| 1 | import {epsilon, splitter, resulterrbound, estimate, vec, sum, scale} from './util.js';
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| 2 |
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| 3 | const o3derrboundA = (7 + 56 * epsilon) * epsilon;
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| 4 | const o3derrboundB = (3 + 28 * epsilon) * epsilon;
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| 5 | const o3derrboundC = (26 + 288 * epsilon) * epsilon * epsilon;
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| 6 |
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| 7 | const bc = vec(4);
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| 8 | const ca = vec(4);
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| 9 | const ab = vec(4);
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| 10 | const at_b = vec(4);
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| 11 | const at_c = vec(4);
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| 12 | const bt_c = vec(4);
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| 13 | const bt_a = vec(4);
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| 14 | const ct_a = vec(4);
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| 15 | const ct_b = vec(4);
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| 16 | const bct = vec(8);
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| 17 | const cat = vec(8);
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| 18 | const abt = vec(8);
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| 19 | const u = vec(4);
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| 20 |
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| 21 | const _8 = vec(8);
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| 22 | const _8b = vec(8);
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| 23 | const _16 = vec(8);
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| 24 | const _12 = vec(12);
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| 25 |
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| 26 | let fin = vec(192);
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| 27 | let fin2 = vec(192);
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| 28 |
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| 29 | function finadd(finlen, alen, a) {
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| 30 | finlen = sum(finlen, fin, alen, a, fin2);
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| 31 | const tmp = fin; fin = fin2; fin2 = tmp;
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| 32 | return finlen;
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| 33 | }
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| 34 |
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| 35 | function tailinit(xtail, ytail, ax, ay, bx, by, a, b) {
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| 36 | let bvirt, c, ahi, alo, bhi, blo, _i, _j, _k, _0, s1, s0, t1, t0, u3, negate;
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| 37 | if (xtail === 0) {
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| 38 | if (ytail === 0) {
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| 39 | a[0] = 0;
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| 40 | b[0] = 0;
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| 41 | return 1;
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| 42 | } else {
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| 43 | negate = -ytail;
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| 44 | s1 = negate * ax;
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| 45 | c = splitter * negate;
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| 46 | ahi = c - (c - negate);
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| 47 | alo = negate - ahi;
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| 48 | c = splitter * ax;
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| 49 | bhi = c - (c - ax);
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| 50 | blo = ax - bhi;
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| 51 | a[0] = alo * blo - (s1 - ahi * bhi - alo * bhi - ahi * blo);
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| 52 | a[1] = s1;
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| 53 | s1 = ytail * bx;
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| 54 | c = splitter * ytail;
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| 55 | ahi = c - (c - ytail);
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| 56 | alo = ytail - ahi;
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| 57 | c = splitter * bx;
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| 58 | bhi = c - (c - bx);
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| 59 | blo = bx - bhi;
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| 60 | b[0] = alo * blo - (s1 - ahi * bhi - alo * bhi - ahi * blo);
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| 61 | b[1] = s1;
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| 62 | return 2;
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| 63 | }
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| 64 | } else {
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| 65 | if (ytail === 0) {
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| 66 | s1 = xtail * ay;
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| 67 | c = splitter * xtail;
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| 68 | ahi = c - (c - xtail);
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| 69 | alo = xtail - ahi;
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| 70 | c = splitter * ay;
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| 71 | bhi = c - (c - ay);
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| 72 | blo = ay - bhi;
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| 73 | a[0] = alo * blo - (s1 - ahi * bhi - alo * bhi - ahi * blo);
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| 74 | a[1] = s1;
