-------------------------------------------------------------------------------------------------------------------------------- ONE CIRCLE INSIDE ANOTHER ------------------------- +++ Input data for three circles C1: 18 3 11 C2: 17 4 5 C3: 4 19 19 +++ Relative positions of C1,C2: INSIDE C1,C3: OVERLAP C2,C3: OVERLAP +++ Intersection points Between C1 and C3: ( 22.095966, 13.208970 ) and ( 7.337663, 0.295455 ) Between C2 and C3: ( 19.656691, 8.235799 ) and ( 12.429603, 1.972323 ) +++ Circle areas area(C1) = 380.132711 area(C2) = 78.539816 area(C3) = 1134.114948 +++ Intersection areas of two circles area(C1,C2) = 78.539816 area(C1,C3) = 120.436360 area(C2,C3) = 28.782463 +++ Intersection area of three circles area(C1,C2,C3) = 28.782463 | | 3 3 3 3 3 3 3 3 3 3 3 3 | 3 3 3 3 3 | 3 3 3 | 3 3 3 | 3 3 3 | 3 3 | 3 3 | 3 3 | 3 3 | 3 3 | 3 3 | 3 3 | 3 3 | 3 3 | 3 3 | 3 3 | 3 3 | 3 3 | 3 3 | 3 3 3 | 3 3 | 3 3 | 3 3 | 3 3 | 1 1 1 1 1 1 1 3 3 | 1 1 3 1 3 | 1 3 1 3 | 1 1 3 1 1 3 | 1 3 1 3 | 1 2 2 2 2 2 3 1 3 | 1 2 3 2 1 3 | 1 2 3 2 1 3 | 1 2 3 2 1 3 | 1 2 3 2 1 3 3 | 1 2 3 3 2 2 1 3 | 1 2 3 1 2 1 3 3 | 1 3 3 2 1 3 3 3 | 1 3 3 3 2 2 1 - - - - - - - - - - - - - - - - - - - - 3 3 3 3 3 3 3 3 3 - - - - - 2 - - - - - 2 - - - - - - - - 1 - - - - - - - - - - - | 1 2 2 2 2 2 1 | 1 1 | 1 1 | 1 1 | 1 1 1 1 | 1 1 | 1 1 1 1 | 1 1 1 1 1 1 1 | | | -------------------------------------------------------------------------------------------------------------------------------- TWO CIRCLES DISJOINT -------------------- +++ Input data for three circles C1: 0 17 13 C2: 20 1 5 C3: 5 9 20 +++ Relative positions of C1,C2: DISJOINT C1,C3: OVERLAP C2,C3: OVERLAP +++ Intersection points Between C1 and C3: ( 5.000000, 29.000000 ) and (-12.977528, 17.764045 ) Between C2 and C3: ( 24.261487, 3.615288 ) and ( 20.202181, -3.995911 ) +++ Circle areas area(C1) = 530.929158 area(C2) = 78.539816 area(C3) = 1256.637061 +++ Intersection areas of two circles area(C1,C2) = 0.000000 area(C1,C3) = 493.245901 area(C2,C3) = 66.152043 +++ Intersection area of three circles area(C1,C2,C3) = 0.000000 | | | | | 1 1 1 1 1 1 1 1 1 1 | 3 3 3 3 3 3 3 3 3 1 3 3 3 1 3 3 3 1 3 3 | 1 3 3 1 3 3 | 1 3 3 1 3 | 1 3 1 3 | 1 3 1 3 | 1 3 1 3 | 1 3 1 3 | 1 3 1 3 | 1 3 1 3 | 1 3 3 | 1 3 3 1 1 3 3 1 | 1 3 3 1 | 1 3 3 1 | 1 3 3 1 | 1 3 3 1 | 1 3 3 1 | 1 3 3 1 | 1 3 3 1 | 3 1 3 3 1 | 1 3 3 1 | 1 3 3 1 | 1 2 2 2 2 2 3 3 1 1 1 | 1 1 1 2 2 3 3 1 1 1 1 1 1 1 2 3 3 | 2 3 2 3 | 2 3 2 3 | 2 2 3 2 - - - - - - - 3 - - - - - - - - - - - - + - - - - - - - - - - - - - - 2 - - - - - - - 3 - 2 - - - - - - - - - - - - - - - 3 | 2 3 2 3 | 2 3 2 3 | 2 3 2 3 | 2 2 