":"55","folderId":"24","text":"this isn't right, but it's almost right, and I don't know how to perfect it"},{"type":"expression","id":"47","folderId":"24","color":"#2d70b3","latex":"\\frac{x^{2}}{\\frac{r}{Z}}+\\left(\\frac{y-\\frac{\\frac{h}{Z+r}+\\frac{h}{Z-r}}{2}}{\\frac{\\frac{h}{Z+r}-\\frac{h}{Z-r}}{2}}\\right)^{2}=1"},{"type":"text","id":"40","text":"number of polygons around each circle"},{"type":"expression","id":"36","color":"#2d70b3","latex":"n=16","slider":{"hardMin":true,"hardMax":true,"min":"1","max":"100","step":"1"}},{"type":"expression","id":"70","color":"#c74440","latex":"T\\left(\\alpha,\\beta\\right)=P\\left(\\left(R_{b}+r\\cos\\left(\\beta\\right)\\right)\\cos\\left(\\alpha\\right),h_{b}+r\\sin\\left(\\beta\\right),Z+R_{b}\\sin\\left(\\alpha\\right)+r\\sin\\left(\\alpha\\right)\\cos\\left(\\beta\\right)\\right)"},{"type":"expression","id":"73","color":"#6042a6","latex":"T_{n}\\left(k,o_{a},o_{b}\\right)=T\\left(2\\pi\\frac{\\operatorname{floor}\\left(\\frac{k}{n}\\right)+o_{a}}{n},2\\pi\\frac{\\operatorname{mod}\\left(k,n\\right)+o_{b}}{n}\\right)"},{"type":"expression","id":"71","color":"#2d70b3","latex":"\\left[\\operatorname{polygon}\\left(T_{n}\\left(k,0,0\\right),T_{n}\\left(k,1,0\\right),T_{n}\\left(k,1,1\\right),T_{n}\\left(k,0,1\\right)\\right)\\operatorname{for}k=\\left[v...\\left(v+30\\right)\\right]\\right]","fillOpacity":"0.3"},{"type":"expression","id":"72","color":"#388c46","latex":"v=248","slider":{"hardMin":true,"hardMax":true,"loopMode":"LOOP_FORWARD","isPlaying":true,"min":"1","max":"n^{2}","step":"1"}}]}}