*** Case (a) +++ Rectangle 1 0.1000000000000000 0.8000000000000000 0.6000000000000000 0.5000000000000000 0.5000000000000000 0.8500000000000000 0.2000000000000000 0.9000000000000000 +++ Rectangle 2 0.3000000000000000 0.3000000000000000 0.8000000000000000 0.0500000000000000 0.9000000000000000 0.4000000000000000 0.4000000000000000 0.5000000000000000 ++================================================================================================================================================================++ || || || || || || || || || || || || || || || DD111111 || || 11 111111111111 || || 1111 111111111111 || || 11 111111111111 || || 1111 1111CC || || 11 11 || || 11 11 || || 1111 11 || || AA11 11 || || 1111 11 || || 11 11 || || 1111 11 || || 1111 11 || || 11 11 || || 1111 11 || || 1111 || || 11 1111 || || 1111 11 || || 1111 11 || || 11 11 || || 1111 11 || || 1111 11 || || 11 11 || || 1111 11 || || 1111 11 || || 11 11 || || 1111 11 || || 1111 11 || || 11 11 || || 1111 11 || || 1111 11 || || 1111 || || DD222222 BB || || 2222 2222222222 || || 22 2222222222 || || 2222 22 2222222222 || || 22 2222222222 || || 2222 2222222222 || || 22 2222222222 || || 2222 2222222222 || || 22 22CC || || 2222 22 || || 22 2222 || || 2222 22 || || 22 22 || || 2222 2222 || || 22 22 || || 2222 22 || || AA22 22 || || 2222 2222 || || 2222 22 || || 2222 22 || || 2222 2222 || || 2222 22 || || 2222 22 || || 2222 22 || || 2222 2222 || || 2222 22 || || 2222 22 || || 2222 2222 || || 2222 22 || || 2222 22 || || 2222 22 || || 2222 2222 || || 2222 22 || || 2222 22 || || 2222 2222 || || 222222 || || BB || || || || || || || || || ++================================================================================================================================================================++ +++ Graphical method N = 10. Area of intersection = 0.0000000000000000 N = 100. Area of intersection = 0.0000000000000000 N = 1000. Area of intersection = 0.0000000000000000 +++ Numerical method N = 10. Area of intersection = 0.0000000000000000 N = 100. Area of intersection = 0.0000000000000000 N = 1000. Area of intersection = 0.0000000000000000 N = 10000. Area of intersection = 0.0000000000000000 N = 100000. Area of intersection = 0.0000000000000000 N = 1000000. Area of intersection = 0.0000000000000000 +++ Geometric method --- Number of edge intersections = 0 Area of intersection = 0.0000000000000000 *** Case (b) +++ Rectangle 1 0.2000000000000000 0.1000000000000000 0.9000000000000000 0.2000000000000000 0.5000000000000000 0.9000000000000000 0.1000000000000000 0.7000000000000000 +++ Rectangle 2 0.2500000000000000 0.5000000000000000 0.4500000000000000 0.2500000000000000 0.6000000000000000 0.6000000000000000 0.4000000000000000 0.7500000000000000 ++================================================================================================================================================================++ || || || || || || || || || || || || || || || 11CC || || 111111 11 || || 111111 11 || || 111111 11 || || 111111 11 || || 111111 11 || || 111111 11 || || 111111 11 || || 111111 11 || || 111111 11 || || 111111 11 || || 111111 11 || || 111111 DD22 11 || || 111111 2222..22 11 || || 111111 22......22 11 || || 111111 22..........2222 11 || || DD11 2222..............22 11 || || 11 22..................22 11 || || 11 2222....................2222 11 || || 11 22..........................22 11 || || 11 22..............................22 11 || || 11 2222................................2222 11 || || 11 22......................................22 11 || || 11 2222........................................22 11 || || 11 22............................................CC 11 || || 11 22............................................2222 11 || || 11 2222............................................22 11 || || 11 22............................................2222 11 || || 11 2222............................................22 11 || || 11 22..............................................22 11 || || 11 22..............................................2222 11 || || 11 2222..............................................22 11 || || 11 AA..............................................2222 11 || || 11 22............................................22 11 || || 11 22..........................................22 11 || || 11 22......................................22 11 || || 11 22....................................22 11 || || 11 22..................................2222 11 || || 11 22................................22 11 || || 11 22............................2222 11 || || 11 22..........................22 11 || || 11 22........................22 11 || || 11 22......................22 11 || || 11 22....................22 11 || || 11 22................2222 11 || || 11 22..............22 11 || || 11 22..........2222 11 || || 11 22..........22 11 || || 11 22........22 11 || || 11 22....2222 11 || || 11 22..22 11 || || 11 2222 11 || || 11 BB 11 || || 11 11 || || 11 11 || || 11 11 || || 11 111111BB || || 11 11111111111111 || || 11 11111111111111 || || 11 11111111111111 || || 11 11111111111111 || || 11 11111111111111 || || 11 11111111111111 || || 11 11111111111111 || || AA111111 || || || || || || || || || || || || || || || || || ++================================================================================================================================================================++ +++ Graphical method N = 10. Area of intersection = 0.0800000000000000 N = 100. Area of intersection = 0.0899000000000000 N = 1000. Area of intersection = 0.0899860000000000 +++ Numerical method N = 10. Area of intersection = 0.0445833333333333 N = 100. Area of intersection = 0.0900000000000000 N = 1000. Area of intersection = 0.0900000000000000 N = 10000. Area of intersection = 0.0900000000000000 N = 100000. Area of intersection = 0.0900000000000001 N = 1000000. Area of intersection = 0.0900000000000000 +++ Geometric method --- Number of edge intersections = 0 --- Number of corners on the intersection polygon = 4 P[0] = (0.2500000000000000, 0.5000000000000000) P[1] = (0.4500000000000000, 0.2500000000000000) P[2] = (0.6000000000000000, 0.6000000000000000) P[3] = (0.4000000000000000, 0.7500000000000000) Area of intersection = 0.0900000000000000 *** Case (c) +++ Rectangle 1 0.2000000000000000 0.3000000000000000 0.7000000000000000 0.4000000000000000 0.3000000000000000 0.9000000000000000 0.1000000000000000 0.7000000000000000 +++ Rectangle 2 0.1500000000000000 0.1000000000000000 0.8000000000000000 0.2000000000000000 0.9000000000000000 0.6000000000000000 0.6000000000000000 0.8000000000000000 ++================================================================================================================================================================++ || || || || || || || || || || || || || || || CC || || 11 11 || || 11 11 || || 11 11 || || 11 11 || || 11 11 || || 11 11 || || 11 11 || || 11 11 DD22 || || 11 11 2222 22 || || 11 11 2222 2222 || || 1111 11 22 22 || || 1111 11 22 2222 || || 1111 11 2222 22 || || 11 11 22 2222 || || 1111 11 2222 22 || || DD11 11 22 2222 || || 11 11 2222 22 || || 11 11 2222 2222 || || 11 1122 22 || || 11 1122 2222 || || 11 222211 22 || || 11 22....11 2222 || || 11 2222......11 22 || || 11 2222..........11 CC || || 11 22............11 22 || || 11 2222..............11 2222 || || 11 2222..................11 22 || || 11 22......................11 22 || || 11 2222........................11 22 || || 11 22..........................11 2222 || || 11 2222............................11 22 || || 11 2222................................11 22 || || 11 22....................................11 22 || || 11 2222......................................11 2222 || || 11 2222........................................11 22 || || 11 22............................................11 22 || || 11 2222..............................................11 22 || || 11 2222..................................................11 2222 || || 11 22......................................................11 22 || || 11 2222..................................................1111BB 22 || || 11 2222..........................................1111111111 22 || || 11 ..................................1111111111 2222 || || 11 2222........................1111111111 22 || || 11 22................1111111111 22 || || 11 2222......1111111111 22 || || 11 221111111111 2222 || || 11 1111111111 22 || || AA111111 2222 22 || || 2222 22 || || 22 2222 || || 2222 22 || || 2222 22 || || 22 22 || || 2222 2222 || || 2222 22 || || 22 222222BB || || 2222 2222222222222222 || || 22 22222222222222 || || 2222 2222222222222222 || || 2222 22222222222222 || || 22 2222222222222222 || || 2222 22222222222222 || || 2222 2222222222222222 || || AA222222 || || || || || || || || || || || || || || || || || ++================================================================================================================================================================++ +++ Graphical method N = 10. Area of intersection = 0.0600000000000000 N = 100. Area of intersection = 0.0586000000000000 N = 1000. Area of intersection = 0.0588160000000000 +++ Numerical method N = 10. Area of intersection = 0.0587777777777778 N = 100. Area of intersection = 0.0588433333333333 N = 1000. Area of intersection = 0.0588378333333332 N = 10000. Area of intersection = 0.0588378506666665 N = 100000. Area of intersection = 0.0588378509877778 N = 1000000. Area of intersection = 0.0588378509982666 +++ Geometric method --- Number of edge intersections = 2 I(0,3) = (0.2901639344262295, 0.3180327868852459) I(1,3) = (0.5019801980198019, 0.6475247524752475) --- Number of corners on the intersection polygon = 3 P[0] = (0.2901639344262295, 0.3180327868852459) P[1] = (0.7000000000000000, 0.4000000000000000) P[2] = (0.5019801980198019, 0.6475247524752475) Area of intersection = 0.0588378509982146 *** Case (d) +++ Rectangle 1 0.1000000000000000 0.2000000000000000 0.5000000000000000 0.3000000000000000 0.4000000000000000 0.8000000000000000 0.1500000000000000 0.7500000000000000 +++ Rectangle 2 0.3000000000000000 0.1000000000000000 0.9000000000000000 0.4000000000000000 0.6000000000000000 0.7000000000000000 0.2000000000000000 0.5000000000000000 ++================================================================================================================================================================++ || || || || || || || || || || || || || || || || || || || || || || || || || || || || || || || 1111CC || || 111111111111 11 || || 1111111111 11 || || 1111111111 11 || || DD1111 11 || || 11 11 || || 11 11 || || 11 11 || || 11 11 22CC22 || || 11 11 222222 22 || || 11 11 222222 22 || || 11 11 222222 22 || || 11 11 222222 22 || || 11 11 222222 22 || || 11 112222 22 || || 11 222211 22 || || 11 222222..11 