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| 75 | negate = -xtail;
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| 76 | s1 = negate * by;
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| 77 | c = splitter * negate;
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| 78 | ahi = c - (c - negate);
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| 79 | alo = negate - ahi;
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| 80 | c = splitter * by;
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| 81 | bhi = c - (c - by);
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| 82 | blo = by - bhi;
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| 83 | b[0] = alo * blo - (s1 - ahi * bhi - alo * bhi - ahi * blo);
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| 84 | b[1] = s1;
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| 85 | return 2;
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| 86 | } else {
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| 87 | s1 = xtail * ay;
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| 88 | c = splitter * xtail;
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| 89 | ahi = c - (c - xtail);
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| 90 | alo = xtail - ahi;
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| 91 | c = splitter * ay;
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| 92 | bhi = c - (c - ay);
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| 93 | blo = ay - bhi;
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| 94 | s0 = alo * blo - (s1 - ahi * bhi - alo * bhi - ahi * blo);
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| 95 | t1 = ytail * ax;
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| 96 | c = splitter * ytail;
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| 97 | ahi = c - (c - ytail);
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| 98 | alo = ytail - ahi;
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| 99 | c = splitter * ax;
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| 100 | bhi = c - (c - ax);
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| 101 | blo = ax - bhi;
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| 102 | t0 = alo * blo - (t1 - ahi * bhi - alo * bhi - ahi * blo);
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| 103 | _i = s0 - t0;
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| 104 | bvirt = s0 - _i;
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| 105 | a[0] = s0 - (_i + bvirt) + (bvirt - t0);
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| 106 | _j = s1 + _i;
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| 107 | bvirt = _j - s1;
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| 108 | _0 = s1 - (_j - bvirt) + (_i - bvirt);
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| 109 | _i = _0 - t1;
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| 110 | bvirt = _0 - _i;
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| 111 | a[1] = _0 - (_i + bvirt) + (bvirt - t1);
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| 112 | u3 = _j + _i;
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| 113 | bvirt = u3 - _j;
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| 114 | a[2] = _j - (u3 - bvirt) + (_i - bvirt);
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| 115 | a[3] = u3;
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| 116 | s1 = ytail * bx;
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| 117 | c = splitter * ytail;
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| 118 | ahi = c - (c - ytail);
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| 119 | alo = ytail - ahi;
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| 120 | c = splitter * bx;
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| 121 | bhi = c - (c - bx);
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| 122 | blo = bx - bhi;
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| 123 | s0 = alo * blo - (s1 - ahi * bhi - alo * bhi - ahi * blo);
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| 124 | t1 = xtail * by;
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| 125 | c = splitter * xtail;
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| 126 | ahi = c - (c - xtail);
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| 127 | alo = xtail - ahi;
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| 128 | c = splitter * by;
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| 129 | bhi = c - (c - by);
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| 130 | blo = by - bhi;
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| 131 | t0 = alo * blo - (t1 - ahi * bhi - alo * bhi - ahi * blo);
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| 132 | _i = s0 - t0;
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| 133 | bvirt = s0 - _i;
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| 134 | b[0] = s0 - (_i + bvirt) + (bvirt - t0);
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| 135 | _j = s1 + _i;
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| 136 | bvirt = _j - s1;
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| 137 | _0 = s1 - (_j - bvirt) + (_i - bvirt);
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| 138 | _i = _0 - t1;
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| 139 | bvirt = _0 - _i;
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| 140 | b[1] = _0 - (_i + bvirt) + (bvirt - t1);
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| 141 | u3 = _j + _i;
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| 142 | bvirt = u3 - _j;
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| 143 | b[2] = _j - (u3 - bvirt) + (_i - bvirt);
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| 144 | b[3] = u3;
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| 145 | return 4;
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| 146 | }
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| 147 | }
