463 lines
14 KiB
JavaScript
463 lines
14 KiB
JavaScript
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import {epsilon, splitter, resulterrbound, estimate, vec, sum, scale} from './util.js';
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const o3derrboundA = (7 + 56 * epsilon) * epsilon;
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const o3derrboundB = (3 + 28 * epsilon) * epsilon;
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const o3derrboundC = (26 + 288 * epsilon) * epsilon * epsilon;
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const bc = vec(4);
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const ca = vec(4);
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const ab = vec(4);
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const at_b = vec(4);
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const at_c = vec(4);
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const bt_c = vec(4);
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const bt_a = vec(4);
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const ct_a = vec(4);
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const ct_b = vec(4);
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const bct = vec(8);
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const cat = vec(8);
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const abt = vec(8);
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const u = vec(4);
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const _8 = vec(8);
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const _8b = vec(8);
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const _16 = vec(8);
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const _12 = vec(12);
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let fin = vec(192);
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let fin2 = vec(192);
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function finadd(finlen, alen, a) {
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finlen = sum(finlen, fin, alen, a, fin2);
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const tmp = fin; fin = fin2; fin2 = tmp;
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return finlen;
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}
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function tailinit(xtail, ytail, ax, ay, bx, by, a, b) {
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let bvirt, c, ahi, alo, bhi, blo, _i, _j, _k, _0, s1, s0, t1, t0, u3, negate;
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if (xtail === 0) {
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if (ytail === 0) {
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a[0] = 0;
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b[0] = 0;
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return 1;
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} else {
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negate = -ytail;
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s1 = negate * ax;
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c = splitter * negate;
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ahi = c - (c - negate);
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alo = negate - ahi;
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c = splitter * ax;
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bhi = c - (c - ax);
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blo = ax - bhi;
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a[0] = alo * blo - (s1 - ahi * bhi - alo * bhi - ahi * blo);
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a[1] = s1;
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s1 = ytail * bx;
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c = splitter * ytail;
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ahi = c - (c - ytail);
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alo = ytail - ahi;
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c = splitter * bx;
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bhi = c - (c - bx);
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blo = bx - bhi;
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b[0] = alo * blo - (s1 - ahi * bhi - alo * bhi - ahi * blo);
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b[1] = s1;
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return 2;
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}
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} else {
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if (ytail === 0) {
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s1 = xtail * ay;
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c = splitter * xtail;
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ahi = c - (c - xtail);
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alo = xtail - ahi;
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c = splitter * ay;
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bhi = c - (c - ay);
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blo = ay - bhi;
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a[0] = alo * blo - (s1 - ahi * bhi - alo * bhi - ahi * blo);
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a[1] = s1;
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negate = -xtail;
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s1 = negate * by;
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c = splitter * negate;
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ahi = c - (c - negate);
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alo = negate - ahi;
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c = splitter * by;
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bhi = c - (c - by);
