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| 1 | +// |
| 2 | +// adjugate.swift |
| 3 | +// |
| 4 | +// |
| 5 | +// Created by Christian Treffs on 02.09.20. |
| 6 | +// |
| 7 | + |
| 8 | +public func adjugate(_ inMat: Mat4x4f) -> Mat4x4f { |
| 9 | + var out = Mat4x4f.identity |
| 10 | + |
| 11 | + out[0, 0] = inMat[1, 1] * inMat[2, 2] * inMat[3, 3] - inMat[1, 1] * inMat[2, 3] * inMat[3, 2] |
| 12 | + out[0, 0] += -inMat[2, 1] * inMat[1, 2] * inMat[3, 3] + inMat[2, 1] * inMat[1, 3] * inMat[3, 2] |
| 13 | + out[0, 0] += inMat[3, 1] * inMat[1, 2] * inMat[2, 3] - inMat[3, 1] * inMat[1, 3] * inMat[2, 2] |
| 14 | + |
| 15 | + out[1, 0] = -inMat[1, 0] * inMat[2, 2] * inMat[3, 3] + inMat[1, 0] * inMat[2, 3] * inMat[3, 2] |
| 16 | + out[1, 0] += inMat[2, 0] * inMat[1, 2] * inMat[3, 3] - inMat[2, 0] * inMat[1, 3] * inMat[3, 2] |
| 17 | + out[1, 0] += -inMat[3, 0] * inMat[1, 2] * inMat[2, 3] + inMat[3, 0] * inMat[1, 3] * inMat[2, 2] |
| 18 | + |
| 19 | + out[2, 0] = inMat[1, 0] * inMat[2, 1] * inMat[3, 3] - inMat[1, 0] * inMat[2, 3] * inMat[3, 1] |
| 20 | + out[2, 0] += -inMat[2, 0] * inMat[1, 1] * inMat[3, 3] + inMat[2, 0] * inMat[1, 3] * inMat[3, 1] |
| 21 | + out[2, 0] += inMat[3, 0] * inMat[1, 1] * inMat[2, 3] - inMat[3, 0] * inMat[1, 3] * inMat[2, 1] |
| 22 | + |
| 23 | + out[3, 0] = -inMat[1, 0] * inMat[2, 1] * inMat[3, 2] + inMat[1, 0] * inMat[2, 2] * inMat[3, 1] |
| 24 | + out[3, 0] += inMat[2, 0] * inMat[1, 1] * inMat[3, 2] - inMat[2, 0] * inMat[1, 2] * inMat[3, 1] |
| 25 | + out[3, 0] += -inMat[3, 0] * inMat[1, 1] * inMat[2, 2] + inMat[3, 0] * inMat[1, 2] * inMat[2, 1] |
| 26 | + |
| 27 | + out[0, 1] = -inMat[0, 1] * inMat[2, 2] * inMat[3, 3] + inMat[0, 1] * inMat[2, 3] * inMat[3, 2] |
| 28 | + out[0, 1] += inMat[2, 1] * inMat[0, 2] * inMat[3, 3] - inMat[2, 1] * inMat[0, 3] * inMat[3, 2] |
| 29 | + out[0, 1] += -inMat[3, 1] * inMat[0, 2] * inMat[2, 3] + inMat[3, 1] * inMat[0, 3] * inMat[2, 2] |
| 30 | + |
| 31 | + out[1, 1] = inMat[0, 0] * inMat[2, 2] * inMat[3, 3] - inMat[0, 0] * inMat[2, 3] * inMat[3, 2] |
| 32 | + out[1, 1] += -inMat[2, 0] * inMat[0, 2] * inMat[3, 3] + inMat[2, 0] * inMat[0, 3] * inMat[3, 2] |
| 33 | + out[1, 1] += inMat[3, 0] * inMat[0, 2] * inMat[2, 3] - inMat[3, 0] * inMat[0, 3] * inMat[2, 2] |