22 || || 11 222222......11 22 || || 11 222222............11 22 || || 11 222222................11 22 || || 11 222222....................11 22 || || 11 222222........................11 22 || || 11 222222............................11 22 || || 11 222222..................................11 22 || || 11 DD22......................................11 22 || || 11 22........................................11 22 || || 11 22......................................11 22 || || 11 22......................................11 22 || || 11 22........................................11 22 || || 11 22........................................11 22 || || 11 22......................................11 22 || || 11 22......................................11 22 || || 11 22......................................11 22BB || || 11 22........................................11 222222 || || 22......................................11 222222 || || 11 22......................................11 222222 || || 11 22......................................11 222222 || || 11 22......................................11 222222 || || 11 22......................................11 222222 || || 11 22......................................11 222222 || || 11 22..................................1111BB 222222 || || 11 22..........................1111111111 222222 || || 11 22................1111111111 222222 || || 1111 22........1111111111 222222 || || 11 221111111111 222222 || || 11 1111111111 222222 || || 11 1111111111 22 222222 || || 11 1111111111 22 222222 || || AA1111 22 222222 || || 22 222222 || || 22 222222 || || 22 222222 || || 22 222222 || || 22 222222 || || 22 222222 || || 22222222 || || AA22 || || || || || || || || || || || || || || || || || ++================================================================================================================================================================++ +++ Graphical method N = 10. Area of intersection = 0.0700000000000000 N = 100. Area of intersection = 0.0735000000000000 N = 1000. Area of intersection = 0.0736910000000000 +++ Numerical method N = 10. Area of intersection = 0.0800000000000000 N = 100. Area of intersection = 0.0738000000000000 N = 1000. Area of intersection = 0.0737171250000000 N = 10000. Area of intersection = 0.0737165812500000 N = 100000. Area of intersection = 0.0737165776125000 N = 1000000. Area of intersection = 0.0737165775405000 +++ Geometric method --- Number of edge intersections = 2 I(0,3) = (0.2647058823529412, 0.2411764705882353) I(1,2) = (0.4363636363636363, 0.6181818181818182) --- Number of corners on the intersection polygon = 4 P[0] = (0.2647058823529412, 0.2411764705882353) P[1] = (0.5000000000000000, 0.3000000000000000) P[2] = (0.4363636363636363, 0.6181818181818182) P[3] = (0.2000000000000000, 0.5000000000000000) Area of intersection = 0.0737165775401070 *** Case (e) +++ Rectangle 1 0.2000000000000000 0.4000000000000000 0.5000000000000000 0.1000000000000000 0.8000000000000000 0.2000000000000000 0.6000000000000000 0.8000000000000000 +++ Rectangle 2 0.4000000000000000 0.3000000000000000 0.9000000000000000 0.5000000000000000 0.3000000000000000 0.9000000000000000 0.1000000000000000 0.7000000000000000 ++================================================================================================================================================================++ || || || || || || || || || || || || || || || CC22 || || 22 22 || || 22 2222 || || 22 22 || || 22 2222 || || 22 22 || || 22 2222 || || 22 22 || || 22 2222 DD || || 22 22 1111 11 || || 22 222222 11 11 || || 2222 2222 11 11 || || 2222 222211 11 || || 2222 1122 11 || || 22 1111....2222 11 || || 2222 11..........22 11 || || DD22 11..............2222 11 || || 22 11....................2211 || || 22 11........................2211 || || 22 1111............................1122 || || 22 11..............................11 2222 || || 22 11..................................11 22 || || 22 11....................................11 2222 || || 22 11......................................11 22 || || 22 1111..........................................11 2222 || || 22 11............................................11 22 || || 22 1111..............................................11 2222 || || 22 11..................................................11 22 || || 22 11....................................................11 2222 || || 22 11......................................................11 22 || || 22 11..........................................................11 2222 || || 22 1111............................................................11 22 || || 22 11..............................................................11 22BB || || 22 11..................................................................11 22222222 || || 11....................................................................11 222222 || || 11 22..................................................................11 22222222 || || 11 22....................................................................11 222222 || || 11 22..................................................................11222222 || || 11 22............................................................222211 || || 11 22....................................................22222222 11 || || AA11 22................................................222222 11 || || 11 22........................................22222222 