import type { Vec3, Vec3Like } from './types';
export interface CatmullRomOptions {
    readonly closed?: boolean;
    readonly parameterization?: 'uniform' | 'centripetal' | 'chordal';
}
export type Curve3Sampler = (out: Vec3, t: number) => Vec3;
/** Whole-path Catmull-Rom, centripetal by default. Open ends extrapolate their
 * neighbours; closed paths wrap without a duplicate control point. No allocation.
 * Empty input writes zero, one point is constant, t is clamped to [0,1].
 */
export declare function catmullRom(out: Vec3, points: readonly Vec3Like[], t: number, options?: CatmullRomOptions): Vec3;
/** Unit direction from the analytic derivative; constant curves write zero. */
export declare function catmullRomTangent(out: Vec3, points: readonly Vec3Like[], t: number, options?: CatmullRomOptions): Vec3;
/** Explicit caller-owned chord-length table for a sampler. out.length-1 is the
 * subdivision count (>=1); rebuild after changing controls. Two Vec3 scratch
 * allocations per build; distance lookup and curve sampling allocate nothing.
 * Approximation, not an analytic arc-length guarantee: increase subdivisions
 * until the application's distance/error budget converges.
 */
export declare function arcLengths(out: Float32Array, sample: Curve3Sampler): Float32Array;
/** Clamp a distance to a valid cumulative table and invert by binary search.
 * Zero-length paths and nonfinite distance return 0; repeated lengths are safe.
 * Table comes from arcLengths; lookups are O(log subdivisions).
 */
export declare function parameterAtDistance(lengths: Float32Array, distance: number): number;
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