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| 148 | }
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| 149 |
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| 150 | function tailadd(finlen, a, b, k, z) {
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| 151 | let bvirt, c, ahi, alo, bhi, blo, _i, _j, _k, _0, s1, s0, u3;
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| 152 | s1 = a * b;
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| 153 | c = splitter * a;
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| 154 | ahi = c - (c - a);
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| 155 | alo = a - ahi;
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| 156 | c = splitter * b;
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| 157 | bhi = c - (c - b);
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| 158 | blo = b - bhi;
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| 159 | s0 = alo * blo - (s1 - ahi * bhi - alo * bhi - ahi * blo);
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| 160 | c = splitter * k;
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| 161 | bhi = c - (c - k);
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| 162 | blo = k - bhi;
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| 163 | _i = s0 * k;
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| 164 | c = splitter * s0;
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| 165 | ahi = c - (c - s0);
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| 166 | alo = s0 - ahi;
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| 167 | u[0] = alo * blo - (_i - ahi * bhi - alo * bhi - ahi * blo);
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| 168 | _j = s1 * k;
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| 169 | c = splitter * s1;
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| 170 | ahi = c - (c - s1);
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| 171 | alo = s1 - ahi;
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| 172 | _0 = alo * blo - (_j - ahi * bhi - alo * bhi - ahi * blo);
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| 173 | _k = _i + _0;
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| 174 | bvirt = _k - _i;
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| 175 | u[1] = _i - (_k - bvirt) + (_0 - bvirt);
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| 176 | u3 = _j + _k;
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| 177 | u[2] = _k - (u3 - _j);
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| 178 | u[3] = u3;
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| 179 | finlen = finadd(finlen, 4, u);
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| 180 | if (z !== 0) {
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| 181 | c = splitter * z;
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| 182 | bhi = c - (c - z);
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| 183 | blo = z - bhi;
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| 184 | _i = s0 * z;
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| 185 | c = splitter * s0;
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| 186 | ahi = c - (c - s0);
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| 187 | alo = s0 - ahi;
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| 188 | u[0] = alo * blo - (_i - ahi * bhi - alo * bhi - ahi * blo);
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| 189 | _j = s1 * z;
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| 190 | c = splitter * s1;
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| 191 | ahi = c - (c - s1);
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| 192 | alo = s1 - ahi;
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| 193 | _0 = alo * blo - (_j - ahi * bhi - alo * bhi - ahi * blo);
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| 194 | _k = _i + _0;
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| 195 | bvirt = _k - _i;
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| 196 | u[1] = _i - (_k - bvirt) + (_0 - bvirt);
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| 197 | u3 = _j + _k;
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| 198 | u[2] = _k - (u3 - _j);
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| 199 | u[3] = u3;
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| 200 | finlen = finadd(finlen, 4, u);
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| 201 | }
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| 202 | return finlen;
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| 203 | }
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| 204 |
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| 205 | function orient3dadapt(ax, ay, az, bx, by, bz, cx, cy, cz, dx, dy, dz, permanent) {
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| 206 | let finlen;
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| 207 | let adxtail, bdxtail, cdxtail;
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| 208 | let adytail, bdytail, cdytail;
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| 209 | let adztail, bdztail, cdztail;
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| 210 | let bvirt, c, ahi, alo, bhi, blo, _i, _j, _k, _0, s1, s0, t1, t0, u3;
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| 211 |
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| 212 | const adx = ax - dx;
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| 213 | const bdx = bx - dx;
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| 214 | const cdx = cx - dx;
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| 215 | const ady = ay - dy;
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| 216 | const bdy = by - dy;
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| 217 | const cdy = cy - dy;
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| 218 | const adz = az - dz;
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| 219 | const bdz = bz - dz;
