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speed up simplify by using more naive distance

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vcoppe
2025-11-15 07:17:11 +01:00
parent 3a65f8dc16
commit 8e63fc6946
1 changed files with 55 additions and 94 deletions
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149
gpx/src/simplify.ts
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@@ -3,8 +3,6 @@ import { Coordinates } from './types';
export type SimplifiedTrackPoint = { point: TrackPoint; distance?: number };
const earthRadius = 6371008.8;
export function ramerDouglasPeucker(
points: TrackPoint[],
epsilon: number = 50,
@@ -72,65 +70,45 @@ export function crossarcDistance(
);
}
const metersPerLatitudeDegree = 111320;
function getMetersPerLongitudeDegree(latitude: number): number {
return Math.cos((latitude * Math.PI) / 180) * metersPerLatitudeDegree;
}
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.
// Calculates the perpendicular distance in meters
// between a line segment (defined by p1 and p2) and a third point, p3.
// Uses simple planar geometry (ignores earth curvature).
const rad = Math.PI / 180;
const lat1 = coord1.lat * rad;
const lat2 = coord2.lat * rad;
const lat3 = coord3.lat * rad;
// Convert to meters using approximate scaling
const metersPerLongitudeDegree = getMetersPerLongitudeDegree(coord1.lat);
const lon1 = coord1.lon * rad;
const lon2 = coord2.lon * rad;
const lon3 = coord3.lon * rad;
const x1 = coord1.lon * metersPerLongitudeDegree;
const y1 = coord1.lat * metersPerLatitudeDegree;
const x2 = coord2.lon * metersPerLongitudeDegree;
const y2 = coord2.lat * metersPerLatitudeDegree;
const x3 = coord3.lon * metersPerLongitudeDegree;
const y3 = coord3.lat * metersPerLatitudeDegree;
// 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);
const dx = x2 - x1;
const dy = y2 - y1;
const segmentLengthSquared = dx * dx + dy * dy;
let diff = Math.abs(bear13 - bear12);
if (diff > Math.PI) {
diff = 2 * Math.PI - diff;
if (segmentLengthSquared === 0) {
// p1 and p2 are the same point
return Math.sqrt((x3 - x1) * (x3 - x1) + (y3 - y1) * (y3 - y1));
}
// Is relative bearing obtuse?
if (diff > Math.PI / 2) {
return dis13;
}
// Project p3 onto the line defined by p1-p2
const t = Math.max(0, Math.min(1, ((x3 - x1) * dx + (y3 - y1) * dy) / segmentLengthSquared));
// Find the cross-track distance.
let dxt = Math.asin(Math.sin(dis13 / earthRadius) * Math.sin(bear13 - bear12)) * earthRadius;
// Find the closest point on the segment
const projX = x1 + t * dx;
const projY = y1 + t * dy;
// 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)
);
// Return distance from p3 to the projected point
return Math.sqrt((x3 - projX) * (x3 - projX) + (y3 - projY) * (y3 - projY));
}
export function projectedPoint(
@@ -146,56 +124,39 @@ export function projectedPoint(
}
function projected(coord1: Coordinates, coord2: Coordinates, coord3: Coordinates): Coordinates {
// Calculates the point on the line defined by p1 and p2
// Calculates the point on the line segment defined by p1 and p2
// that is closest to the third point, p3.
// Input lat1,lon1,lat2,lon2,lat3,lon3 in degrees.
// Uses simple planar geometry (ignores earth curvature).
const rad = Math.PI / 180;
const lat1 = coord1.lat * rad;
const lat2 = coord2.lat * rad;
const lat3 = coord3.lat * rad;
// Convert to meters using approximate scaling
const metersPerLongitudeDegree = getMetersPerLongitudeDegree(coord1.lat);
const lon1 = coord1.lon * rad;
const lon2 = coord2.lon * rad;
const lon3 = coord3.lon * rad;
const x1 = coord1.lon * metersPerLongitudeDegree;
const y1 = coord1.lat * metersPerLatitudeDegree;
const x2 = coord2.lon * metersPerLongitudeDegree;
const y2 = coord2.lat * metersPerLatitudeDegree;
const x3 = coord3.lon * metersPerLongitudeDegree;
const y3 = coord3.lat * metersPerLatitudeDegree;
// 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);
const dx = x2 - x1;
const dy = y2 - y1;
const segmentLengthSquared = dx * dx + dy * dy;
let diff = Math.abs(bear13 - bear12);
if (diff > Math.PI) {
diff = 2 * Math.PI - diff;
}
// Is relative bearing obtuse?
if (diff > Math.PI / 2) {
if (segmentLengthSquared === 0) {
// p1 and p2 are the same point
return coord1;
}
// Find the cross-track distance.
let dxt = Math.asin(Math.sin(dis13 / earthRadius) * Math.sin(bear13 - bear12)) * earthRadius;
// Project p3 onto the line defined by p1-p2
const t = Math.max(0, Math.min(1, ((x3 - x1) * dx + (y3 - y1) * dy) / segmentLengthSquared));
// 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 coord2;
} else {
// Determine the closest point (p4) on the great circle
const f = dis14 / earthRadius;
const lat4 = Math.asin(
Math.sin(lat1) * Math.cos(f) + Math.cos(lat1) * Math.sin(f) * Math.cos(bear12)
);
const lon4 =
lon1 +
Math.atan2(
Math.sin(bear12) * Math.sin(f) * Math.cos(lat1),
Math.cos(f) - Math.sin(lat1) * Math.sin(lat4)
);
// Find the closest point on the segment
const projX = x1 + t * dx;
const projY = y1 + t * dy;
return { lat: lat4 / rad, lon: lon4 / rad };
}
// Convert back to degrees
return {
lat: projY / metersPerLatitudeDegree,
lon: projX / metersPerLongitudeDegree,
};
}