11 || || 11 22..................................222222 11 || || 11 22..........................22222222 11 || || 11 22......................222222 11 || || 11 22..............22222222 11 || || 11 22........222222 11 || || 11 2222222222 11 || || 11 AA22 11 || || 11 11 || || 11 11 || || 11 11 || || 11 11 || || 11 11 || || 11 11 || || 11 11 || || 1111 CC || || 1111 11111111 || || 1111 111111 || || 1111 111111 || || 11 111111 || || 1111 111111 || || 1111 111111 || || 1111 111111 || || BB11 || || || || || || || || || || || || || || || || || ++================================================================================================================================================================++ +++ Graphical method N = 10. Area of intersection = 0.1000000000000000 N = 100. Area of intersection = 0.1111000000000000 N = 1000. Area of intersection = 0.1119970000000000 +++ Numerical method N = 10. Area of intersection = 0.1136666666666667 N = 100. Area of intersection = 0.1120700000000000 N = 1000. Area of intersection = 0.1120834666666667 N = 10000. Area of intersection = 0.1120840333333335 N = 100000. Area of intersection = 0.1120840336200002 N = 1000000. Area of intersection = 0.1120840336129667 +++ Geometric method --- Number of edge intersections = 4 I(3,3) = (0.2714285714285715, 0.4714285714285715) I(2,0) = (0.7235294117647060, 0.4294117647058824) I(2,1) = (0.6428571428571429, 0.6714285714285714) I(3,1) = (0.5400000000000000, 0.7400000000000000) --- Number of corners on the intersection polygon = 5 P[0] = (0.2714285714285715, 0.4714285714285715) P[1] = (0.4000000000000000, 0.3000000000000000) P[2] = (0.7235294117647060, 0.4294117647058824) P[3] = (0.6428571428571429, 0.6714285714285714) P[4] = (0.5400000000000000, 0.7400000000000000) Area of intersection = 0.1120840336134454 *** Case (f) +++ Rectangle 1 0.2000000000000000 0.2000000000000000 0.8000000000000000 0.1000000000000000 0.9000000000000000 0.9000000000000000 0.0500000000000000 0.8000000000000000 +++ Rectangle 2 0.5000000000000000 0.0500000000000000 0.9500000000000000 0.3000000000000000 0.4000000000000000 0.7000000000000000 0.2500000000000000 0.5000000000000000 ++================================================================================================================================================================++ || || || || || || || || || || || || || || || 11111111CC || || 11111111111111111111 11 || || 111111111111111111 11 || || 11111111111111111111 11 || || 111111111111111111 1111 || || 11111111111111111111 11 || || 111111111111111111 11 || || 11111111111111111111 11 || || DD11111111 11 || || 11 11 || || 11 11 || || 11 11 || || 11 1111 || || 11 11 || || 11 11 || || 11 11 || || 11 CC22 11 || || 11 2222..22 11 || || 11 2222......22 11 || || 11 2222..........2222 11 || || 11 22................22 1111 || || 11 2222..................2222 11 || || 11 2222........................22 11 || || 11 2222............................22 11 || || 11 22................................2222 11 || || 11 2222....................................22 11 || || 11 2222........................................22 11 || || 11 2222............................................2222 11 || || 11 22..................................................22 1111 || || 11 2222....................................................2222 11 || || 11 2222..........................................................22 11 || || 11 2222..............................................................22 11 || || 11 DD..................................................................2222 11 || || 11 22....................................................................22 11 || || 11 22......................................................................22 11 || || 11 22......................................................................2222 11 || || 11 2222........................................................................22 1111 || || 11 22..........................................................................2222 11 || || 11 22............................................................................22 11 || || 11 22..............................................................................22 11 || || 11 22..............................................................................222211 || || 11 22..................................................................................11 || || 11 22................................................................................1122 || || 11 22................................................................................11 2222 || || 11 22............................................................................1111 22 || || 11 22............................................................................11 2222 || || 11 22..........................................................................11 22 || || 11 22........................................................................11 22 || || 11 22........................................................................11 22BB || || 11 22......................................................................11 222222 || || 11 22......................................................................11 2222 || || 11 22....................................................................11 2222 || || 11 22..................................................................1111 