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| 220 | const cdz = cz - dz;
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| 221 |
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| 222 | s1 = bdx * cdy;
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| 223 | c = splitter * bdx;
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| 224 | ahi = c - (c - bdx);
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| 225 | alo = bdx - ahi;
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| 226 | c = splitter * cdy;
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| 227 | bhi = c - (c - cdy);
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| 228 | blo = cdy - bhi;
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| 229 | s0 = alo * blo - (s1 - ahi * bhi - alo * bhi - ahi * blo);
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| 230 | t1 = cdx * bdy;
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| 231 | c = splitter * cdx;
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| 232 | ahi = c - (c - cdx);
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| 233 | alo = cdx - ahi;
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| 234 | c = splitter * bdy;
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| 235 | bhi = c - (c - bdy);
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| 236 | blo = bdy - bhi;
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| 237 | t0 = alo * blo - (t1 - ahi * bhi - alo * bhi - ahi * blo);
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| 238 | _i = s0 - t0;
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| 239 | bvirt = s0 - _i;
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| 240 | bc[0] = s0 - (_i + bvirt) + (bvirt - t0);
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| 241 | _j = s1 + _i;
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| 242 | bvirt = _j - s1;
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| 243 | _0 = s1 - (_j - bvirt) + (_i - bvirt);
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| 244 | _i = _0 - t1;
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| 245 | bvirt = _0 - _i;
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| 246 | bc[1] = _0 - (_i + bvirt) + (bvirt - t1);
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| 247 | u3 = _j + _i;
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| 248 | bvirt = u3 - _j;
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| 249 | bc[2] = _j - (u3 - bvirt) + (_i - bvirt);
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| 250 | bc[3] = u3;
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| 251 | s1 = cdx * ady;
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| 252 | c = splitter * cdx;
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| 253 | ahi = c - (c - cdx);
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| 254 | alo = cdx - ahi;
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| 255 | c = splitter * ady;
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| 256 | bhi = c - (c - ady);
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| 257 | blo = ady - bhi;
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| 258 | s0 = alo * blo - (s1 - ahi * bhi - alo * bhi - ahi * blo);
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| 259 | t1 = adx * cdy;
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| 260 | c = splitter * adx;
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| 261 | ahi = c - (c - adx);
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| 262 | alo = adx - ahi;
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| 263 | c = splitter * cdy;
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| 264 | bhi = c - (c - cdy);
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| 265 | blo = cdy - bhi;
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| 266 | t0 = alo * blo - (t1 - ahi * bhi - alo * bhi - ahi * blo);
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| 267 | _i = s0 - t0;
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| 268 | bvirt = s0 - _i;
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| 269 | ca[0] = s0 - (_i + bvirt) + (bvirt - t0);
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| 270 | _j = s1 + _i;
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| 271 | bvirt = _j - s1;
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| 272 | _0 = s1 - (_j - bvirt) + (_i - bvirt);
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| 273 | _i = _0 - t1;
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| 274 | bvirt = _0 - _i;
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| 275 | ca[1] = _0 - (_i + bvirt) + (bvirt - t1);
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| 276 | u3 = _j + _i;
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| 277 | bvirt = u3 - _j;
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| 278 | ca[2] = _j - (u3 - bvirt) + (_i - bvirt);
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| 279 | ca[3] = u3;
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| 280 | s1 = adx * bdy;
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| 281 | c = splitter * adx;
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| 282 | ahi = c - (c - adx);
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| 283 | alo = adx - ahi;
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| 284 | c = splitter * bdy;
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| 285 | bhi = c - (c - bdy);
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| 286 | blo = bdy - bhi;
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| 287 | s0 = alo * blo - (s1 - ahi * bhi - alo * bhi - ahi * blo);
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| 288 | t1 = bdx * ady;
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| 289 | c = splitter * bdx;
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| 290 | ahi = c - (c - bdx);
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| 291 | alo = bdx - ahi;
