/**
 * Great-circle helpers for arc and route marks.
 *
 * Why this exists rather than drawing straight lines: a straight segment between
 * two points on a projected map is not the path anything travels. Tokyo to New
 * York arcs over the Arctic; in Web Mercator the true route looks like a curve
 * bending sharply north, and a straight line between the two is both wrong and
 * misleadingly long. Many libraries draw the straight line and hope.
 *
 * The output is a GeoJSON LineString in lon/lat, deliberately, so that d3-geo's
 * own clipping and antimeridian cutting handle the hard cases: a Tokyo to Los
 * Angeles arc crossing the antimeridian is split into two rendered segments
 * automatically instead of streaking back across the whole map.
 *
 * @module geo/Geodesic
 */
import type { LineString } from 'geojson';
import type { LonLat, WorldPoint } from '../types';
/**
 * Angular distance between two points, in degrees along a great circle.
 */
export declare function angularDistance(from: LonLat, to: LonLat): number;
/**
 * How many intermediate points a geodesic needs.
 *
 * Scaled by arc length so a 200 km hop is not sampled as densely as a
 * trans-Pacific route, and clamped so neither end degenerates: too few points
 * makes a great circle look like a polyline, too many wastes memory on every arc
 * in a 5,000-route network.
 */
export declare function segmentsFor(degrees: number, { min, max, perDegree }?: {
    min?: number | undefined;
    max?: number | undefined;
    perDegree?: number | undefined;
}): number;
/**
 * Sample a great circle between two points.
 *
 * Returns lon/lat coordinates including both endpoints.
 */
export declare function greatCircle(from: LonLat, to: LonLat, segments?: number): LonLat[];
/**
 * A great circle as a GeoJSON LineString, ready to hand to a d3 path generator.
 */
export declare function greatCircleLine(from: LonLat, to: LonLat, segments?: number): LineString;
/**
 * The midpoint of a great circle, useful for anchoring a tooltip or a label on an
 * arc.
 */
export declare function greatCircleMidpoint(from: LonLat, to: LonLat): LonLat;
/**
 * A quadratic bezier through world space, bulging perpendicular to the chord.
 *
 * This is the decorative alternative to a true geodesic, and it is worth being
 * explicit that it is decorative: the curve is not a path anything follows, and
 * its height carries no meaning. It reads well for hub-and-spoke marketing maps
 * and for keeping many parallel routes visually distinguishable, which is why it
 * is offered at all.
 *
 * The bulge is always drawn to the same side of the chord (left, in screen terms)
 * so that a set of arcs fans consistently instead of alternating.
 *
 * @param curvature 0 is a straight chord; 0.3 is a gentle arc; 1 is extreme.
 */
export declare function bezierArc(from: WorldPoint, to: WorldPoint, curvature: number): string;
/**
 * Total length of a projected polyline in world pixels, used to seed
 * stroke-dasharray for draw-on animations.
 */
export declare function polylineLength(points: WorldPoint[]): number;
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