s2-tools/dist/geometry/predicates/orient2d.js

A collection of geospatial tools primarily designed for WGS84, Web Mercator, and S2.

import { estimate, predSum, resulterrbound, splitter, vec } from './util';
const ccwerrboundA = 3.3306690738754716e-16; // (3 + 16 * epsilon) * epsilon;
const ccwerrboundB = 2.2204460492503146e-16; // (2 + 12 * epsilon) * epsilon;
const ccwerrboundC = 1.1093356479670487e-31; // (9 + 64 * epsilon) * epsilon * epsilon;
let constants;
/**
 * build constants for future reuse
 * @returns - the constants
 */
function buildConstants() {
    return {
        B: vec(4),
        C1: vec(8),
        C2: vec(12),
        D: vec(16),
        u: vec(4),
    };
}
/**
 * @param ax - x coordinate of first point
 * @param ay - y coordinate of first point
 * @param bx - x coordinate of second point
 * @param by - y coordinate of second point
 * @param cx - x coordinate of comparison point
 * @param cy - y coordinate of comparison point
 * @param detsum - sum of the determinants of all intermediate cross products
 * @returns - a negative value if the points a, b, and c occur in counterclockwise order
 * (c lies to the left of the directed line defined by points a and b).
 * - Returns a positive value if they occur in clockwise order (c lies to the right of the directed line ab).
 * - Returns zero if they are collinear.
 */
function orient2dadapt(ax, ay, bx, by, cx, cy, detsum) {
    if (constants === undefined)
        constants = buildConstants();
    const { B, C1, C2, D, u } = constants;
    let bvirt, c, ahi, alo, bhi, blo, _i, _j, _0, s1, s0, t1, t0, u3;
    const acx = ax - cx;
    const bcx = bx - cx;
    const acy = ay - cy;
    const bcy = by - cy;
    s1 = acx * bcy;
    c = splitter * acx;
    ahi = c - (c - acx);
    alo = acx - ahi;
    c = splitter * bcy;
    bhi = c - (c - bcy);
    blo = bcy - bhi;
    s0 = alo * blo - (s1 - ahi * bhi - alo * bhi - ahi * blo);
    t1 = acy * bcx;
    c = splitter * acy;
    ahi = c - (c - acy);
    alo = acy - ahi;
    c = splitter * bcx;
    bhi = c - (c - bcx);
    blo = bcx - bhi;
    t0 = alo * blo - (t1 - ahi * bhi - alo * bhi - ahi * blo);
    _i = s0 - t0;
    bvirt = s0 - _i;
    B[0] = s0 - (_i + bvirt) + (bvirt - t0);
    _j = s1 + _i;
    bvirt = _j - s1;
    _0 = s1 - (_j - bvirt) + (_i - bvirt);
    _i = _0 - t1;
    bvirt = _0 - _i;
    B[1] = _0 - (_i + bvirt) + (bvirt - t1);
    u3 = _j + _i;
    bvirt = u3 - _j;
    B[2] = _j - (u3 - bvirt) + (_i - bvirt);
    B[3] = u3;
    let det = estimate(4, B);
    let errbound = ccwerrboundB * detsum;
    if (det >= errbound || -det >= errbound) {
        return det;
    }
    bvirt = ax - acx;
    const acxtail = ax - (acx + bvirt) + (bvirt - cx);
    bvirt = bx - bcx;
    const bcxtail = bx - (bcx + bvirt) + (bvirt - cx);
    bvirt = ay - acy;
    const acytail = ay - (acy + bvirt) + (bvirt - cy);
    bvirt = by - bcy;
    const bcytail = by - (bcy + bvirt) + (bvirt - cy);
    if (acxtail === 0 && acytail === 0 && bcxtail === 0 && bcytail === 0) {
        return det;
    }
    errbound = ccwerrboundC * detsum + resulterrbound * Math.abs(det);
    det += acx * bcytail + bcy * acxtail - (acy * bcxtail + bcx * acytail);
    if (det >= errbound || -det >= errbound)
        return det;
    s1 = acxtail * bcy;
    c = splitter * acxtail;
    ahi = c - (c - acxtail);
    alo = acxtail - ahi;
    c = splitter * bcy;
    bhi = c - (c - bcy);
    blo = bcy - bhi;
    s0 = alo * blo - (s1 - ahi * bhi - alo * bhi - ahi * blo);
    t1 = acytail * bcx;
    c = splitter * acytail;
    ahi = c - (c - acytail);
    alo = acytail - ahi;
    c = splitter * bcx;
    bhi = c - (c - bcx);
    blo = bcx - bhi;
    t0 = alo * blo - (t1 - ahi * bhi - alo * bhi - ahi * blo);
    _i = s0 - t0;
    bvirt = s0 - _i;
    u[0] = s0 - (_i + bvirt) + (bvirt - t0);