| 34 | + |
| 35 | + out[2, 1] = -inMat[0, 0] * inMat[2, 1] * inMat[3, 3] + inMat[0, 0] * inMat[2, 3] * inMat[3, 1] |
| 36 | + out[2, 1] += inMat[2, 0] * inMat[0, 1] * inMat[3, 3] - inMat[2, 0] * inMat[0, 3] * inMat[3, 1] |
| 37 | + out[2, 1] += -inMat[3, 0] * inMat[0, 1] * inMat[2, 3] + inMat[3, 0] * inMat[0, 3] * inMat[2, 1] |
| 38 | + |
| 39 | + out[3, 1] = inMat[0, 0] * inMat[2, 1] * inMat[3, 2] - inMat[0, 0] * inMat[2, 2] * inMat[3, 1] |
| 40 | + out[3, 1] += -inMat[2, 0] * inMat[0, 1] * inMat[3, 2] + inMat[2, 0] * inMat[0, 2] * inMat[3, 1] |
| 41 | + out[3, 1] += inMat[3, 0] * inMat[0, 1] * inMat[2, 2] - inMat[3, 0] * inMat[0, 2] * inMat[2, 1] |
| 42 | + |
| 43 | + out[0, 2] = inMat[0, 1] * inMat[1, 2] * inMat[3, 3] - inMat[0, 1] * inMat[1, 3] * inMat[3, 2] |
| 44 | + out[0, 2] += -inMat[1, 1] * inMat[0, 2] * inMat[3, 3] + inMat[1, 1] * inMat[0, 3] * inMat[3, 2] |
| 45 | + out[0, 2] += inMat[3, 1] * inMat[0, 2] * inMat[1, 3] - inMat[3, 1] * inMat[0, 3] * inMat[1, 2] |
| 46 | + |
| 47 | + out[1, 2] = -inMat[0, 0] * inMat[1, 2] * inMat[3, 3] + inMat[0, 0] * inMat[1, 3] * inMat[3, 2] |
| 48 | + out[1, 2] += inMat[1, 0] * inMat[0, 2] * inMat[3, 3] - inMat[1, 0] * inMat[0, 3] * inMat[3, 2] |
| 49 | + out[1, 2] += -inMat[3, 0] * inMat[0, 2] * inMat[1, 3] + inMat[3, 0] * inMat[0, 3] * inMat[1, 2] |
| 50 | + |
| 51 | + out[2, 2] = inMat[0, 0] * inMat[1, 1] * inMat[3, 3] - inMat[0, 0] * inMat[1, 3] * inMat[3, 1] |
| 52 | + out[2, 2] += -inMat[1, 0] * inMat[0, 1] * inMat[3, 3] + inMat[1, 0] * inMat[0, 3] * inMat[3, 1] |
| 53 | + out[2, 2] += inMat[3, 0] * inMat[0, 1] * inMat[1, 3] - inMat[3, 0] * inMat[0, 3] * inMat[1, 1] |
| 54 | + |
| 55 | + out[3, 2] = -inMat[0, 0] * inMat[1, 1] * inMat[3, 2] + inMat[0, 0] * inMat[1, 2] * inMat[3, 1] |
| 56 | + out[3, 2] += inMat[1, 0] * inMat[0, 1] * inMat[3, 2] - inMat[1, 0] * inMat[0, 2] * inMat[3, 1] |
| 57 | + out[3, 2] += -inMat[3, 0] * inMat[0, 1] * inMat[1, 2] + inMat[3, 0] * inMat[0, 2] * inMat[1, 1] |
| 58 | + |
| 59 | + out[0, 3] = -inMat[0, 1] * inMat[1, 2] * inMat[2, 3] + inMat[0, 1] * inMat[1, 3] * inMat[2, 2] |
| 60 | + out[0, 3] += inMat[1, 1] * inMat[0, 2] * inMat[2, 3] - inMat[1, 1] * inMat[0, 3] * inMat[2, 2] |