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blo = by - bhi;
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b[0] = alo * blo - (s1 - ahi * bhi - alo * bhi - ahi * blo);
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b[1] = s1;
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return 2;
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} else {
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s1 = xtail * ay;
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c = splitter * xtail;
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ahi = c - (c - xtail);
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alo = xtail - ahi;
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c = splitter * ay;
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bhi = c - (c - ay);
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blo = ay - bhi;
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s0 = alo * blo - (s1 - ahi * bhi - alo * bhi - ahi * blo);
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t1 = ytail * ax;
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c = splitter * ytail;
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ahi = c - (c - ytail);
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alo = ytail - ahi;
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c = splitter * ax;
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bhi = c - (c - ax);
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blo = ax - bhi;
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t0 = alo * blo - (t1 - ahi * bhi - alo * bhi - ahi * blo);
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_i = s0 - t0;
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bvirt = s0 - _i;
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a[0] = s0 - (_i + bvirt) + (bvirt - t0);
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_j = s1 + _i;
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bvirt = _j - s1;
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_0 = s1 - (_j - bvirt) + (_i - bvirt);
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_i = _0 - t1;
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bvirt = _0 - _i;
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a[1] = _0 - (_i + bvirt) + (bvirt - t1);
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u3 = _j + _i;
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bvirt = u3 - _j;
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a[2] = _j - (u3 - bvirt) + (_i - bvirt);
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a[3] = u3;
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s1 = ytail * bx;
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c = splitter * ytail;
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ahi = c - (c - ytail);
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alo = ytail - ahi;
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c = splitter * bx;
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bhi = c - (c - bx);
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blo = bx - bhi;
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s0 = alo * blo - (s1 - ahi * bhi - alo * bhi - ahi * blo);
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t1 = xtail * by;
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c = splitter * xtail;
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ahi = c - (c - xtail);
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alo = xtail - ahi;
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c = splitter * by;
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bhi = c - (c - by);
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blo = by - bhi;
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t0 = alo * blo - (t1 - ahi * bhi - alo * bhi - ahi * blo);
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_i = s0 - t0;
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bvirt = s0 - _i;
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b[0] = s0 - (_i + bvirt) + (bvirt - t0);
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_j = s1 + _i;
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bvirt = _j - s1;
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_0 = s1 - (_j - bvirt) + (_i - bvirt);
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_i = _0 - t1;
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bvirt = _0 - _i;
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b[1] = _0 - (_i + bvirt) + (bvirt - t1);
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u3 = _j + _i;
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bvirt = u3 - _j;
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b[2] = _j - (u3 - bvirt) + (_i - bvirt);
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b[3] = u3;
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return 4;
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}
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}
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}
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function tailadd(finlen, a, b, k, z) {
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let bvirt, c, ahi, alo, bhi, blo, _i, _j, _k, _0, s1, s0, u3;
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s1 = a * b;
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c = splitter * a;
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ahi = c - (c - a);
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alo = a - ahi;
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c = splitter * b;
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bhi = c - (c - b);
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blo = b - bhi;
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s0 = alo * blo - (s1 - ahi * bhi - alo * bhi - ahi * blo);