222222 || || 11 22................................................................11222222 || || 11 22..............................................................221122 || || 11 22..........................................................222211 || || AA111111 22....................................................2222 11 || || 11111111111111 22................................................222222 11 || || 111111111111 22..........................................222222 11 || || 111111111111..................................222222 11 || || 22 111111111111....................2222 1111 || || 22 111111111111....2222 11 || || 22 111111111111 11 || || 22 222222 111111111111 11 || || 22 222222 1111BB || || 22 2222 || || 22 222222 || || 22222222 || || AA22 || || || || || || || || || ++================================================================================================================================================================++ +++ Graphical method N = 10. Area of intersection = 0.1900000000000000 N = 100. Area of intersection = 0.1975000000000000 N = 1000. Area of intersection = 0.1976200000000000 +++ Numerical method N = 10. Area of intersection = 0.1909292929292929 N = 100. Area of intersection = 0.1976233333333333 N = 1000. Area of intersection = 0.1976429479797980 N = 10000. Area of intersection = 0.1976431889545456 N = 100000. Area of intersection = 0.1976431861281818 N = 1000000. Area of intersection = 0.1976431861495818 +++ Geometric method --- Number of edge intersections = 4 I(0,3) = (0.4387755102040816, 0.1602040816326531) I(0,0) = (0.6384615384615385, 0.1269230769230769) I(1,0) = (0.8156716417910449, 0.2253731343283582) I(1,1) = (0.8354166666666669, 0.3833333333333333) --- Number of corners on the intersection polygon = 6 P[0] = (0.4387755102040816, 0.1602040816326531) P[1] = (0.6384615384615385, 0.1269230769230769) P[2] = (0.8156716417910449, 0.2253731343283582) P[3] = (0.8354166666666669, 0.3833333333333333) P[4] = (0.4000000000000000, 0.7000000000000000) P[5] = (0.2500000000000000, 0.5000000000000000) Area of intersection = 0.1976431861493163 *** Case (g) +++ Rectangle 1 0.7000000000000000 0.9000000000000000 0.1500000000000000 0.7000000000000000 0.4500000000000000 0.3000000000000000 0.9000000000000000 0.4000000000000000 +++ Rectangle 2 0.8000000000000000 0.1000000000000000 0.8500000000000000 0.7500000000000000 0.3500000000000000 0.9500000000000000 0.1000000000000000 0.2000000000000000 ++================================================================================================================================================================++ || || || || || || || CC22 || || 2222 222222 || || 22 2222 || || 22 222222 || || 22 2222 11AA || || 22 222222 11111111 11 || || 22 2222 11111111 11 || || 22 2211111111 11 || || 22 111111..2222 11 || || 22 11111111..........222222 11 || || 22 11111111......................2222 11 || || 22 11111111................................222222 11 || || 22 111111............................................2211 || || 22 11111111....................................................112222 || || 22 11111111..........................................................11 2222 || || 2211111111..................................................................11 222222 || || 111111........................................................................11 BB || || 1111111122..........................................................................11 22 || || 111111 22..............................................................................11 22 || || 11111111 22..............................................................................11 22 || || BB11 22..................................................................................11 22 || || 11 ..................................................................................11 22 || || 11 22..................................................................................11 22 || || 11 22......................................................................................11 2222 || || 11 22......................................................................................11 22 || || 11 22........................................................................................11 22 || || 11 22..........................................................................................11 22 || || 1122..........................................................................................11 22 || || 1122............................................................................................1122 || || 2211............................................................................................1122 || || 22 11............................................................................................11 || || 22 11..........................................................................................11 || || 22 11..........................................................................................11 || || 22 11........................................................................................2211 || || 22 11......................................................................................2211 || || 22 11....................................................................................22 11 || || 22 