)u capm ]nnk~]]Ur8<A' ff@/hqOsj(0fTfTH /h hwWritten by: Ken Koedinger, School of Computer Science, Carnegie Mellon University, Pittsburgh, PA 15213 (412) 268-7667 Email: koedinger@cs.cmu.edududu$`UEhDteaseo  e r8<A' ff@/hqOsj(0fTfTH /hr)UMoving the point moves the player's path further out the wing. A locus of points is traced that indicates the player's optimal position to maximize the goal angle. (I used the "Quadrature of the rectangle" construction to do this construction.)n.)<<L _@@GojHHr8<A' ff@/hqOsj(0fTfTH /hAClchr8<B' ff@/hqOsj(0fTfTH /hCCl3Cl r8<' ff@/hqOsj(0fTfTH /hf%BbConclusion: When streaking down the wing, the maximum goal angle subtended occurs when you are a little less than 45 degrees from the goal center. The further out on the wing you are the optimal position gets closer to 45 degress.UCN?@mv(٦L`ci]'Ur8<j' ff@/hqOsj(0fTfTH /hAClCCl?>,Kr8< MOVE THIS POINTff@/hqOsj(0fTfTH /hCCl?f r8< post1' ff@/hqOsj(0fTfTH /hC[ClSX?s r8< post2' ff@/hqOsj(0fTfTH /hCCl 'Y r8< player's pathNTff@/hqOsj(0fTfTH /hCBCC@?1c XH r8<GOAL THIS POINTff@/hqOsj(0fTfTH /hC[ClCCl?C%>i  1Br8<1OVE THIS POINTff@/hqOsj(0fTfTH /hCClB?5%F?5%F r8<tOVE THIS POINTff@/hqOsj(0fTfTH /hCClC[Cl?/4r8< Goal-centerthNTff@/hqOsj(0fTfTH /hBDCl r8< goal-centerthNTff@/hqOsj(0fTfTH /hCCl  + r8<1layer's pathNTff@/hqOsj(0fTfTH /h GOAL = 0o8/{ounp!!|h@p(#o-!`Rp0pP.O h@p@^dp!`^z"*DRounh@p `>T4ph@p Goal mouth = `q.B-0Ha:aRecs():4TpTp4aĸq*!zound4,rP|q@qXa2q|2|qs():qIPHPyPհPP٨PGs$Ë**!qr@r,4rZPr@s8r JKPHPyrcPհ`P٨PGs$,x,  `|WDjtPdc~s + r8<2layer's pathNTff@/hqOsj(0fTfTH /h m {S:MOVE THIS POINTpost1} = ounp!!|h@p(#o-!`Rp0pP.O h@p@^dp!`^z"*DRounh@p `>T4ph@pDistance out on wing = B-0Ha:aRecs():4TpTp4aĸq*!zound4,rP|q@qXa2q|2|qs():qIPHPyPհPP٨PGs$Ë**!qr@r,4rZPr@s8r JKPHPyrcPհ`P٨PGs$,x,  `|WDjtPdc~s .X r8<noal-centerthNTff@/hqOsj(0fTfTH /hBDClCCl? 'X r8<roal-centerthNTff@/hqOsj(0fTfTH /hCBCC@?h;r8<Hoal-centerthNTff@/hqOsj(0fTfTH /hCCClkp>r8< Loal-centerthNTff@/hqOsj(0fTfTH /hCBZ1Vr8<2oal-centerthNTff@/hqOsj(0fTfTH /hCCClC?5%F?5%F Y r8<soal-centerthNTff@/hqOsj(0fTfTH /hCClChCT4ph@pAngle(post1 player post2) = B-0Ha:aRecs():4TpTp4aĸq*!zound4,rP|q@qXa2q|2|qs():qIPHPyPհPP٨PGs$Ë**!qr@r,4rZPr@s8r JKPHPyrcPհ`P٨PGs$,x,  `|WDjtPdc~s d r8<ulayerenterthNTff@/hqOsj(0fTfTH /hCClCBε,?(  r8<6layerenterthNTff@/hqOsj(0fTfTH /h m{!:A}post1goal-centerplayer = ounp!!|h@p(#o-!`Rp0pP.O h@p@^dp!`^z"*DRounh@p `>T4ph@p"Angle(post1 goal-center player) = Ha:aRecs():4TpTp4aĸq*!zound4,rP|q@qXa2q|2|qs():qIPHPyPհPP٨PGs$Ë**!qr@r,4rZPr@s8r JKPHPyrcPհ`P٨PGs$,x,  `|WDjtPdc~s