    _j = s1 + _i;
    bvirt = _j - s1;
    _0 = s1 - (_j - bvirt) + (_i - bvirt);
    _i = _0 - t1;
    bvirt = _0 - _i;
    u[1] = _0 - (_i + bvirt) + (bvirt - t1);
    u3 = _j + _i;
    bvirt = u3 - _j;
    u[2] = _j - (u3 - bvirt) + (_i - bvirt);
    u[3] = u3;
    const C1len = predSum(4, B, 4, u, C1);
    s1 = acx * bcytail;
    c = splitter * acx;
    ahi = c - (c - acx);
    alo = acx - ahi;
    c = splitter * bcytail;
    bhi = c - (c - bcytail);
    blo = bcytail - bhi;
    s0 = alo * blo - (s1 - ahi * bhi - alo * bhi - ahi * blo);
    t1 = acy * bcxtail;
    c = splitter * acy;
    ahi = c - (c - acy);
    alo = acy - ahi;
    c = splitter * bcxtail;
    bhi = c - (c - bcxtail);
    blo = bcxtail - bhi;
    t0 = alo * blo - (t1 - ahi * bhi - alo * bhi - ahi * blo);
    _i = s0 - t0;
    bvirt = s0 - _i;
    u[0] = s0 - (_i + bvirt) + (bvirt - t0);
    _j = s1 + _i;
    bvirt = _j - s1;
    _0 = s1 - (_j - bvirt) + (_i - bvirt);
    _i = _0 - t1;
    bvirt = _0 - _i;
    u[1] = _0 - (_i + bvirt) + (bvirt - t1);
    u3 = _j + _i;
    bvirt = u3 - _j;
    u[2] = _j - (u3 - bvirt) + (_i - bvirt);
    u[3] = u3;
    const C2len = predSum(C1len, C1, 4, u, C2);
    s1 = acxtail * bcytail;
    c = splitter * acxtail;
    ahi = c - (c - acxtail);
    alo = acxtail - ahi;
    c = splitter * bcytail;
    bhi = c - (c - bcytail);
    blo = bcytail - bhi;
    s0 = alo * blo - (s1 - ahi * bhi - alo * bhi - ahi * blo);
    t1 = acytail * bcxtail;
    c = splitter * acytail;
    ahi = c - (c - acytail);
    alo = acytail - ahi;
    c = splitter * bcxtail;
    bhi = c - (c - bcxtail);
    blo = bcxtail - bhi;
    t0 = alo * blo - (t1 - ahi * bhi - alo * bhi - ahi * blo);
    _i = s0 - t0;
    bvirt = s0 - _i;
    u[0] = s0 - (_i + bvirt) + (bvirt - t0);
    _j = s1 + _i;
    bvirt = _j - s1;
    _0 = s1 - (_j - bvirt) + (_i - bvirt);
    _i = _0 - t1;
    bvirt = _0 - _i;
    u[1] = _0 - (_i + bvirt) + (bvirt - t1);
    u3 = _j + _i;
    bvirt = u3 - _j;
    u[2] = _j - (u3 - bvirt) + (_i - bvirt);
    u[3] = u3;
    const Dlen = predSum(C2len, C2, 4, u, D);
    return D[Dlen - 1];
}
/**
 * @param ax - x coordinate of first point
 * @param ay - y coordinate of first point
 * @param bx - x coordinate of second point
 * @param by - y coordinate of second point
 * @param cx - x coordinate of comparison point
 * @param cy - y coordinate of comparison point
 * @returns - a positive value if the points a, b, and c occur in counterclockwise order
 * (c lies to the left of the directed line defined by points a and b).
 * - Returns a negative value if they occur in clockwise order (c lies to the right of the directed line ab).
 * - Returns zero if they are collinear.
 */
export function orient2d(ax, ay, bx, by, cx, cy) {
    const { abs } = Math;
    const detleft = (ay - cy) * (bx - cx);
    const detright = (ax - cx) * (by - cy);
    const det = detleft - detright;
    const detsum = abs(detleft + detright);
    if (abs(det) >= ccwerrboundA * detsum)
        return det;
    return -orient2dadapt(ax, ay, bx, by, cx, cy, detsum);
}
/**
 * @param ax - x coordinate of first point
 * @param ay - y coordinate of first point
 * @param bx - x coordinate of second point
 * @param by - y coordinate of second point
 * @param cx - x coordinate of comparison point
 * @param cy - y coordinate of comparison point
 * @returns - a positive value if the points a, b, and c occur in counterclockwise order
 * (c lies to the left of the directed line defined by points a and b).
 * - Returns a negative value if they occur in clockwise order (c lies to the right of the directed line ab).
 * - Returns zero if they are collinear.
 */
export function orient2dfast(ax, ay, bx, by, cx, cy) {
    return (ay - cy) * (bx - cx) - (ax - cx) * (by - cy);
}
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