11..................................................................................2222 11 || || 2222 11................................................................................22 11 || || 22 11..............................................................................22 11 || || 22 11............................................................................22 11 || || 22 11............................................................................22 11 || || 22 11..........................................................................22 11 || || 22 11........................................................................22 11 || || 22 11......................................................................22 11 || || 22 11......................................................................22 1111DD || || 22 11..................................................................111111111111 || || 22 11........................................................111111111122 || || 22 11............................................111111111111 22 || || 22 11....................................1111111111 22 || || 22 11........................111111111111 22 || || 22 11..............1111111111 22 || || 22 11..111111111111 22 || || 22 CC1111 22 || || 22 22 || || 22 22 || || 22 22 || || 22 22 || || 22 22 || || 22 22 || || 22 22 || || DD22222222 22 || || 22222222222222 22 || || 22222222222222 22 || || 22222222222222 22 || || 22222222222222 22 || || 22222222222222 22 || || 22222222222222 22 || || 22222222222222 22 || || 2222AA || || || || || || || || || || || || || || || || || ++================================================================================================================================================================++ +++ Graphical method N = 10. Area of intersection = 0.2400000000000000 N = 100. Area of intersection = 0.2389000000000000 N = 1000. Area of intersection = 0.2393030000000000 +++ Numerical method N = 10. Area of intersection = 0.1839848484848485 N = 100. Area of intersection = 0.2391776767676767 N = 1000. Area of intersection = 0.2392959545454545 N = 10000. Area of intersection = 0.2392973542424241 N = 100000. Area of intersection = 0.2392973435419192 N = 1000000. Area of intersection = 0.2392973436403864 +++ Geometric method --- Number of edge intersections = 6 I(1,2) = (0.2307692307692307, 0.5923076923076923) I(2,0) = (0.8217391304347825, 0.3826086956521739) I(3,0) = (0.8354838709677419, 0.5612903225806447) I(3,1) = (0.7428571428571428, 0.7928571428571428) I(0,1) = (0.5821428571428570, 0.8571428571428572) I(0,2) = (0.2827586206896551, 0.7482758620689655) --- Number of corners on the intersection polygon = 7 P[0] = (0.2307692307692307, 0.5923076923076923) P[1] = (0.4500000000000000, 0.3000000000000000) P[2] = (0.8217391304347825, 0.3826086956521739) P[3] = (0.8354838709677419, 0.5612903225806447) P[4] = (0.7428571428571428, 0.7928571428571428) P[5] = (0.5821428571428570, 0.8571428571428572) P[6] = (0.2827586206896551, 0.7482758620689655) Area of intersection = 0.2392973436403032 *** Case (h) +++ Rectangle 1 0.9500000000000000 0.6000000000000000 0.4000000000000000 0.9500000000000000 0.0500000000000000 0.5000000000000000 0.5000000000000000 0.0500000000000000 +++ Rectangle 2 0.1000000000000000 0.3000000000000000 0.7000000000000000 0.1000000000000000 0.8000000000000000 0.9000000000000000 0.2000000000000000 0.8000000000000000 ++================================================================================================================================================================++ || || || || || || || BB11 || || 1111 11 || || 1111 1111 || || 1111 1111 || || 11 11 222222CC || || 11 1111 22222222222222 22 || || 1111 11 22222222222222 22 || || 1111 11112222222222 22 || || 1111 22222222222222..11 2222 || || 11 22222222222222..............111111 22 || || 1111222222222222................................1111 22 || || 22222222111122................................................11 22 || || DD222222 1111......................................................1111 22 || || 22 11............................................................11 22 || || 22 1111..............................................................1111 22 || || 22 1111....................................................................11 22 || || 22 1111........................................................................1111 2222 || || 22 1111..............................................................................1111 22 || || 22 11....................................................................................1122 || || 22 1111......................................................................................1111 || || 22 1111........................................................................................22 11 || || 221111..........................................................................................22 1111 || || 2211............................................................................................22 11 || || 11..............................................................................................22 1111 || || 1111............................................................................................2222 1111 || || 1111..............................................................................................22 11 || || 