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c = splitter * k;
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bhi = c - (c - k);
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blo = k - bhi;
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_i = s0 * k;
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c = splitter * s0;
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ahi = c - (c - s0);
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alo = s0 - ahi;
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u[0] = alo * blo - (_i - ahi * bhi - alo * bhi - ahi * blo);
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_j = s1 * k;
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c = splitter * s1;
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ahi = c - (c - s1);
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alo = s1 - ahi;
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_0 = alo * blo - (_j - ahi * bhi - alo * bhi - ahi * blo);
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_k = _i + _0;
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bvirt = _k - _i;
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u[1] = _i - (_k - bvirt) + (_0 - bvirt);
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u3 = _j + _k;
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u[2] = _k - (u3 - _j);
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u[3] = u3;
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finlen = finadd(finlen, 4, u);
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if (z !== 0) {
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c = splitter * z;
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bhi = c - (c - z);
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blo = z - bhi;
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_i = s0 * z;
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c = splitter * s0;
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ahi = c - (c - s0);
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alo = s0 - ahi;
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u[0] = alo * blo - (_i - ahi * bhi - alo * bhi - ahi * blo);
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_j = s1 * z;
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c = splitter * s1;
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ahi = c - (c - s1);
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alo = s1 - ahi;
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_0 = alo * blo - (_j - ahi * bhi - alo * bhi - ahi * blo);
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_k = _i + _0;
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bvirt = _k - _i;
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u[1] = _i - (_k - bvirt) + (_0 - bvirt);
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u3 = _j + _k;
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u[2] = _k - (u3 - _j);
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u[3] = u3;
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finlen = finadd(finlen, 4, u);
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}
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return finlen;
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}
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function orient3dadapt(ax, ay, az, bx, by, bz, cx, cy, cz, dx, dy, dz, permanent) {
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let finlen;
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let adxtail, bdxtail, cdxtail;
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let adytail, bdytail, cdytail;
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let adztail, bdztail, cdztail;
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let bvirt, c, ahi, alo, bhi, blo, _i, _j, _k, _0, s1, s0, t1, t0, u3;
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const adx = ax - dx;
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const bdx = bx - dx;
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const cdx = cx - dx;
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const ady = ay - dy;
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const bdy = by - dy;
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const cdy = cy - dy;
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const adz = az - dz;
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const bdz = bz - dz;
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const cdz = cz - dz;
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s1 = bdx * cdy;
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c = splitter * bdx;
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ahi = c - (c - bdx);
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alo = bdx - ahi;
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c = splitter * cdy;
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bhi = c - (c - cdy);
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blo = cdy - bhi;
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s0 = alo * blo - (s1 - ahi * bhi - alo * bhi - ahi * blo);
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t1 = cdx * bdy;
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c = splitter * cdx;
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ahi = c - (c - cdx);
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alo = cdx - ahi;
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c = splitter * bdy;
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bhi = c - (c - bdy);
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blo = bdy - bhi;
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t0 = alo * blo - (t1 - ahi * bhi - alo * bhi - ahi * blo);
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_i = s0 - t0;
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bvirt = s0 - _i;