3 2 2 3 | 3 3 | 3 3 | 3 3 3 | 3 3 3 3 | 3 3 3 3 3 3 3 3 | 3 3 3 3 3 3 3 3 3 | | | | | | -------------------------------------------------------------------------------------------------------------------------------- MUTUAL OVERLAP: CASE 5(a) ------------------------- +++ Input data for three circles C1: 0 4 20 C2: 10 20 16 C3: 16 9 15 +++ Relative positions of C1,C2: OVERLAP C1,C3: OVERLAP C2,C3: OVERLAP +++ Intersection points Between C1 and C2: ( 19.726556, 7.295902 ) and ( -5.681613, 23.176008 ) Between C1 and C3: ( 17.355813, -5.938600 ) and ( 8.608600, 22.052479 ) Between C2 and C3: ( 25.998973, 20.181258 ) and ( 1.185740, 6.646767 ) +++ Circle areas area(C1) = 1256.637061 area(C2) = 804.247719 area(C3) = 706.858347 +++ Intersection areas of two circles area(C1,C2) = 366.271146 area(C1,C3) = 389.025329 area(C2,C3) = 376.636110 +++ Intersection area of three circles --- Case 5(a) area(C1,C2,C3) = 237.074143 | | | | | 2 2 2 2 2 2 2 | 2 2 2 2 2 2 | 2 2 2 2 | 2 2 2 2 2 2 2 | 2 2 | 2 2 | 2 2 | 2 2 | 2 2 | 2 2 | 2 2 1 1 1 1 1 1 1 1 1 3 3 3 3 3 3 3 2 1 2 1 | 1 1 1 3 3 3 3 3 3 2 1 1 2 | 3 3 3 3 2 1 1 2 | 3 1 1 3 2 1 2 | 3 2 1 3 1 2 | 3 1 2 3 1 2 | 3 1 2 3 1 2 | 3 1 2 3 1 2 | 3 1 2 3 1 2 | 3 1 2 3 1 2 | 3 1 2 3 1 2 | 3 1 2 3 1 2 | 3 1 2 3 1 2 | 3 1 2 3 1 2 | 3 1 2 3 1 2 | 3 3 1 2 3 1 2 2 3 2 2 3 1 | 3 2 1 3 1 | 3 2 2 2 2 1 3 1 | 3 2 2 2 2 2 2 1 3 1 1 3 2 2 2 2 2 2 2 1 3 1 | 3 1 3 1 | 3 1 3 1 | 3 1 3 1 - - - - - - - - - - - - - - - - - - - + - - - 3 - - - - - - - - - - - - - - - 1 - - - - - - - 3 - - - - - - - - - - - - 1 | 3 1 3 1 | 3 1 3 1 | 3 1 3 1 | 3 3 1 3 3 1 | 3 3 3 1 3 3 3 1 | 3 3 3 3 3 3 3 1 | 1 1 | 1 1 | 1 1 | 1 1 | 1 1 | 1 1 1 | 1 1 1 1 | 1 1 1 1 1 | 1 1 1 1 1 1 1 1 1 1 1 1 | | | -------------------------------------------------------------------------------------------------------------------------------- MUTUAL OVERLAP: CASE 5(b)(i) ---------------------------- +++ Input data for three circles C1: 16 14 18 C2: 17 1 10 C3: 19 20 18 +++ Relative positions of C1,C2: OVERLAP C1,C3: OVERLAP C2,C3: OVERLAP +++ Intersection points Between C1 and C2: ( 26.913246, -0.314366 ) and ( 7.404401, -1.815046 ) Between C1 and C3: ( 33.317712, 9.091144 ) and ( 1.682288, 24.908856 ) Between C2 and C3: ( 26.629473, 3.696898 ) and ( 8.143130, 5.642828 ) +++ Circle areas area(C1) = 1017.876020 area(C2) = 314.159265 area(C3) = 1017.876020 +++ Intersection areas of two circles area(C1,C2) = 236.556673 area(C1,C3) = 777.785591 area(C2,C3) = 117.514378 +++ Intersection area of three circles area(C1,C2,C3) = 117.514378 | | | 3 3 3 3 3 3 3 3 3 | 3 3 3 3 3 3 | 3 3 3 3 | 3 3 | 3 3 | 3 3 | 3 1 1 1 1 1 1 1 1 1 3 | 3 1 1 1 1 1 1 3 | 3 1 1 1 1 3 | 3 1 1 3 | 3 1 1 3 | 3 1 1 3 | 3 1 1 3 | 3 1 3 | 3 1 3 1 3 1 3 1 3 1 3 1 | 3 1 3 1 | 3 3 1 3 1 | 3 1 3 1 | 3 1 3 1 | 3 1 3 1 | 3 1 3 1 | 3 1 3 1 | 3 1 1 3 1 | 3 1 3 1 | 3 1 3 1 | 3 2 2 2 2 2 2 2 1 3 1 | 3 2 2 2 2 3 1 | 3 2 2 3 1 | 3 2 2 3 1 1 | 3 2 2 3 1 1 3 2 3 1 1 2 3 2 3 1 | 1 2 3 3 3 3 1 | 1 2 3 3 3 3 3 3 2 1 | 1 2 3 3 3 3 3 3 3 3 3 2 1 | 1 2 2 2 1 - - - - - - - - - - - - - - - - - - - - + - - - - 1 - 2 - - - - - - - - - - - - - - - - - - - 2 - - - - - - - - - - - - - | 1 2 1 2 | 2 1 1 1 2 | 2 1 1 1 1 1 1 2 | 2 1 1 1 1 1 1 1 1 1 2 | 2 2 | 2 2 | 2 2 | 2 2 2 2 | 2 2 2 2 2 2 2 | | | -------------------------------------------------------------------------------------------------------------------------------- MUTUAL OVERLAP: CASE 5(b)(ii) ----------------------------- +++ Input data for three circles C1: 0 13 15 C2: 19 2 9 C3: 20 19 10 +++ Relative positions of C1,C2: OVERLAP C1,C3: OVERLAP C2,C3: OVERLAP +++ Intersection points Between C1 and C2: ( 14.674573, 9.892445 ) and ( 10.001775, 1.821248 ) Between C1 and C3: ( 14.784699, 10.467671 ) and ( 10.949246, 23.252512 ) Between C2 and C3: ( 23.665788, 9.696130 ) and ( 15.268694, 10.190077 ) +++ Circle areas area(C1) = 706.858347 area(C2) = 254.469005 area(C3) = 314.159265 +++ Intersection areas of two circles area(C1,C2) = 12.866247 area(C1,C3) = 37.460354 area(C2,C3) = 11.172278 +++ Intersection area of three circles area(C1,C2,C3) = 0.000000 | | | | | | | | | 3 3 3 3 3 3 3 1 1 1 1 1 1 1 3 3 3 3 1 1 1 | 1 1 1 3 3 1 1 | 1 1 3 3 1 | 1 3 3 1 | 1 3 3 1 | 3 3 1 | 3 1 3 1 | 3 1 3 1 | 3 1 3 1 | 3 1 3 3 1 | 3 1 3 1 | 3 1 3 1 | 3 1 3 1 | 3 1 3 1 | 3 1 3 1 1 3 1 3 1 | 3 1 3 1 | 3 1 2 2 2 2 2 3 1 | 3 3 2 2 3 3 1 | 2 2 3 3 3 3 3 3 3 2 2 1 | 2 1 2 1 | 2 1 2 1 | 2 1 2 1 | 2 1 2 1 | 2 1 2 1 | 2 1 2 1 | 2 2 2 1 | 1 2 2 - - - - - - - - - - - - 1 1 - - - - - - + - - - - - - 1 1 - 2 - - - - - - - - - - - - - - - - - 2 - - - - - - - - - - - - 1 1 1 | 1 1 1 2 2 1 1 1 1 1 1 1 2 2 | 2 2 | 2 2 | 2 2 2 2 | 2 2 2 2 | 2 2 2 2 2 | | | | | | | -------------------------------------------------------------------------------------------------------------------------------- MUTUAL OVERLAP: CASE 5(c)(i) ---------------------------- +++ Input data for three circles C1: 13 5 12 C2: 15 16 14 C3: 17 20 14 +++ Relative positions of C1,C2: OVERLAP C1,C3: OVERLAP C2,C3: OVERLAP +++ Intersection points Between C1 and C2: ( 24.945120, 6.146342 ) and ( 2.222880, 10.277658 ) Between C1 and C3: ( 24.560709, 8.217144 ) and ( 4.576221, 13.546341 ) Between C2 and C3: ( 28.361230, 11.819385 ) and ( 3.638770, 