| 61 | + out[0, 3] += -inMat[2, 1] * inMat[0, 2] * inMat[1, 3] + inMat[2, 1] * inMat[0, 3] * inMat[1, 2] |
| 62 | + |
| 63 | + out[1, 3] = inMat[0, 0] * inMat[1, 2] * inMat[2, 3] - inMat[0, 0] * inMat[1, 3] * inMat[2, 2] |
| 64 | + out[1, 3] += -inMat[1, 0] * inMat[0, 2] * inMat[2, 3] + inMat[1, 0] * inMat[0, 3] * inMat[2, 2] |
| 65 | + out[1, 3] += inMat[2, 0] * inMat[0, 2] * inMat[1, 3] - inMat[2, 0] * inMat[0, 3] * inMat[1, 2] |
| 66 | + |
| 67 | + out[2, 3] = -inMat[0, 0] * inMat[1, 1] * inMat[2, 3] + inMat[0, 0] * inMat[1, 3] * inMat[2, 1] |
| 68 | + out[2, 3] += inMat[1, 0] * inMat[0, 1] * inMat[2, 3] - inMat[1, 0] * inMat[0, 3] * inMat[2, 1] |
| 69 | + out[2, 3] += -inMat[2, 0] * inMat[0, 1] * inMat[1, 3] + inMat[2, 0] * inMat[0, 3] * inMat[1, 1] |
| 70 | + |
| 71 | + out[3, 3] = inMat[0, 0] * inMat[1, 1] * inMat[2, 2] - inMat[0, 0] * inMat[1, 2] * inMat[2, 1] |
| 72 | + out[3, 3] += -inMat[1, 0] * inMat[0, 1] * inMat[2, 2] + inMat[1, 0] * inMat[0, 2] * inMat[2, 1] |
| 73 | + out[3, 3] += inMat[2, 0] * inMat[0, 1] * inMat[1, 2] - inMat[2, 0] * inMat[0, 2] * inMat[1, 1] |
| 74 | + |
| 75 | + return out |
| 76 | +} |
| 77 | + |
| 78 | +public func adjugate(_ inMat: Mat4x4d) -> Mat4x4d { |
| 79 | + var out = Mat4x4d.identity |
| 80 | + |
| 81 | + out[0, 0] = inMat[1, 1] * inMat[2, 2] * inMat[3, 3] - inMat[1, 1] * inMat[2, 3] * inMat[3, 2] |
| 82 | + out[0, 0] += -inMat[2, 1] * inMat[1, 2] * inMat[3, 3] + inMat[2, 1] * inMat[1, 3] * inMat[3, 2] |
| 83 | + out[0, 0] += inMat[3, 1] * inMat[1, 2] * inMat[2, 3] - inMat[3, 1] * inMat[1, 3] * inMat[2, 2] |
| 84 | + |
| 85 | + out[1, 0] = -inMat[1, 0] * inMat[2, 2] * inMat[3, 3] + inMat[1, 0] * inMat[2, 3] * inMat[3, 2] |
| 86 | + out[1, 0] += inMat[2, 0] * inMat[1, 2] * inMat[3, 3] - inMat[2, 0] * inMat[1, 3] * inMat[3, 2] |
| 87 | + out[1, 0] += -inMat[3, 0] * inMat[1, 2] * inMat[2, 3] + inMat[3, 0] * inMat[1, 3] * inMat[2, 2] |
| 88 | + |
| 89 | + out[2, 0] = inMat[1, 0] * inMat[2, 1] * inMat[3, 3] - inMat[1, 0] * inMat[2, 3] * inMat[3, 1] |
| 90 | + out[2, 0] += -inMat[2, 0] * inMat[1, 1] * inMat[3, 3] + inMat[2, 0] * inMat[1, 3] * inMat[3, 1] |
| 91 | + out[2, 0] += inMat[3, 0] * inMat[1, 1] * inMat[2, 3] - inMat[3, 0] * inMat[1, 3] * inMat[2, 1] |