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bc[0] = s0 - (_i + bvirt) + (bvirt - t0);
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_j = s1 + _i;
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bvirt = _j - s1;
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_0 = s1 - (_j - bvirt) + (_i - bvirt);
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_i = _0 - t1;
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bvirt = _0 - _i;
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bc[1] = _0 - (_i + bvirt) + (bvirt - t1);
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u3 = _j + _i;
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bvirt = u3 - _j;
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bc[2] = _j - (u3 - bvirt) + (_i - bvirt);
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bc[3] = u3;
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s1 = cdx * ady;
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c = splitter * cdx;
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ahi = c - (c - cdx);
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alo = cdx - ahi;
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c = splitter * ady;
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bhi = c - (c - ady);
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blo = ady - bhi;
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s0 = alo * blo - (s1 - ahi * bhi - alo * bhi - ahi * blo);
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t1 = adx * cdy;
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c = splitter * adx;
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ahi = c - (c - adx);
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alo = adx - ahi;
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c = splitter * cdy;
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bhi = c - (c - cdy);
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blo = cdy - bhi;
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t0 = alo * blo - (t1 - ahi * bhi - alo * bhi - ahi * blo);
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_i = s0 - t0;
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bvirt = s0 - _i;
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ca[0] = s0 - (_i + bvirt) + (bvirt - t0);
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_j = s1 + _i;
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bvirt = _j - s1;
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_0 = s1 - (_j - bvirt) + (_i - bvirt);
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_i = _0 - t1;
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bvirt = _0 - _i;
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ca[1] = _0 - (_i + bvirt) + (bvirt - t1);
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u3 = _j + _i;
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bvirt = u3 - _j;
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ca[2] = _j - (u3 - bvirt) + (_i - bvirt);
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ca[3] = u3;
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s1 = adx * bdy;
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c = splitter * adx;
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ahi = c - (c - adx);
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alo = adx - ahi;
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c = splitter * bdy;
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bhi = c - (c - bdy);
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blo = bdy - bhi;
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s0 = alo * blo - (s1 - ahi * bhi - alo * bhi - ahi * blo);
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t1 = bdx * ady;
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c = splitter * bdx;
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ahi = c - (c - bdx);
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alo = bdx - ahi;
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c = splitter * ady;
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bhi = c - (c - ady);
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blo = ady - bhi;
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t0 = alo * blo - (t1 - ahi * bhi - alo * bhi - ahi * blo);
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_i = s0 - t0;
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bvirt = s0 - _i;
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ab[0] = s0 - (_i + bvirt) + (bvirt - t0);
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_j = s1 + _i;
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bvirt = _j - s1;
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_0 = s1 - (_j - bvirt) + (_i - bvirt);
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_i = _0 - t1;
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bvirt = _0 - _i;
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ab[1] = _0 - (_i + bvirt) + (bvirt - t1);
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u3 = _j + _i;
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bvirt = u3 - _j;
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ab[2] = _j - (u3 - bvirt) + (_i - bvirt);
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ab[3] = u3;
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finlen = sum(
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sum(
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scale(4, bc, adz, _8), _8,
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scale(4, ca, bdz, _8b), _8b, _16), _16,
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scale(4, ab, cdz, _8), _8, fin);
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let det = estimate(finlen, fin);
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let errbound = o3derrboundB * permanent;