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| 292 | c = splitter * ady;
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| 293 | bhi = c - (c - ady);
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| 294 | blo = ady - bhi;
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| 295 | t0 = alo * blo - (t1 - ahi * bhi - alo * bhi - ahi * blo);
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| 296 | _i = s0 - t0;
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| 297 | bvirt = s0 - _i;
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| 298 | ab[0] = s0 - (_i + bvirt) + (bvirt - t0);
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| 299 | _j = s1 + _i;
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| 300 | bvirt = _j - s1;
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| 301 | _0 = s1 - (_j - bvirt) + (_i - bvirt);
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| 302 | _i = _0 - t1;
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| 303 | bvirt = _0 - _i;
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| 304 | ab[1] = _0 - (_i + bvirt) + (bvirt - t1);
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| 305 | u3 = _j + _i;
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| 306 | bvirt = u3 - _j;
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| 307 | ab[2] = _j - (u3 - bvirt) + (_i - bvirt);
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| 308 | ab[3] = u3;
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| 309 |
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| 310 | finlen = sum(
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| 311 | sum(
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| 312 | scale(4, bc, adz, _8), _8,
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| 313 | scale(4, ca, bdz, _8b), _8b, _16), _16,
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| 314 | scale(4, ab, cdz, _8), _8, fin);
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| 315 |
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| 316 | let det = estimate(finlen, fin);
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| 317 | let errbound = o3derrboundB * permanent;
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| 318 | if (det >= errbound || -det >= errbound) {
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| 319 | return det;
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| 320 | }
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| 321 |
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| 322 | bvirt = ax - adx;
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| 323 | adxtail = ax - (adx + bvirt) + (bvirt - dx);
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| 324 | bvirt = bx - bdx;
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| 325 | bdxtail = bx - (bdx + bvirt) + (bvirt - dx);
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| 326 | bvirt = cx - cdx;
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| 327 | cdxtail = cx - (cdx + bvirt) + (bvirt - dx);
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| 328 | bvirt = ay - ady;
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| 329 | adytail = ay - (ady + bvirt) + (bvirt - dy);
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| 330 | bvirt = by - bdy;
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| 331 | bdytail = by - (bdy + bvirt) + (bvirt - dy);
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| 332 | bvirt = cy - cdy;
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| 333 | cdytail = cy - (cdy + bvirt) + (bvirt - dy);
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| 334 | bvirt = az - adz;
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| 335 | adztail = az - (adz + bvirt) + (bvirt - dz);
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| 336 | bvirt = bz - bdz;
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| 337 | bdztail = bz - (bdz + bvirt) + (bvirt - dz);
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| 338 | bvirt = cz - cdz;
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| 339 | cdztail = cz - (cdz + bvirt) + (bvirt - dz);
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| 340 |
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| 341 | if (adxtail === 0 && bdxtail === 0 && cdxtail === 0 &&
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| 342 | adytail === 0 && bdytail === 0 && cdytail === 0 &&
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| 343 | adztail === 0 && bdztail === 0 && cdztail === 0) {
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| 344 | return det;
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| 345 | }
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| 346 |
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| 347 | errbound = o3derrboundC * permanent + resulterrbound * Math.abs(det);
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| 348 | det +=
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| 349 | adz * (bdx * cdytail + cdy * bdxtail - (bdy * cdxtail + cdx * bdytail)) + adztail * (bdx * cdy - bdy * cdx) +
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| 350 | bdz * (cdx * adytail + ady * cdxtail - (cdy * adxtail + adx * cdytail)) + bdztail * (cdx * ady - cdy * adx) +
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| 351 | cdz * (adx * bdytail + bdy * adxtail - (ady * bdxtail + bdx * adytail)) + cdztail * (adx * bdy - ady * bdx);
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| 352 | if (det >= errbound || -det >= errbound) {
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| 353 | return det;
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| 354 | }
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| 355 |
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| 356 | const at_len = tailinit(adxtail, adytail, bdx, bdy, cdx, cdy, at_b, at_c);
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| 357 | const bt_len = tailinit(bdxtail, bdytail, cdx, cdy, adx, ady, bt_c, bt_a);