| 92 | + |
| 93 | + out[3, 0] = -inMat[1, 0] * inMat[2, 1] * inMat[3, 2] + inMat[1, 0] * inMat[2, 2] * inMat[3, 1] |
| 94 | + out[3, 0] += inMat[2, 0] * inMat[1, 1] * inMat[3, 2] - inMat[2, 0] * inMat[1, 2] * inMat[3, 1] |
| 95 | + out[3, 0] += -inMat[3, 0] * inMat[1, 1] * inMat[2, 2] + inMat[3, 0] * inMat[1, 2] * inMat[2, 1] |
| 96 | + |
| 97 | + out[0, 1] = -inMat[0, 1] * inMat[2, 2] * inMat[3, 3] + inMat[0, 1] * inMat[2, 3] * inMat[3, 2] |
| 98 | + out[0, 1] += inMat[2, 1] * inMat[0, 2] * inMat[3, 3] - inMat[2, 1] * inMat[0, 3] * inMat[3, 2] |
| 99 | + out[0, 1] += -inMat[3, 1] * inMat[0, 2] * inMat[2, 3] + inMat[3, 1] * inMat[0, 3] * inMat[2, 2] |
| 100 | + |
| 101 | + out[1, 1] = inMat[0, 0] * inMat[2, 2] * inMat[3, 3] - inMat[0, 0] * inMat[2, 3] * inMat[3, 2] |
| 102 | + out[1, 1] += -inMat[2, 0] * inMat[0, 2] * inMat[3, 3] + inMat[2, 0] * inMat[0, 3] * inMat[3, 2] |
| 103 | + out[1, 1] += inMat[3, 0] * inMat[0, 2] * inMat[2, 3] - inMat[3, 0] * inMat[0, 3] * inMat[2, 2] |
| 104 | + |
| 105 | + out[2, 1] = -inMat[0, 0] * inMat[2, 1] * inMat[3, 3] + inMat[0, 0] * inMat[2, 3] * inMat[3, 1] |
| 106 | + out[2, 1] += inMat[2, 0] * inMat[0, 1] * inMat[3, 3] - inMat[2, 0] * inMat[0, 3] * inMat[3, 1] |
| 107 | + out[2, 1] += -inMat[3, 0] * inMat[0, 1] * inMat[2, 3] + inMat[3, 0] * inMat[0, 3] * inMat[2, 1] |
| 108 | + |
| 109 | + out[3, 1] = inMat[0, 0] * inMat[2, 1] * inMat[3, 2] - inMat[0, 0] * inMat[2, 2] * inMat[3, 1] |
| 110 | + out[3, 1] += -inMat[2, 0] * inMat[0, 1] * inMat[3, 2] + inMat[2, 0] * inMat[0, 2] * inMat[3, 1] |
| 111 | + out[3, 1] += inMat[3, 0] * inMat[0, 1] * inMat[2, 2] - inMat[3, 0] * inMat[0, 2] * inMat[2, 1] |
| 112 | + |
| 113 | + out[0, 2] = inMat[0, 1] * inMat[1, 2] * inMat[3, 3] - inMat[0, 1] * inMat[1, 3] * inMat[3, 2] |
| 114 | + out[0, 2] += -inMat[1, 1] * inMat[0, 2] * inMat[3, 3] + inMat[1, 1] * inMat[0, 3] * inMat[3, 2] |
| 115 | + out[0, 2] += inMat[3, 1] * inMat[0, 2] * inMat[1, 3] - inMat[3, 1] * inMat[0, 3] * inMat[1, 2] |
| 116 | + |
| 117 | + out[1, 2] = -inMat[0, 0] * inMat[1, 2] * inMat[3, 3] + inMat[0, 0] * inMat[1, 3] * inMat[3, 2] |
| 118 | + out[1, 2] += inMat[1, 0] * inMat[0, 2] * inMat[3, 3] - inMat[1, 0] * inMat[0, 3] * inMat[3, 2] |
