{"version":9,"randomSeed":"1f5c499dcdd8960965a9721f4f1e737a","graph":{"viewport":{"xmin":-10.000000000000002,"ymin":-6.929235918734245,"xmax":9.999999999999998,"ymax":6.929235918734245},"showGrid":false,"showXAxis":false,"showYAxis":false},"expressions":{"list":[{"type":"image","id":"49","image_url":"data:image/png;base64,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","name":"cannon.png","center":"P","angle":"A_{S}-\\frac{\\pi}{2}","width":"2","height":"2"},{"type":"image","id":"48","image_url":"data:image/jpeg;base64,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","name":"space_invader.jpeg","center":"E","width":"1","height":"0.8"},{"type":"expression","id":"1","color":"#2d70b3","latex":"P=\\left(-4,-1\\right)","hidden":true,"dragMode":"NONE","pointOpacity":"1","pointSize":"30"},{"type":"expression","id":"23","color":"#2d70b3","latex":"C_{P}=\\left[\\left(0,1\\right),\\left(1,0\\right),\\left(0,-1\\right),\\left(-1,0\\right)\\right]","hidden":true,"labelSize":"medium"},{"type":"text","id":"41","text":"click to move player"},{"type":"expression","id":"24","color":"#fa7e19","latex":"P+C_{P}","pointOpacity":"1","pointSize":"20","clickableInfo":{"enabled":true,"latex":"P\\to P+C_{P}\\left[\\operatorname{index}\\right]"}},{"type":"expression","id":"25","color":"#c74440","latex":"E=\\left[\\left(-3,-5\\right),\\left(-2,0\\right),\\left(-2,-4\\right),\\left(0,6\\right),\\left(7,3\\right),\\left(-4,2\\right),\\left(3,5\\right),\\left(-6,3\\right),\\left(-5,-3\\right),\\left(0,2\\right)\\right]","label":"${K}","hidden":true,"pointSize":"15"},{"type":"expression","id":"27","color":"#c74440","latex":"N_{E}=10","slider":{"hardMin":true,"hardMax":true,"min":"1","max":"100","step":"1"}},{"type":"text","id":"47","text":"reset game"},{"type":"expression","id":"26","color":"#000000","latex":"E\\to\\left(\\operatorname{round}\\left(16\\operatorname{random}\\left(N_{E}\\right)-8\\right),\\operatorname{round}\\left(16\\operatorname{random}\\left(N_{E}\\right)-8\\right)\\right)"},{"type":"expression","id":"28","color":"#2d70b3","latex":"A_{S}=0.82","slider":{"hardMin":true,"min":"0","max":"54"}},{"type":"text","id":"43","text":"drag to rotate \"gun\""},{"type":"expression","id":"37","color":"#6042a6","latex":"V_{S}=\\left(\\cos A_{S},\\sin A_{S}\\right)","labelSize":"medium"},{"type":"expression","id":"29","color":"#388c46","latex":"P+\\frac{3}{2}V_{S}","hidden":true,"pointSize":"15","clickableInfo":{"enabled":true,"latex":"A_{S}\\to A_{S}+1"}},{"type":"expression","id":"32","color":"#c74440","latex":"P_{D}\\left(u,v\\right)=u.x\\cdot v.x+u.y\\cdot v.y"},{"type":"expression","id":"35","color":"#6042a6","latex":"C_{L}\\left(a,b,x\\right)=\\left\\{x\\le a:a,x\\ge b:b,x\\right\\}"},{"type":"expression","id":"30","color":"#6042a6","latex":"D\\left(a,b,x\\right)=\\operatorname{distance}\\left(x-a,\\left(b-a\\right)\\cdot C_{L}\\left(0,999,\\frac{P_{D}\\left(x-a,b-a\\right)}{P_{D}\\left(b-a,b-a\\right)}\\right)\\right)"},{"type":"expression","id":"34","color":"#388c46","latex":"K=\\left[1...N_{E}\\right]"},{"type":"text","id":"45","text":"click to \"shoot\""},{"type":"expression","id":"36","color":"#000000","latex":"E\\to E\\left[D\\left(P,P+V_{S},E\\right)>1\\right]"},{"type":"expression","id":"38","color":"#c74440","latex":"y-P.y=\\frac{V_{S}.y}{V_{S}.x}\\cdot\\left(x-P.x\\right)","hidden":true,"labelSize":"medium"},{"type":"expression","id":"39","color":"#000000","latex":"\\left(0,5-999\\operatorname{length}\\left(E\\right)\\right)","showLabel":true,"label":"You win!","hidden":true,"labelSize":"2"}]}}