111122..............................................................................................22 1111 || || 11 22..............................................................................................22 11 || || 1111 22..............................................................................................22 AA || || 1111 22..............................................................................................22 1111 || || 1111 22................................................................................................22 1111 || || 1111 22................................................................................................22 1111 || || 11 22..............................................................................................2222 1111 || || 1111 22..............................................................................................22 11 || || 1111 22..............................................................................................22 11 || || 1111 22................................................................................................22 1111 || || CC11 22................................................................................................22 1111 || || 11 22................................................................................................22 1111 || || 11 22................................................................................................22 1111 || || 11 22................................................................................................22 11 || || 1122................................................................................................2222 1111 || || 11................................................................................................22 1111 || || 2211..............................................................................................22 1111 || || 22 11............................................................................................22 1111 || || 22 11..........................................................................................22 11 || || 22 11........................................................................................22 11 || || 22 11......................................................................................22 1111 || || 22 11....................................................................................221111 || || 22 11................................................................................221111 || || 22 11..............................................................................1111 || || 22 11............................................................................11 || || 22 11........................................................................1111 || || AA22 11....................................................................111122 || || 22222222 11................................................................1111 22 || || 222222 11............................................................1111 22 || || 222222 11..........................................................11 22 || || 222222 11......................................................11 2222 || || 22222211..................................................1111 22 || || 221122............................................1111 22 || || 2211222222....................................1111 22 || || 11 2222..............................1111 22 || || 11 222222........................11 22 || || 11 222222................1111 22 || || 11 22222222......1111 22 || || 11 22221111 2222 || || 11 1111222222 22 || || 11 11 222222 22 || || 11 11 222222 22 || || 11 1111 22BB || || 11 1111 || || 11 1111 || || 1111 || || DD || || || || || || || || || ++================================================================================================================================================================++ +++ Graphical method N = 10. Area of intersection = 0.3400000000000001 N = 100. Area of intersection = 0.3334000000000000 N = 1000. Area of intersection = 0.3346090000000000 +++ Numerical method N = 10. Area of intersection = 0.3363203463203464 N = 100. Area of intersection = 0.3346767316017316 N = 1000. Area of intersection = 0.3347552103174601 N = 10000. Area of intersection = 0.3347552041269845 N = 100000. Area of intersection = 0.3347551995426409 N = 1000000. Area of intersection = 0.3347551995691037 +++ Geometric method --- Number of edge intersections = 8 I(2,3) = (0.1250000000000000, 0.4250000000000000) I(2,0) = (0.3250000000000001, 0.2249999999999999) I(3,0) = (0.5750000000000001, 0.1416666666666667) I(3,1) = (0.7286885245901640, 0.3295081967213115) I(0,1) = (0.7763157894736843, 0.7105263157894738) I(0,2) = (0.5452830188679245, 0.8575471698113207) I(1,2) = (0.2957446808510638, 0.8159574468085107) I(1,3) = (0.1711538461538462, 0.6557692307692309) --- Number of corners on the intersection polygon = 8 P[0] = (0.1250000000000000, 0.4250000000000000) P[1] = (0.3250000000000001, 0.2249999999999999) P[2] = (0.5750000000000001, 0.1416666666666667) P[3] = (0.7286885245901640, 0.3295081967213115) P[4] = (0.7763157894736843, 0.7105263157894738) P[5] = (0.5452830188679245, 0.8575471698113207) P[6] = (0.2957446808510638, 0.8159574468085107) P[7] = (0.1711538461538462, 0.6557692307692309) Area of intersection = 0.3347551995684276