gpx.studio/website/src/lib/components/toolbar/tools/routing/Simplify.ts

import type { Coordinates, GPXFile, TrackPoint, TrackSegment } from "gpx";

type SimplifiedTrackPoint = { point: TrackPoint, distance?: number };

const earthRadius = 6371008.8;

export function getZoomLevelForDistance(latitude: number, distance?: number): number {
    if (distance === undefined) {
        return 0;
    }

    const rad = Math.PI / 180;
    const lat = latitude * rad;

    return Math.min(20, Math.max(0, Math.floor(Math.log2((earthRadius * Math.cos(lat)) / distance))));
}

export function updateAnchorPoints(file: GPXFile) {
    let segments = file.getSegments();

    for (let segment of segments) {
        if (!segment._data.anchors) { // New segment, compute anchor points for it
            computeAnchorPoints(segment);
            continue;
        }

        if (segment.trkpt.length > 0) {
            if (!segment.trkpt[0]._data.anchor) { // First point is not an anchor, make it one
                segment.trkpt[0]._data.anchor = true;
                segment.trkpt[0]._data.zoom = 0;
            }

            if (!segment.trkpt[segment.trkpt.length - 1]._data.anchor) { // Last point is not an anchor, make it one
                segment.trkpt[segment.trkpt.length - 1]._data.anchor = true;
                segment.trkpt[segment.trkpt.length - 1]._data.zoom = 0;
            }
        }
    }
}

function computeAnchorPoints(segment: TrackSegment) {
    let points = segment.trkpt;
    let anchors = ramerDouglasPeucker(points);
    anchors.forEach((anchor) => {
        let point = anchor.point;
        point._data.anchor = true;
        point._data.zoom = getZoomLevelForDistance(point.getLatitude(), anchor.distance);
    });
    segment._data.anchors = true;
}

export function ramerDouglasPeucker(points: readonly TrackPoint[], epsilon: number = 50, start: number = 0, end: number = points.length - 1): SimplifiedTrackPoint[] {
    if (points.length == 0) {
        return [];
    } else if (points.length == 1) {
        return [{
            point: points[0]
        }];
    }

    let simplified = [{
        point: points[start]
    }];
    ramerDouglasPeuckerRecursive(points, epsilon, start, end, simplified);
    simplified.push({
        point: points[end]
    });
    return simplified;
}

function ramerDouglasPeuckerRecursive(points: readonly TrackPoint[], epsilon: number, start: number, end: number, simplified: SimplifiedTrackPoint[]) {
    let largest = {
        index: 0,
        distance: 0
    };

    for (let i = start + 1; i < end; i++) {
        let distance = crossarc(points[start].getCoordinates(), points[end].getCoordinates(), points[i].getCoordinates());
        if (distance > largest.distance) {
            largest.index = i;
            largest.distance = distance;
        }
    }

    if (largest.distance > epsilon) {
        ramerDouglasPeuckerRecursive(points, epsilon, start, largest.index, simplified);
        simplified.push({ point: points[largest.index], distance: largest.distance });
        ramerDouglasPeuckerRecursive(points, epsilon, largest.index, end, simplified);
    }
}

function crossarc(coord1: Coordinates, coord2: Coordinates, coord3: Coordinates): number {
    // Calculates the shortest distance in meters 
    // between an arc (defined by p1 and p2) and a third point, p3.
    // Input lat1,lon1,lat2,lon2,lat3,lon3 in degrees.

    const rad = Math.PI / 180;
    const lat1 = coord1.lat * rad;
    const lat2 = coord2.lat * rad;
    const lat3 = coord3.lat * rad;

    const lon1 = coord1.lon * rad;
    const lon2 = coord2.lon * rad;
    const lon3 = coord3.lon * rad;

    // Prerequisites for the formulas
    const bear12 = bearing(lat1, lon1, lat2, lon2);
    const bear13 = bearing(lat1, lon1, lat3, lon3);
    let dis13 = distance(lat1, lon1, lat3, lon3);

    let diff = Math.abs(bear13 - bear12);
    if (diff > Math.PI) {
        diff = 2 * Math.PI - diff;
    }

    // Is relative bearing obtuse?
    if (diff > (Math.PI / 2)) {
        return dis13;
    }

    // Find the cross-track distance.
    let dxt = Math.asin(Math.sin(dis13 / earthRadius) * Math.sin(bear13 - bear12)) * earthRadius;

    // Is p4 beyond the arc?
    let dis12 = distance(lat1, lon1, lat2, lon2);
    let dis14 = Math.acos(Math.cos(dis13 / earthRadius) / Math.cos(dxt / earthRadius)) * earthRadius;
    if (dis14 > dis12) {
        return distance(lat2, lon2, lat3, lon3);
    } else {
        return Math.abs(dxt);
    }
}

function distance(latA: number, lonA: number, latB: number, lonB: number): number {
    // Finds the distance between two lat / lon points.
    return Math.acos(Math.sin(latA) * Math.sin(latB) + Math.cos(latA) * Math.cos(latB) * Math.cos(lonB - lonA)) * earthRadius;
}


function bearing(latA: number, lonA: number, latB: number, lonB: number): number {
    // Finds the bearing from one lat / lon point to another.
    return Math.atan2(Math.sin(lonB - lonA) * Math.cos(latB),
        Math.cos(latA) * Math.sin(latB) - Math.sin(latA) * Math.cos(latB) * Math.cos(lonB - lonA));
}