@uor-foundation/geometry/dist/embedding.d.ts

Layer 5: Geometric manifolds - the shape of mathematical space

import type { PageTopology } from '@uor-foundation/topology';
export interface Point2D {
    x: number;
    y: number;
}
export interface CurveSegment {
    start: bigint;
    end: bigint;
    curvature: number;
    points: Point2D[];
}
export interface GeometricEmbedding {
    folio: bigint;
    curve: Point2D[];
    segments: CurveSegment[];
    totalRotation: number;
}
export interface RotationMatrix {
    cos: number;
    sin: number;
}
export declare class ContinuousEmbedding {
    private topology;
    private readonly LAMBDA;
    private readonly FOLIO_SIZE;
    private readonly rotationCache;
    constructor(topology: PageTopology);
    embedFolio(startIndex?: bigint): GeometricEmbedding;
    computeCurvature(n: bigint): number;
    getEmbedding(n: bigint): Point2D;
    computeGeodesic(a: bigint, b: bigint): Point2D[];
    embeddingDistance(a: bigint, b: bigint): number;
    intrinsicDistance(a: bigint, b: bigint): bigint;
    biLipschitzBounds(a: bigint, b: bigint): {
        lower: number;
        upper: number;
    };
    computeArcLength(path: Point2D[]): number;
    findCriticalCurvaturePoints(start: bigint, end: bigint): bigint[];
    visualizeEmbedding(embedding: GeometricEmbedding, width?: number, height?: number): string[];
    getWindingNumber(embedding: GeometricEmbedding): number;
    interpolateOnCurve(n: bigint, t: number): Point2D;
    private precomputeRotations;
    private getRotation;
    extendToComplexPlane(n: bigint): {
        real: number;
        imag: number;
    };
    computeSpectralGap(start: bigint, end: bigint): number;
    detectBottlenecks(embedding: GeometricEmbedding): bigint[];
}
//# sourceMappingURL=embedding.d.ts.map