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| 358 | const ct_len = tailinit(cdxtail, cdytail, adx, ady, bdx, bdy, ct_a, ct_b);
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| 359 |
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| 360 | const bctlen = sum(bt_len, bt_c, ct_len, ct_b, bct);
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| 361 | finlen = finadd(finlen, scale(bctlen, bct, adz, _16), _16);
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| 362 |
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| 363 | const catlen = sum(ct_len, ct_a, at_len, at_c, cat);
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| 364 | finlen = finadd(finlen, scale(catlen, cat, bdz, _16), _16);
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| 365 |
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| 366 | const abtlen = sum(at_len, at_b, bt_len, bt_a, abt);
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| 367 | finlen = finadd(finlen, scale(abtlen, abt, cdz, _16), _16);
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| 368 |
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| 369 | if (adztail !== 0) {
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| 370 | finlen = finadd(finlen, scale(4, bc, adztail, _12), _12);
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| 371 | finlen = finadd(finlen, scale(bctlen, bct, adztail, _16), _16);
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| 372 | }
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| 373 | if (bdztail !== 0) {
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| 374 | finlen = finadd(finlen, scale(4, ca, bdztail, _12), _12);
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| 375 | finlen = finadd(finlen, scale(catlen, cat, bdztail, _16), _16);
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| 376 | }
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| 377 | if (cdztail !== 0) {
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| 378 | finlen = finadd(finlen, scale(4, ab, cdztail, _12), _12);
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| 379 | finlen = finadd(finlen, scale(abtlen, abt, cdztail, _16), _16);
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| 380 | }
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| 381 |
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| 382 | if (adxtail !== 0) {
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| 383 | if (bdytail !== 0) {
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| 384 | finlen = tailadd(finlen, adxtail, bdytail, cdz, cdztail);
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| 385 | }
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| 386 | if (cdytail !== 0) {
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| 387 | finlen = tailadd(finlen, -adxtail, cdytail, bdz, bdztail);
|
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| 388 | }
|
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| 389 | }
|
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| 390 | if (bdxtail !== 0) {
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|---|
| 391 | if (cdytail !== 0) {
|
|---|
| 392 | finlen = tailadd(finlen, bdxtail, cdytail, adz, adztail);
|
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| 393 | }
|
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| 394 | if (adytail !== 0) {
|
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| 395 | finlen = tailadd(finlen, -bdxtail, adytail, cdz, cdztail);
|
|---|
| 396 | }
|
|---|
| 397 | }
|
|---|
| 398 | if (cdxtail !== 0) {
|
|---|
| 399 | if (adytail !== 0) {
|
|---|
| 400 | finlen = tailadd(finlen, cdxtail, adytail, bdz, bdztail);
|
|---|
| 401 | }
|
|---|
| 402 | if (bdytail !== 0) {
|
|---|
| 403 | finlen = tailadd(finlen, -cdxtail, bdytail, adz, adztail);
|
|---|
| 404 | }
|
|---|
| 405 | }
|
|---|
| 406 |
|
|---|
| 407 | return fin[finlen - 1];
|
|---|
| 408 | }
|
|---|
| 409 |
|
|---|
| 410 | export function orient3d(ax, ay, az, bx, by, bz, cx, cy, cz, dx, dy, dz) {
|
|---|
| 411 | const adx = ax - dx;
|
|---|
| 412 | const bdx = bx - dx;
|
|---|
| 413 | const cdx = cx - dx;
|
|---|
| 414 | const ady = ay - dy;
|
|---|
| 415 | const bdy = by - dy;
|
|---|
| 416 | const cdy = cy - dy;
|
|---|
| 417 | const adz = az - dz;
|
|---|
| 418 | const bdz = bz - dz;
|
|---|
| 419 | const cdz = cz - dz;
|
|---|
| 420 |
|
|---|
| 421 | const bdxcdy = bdx * cdy;
|
|---|
| 422 | const cdxbdy = cdx * bdy;
|
|---|
| 423 |
|
|---|
| 424 | const cdxady = cdx * ady;
|
|---|
| 425 | const adxcdy = adx * cdy;
|
|---|
| 426 |
|
|---|
| 427 | const adxbdy = adx * bdy;
|
|---|
| 428 | const bdxady = bdx * ady;
|
|---|
| 429 |
|
|---|
| 430 | const det =
|
|---|
| 431 | adz * (bdxcdy - cdxbdy) +
|
|---|
| 432 | bdz * (cdxady - adxcdy) +
|
|---|
| 433 | cdz * (adxbdy - bdxady);
|
|---|
| 434 |
|
|---|
| 435 | const permanent =
|
|---|
| 436 | (Math.abs(bdxcdy) + Math.abs(cdxbdy)) * Math.abs(adz) +
|
|---|
| 437 | (Math.abs(cdxady) + Math.abs(adxcdy)) * Math.abs(bdz) +
|
|---|
| 438 | (Math.abs(adxbdy) + Math.abs(bdxady)) * Math.abs(cdz);
|
|---|
| 439 |
|
|---|
| 440 | const errbound = o3derrboundA * permanent;
|
|---|
| 441 | if (det > errbound || -det > errbound) {
|
|---|
| 442 | return det;
|
|---|
| 443 | }
|
|---|
| 444 |
|
|---|
| 445 | return orient3dadapt(ax, ay, az, bx, by, bz, cx, cy, cz, dx, dy, dz, permanent);
|
|---|
| 446 | }
|
|---|
| 447 |
|
|---|
| 448 | export function orient3dfast(ax, ay, az, bx, by, bz, cx, cy, cz, dx, dy, dz) {
|
|---|
| 449 | const adx = ax - dx;
|
|---|
| 450 | const bdx = bx - dx;
|
|---|
| 451 | const cdx = cx - dx;
|
|---|
| 452 | const ady = ay - dy;
|
|---|
| 453 | const bdy = by - dy;
|
|---|
| 454 | const cdy = cy - dy;
|
|---|
| 455 | const adz = az - dz;
|
|---|
| 456 | const bdz = bz - dz;
|
|---|
| 457 | const cdz = cz - dz;
|
|---|
| 458 |
|
|---|
| 459 | return adx * (bdy * cdz - bdz * cdy) +
|
|---|
| 460 | bdx * (cdy * adz - cdz * ady) +
|
|---|
| 461 | cdx * (ady * bdz - adz * bdy);
|
|---|
| 462 | }
|
|---|