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if (det >= errbound || -det >= errbound) {
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return det;
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}
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bvirt = ax - adx;
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adxtail = ax - (adx + bvirt) + (bvirt - dx);
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bvirt = bx - bdx;
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bdxtail = bx - (bdx + bvirt) + (bvirt - dx);
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bvirt = cx - cdx;
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cdxtail = cx - (cdx + bvirt) + (bvirt - dx);
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bvirt = ay - ady;
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adytail = ay - (ady + bvirt) + (bvirt - dy);
|
||
|
|
bvirt = by - bdy;
|
||
|
|
bdytail = by - (bdy + bvirt) + (bvirt - dy);
|
||
|
|
bvirt = cy - cdy;
|
||
|
|
cdytail = cy - (cdy + bvirt) + (bvirt - dy);
|
||
|
|
bvirt = az - adz;
|
||
|
|
adztail = az - (adz + bvirt) + (bvirt - dz);
|
||
|
|
bvirt = bz - bdz;
|
||
|
|
bdztail = bz - (bdz + bvirt) + (bvirt - dz);
|
||
|
|
bvirt = cz - cdz;
|
||
|
|
cdztail = cz - (cdz + bvirt) + (bvirt - dz);
|
||
|
|
|
||
|
|
if (adxtail === 0 && bdxtail === 0 && cdxtail === 0 &&
|
||
|
|
adytail === 0 && bdytail === 0 && cdytail === 0 &&
|
||
|
|
adztail === 0 && bdztail === 0 && cdztail === 0) {
|
||
|
|
return det;
|
||
|
|
}
|
||
|
|
|
||
|
|
errbound = o3derrboundC * permanent + resulterrbound * Math.abs(det);
|
||
|
|
det +=
|
||
|
|
adz * (bdx * cdytail + cdy * bdxtail - (bdy * cdxtail + cdx * bdytail)) + adztail * (bdx * cdy - bdy * cdx) +
|
||
|
|
bdz * (cdx * adytail + ady * cdxtail - (cdy * adxtail + adx * cdytail)) + bdztail * (cdx * ady - cdy * adx) +
|
||
|
|
cdz * (adx * bdytail + bdy * adxtail - (ady * bdxtail + bdx * adytail)) + cdztail * (adx * bdy - ady * bdx);
|
||
|
|
if (det >= errbound || -det >= errbound) {
|
||
|
|
return det;
|
||
|
|
}
|
||
|
|
|
||
|
|
const at_len = tailinit(adxtail, adytail, bdx, bdy, cdx, cdy, at_b, at_c);
|
||
|
|
const bt_len = tailinit(bdxtail, bdytail, cdx, cdy, adx, ady, bt_c, bt_a);
|
||
|
|
const ct_len = tailinit(cdxtail, cdytail, adx, ady, bdx, bdy, ct_a, ct_b);
|
||
|
|
|
||
|
|
const bctlen = sum(bt_len, bt_c, ct_len, ct_b, bct);
|
||
|
|
finlen = finadd(finlen, scale(bctlen, bct, adz, _16), _16);
|
||
|
|
|
||
|
|
const catlen = sum(ct_len, ct_a, at_len, at_c, cat);
|
||
|
|
finlen = finadd(finlen, scale(catlen, cat, bdz, _16), _16);
|
||
|
|
|
||
|
|
const abtlen = sum(at_len, at_b, bt_len, bt_a, abt);
|
||
|
|
finlen = finadd(finlen, scale(abtlen, abt, cdz, _16), _16);
|
||
|
|
|
||
|
|
if (adztail !== 0) {
|
||
|
|
finlen = finadd(finlen, scale(4, bc, adztail, _12), _12);
|
||
|
|
finlen = finadd(finlen, scale(bctlen, bct, adztail, _16), _16);
|
||
|
|
}
|
||
|
|
if (bdztail !== 0) {
|
||
|
|
finlen = finadd(finlen, scale(4, ca, bdztail, _12), _12);
|
||
|
|
finlen = finadd(finlen, scale(catlen, cat, bdztail, _16), _16);
|
||
|
|
}
|
||
|
|
if (cdztail !== 0) {
|
||
|
|
finlen = finadd(finlen, scale(4, ab, cdztail, _12), _12);
|
||
|
|
finlen = finadd(finlen, scale(abtlen, abt, cdztail, _16), _16);
|
||
|
|
}
|
||
|
|
|
||
|
|
if (adxtail !== 0) {
|
||
|
|
if (bdytail !== 0) {
|
||
|
|
finlen = tailadd(finlen, adxtail, bdytail, cdz, cdztail);
|
||
|
|
}
|
||
|
|
if (cdytail !== 0) {
|
||
|
|
finlen = tailadd(finlen, -adxtail, cdytail, bdz, bdztail);
|
||
|
|
}
|
||
|
|
}
|
||
|
|
if (bdxtail !== 0) {
|
||
|
|
if (cdytail !== 0) {
|
||
|
|
finlen = tailadd(finlen, bdxtail, cdytail, adz, adztail);
|
||
|
|
}
|
||
|
|
if (adytail !== 0) {
|
||
|
|
finlen = tailadd(finlen, -bdxtail, adytail, cdz, cdztail);
|
||
|
|
}
|
||
|
|
}
|
||
|
|
if (cdxtail !== 0) {
|
||
|
|
if (adytail !== 0) {
|
||
|
|
finlen = tailadd(finlen, cdxtail, adytail, bdz, bdztail);
|
||
|
|
}
|
||
|
|
if (bdytail !== 0) {
|
||
|
|
finlen = tailadd(finlen, -cdxtail, bdytail, adz, adztail);
|
||
|
|
}
|
||
|
|
}
|
||
|
|
|
||
|
|
return fin[finlen - 1];
|
||
|
|
}
|
||
|
|
|
||
|
|
export function orient3d(ax, ay, az, bx, by, bz, cx, cy, cz, dx, dy, dz) {
|
||
|
|
const adx = ax - dx;
|
||
|
|
const bdx = bx - dx;
|
||
|
|
const cdx = cx - dx;
|
||
|
|
const ady = ay - dy;
|
||
|
|
const bdy = by - dy;
|
||
|
|
const cdy = cy - dy;
|
||
|
|
const adz = az - dz;
|
||
|
|
const bdz = bz - dz;
|
||
|
|
const cdz = cz - dz;
|
||
|
|
|
||
|
|
const bdxcdy = bdx * cdy;
|
||
|
|
const cdxbdy = cdx * bdy;
|
||
|
|
|
||
|
|
const cdxady = cdx * ady;
|
||
|
|
const adxcdy = adx * cdy;
|
||
|
|
|
||
|
|
const adxbdy = adx * bdy;
|
||
|
|
const bdxady = bdx * ady;
|
||
|
|
|
||
|
|
const det =
|
||
|
|
adz * (bdxcdy - cdxbdy) +
|
||
|
|
bdz * (cdxady - adxcdy) +
|
||
|
|
cdz * (adxbdy - bdxady);
|
||
|
|
|
||
|
|
const permanent =
|
||
|
|
(Math.abs(bdxcdy) + Math.abs(cdxbdy)) * Math.abs(adz) +
|
||
|
|
(Math.abs(cdxady) + Math.abs(adxcdy)) * Math.abs(bdz) +
|
||
|
|
(Math.abs(adxbdy) + Math.abs(bdxady)) * Math.abs(cdz);
|
||
|
|
|
||
|
|
const errbound = o3derrboundA * permanent;
|
||
|
|
if (det > errbound || -det > errbound) {
|
||
|
|
return det;
|
||
|
|
}
|
||
|
|
|
||
|
|
return orient3dadapt(ax, ay, az, bx, by, bz, cx, cy, cz, dx, dy, dz, permanent);
|
||
|
|
}
|
||
|
|
|
||
|
|
export function orient3dfast(ax, ay, az, bx, by, bz, cx, cy, cz, dx, dy, dz) {
|
||
|
|
const adx = ax - dx;
|
||
|
|
const bdx = bx - dx;
|
||
|
|
const cdx = cx - dx;
|
||
|
|
const ady = ay - dy;
|
||
|
|
const bdy = by - dy;
|
||
|
|
const cdy = cy - dy;
|
||
|
|
const adz = az - dz;
|
||
|
|
const bdz = bz - dz;
|
||
|
|
const cdz = cz - dz;
|
||
|
|
|
||
|
|
return adx * (bdy * cdz - bdz * cdy) +
|
||
|
|
bdx * (cdy * adz - cdz * ady) +
|
||
|
|
cdx * (ady * bdz - adz * bdy);
|
||
|
|
}
|