24.180615 ) +++ Circle areas area(C1) = 452.389342 area(C2) = 615.752160 area(C3) = 615.752160 +++ Intersection areas of two circles area(C1,C2) = 247.509775 area(C1,C3) = 151.937575 area(C2,C3) = 491.066807 +++ Intersection area of three circles area(C1,C2,C3) = 151.937575 | | | | | 3 3 3 3 3 3 3 | 3 3 3 3 3 3 | 3 3 | 3 3 3 3 | 3 2 2 2 2 2 2 2 3 | 3 2 2 2 2 2 2 3 | 3 2 2 3 | 3 2 2 2 2 3 | 3 2 2 3 | 3 2 3 | 3 2 3 | 3 2 3 | 2 3 2 3 | 2 3 2 3 | 2 3 3 2 3 | 2 3 2 3 | 2 3 2 3 | 2 3 1 1 1 1 1 1 1 2 3 | 2 3 1 1 2 1 1 2 3 | 2 3 1 1 1 1 2 3 | 2 3 1 1 2 3 | 2 1 3 1 3 | 2 1 3 1 3 | 2 1 3 1 3 | 2 3 1 3 2 | 1 2 3 3 1 3 3 2 | 1 2 3 3 1 2 | 1 2 3 3 3 3 3 3 1 2 | 1 2 3 3 3 3 3 3 3 2 | 1 2 2 1 2 2 1 | 1 2 2 1 | 1 2 2 2 2 2 2 1 | 1 2 2 2 2 2 2 2 1 | 1 1 - - - - - - - - - - - - - - - - - - - - + - 1 - - - - - - - - - - - - - - - - - - - - - 1 - - - - - - - - - - - - - - - - | 1 1 | 1 1 | 1 1 | 1 1 | 1 1 1 1 | 1 1 1 1 | 1 1 1 1 1 1 1 | | | | -------------------------------------------------------------------------------------------------------------------------------- MUTUAL OVERLAP: CASE 5(c)(ii) ----------------------------- +++ Input data for three circles C1: 0 13 20 C2: 12 17 11 C3: 19 19 14 +++ Relative positions of C1,C2: OVERLAP C1,C3: OVERLAP C2,C3: OVERLAP +++ Intersection points Between C1 and C2: ( 19.606915, 9.054256 ) and ( 13.318085, 27.920744 ) Between C1 and C3: ( 18.337147, 5.015701 ) and ( 10.426077, 30.067423 ) Between C2 and C3: ( 13.540458, 6.108398 ) and ( 7.553882, 27.061413 ) +++ Circle areas area(C1) = 1256.637061 area(C2) = 380.132711 area(C3) = 615.752160 +++ Intersection areas of two circles area(C1,C2) = 325.891653 area(C1,C3) = 263.531575 area(C2,C3) = 302.230084 +++ Intersection area of three circles area(C1,C2,C3) = 247.989026 | | | | | | | 1 1 1 1 1 1 1 1 1 3 3 3 3 3 3 3 1 1 1 | 1 1 1 3 3 3 3 3 3 1 1 | 1 1 3 3 1 1 | 3 3 3 3 1 | 3 1 3 1 | 3 2 2 2 2 2 2 2 3 1 | 2 3 1 2 2 3 1 | 2 3 1 2 3 1 | 2 2 3 1 2 2 3 1 | 2 3 1 2 3 1 | 2 3 1 2 3 1 | 2 3 1 2 3 1 | 2 3 1 2 3 1 | 2 3 1 2 3 1 | 2 3 3 2 3 1 | 2 3 1 2 3 1 | 2 3 2 1 2 3 1 | 2 3 1 2 3 1 | 2 3 1 2 3 1 | 2 3 1 2 3 1 1 2 3 1 2 3 1 | 2 3 1 2 3 1 | 2 3 1 2 3 1 | 2 3 2 3 1 | 2 2 3 2 2 3 1 | 2 3 3 2 1 3 3 1 | 2 2 3 2 2 1 3 1 | 2 2 2 2 3 3 3 1 3 3 3 1 | 3 3 3 3 3 3 3 1 | 1 1 | 1 1 | 1 1 | 1 - - - - - 1 - - - - - - - - - - - - - - + - - - - - - - - - - - - - - 1 - - - - - - - - - - - - - - - - - - - - - - - - - 1 | 1 1 | 1 1 | 1 1 1 | 1 1 1 1 | 1 1 1 1 1 | 1 1 1 1 1 1 1 1 1 1 1 1 | | | | | | | --------------------------------------------------------------------------------------------------------------------------------