| 119 | + out[1, 2] += -inMat[3, 0] * inMat[0, 2] * inMat[1, 3] + inMat[3, 0] * inMat[0, 3] * inMat[1, 2] |
| 120 | + |
| 121 | + out[2, 2] = inMat[0, 0] * inMat[1, 1] * inMat[3, 3] - inMat[0, 0] * inMat[1, 3] * inMat[3, 1] |
| 122 | + out[2, 2] += -inMat[1, 0] * inMat[0, 1] * inMat[3, 3] + inMat[1, 0] * inMat[0, 3] * inMat[3, 1] |
| 123 | + out[2, 2] += inMat[3, 0] * inMat[0, 1] * inMat[1, 3] - inMat[3, 0] * inMat[0, 3] * inMat[1, 1] |
| 124 | + |
| 125 | + out[3, 2] = -inMat[0, 0] * inMat[1, 1] * inMat[3, 2] + inMat[0, 0] * inMat[1, 2] * inMat[3, 1] |
| 126 | + out[3, 2] += inMat[1, 0] * inMat[0, 1] * inMat[3, 2] - inMat[1, 0] * inMat[0, 2] * inMat[3, 1] |
| 127 | + out[3, 2] += -inMat[3, 0] * inMat[0, 1] * inMat[1, 2] + inMat[3, 0] * inMat[0, 2] * inMat[1, 1] |
| 128 | + |
| 129 | + out[0, 3] = -inMat[0, 1] * inMat[1, 2] * inMat[2, 3] + inMat[0, 1] * inMat[1, 3] * inMat[2, 2] |
| 130 | + out[0, 3] += inMat[1, 1] * inMat[0, 2] * inMat[2, 3] - inMat[1, 1] * inMat[0, 3] * inMat[2, 2] |
| 131 | + out[0, 3] += -inMat[2, 1] * inMat[0, 2] * inMat[1, 3] + inMat[2, 1] * inMat[0, 3] * inMat[1, 2] |
| 132 | + |
| 133 | + out[1, 3] = inMat[0, 0] * inMat[1, 2] * inMat[2, 3] - inMat[0, 0] * inMat[1, 3] * inMat[2, 2] |
| 134 | + out[1, 3] += -inMat[1, 0] * inMat[0, 2] * inMat[2, 3] + inMat[1, 0] * inMat[0, 3] * inMat[2, 2] |
| 135 | + out[1, 3] += inMat[2, 0] * inMat[0, 2] * inMat[1, 3] - inMat[2, 0] * inMat[0, 3] * inMat[1, 2] |
| 136 | + |
| 137 | + out[2, 3] = -inMat[0, 0] * inMat[1, 1] * inMat[2, 3] + inMat[0, 0] * inMat[1, 3] * inMat[2, 1] |
| 138 | + out[2, 3] += inMat[1, 0] * inMat[0, 1] * inMat[2, 3] - inMat[1, 0] * inMat[0, 3] * inMat[2, 1] |
| 139 | + out[2, 3] += -inMat[2, 0] * inMat[0, 1] * inMat[1, 3] + inMat[2, 0] * inMat[0, 3] * inMat[1, 1] |
| 140 | + |
| 141 | + out[3, 3] = inMat[0, 0] * inMat[1, 1] * inMat[2, 2] - inMat[0, 0] * inMat[1, 2] * inMat[2, 1] |
| 142 | + out[3, 3] += -inMat[1, 0] * inMat[0, 1] * inMat[2, 2] + inMat[1, 0] * inMat[0, 2] * inMat[2, 1] |
| 143 | + out[3, 3] += inMat[2, 0] * inMat[0, 1] * inMat[1, 2] - inMat[2, 0] * inMat[0, 2] * inMat[1, 1] |
| 144 | + |
| 145 | + return out |
| 146 | +} |
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